On May 8, 2012, Bill Nye and Neil deGrasse Tyson brought their unique brand of motivational speaking to Capitol Hill. In a standing-room-only lunch discussion in one of the meeting rooms for the Committee on Space, Science, Technology, these two space superstars, along with planetary scientist Louise Prockter, explained to members of Congress, staffers, and media why we must continue to invest in planetary exploration.

I have just received an invitation to take part in the program “Computational Challenges in Probability” organised by ICERM (Institute for Computational and Experimental Research in Mathematics, located in what sounds like a terrific building!) next semester. Here is the purpose statement:

The Fall 2012 Semester on “Computational Challenges in Probability” aims to bring together leading experts and young researchers who are advancing the use of probabilistic and computational methods to study complex models in a variety of fields. The goal is to identify common challenges, exchange existing tools, reveal new application areas and forge new collaborative efforts. The semester includes four workshops – Bayesian Nonparametrics, Uncertainty Quantification, Monte Carlo Methods in the Physical and Biological Sciences and Performance Analysis of Monte Carlo Methods. In addition, synergistic activities will be planned throughout the duration of the semester. In particular, there will be several short courses and plenary invited talks by experts on related topics such as graphical models, randomized algorithms and stochastic networks, regular weekly seminars and relevant film screenings.

There are thus four workshops organised over the period and an impressive collection of long-term participants. I will most likely take part in the last workshop, “Performance Analysis of Monte Carlo Methods”, although I would like to attend all of them! (Interesting side remark: while looking at the ICERM website, I found that May 18th is the Day of Data! Great, except that neither the word statistitics nor the word statistician appear on the page…)

Filed under: Statistics, Travel, University life Tagged: Bayesian nonparametrics, Brown University, computational statistics, conference, ICERM, Monte Carlo methods, probability theory, Providence, thematic semester, workshop

Cross posted from Nature Medicine’s Spoonful of Medicine blog. Author: Elie Dolgin.

The US Food and Drug Administration is often criticized for taking a plodding approach to drug regulation. But when it comes to approving novel therapeutics, the agency is actually much speedier than its European and Canadian counterparts.

“Many of the criticisms that the FDA has been facing over the past couple years were not based on concrete data,” says Jeff Allen, executive director of Friends of Cancer Research, an advocacy organization based in Washington, DC. “Hopefully this will let people really focus on the challenges facing drug regulation, rather than falling into talking points about approval speed.”

Using publically available records, a team from the Yale University School of Medicinein New Haven, Connecticut compared the review times of all small molecule and biologic drugs approved by the FDA, the European Medicines Agency (EMA) and Health Canada from 2001 through 2010. Reporting online today in the New England Journal of Medicine, the researchers found that, regardless of drug type, orphan designation or priority review status, the FDA cleared new medicines, on average, at least a month faster than the other two agencies (see chart).

“Pretty consistently the FDA was coming out on top,” says Yale medical student Nicholas Downing, who led the work. For example, when considering just the 72 agents approved by all three regulators, the median review time at the FDA was a full three months shorter than at the other agencies—under nine months at the FDA, compared to almost a year at the EMA and Health Canada .

Strength in numbers

The results should help shield the FDA against some recent attacks, especially as Congress gears up to renew the Prescription Drug User Fee Act, which allows the FDA to collect ‘user fees’ from pharmaceutical companies to support the infrastructure needed to provide timely and scientifically thorough reviews. But the findings should come as no surprise to people who have actually considered the hard numbers.

Last year, for instance, Allen and his colleagues examined 35 cancer drugs that were reviewed by the FDA and the EMA between 2003 and 2010, and showed that the median approval time was almost six months faster in the US than in Europe. Before that, a team from what is now known as the Centre for Innovation in Regulatory Science in London compared the regulatory review process between 1997 and 2002 across the US, EU, Canada, Switzerland and Australia; they found that the FDA was routinely at the top of the charts for speed. A March 2012 report from the US Government Accountability Office (GAO) also concluded that the FDA met its performance goals for timely drug reviews in all but one year between 2000 and 2010.

“The idea that the FDA somehow inhibits innovation is just based on false premises,” says Michael Halpern, manager for the Scientific Integrity program at the Union of Concerned Scientists, a nonprofit science advocacy group based in Cambridge, Massachusetts. “The agency is able to effectively balance speed without compromising health and safety in a way that suggests Congress should not view the FDA as an obstacle that needs to be reined in, but they need to give the agency the resources and independence so that it effectively protects people.”

The FDA’s track record on medical devices has not been as exemplary, however. Two years ago, researchers from Stanford University in California put out a damning report that compared regulatory timelines for medical devices in Europe and the US. The authors surveyed more than 200 companies, and found that approvals were about two years slower, on average, at the FDA (31 months) compared to the EMA (7 months) for most devices. Adding insult to injury, a GAO report released earlier this year found that the review times for medical device approvals have been creeping upwards in recent years.

The situation could be turning around, though. According to FDA Commissioner Margaret Hamburg, device approval times started to drop finally in 2011. “For the majority of devices that we review, we are as fast or faster than our European colleagues,” Hamburg told attendees of last month’s TEDMED conference in Washington, DC (as reported by the Device Talk blog).

I hope Hamburg is correct. Now we just need to wait for the hard numbers to back her up.

A little while back, I wrote about Jupiter appearing in an image from NASA’s SOHO Sun-observing satellite. I promised that it would soon appear in a SOHO camera that had higher magnification, and we’d be able to see its moons.

I am not one to break promises:

Awesome. It helps to set the resolution to 720p to see the moons when they’re pointed out.

And just you wait: in early June, Venus will appear in the LASCO C3 and C2 cameras, on its way for a date transiting the Sun for the last time in over a century. I’ll have more about that event in a few days… I promise!

Tip o’ the occulting bar to SungrazerComets on Twitter.

Related Posts:

- Jupiter, acting all superior
- Lovejoy lives!
- The Sun fries a comet and we got to watch
- The Galilean Revolution, 400 years later

Hey, if you want to read about the history of particle colliders, and the prospect for it in the next 20 years, this article might be something that interest you.

Abstract: Particle colliders for high energy physics have been in the forefront of scientific discoveries for more than half a century. The accelerator technology of the collider has progressed immensely, while the beam energy, luminosity, facility size and the cost have grown by several orders of magnitude. The method of colliding beams has not fully exhausted its potential but its pace of progress has greatly slowed down. In this paper we very briefly review the method and the history of colliders, discuss in detail the developments over the past two decades and the directions of the R&D toward near future colliders which are currently being explored. Finally, we make an attempt to look beyond the current horizon and outline the changes in the paradigm required for the next breakthroughs. 

Zz.

On Sunday, May 20, the Moon will pass between the Earth and the Sun, creating a solar eclipse.

However, this isn’t your usual event: because the Moon will be at apogee (the farthest point in its orbit), it won’t completely cover the face of the Sun. Instead of the Sun being totally blocked and the ethereal glow of its corona visible, we’ll see an annular eclipse, also called a "Ring of Fire" eclipse. The picture here — from the October 2005 annular eclipse — makes it clear why!

The eclipse begins at 20:56 UTC (16:56 Eastern US time) on May 20, and ends at 02:49 UTC May 21 (22:49 on May 20 Eastern time). Folks on the east coast of the US will not see the entire eclipse (for those on the extreme east coast, the Sun sets before the eclipse starts for that location [UPDATE: here's a good map to show you if you can see it or not, from the AstroGuyz site]), whereas people on the west coast will barely see the whole thing. For me, in Boulder, Colorado, the Sun ...

By James Dacey

His eponymous particle may be famously elusive, but Peter Higgs has been seemingly omnipresent in Bristol over the past couple of days. He has spent today at Physics World headquarters, having appeared last night at the Bristol Festival of Ideas, and he has just shot off to the University of Bristol to meet with academics and give a special colloquium. Last night he also managed to squeeze in an appearance on the local news programme BBC Points West, which documented Higgs returning to Cotham School, where he was a pupil for five years. You can read full details of Higgs' Bristol trip in this blog entry by Physics World editor Matin Durrani, who spent time with Higgs today to record an interview that will be appearing on physicworld.com.

In Higgs' talk last night, he was joined on stage by the science editor of the Observer, Robin McKie, and naturally the questions turned to the particle that now bears his name. When asked about how he came up with his boson, Higgs lived up to his famous modesty, explaining how the idea had emerged without grand designs from his work on a problem relating to superconductivity. He seemed slightly embarrassed that the particle has been named after him when there were several other theorists working on the same issues.

Higgs was also humble when questioned about how he felt about the vast investments that have been made in constructing particle accelerators to hunt (in part) for the fruit of his work. When asked by a member of the audience whether he would celebrate the discovery of his boson, Higgs replied in his typically understated manner that he has a bottle of champagne left over from Christmas, but he that he hadn't yet "put it in the fridge".

In this week's Facebook poll we want to know how you feel about the hunt for the Higgs boson.

How significant would the discovery of the Higgs boson be?

It would answer the biggest outstanding question in physics
It would answer the most important question in particle physics
There are other more important questions in particle physics

Let us know by visiting our Facebook page. And please feel free to explain your response by posting a comment on the Facebook poll.

In last week's poll we asked "What is your primary source of online physics news?". 78% of respondents said they get the majority of their updates from specialist news sites. 9% said they rely on general news sites. 6% use social media, another 6% rely on blogs, and just 1% get their news via Internet radio and podcasts.

Thank you for your participation and we look forward to hearing from you in this week's poll.

By Matin Durrani

It's been a hectic few days for 82-year-old Peter Higgs.

The retired Edinburgh University particle theorist, after whom the famous boson is named, has been in Bristol for the last two days undertaking a series of public engagements.

First up was a visit yesterday to Cotham School, where Higgs was a pupil for five years during the Second World War when his father – a BBC engineer – was posted to the city. Higgs is in fact not the only great physicist the school has produced – the other stellar pupil was Paul Dirac, whose name the young Higgs used to see displayed prominently on the school's honours boards. Higgs, who was back at the school for the first time since the war, signed autographs as he opened a new science block, appropriately named The Dirac–Higgs Science Centre, accompanied by the media.

In the evening, the self-effacing Higgs then took part in an event at St George's Bristol that was part of the city's Festival of Ideas. In front of an audience of several hundred people, he was joined on stage by Graham Farmelo, author of the award-winning Dirac biography The Strangest Man, who outlined Dirac's achievements and his links with Bristol. Higgs then took part in a conversation with Observer science editor Robin McKie, who asked him, among other things, how he would celebrate if the Higgs boson is found. To much amusement, Higgs replied that he had "a leftover bottle of champagne from Christmas" but that he hadn't yet "put it in the fridge".

Today, Higgs paid a visit to IOP Publishing, where I interviewed him for Physics World. Inspired by questions posted by readers on our Facebook page and sent to us via Twitter, I quizzed Higgs about his early work on symmetry breaking, his thoughts about the search for the Higgs at CERN and his wider views on physics. We'll be posting the interview online in the next month or two, so stay tuned for that.

Higgs still remains embarrassed at having a particle named after him, feeling that it places too much of the credit on him at the expense of other theorists. But during our interview, even he on occasion dropped the "so-called" from the "so-called Higgs boson", the "so-called Higgs field" and the "so-called Higgs mechanism". It just gets tiring after a while, I suppose.

As I write, the indefatigable Higgs is off to give a colloquium in the main lecture theatre at the physics department at the University of Bristol, entitled "My life as a boson". Over lunch I asked Higgs if that wouldn't be the perfect title for his autobiography. Self-effacing as ever, Higgs replied that, when it came to writing books, he was simply "too lazy". So if you want to hear more about his life, you'll have to wait for the Physics World interview.

This Saturday, SpaceX will attempt to make history by launching the first commercial spacecraft to berth with the International Space Station.

On the heels of Nobel laureate Al Gilman’s announcement that he plans to resign as the chief scientific officer of the US$3-billion Cancer Research Institute of Texas (CPRIT) and the leaking of his resignation letter, which raised concerns about the institute’s peer-review process, similar concerns and supporting details are now trickling out from the independent group of scientists who evaluate the Austin-based institute’s research grant applications.

In a letter dated 14 May, the organization’s scientific review council, chaired by Phillip Sharp of the Massachusetts Institute of Technology in Cambridge, criticizes actions taken by the CPRIT management and oversight committee — actions that they say are “inconsistent” with statements by CPRIT’s executive director William Gimson defending the integrity of the institute’s peer-review system.  The letter also reiterates the council’s faith in Gilman. In his 8 May resignation letter, Gilman had expressed concerns about CPRIT maintaining a “functional peer review system”.

Gilman told Nature in an e-mail that he believes that both letters address “the same basic issues”.

Among the most damning of the council’s concerns is their assertion that they were not consulted about a $20-million ‘incubator’ award  — the largest ever made by CPRIT — that went to Rice University and the University of Texas MD Anderson Cancer Center, both in Houston. Although the MD Anderson Cancer Center is slated to receive $18 million from the award, the council found their proposal too short (only 6.5 pages), too last-minute (it was approved three weeks after submission) and too skimpy on scientific detail.

“We will be viewed to have approved this award, and the failure to include us in the process calls into question our roles and the integrity of the review program in general. More importantly, this by-pass is inherently unfair to every scientist in Texas who participates in the CPRIT program,” the review council writes.

Incubator grants — to fund programmes and services aimed at commercializing new products for cancer diagnosis, treatment and prevention — are not defined by CPRIT as requiring scientific peer review. But the council argues that the activities laid out in MD Anderson’s proposal sound like research. Additionally, “no product candidates were mentioned,” said the letter, “nor is a company involved”. This marked the first time CPRIT has issued an award in this grant category.

“It is clear that the rules surrounding submission, evaluation, and funding of incubators must be clarified,” Gimson said in a statement. “It is my intent to address the concerns that have arisen about the commercialization review process by soliciting input from CPRIT’s stakeholders.”

The review council also criticizes CPRIT’s oversight committee for putting on hold seven multi-investigator research applications that the review council recommended for funding. The letter alleges that this was done because of opposition from certain committee members to a significant amount of the funding going to the University of Texas Southwestern Medical School in Dallas, where Gilman once served as dean. The review council writes that this amounts to an unfounded accusation of bias on the part of both the council and Gilman, which they “vigorously deny”.

Gimson said that the decision was related to timing and budget issues and confirmed that all seven projects are up for consideration at a meeting of the oversight committee scheduled for 26 July. In his resignation letter, Gilman suggests that he wants to remain in his role through the summer, in part to prevent ”negative decisions” about funding from being made at the same meeting.

This has been out for a little while now, and Chris has been promoting it very heavily, and it's sort of interesting to see the reactions. It's really something of a Rorschach blot of a book, with a lot of what's been written about it telling you more about what the writer wants to be in the book than what's actually in it. A lot of conservative responses to it are basically case studies in the sort of motivated reasoning Chris is writing about, but I've even seen some liberals jumping on it as completely confirming their own pre-existing biases, for example, claiming that this means Chris has renounced the whole idea of "framing" that led to so much bickering a few years back.

The premise of the book is certainly inflammatory, as you can tell from the full title: The Republican Brain: The Science of Why They Deny Science--and Reality. That's eye-catching, all right, well chosen to stir up some excitement. And it pretty much tells you what you're going to get: an argument, based on recent cognitive science experiments, that people who are inclined to be politically conservative will approach facts and data in a fundamentally different way than people who are inclined to be politically liberal.

What's striking about the book, especially given the title, is how careful it is. This perhaps shouldn't be surprising, given that Chris is a liberal guy, and thus more comfortable with nuance and uncertainty (according to the research he cites), but he does a really good job of avoiding extreme overreach. The research results that he describes are presented with most of the caveats you would like to see from a responsible science journalist. This isn't 274 pages of "Repubs R Dum LOL!", it's a carefully constructed argument, presented in a very calm manner. He's also very careful to note the limitations of everything-- that while an individual's innate personality type may incline them toward one ideology or another, in the end, political affiliation is a complicated mix of innate traits and environmental influences (family, local political context, media, etc.).

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The elevator that sinks into the Vale Creighton Mine near Sudbury, Ontario, is a gateway to two different worlds. One is Canada’s largest nickel mine, opened at the turn of the last century and still in operation. The other is SNOLAB, a large underground particle physics laboratory, the grand opening of which will take place today.

One of the things I love about the internet, and specifically Twitter, is how an offhand comment turns into awesome. And it happens within seconds.

For some reason, a super-hi-res picture of the Earth is making the rounds right now. It’s a gorgeous pic, and lots of people are sending me the link via email and Twitter. The thing is, I wrote about this picture back in April, on Earth Day. But such is the nature of the interwebz that stuff pops back up.

I appreciate that folks think enough of me to send me stuff, in case I hadn’t seen it. But in this case I figured I’d better stem the tide, so I tweeted about it, just basically saying thanks, but I already wrote about it.

Right after tweeting that, I realized how hipster it sounded. So I decided to go full hipster, tweeting:

It says, "I wrote about the Earth, it’s an obscure planet, you’ve probably never heard of it. #BadAstrohipster". I added the #BadAstrohipster hashtag as an afterthought; hashtags were originally meant to be used as a way to organize and categorize tweets, but now most ...

In case you missed it, here's the press release on the inauguration of SNOLAB:

The lab is situated 2km beneath the surface of the Earth and will enable researchers ton answer fundamental questions about the history and the composition of the Universe. They will also be able to use the infrastructure to conduct research into the nature of supernovas, our own star – the Sun – and Earth itself. SNOLAB will indeed be at the heart of a wide range of experiments, including PICASSO, an international project that is being lead by UdeM researchers. “In terms of current and future experiments, around half about the detection of dark matter in the Universe and ‘weakly interacting massive particles’ or ‘WIMPs’ in particular. PICASSO is one such research project. WIMPs are in fact particules that we do not know anything about and that would be a part of what we call ‘new physics’,” explained PICASSO Project Leader Professor Viktor Zacek, of the University of Montreal’s Department of Physics. “In fact, the presence of dark energy and dark matter are proof that we are still very far from having completely understood physics and the world that surrounds us.”

A lot of physics are now done underground, literally! :)

Zz.

Geneviève Fioraso, deputy mayor of Grenoble, and a Socialist member of the National Assembly (the French parliament), representing the Isère constituency, has been appointed minister of higher education and research in the first goverment of French president François Hollande and prime minister Jean-Marc Ayrault. Fioraso is no stranger to research and innovation issues, which has been her speciality both as a member of parliament, and as deputy mayor of Grenoble, while she is also a member of the Parliamentary Office for the Evaluation of Scientific and Technological Choices. Most recently, she was rapporteur of the office’s February report on the challenges of synthetic biology. She was also part of the group of advisers on innovation in François Hollande’s election campaign team.

Fioraso, who is 57 years old, has had a diverse career. Starting out as a lecturer in English and economics, she took a post at the Grenoble city hall in 1979, and became a parliamentary assistant in 1983. In 1989, she took on a management role at the high-tech start-up Corys, where she worked on the safety of nuclear and coal-fired power plants. In 1995, she became head of the office of Grenoble’s deputy mayor, Michel Destot, and in the early 2000′s worked as a marketing executive for France Telecom in emerging social and health applications. Elected to parliament in 2007, she is also chief executive officer of Sem Minatec Entreprises, the business incubator wing of Minatec, the renowned Grenoble innovation campus for nanotechnology and electronics, which has some 2400 researchers, 1200 students and 600 industrial staff.

Fioraso is one of 17 women among the 34 ministers nominated to the new government. This parity, promised by Hollande, is a first for France. The new government may undergo a reshuffle after the upcoming parliamentary elections, however, the first round of which will be held on 10 June with the final round being held on 17 June. For the full government line-up see the newspaper Le Monde’s summary.

Other links: Fioraso’s blog and page at the National Assembly.

Nature’s Q&A’s with Nicolas Sarkozy and François Hollande in the run up to the presidential election – “A question of science.”

Some experiment with pictures taken with my new pocket camera, a Canon Ixus 115 H5 I bought in replacement of the (mediocre) Nikon Coolpix I lost on Ben Nevis… (I am afraid the “miniature” option giving the impression of a small scale mode is going to get overused…!)

Filed under: pictures, Travel

In a deadly flu outbreak, shutting airports should reduce the spread of the disease. But networks scientists have discovered a better approach that's just as effective.

One of the nightmare scenarios for modern society is the possibility of a global flu pandemic like the 1918 Spanish influenza which infected about a quarter of the global population and killed as many as 130 million of them. 

An important question for policy makers is how best to limit the spread of such a disease if a new outbreak were to occur. (The Spanish flu was caused by the H1N1 flu virus that was also responsible for the 2009 swine flu outbreak.)

One obvious idea is to close international airports to prevent, or at least dramatically reduce, the movement of potentially infected individuals between countries. But is this the best approach?

Today, Jose Marcelino and Marcus Kaiser at Newcastle University in the UK, provide an answer. They say a better approach is to cut specific flights between airports because it can achieve the same reduction in the spread of the disease with far less drastic action.

These guys used a standard disease-spreading model to simulate the spread of an H1N1-type infection across a network consisting of the world's top 500 airports and the flights between them. The disease started in Mexico City.

They then reran the simulation to see how different strategies could reduce the spread. They found that shutting entire airports can obviously reduce infection. 

But they also studied less obvious strategies such as looking for cities that play an important role in the network and reducing the flights between them by 25 per cent. This turned out to be a much more effective strategy.

They found that shutting entire airports only had a significant effect on spreading if it reduced travel by 95 per cent. By contrast,  they could achieve the same effect by removing just 18 per cent of flights between cities ranked by a network measure called edge betweenness.  

At best shutting entire airports could only cut infections by 18 per cent whereas removing specific flights reduced infections by up to 37 per cent. 

"Selecting highly ranked single connections between cities for cancellation was more effective, resulting in fewer individuals infected with influenza, compared to shutting down whole airports," say Marcelino and Kaiser. This approach has the added benefit that it disrupts far fewer individuals 

Because these guys used a model of the actual global network of airports and flights they were able to identify the specific connections that would need to be targeted. For an infection that starts in Mexico City, the highest ranked routes that would need to be targeted are Sao Paulo to Beijing, Sapporo to New York and Montevideo to Paris.

That seems an eminently sensible suggestion. However, policy makers might want to study this approach in more detail to check that the conclusions still hold if outbreaks occur in other places too. 

Another idea worth checking is to see whether smaller airports could also play an important role in disease spreading.  Marcelino and Kaiser study a network consisting of the top 500 airports but the world is blessed with some 4000 airports in total. 

It's not inconceivable that some of these could play a crucial role in linking different parts of the world in a way that could facilitate disease spreading. 

Ref: http://arxiv.org/abs/1205.3245: Critical Paths In A Metapopulation Model Of H1N1: Efficiently Delaying Influenza Spreading Through Fight Cancellation

Today, 17th May, is International day Against Homophobia and Transphobia (IDAHO). There are events going on all round the world, including the UK (for which you can find a list here).

As an oldie, I find it quite amazing how much attitudes have changed in the general population, and even within the police force, but sadly that doesn’t mean that homophobic hate crimes no longer happen. In fact, they are still depressingly commonplace. The path that leads to violence (and even murder) starts with verbal abuse, and this will only stop when all fair-minded people (straight, gay, bisexual, transexual and undecided) are prepared to confront the bigots. Maybe one day IDAHO will not be needed, but that day remains a long way off.

Here is the official IDAHO video

And here is a special message from these parts made by Stonewall Cymru and the Welsh Assembly

Follow @telescoper

The Euler characteristic of topological spaces behaves something like a measure. For example, under suitable hypotheses,

$$\chi (X\cup Y)=\chi (X)+\chi (Y)-\chi (X\cap Y).$$

One of the main things you can do with a measure is integrate with respect to it — or ‘against’ it, as they say.

So: what happens if you try to integrate against the Euler characteristic?

I don’t completely understand the answer myself, but I’ll explain as well as I can. Along the way, we’ll see:

• how this train of thought helps us to define Euler characteristic
• how it also leads to the notion of curvature.

Simple functions on the line

Let’s begin in one dimension. Our aim is to define the integral $\int fd\chi$ for suitable functions $f:R\to R$.

Whatever we think Euler characteristic is, the Euler characteristic of a compact, nonempty interval $A$ should be $1$. So, writing $I_A$ for the indicator function (or characteristic function) of $A$, we should have

$$\int I_{A}d\chi =1.$$

Since integration is supposed to be linear, this tells us how we must integrate any finite linear combination of indicator functions of compact nonempy intervals. I’ll call these simple functions on $R$. So, for a simple function

$$f=\sum _{r=1}^k{c}_r{I}_{A_r},$$

where each $A_r$ is a compact nonempty interval, we should have

$$\int fd\chi =\sum _{r=1}^k{c}_r.$$

Do I hear you sigh? If you’ve seen this kind of thing before, you’ll recognize the standard problem: the definition isn’t obviously consistent, since $f$ can be expressed as a combination of indicator functions in multiple ways, and maybe these give multiple different values for the integral. In that case, you’ll also know that the standard solution, involving common refinements, is pretty tedious work.

Happily, we can avoid it. Here’s how. For a simple function $f$, put

$$J(f)=\sum _{x\in R}(f(x)-f(x-))$$

where $f(x-)$ means ${\lim }_{\epsilon \to 0+}f(x-\epsilon )$. This quantity $J(f)$ is well-defined, linear in $f$, and takes value $1$ when $f$ is the indicator function of a compact nonempty interval. So, $J(f)=\sum c_r$ whenever $f=\sum c_r{I}_{A_r}$. We therefore put

$$\int fd\chi =J(f),$$

and the consistency problem evaporates.

Let’s have some examples. What, for instance, is the integral against the Euler characteristic of this function?

The solid and empty circles indicate that $f(a)=f(b)=0$. So

$$f=3I_{(a,b)}=3I_{[a,b]}-3I_{[a,a]}-3I_{[b,b]}$$

and

$$\int fd\chi =3-3-3=-3.$$

Since $f=3I_{(a,b)}$, this tells us that we’re treating the Euler characteristic of the open interval $(a,b)$ as $-1$. That might strike you as wrong if you’re used to Euler characteristic being invariant under homotopy equivalence. But as James Propp pointed out long ago, there’s a tension between the requirement that Euler characteristic is homotopy-invariant and the requirement that it behaves like a finitely additive measure. You can’t have both at once. (See also John Baez’s excellent talk on the mysteries of counting.) Here we’re not worrying about homotopy invariance; we’re using what Propp would call ‘Euler measure’.

What about this function?

It’s not hard to see that $\int gd\chi =7$, whatever the unlabelled values on the axes might happen to be. I chose the letter $J$ to stand for ‘jump’: $J(f)=\int fd\chi$ is the total vertical jump occurring at jump discontinuities from the left.

One more example: what is the integral against the Euler characteristic of the following function?

Here

$$h=3I_{[a,d]}+5I_{[a,b]}+I_{[c,d]},$$

so

$$\int hd\chi =3+5+1=9$$

(regardless of the values of $a$, $b$, $c$ and $d$). Alternatively, you can calculate $\int hd\chi$ via the formula for $J(f)$, giving $8+(4-3)=9$ again.

More general functions on the line

Classical measure theory also involves things called ‘simple functions’ (with a different but analogous meaning). There, defining integration for simple functions is just a prelude to defining integration for a larger class of functions. Can we do something similar here, extending our integral to a larger class of functions?

We can. Indeed, the formula

$$\sum _{x\in R}(f(x)-f(x-))$$

for $\int fd\chi$ immediately makes sense for more than just the simple functions.

But before we charge ahead and generalize, let’s correct the ugly asymmetry you see here. In everything so far, we could equally well have used the formula

$$\sum _{x\in R}(f(x)-f(x+)).$$

It makes no difference: this is still equal to $\int fd\chi$ for simple functions $f$. Of course, it’s just as asymmetric. However, taking the average of the two formulas, we also have

$$\int fd\chi =\frac{1}{2}\sum _{x\in R}[-f(x-)+2f(x)-f(x+)].$$

This is now symmetric, and therefore more likely to give us a useful definition for more general functions $f$.

(Maybe you can see a hint of how curvature is going to enter the story: this looks like the expression $$f″(x)={\displaystyle \underset{\epsilon \to 0}{\lim }\frac{f(x-\epsilon )-2f(x)+f(x+\epsilon )}{{\epsilon }^2}}$$ for a second derivative, and second derivatives have something to do with curvature.)

So: let $f:R\to R$ be a function such that the limits $f(x-)$ and $f(x+)$ exist for all $x\in R$, and are equal to $f(x)$ for all but finitely many $x\in R$. In other words, $f$ is continuous except for a finite number of jump discontinuities. The integral against the Euler characteristic of such a function $f$ is defined by the formula above:

$$\int fd\chi =\frac{1}{2}\sum _{x\in R}[-f(x-)+2f(x)-f(x+)].$$

Be warned: this has some properties that you might not expect of an integral. For instance, the integral of any continuous function is $0$, the integral of a function that is everywhere strictly positive can be strictly negative, and changing the value of a function at a single point can change the value of the integral. On the other hand, this integral has some interesting properties too, as we’ll see when we get to higher dimensions.

Simple functions in higher dimensions

Let’s now consider functions on $R^n$, for $n\ge 1$. The role of intervals will be played by convex sets. For brevity, I’ll use ‘convex’ to mean ‘compact, nonempty and convex’.

A function $f:R^n\to R$ is simple if it can be expressed as a finite linear combination of indicator functions of convex sets. Again, we want to ‘define’

$$\int fd\chi =\sum _{r=1}^k{c}_r$$

whenever $f={\sum }_{r=1}^k{c}_r{I}_{A_r}$ for some convex sets $A_r$, and again we might groan at the prospect of having to do those tedious consistency checks.

But once more, the jump functional $J$ comes to the rescue. I’ll explain in the case $n=2$; the strategy for higher dimensions should be clear. Let $f:R^2\to R$ be a simple function. For each $x\in R$, the function

$$f(x,-):R\to R$$

is simple, and so we can define a function $F:R\to R$ by $F(x)=J(f(x,-))$. This function $F$, too, is simple, so we get a real number $J(F)$. We define $J(f)$ to be this number: $J(f)=J(F)$.

Thus, we have defined $J(f)$ for every simple function $f$ on $R^2$. It is linear in $f$, with $J(1_A)=1$ whenever $A$ is convex. So just as in the one-dimensional case, $J(f)=\sum c_r$ when $f=\sum c_r{I}_{A_r}$. This solves the consistency problem, and $\int fd\chi =J(f)$.

I learned this from Chapter 5 of Klain and Rota’s Introduction to Geometric Probability (source of so many wonderful things). It is remarkably little effort, and is even based on a very standard technique: reducing a multivariable integral to a sequence of single-variable integrals. But it has an immediate nontrivial consequence: the definition of Euler characteristic for a large class of subsets of $R^n$.

Indeed, call a subset $S$ of $R^n$ polyconvex if it can be expressed as a finite union of convex sets. For example, any picture on a black and white television is polyconvex (assuming that each pixel is convex). And quite simply, we define

$$\chi (S)=\int I_{S}d\chi .$$

You can prove, as Klain and Rota do, that this coincides with the usual definition.

More general functions in higher dimensions, and curvature

The rough idea now is that given a function $f:R^n\to R$ whose discontinuities are no worse than those of a simple function, we should be able to define $\int fd\chi$ by repeating verbatim the definition for simple functions.

In the one-dimensional case, we first had to deal with the pesky problem that the formula

$$J(f)=\sum _{x\in R}(f(x)-f(x-))$$

isn’t symmetric, so probably wouldn’t generalize well. To fix that, we considered the formula $\sum (f(x)-f(x+))$ obtained by reversing the orientation of the line, and then we averaged over the two orientations to get something symmetric.

In higher dimensions, the asymmetry problem can no longer be brushed aside with this algebraic flick of the wrist. In fact, some interesting geometry comes in here. This asymmetry issue, which looked like a nuisance distracting us from the main business, turns out to be exactly the reason why integration against the Euler characteristic is closely related to curvature.

Again I’ll stick to $n=2$, leaving higher dimensions to your imagination.

In defining $J(f)$ for simple functions $f:R^2\to R$, we used the standard coordinate system on $R^2$. When $f$ is simple, the choice of basis does not affect the value of $J(f)$ (which is always equal to $\sum c_r$, if $f=\sum c_r{I}_{A_r}$). But for more general functions $f$, it certainly does make a difference. What we should do is consider all ordered orthonormal bases of $R^2$, calculate $J(f)$ with respect to each basis, and define $\int fd\chi$ to be the average.

(You can see that this generalizes what we did for $R^1$: there we took the average of two things, and there are two orthonormal bases of $R^1$.)

I don’t want to make this post any longer by explaining exactly what, for instance, ‘average’ means. Nor will I say much about which functions $f$ this will be a reasonable definition for. Instead, I’ll focus on the geometric interpretation of $\int fd\chi$.

Let’s think about a function $f:R^2\to R$ of the form $g\cdot I_A$, where $g$ is continuous and $A$ is convex. Thus, $f$ is supported on $A$ and continuous everywhere except perhaps on the boundary of $A$, where it might jump in value as it crosses the boundary. I’ve just been reading something that talks about functions `suffering a jump discontinuity’. The suffering of $f$ is limited to $\partial A$.

What is $\int fd\chi$? How can we understand it?

Well, $\int fd\chi$ is the average over all orthonormal bases of the quantity “$J(f)$ with respect to that basis”. So, take an orthonormal basis — a coordinate system — and let’s consider $J(f)$.

Recall that the definition of $J(f)$ was slicewise. For each $x\in R$, we take the function $f(x,-):R\to R$ and put $F(x)=J(f(x,-))$. In the picture, the value of $x$ shown is in the vertical shadow of $A$, so $F(x)$ is equal to $f(x,y)$.

Now since $f$ is continuous, $F$ is too, except that $F$ has a jump discontinuity at each end of the shadow. So, $J(F)=f(x_0,y_0)$. Finally, by definition, $J(f)=J(F)$, and so $J(f)=f(x_0,y_0)$.

So in the end, $J(f)$ is something really trivial:

$J(f)$ is the value of $f$ at the leftmost point of $A$

where ‘leftmost’ refers to the basis concerned. (I’m assuming for simplicity that the boundary of $A$ is smooth and contains no line segments. This isn’t crucial.)

But this isn’t the same as $\int fd\chi$. To get that, we have to average over all orthonormal bases of $R^2$. That is, we slowly rotate our coordinate axes through ${360}^{\circ }$, at each moment recording the value of $f$ at the ‘leftmost’ point of $A$ (with respect to the current axes), then taking the mean. As we rotate, that leftmost point works itself around the whole boundary of $A$, never backtracking. And here’s the important thing:

It spends more time at some boundary points than others.

To see why, consider a convex set like this:

For almost all choices of axes, the leftmost point of $A$ will be in one of the red parts of the boundary. Only rarely will it be elsewhere.

So as we rotate the axes, the leftmost point with respect to the axes moves quickly over parts of the boundary with low curvature, and lingers where the curvature is high. We’d therefore imagine that $\int fd\chi$ would be the integral of $f$ over the boundary of $A$ with respect to some kind of curvature measure on $\partial A$.

This turns out to be true. In fact,

$$\int fd\chi ={\int }_{\partial A}fd\varphi$$

where $\varphi$ is the angle that the tangent makes with some fixed, arbitrarily chosen reference line:

This is good, but there’s another way to put it too. When we integrate along a curve, we usually do it with respect to the arclength measure, typically written as $ds$. And the rate of change of the angle $\varphi$ per unit arclength is nothing but the classical curvature $\kappa$. That is, $\kappa =d\varphi /ds$. Putting this together with the last equation, we get

$$\int fd\chi ={\int }_{\partial A}f\cdot \kappa ds.$$

So, the integral against the Euler characteristic of a function of this type is naturally expressed in terms of curvature.

You can go further down this track. If you know about intrinsic volumes, you can ask and answer the question: what does it mean to integrate against an intrinsic volume? You’ll see that each intrinsic volume corresponds to a different curvature measure; in $n$ dimensions, we get $n$ different curvature measures on the boundary of a convex set.

What I’d like to know is how much of this story is well-known. Curvature measures are extremely well-studied, and connections between curvature and Euler characteristic go back to the Gauss–Bonnet theorem at least. On the other hand, I’ve never heard anyone talking explicitly about integration against the Euler characteristic. Does anyone know where this stuff is written up?

How to enjoy a solar eclipse with your kids, making shadow magic with a pinhole viewer.

• Title: Linking Type Ia Supernovae Progenitors and the Resulting Explosions
• Authors: Ryan J. Foley et al.
• First Author’s Institution:  Harvard-Smithsonian Center for Astrophysics

Background

You probably heard that the 2011 Nobel Prize in Physics went to Perlmutter, Schmidt, and Riess for their discovery of the accelerating universe.  You might even know that they measured the universe’s expansion with type Ia supernovae.  We can estimate the luminosity of these so-called standard candles very precisely and thus infer how far away the supernova is.  However, one outstanding question discussed in a previous astrobite is, “How standard are standard candles?”  If we have overlooked a process that allows some type Ia supernovae to be brighter than others, there are inherent errors in our measurement of the universe’s acceleration.

Two different populations of stars might lead to type Ia supernovae.  The two different progenitor systems are classified as single-degenerate or double-degenerate.  A single-degenerate system includes a white dwarf orbiting another star at such a close distance that the white dwarf’s gravity strips gas from the other star.  The  gas forms an accretion disk around the white dwarf as it spirals onto the white dwarf’s surface.  Eventually, the mass of the white dwarf exceeds the Chandrasekhar limit, and the white dwarf can no longer hold itself up by electron degeneracy pressure; it explodes in a type Ia supernova.  A double-degenerate system consists of two white dwarfs that collide, creating a type Ia supernova.  So how can we tell these two progenitor systems apart from the properties of a type Ia supernova?

In this paper

The authors claim: “For the first time, we have shown a direct connection between the progenitor system of a SN Ia and its explosion properties.”  The authors examined 23 bright supernovae with high-resolution spectra to look for correlations between the sodium D absorption line, which is a relic of the progenitor environment, and the explosion properties.  They found that progenitors that have blue-shifted sodium D lines produce redder, higher-velocity explosions, with 98.9-99.9% confidence (see figure below).  Here is a brief recap of the three different types of measurements the authors made that differentiated between the two type Ia supernova populations:

Is the circumstellar sodium D absorption line blue-shifted?

The authors examine the sodium D region of the spectrum for narrow absorption lines in addition to the host galaxy’s sodium D line.  Because supernovae happen in galaxies, a spectrum of a supernova also contains information about the host galaxy, and it is critical to disentangle the two.  Future work has found that some supernovae exhibit variable sodium D absorption lines.  Because galaxies change on extremely slow timescales, their spectra do not vary; therefore, the variale sodium D line must come from the region around the supernova.

The supernova’s sodium D line is blue-shifted, red-shifted, or symmetric (i.e. indistinguishable) relative to the host galaxy’s sodium D absorption line, or the host galaxy has no reference sodium D line.  Previous studies have shown that many more supernovae have blue-shifted than red-shifted circumstellar sodium D lines, indicating that there is a population of progenitors characterized by strong outflows relative to the host galaxy’s velocity.  This study agrees, finding 6 supernovae with red-shifted and 10 with blue-shifted lines.

• Blue-shifted: indicates either strong outflow from progenitor or statistical deviation due to interstellar medium.
• Red-shifted: indicates either inflow into progenitor or statistical deviation due to interstellar medium.
• Single/symmetric: indicates weak or no outflow from the progenitor.
• No absorption: host galaxy lacked sodium D absorption line.

Going back to single- versus double-degenerate progenitors, we might expect the the single-degenerate system, which requires the white dwarf to slowly accrete matter from its companion, to develop outflows, whereas the catastrophic merger scenario of the double-degenerate case would not have time to form a steady outflow.

Does the light curve have a red pseudo-color?

The authors measure the magnitude in the blue (B) filter at the time of maximum brightness in the blue filter minus the magnitude in the visible (V) filter at the same time.  After a correction for galactic extinction, this serves as a proxy for the extinction due to circumstellar material and is thus a good indicator of gas around the supernova.

• Higher B-V (redder): progenitor lived in a gas-rich environment.
• Lower B-V (bluer): progenitor lived in a gas-poor environment.

Because a single-degenerate system involves the white dwarf messily acquiring the gaseous outer layer of its companion, this would lead to a supernova in a gas-rich environment.  White dwarfs are very gas-poor objects (they are basically giant balls of carbon), and so the double-degenerate scenario does not involve a gaseous environment.

Is the supernova’s ejection velocity unusually high?

The authors measure from the red-shift of the Silicon II line at the time of the supernova’s maximum brightness and use the Doppler formula to convert this to an ejection velocity (i.e. energy per unit mass).  This is the velocity (about 12,000 km/s) of the supernova’s explosion front, and it is completely different from the progenitor outflow velocity measured in the blue-shifted sodium D lines, which results from the comparatively lethargic dribbling of gas from the progenitor.

• Higher velocity: more energetic explosion!
• Normal velocity: explosion was pretty meh (by supernova standards).

It is not obvious to me whether the single- or double-degenerate supernova would produce a more energetic explosion.

Since you asked, here's an update on The Project. I was a bit quiet on it the last two weeks with the end of semester duties taking up lots of time (setting finals, grading them, extra homeworks and so forth - see several recent posts). Just before that however, I did a bit of a push to finish some pages that I wanted to include in my presentation to the Los Angeles Institute for the Humanities (I mentioned that to you before - see here. It went very well by the way, with lots of enthusiasm from lots of those who were kind enough to attend.) Over the four or five days I've started on a new aspect of the project that has led me in an interesting direction - revisiting some of the original pages I did, two years ago. I decided then that the best thing to do to learn what I needed to learn about production of a graphic novel is just to... produce one. So I set upon a prototype, learning lots of techniques along the way, making lots of twists and turns in developing the methods that worked best for me, and so forth. I've refined the route I take from pencil to final product over the time (I've described it to you a number of times here on the blog), and in addition, my basic drawing skills have moved along a lot too... Anyway, looking back, I see that the first few pages especially are quite dreadful, a combination of bad drawing and also the struggle with digital inking techniques that I decided to abandon in favour of old school nib pens and ink. (It is actually satisfying to see just how far I've come in a short time... fixing various things took a relatively short time compared to how long I'd have agonized over them back then...) So since I want to show this prototype to people, I've decided to re-draw and [...]

As part of an on-going paper with Kerrie Mengersen and Pierre Pudlo, we are using a GARCH(1,1) model as a target. Thus, the model is of the form

which is a somehow puzzling object: the latent (variance) part is deterministic and can be reconstructed exactly given the series and the parameters. However, estimation is not such an easy task and using the garch() function in the tseries package leads to puzzling results! Indeed, simulating data shows some high variability of the procedure against starting values:

genedata=function(para,nobs){

   pata=epst=sigt=rnorm(nobs)
   sigt[1]=sqrt(para[1])
   pata[1]=epst[1]*sigt[1]
   for (t in 2:nobs){
      sigt[t]=sqrt(para[1]+para[2]*pata[t-1]^2+para[3]*sigt[t-1]^2)
      pata[t]=epst[t]*sigt[t]
      }
   list(pata=pata,sigt=sigt,epst=epst)
}
> x = genedata(c(1, 0.3, 0.2),1000)$pata
> garch(x,trace=FALSE)

Call:
garch(x = x, trace = FALSE)

Coefficient(s):
       a0         a1         b1
4.362e+00  1.976e-01  6.805e-14
> garch(x,trace=FALSE,start=c(1,.3,.2))

Call:
garch(x = x, trace = FALSE, start = c(1, 0.3, 0.2))

Coefficient(s):
    a0      a1      b1
0.8025  0.2592  0.3255
> simgarch=genedata(c(1, 0.2, 0.7),1000)

Call:
garch(x = simgarch$pat, trace = FALSE)

Coefficient(s):
a0         a1         b1
8.044e+00  1.826e-01  4.051e-14
> garch(simgarch$pat,trace=FALSE,star=c(1, 0.2, 0.7))

Call:
garch(x = simgarch$pat, trace = FALSE, star = c(1, 0.2, 0.7))

Coefficient(s):
a0      a1      b1
1.1814  0.2079  0.6590

The above code clearly shows the huge impact of the starting value on the final estimate….

Filed under: R, Statistics, University life Tagged: GARCH, R, times series, tseries

SpaceX and NASA have completed a successful flight readiness review (FRR) for the Dragon's upcoming visit to the International Space Station.

I've finally succumbed to the sickness sweeping the land, and find myself wide awake at 5am (this is not really a natural state for an astronomer). So, as I sit here with sore throat, a quick post for you.

Blair Conn, my ex-student and now Humboldt Fellow in Heidelberg, and I, have had a paper accepted for publication in the  Astrophysical Journal. The focus of the paper is the Monoceros Ring, a vast "stream" of stars that appears to circle at the outer edge of the Milky Way galaxy.



The ring has had a bit of a checkered past, not its existence, but its origin.

People generally fall into two camps, those that think that Monoceros is just a natural piece of galaxy, a region of the stellar disk that has been puffed up (also known as the flare or warp of the disk), whereas others think the ring is the debris from a dwarf galaxy which was tidally disrupted when it came to close to the disk of the Milky Way. Potentially it is the debris from the Canis Major Dwarf Galaxy, a little galaxy thought to be nestled into the disk of the Milky Way.

The problem is that the Monoceros Ring is immense on the sky, and to map it in detail takes a lot of work. But it is this mapping that is required to get a chance to tell the difference between the two ideas.

Which brings us to Blair's paper. If you want to map an immense structure, you need a big field of view, and one of the biggest, on one of the best telescopes, is Suprime-Cam on Subaru in Hawaii.

IMHO, this is one of the best imagers in the world (and it's only going to get better, but that's for another post).

Superime-Cam was used to take a number of deep fields in directions away from the disk of the Milky Way in three strips.
The red regions are the fields (distorted as we are looking at a large patch of sky on flat paper). The grey underneath is the extinction due to galactic dust. This dust is the real bane of astronomers!

 Cutting to the chase (as I need to get a shower and get to work) what do we find. Well, the distribution of stars in these fields (in terms of how many and how far they are) appear to match both the models, the galactic and extra-galactic source for Canis Major.

But!!! it appears that the chemical composition of stars in the ring is different to that in the disk of the Milky Way, strongly suggesting that the stars in the ring are not simply puffed up from the galactic disk. Maybe Monoceros really is an extragalactic invader?

However, experience has taught me that evidence doesn't strongly sway peoples' viewpoint on things, and I am sure that we will here counter claims about its origin. But this is fun and how science is done. Well done Blair!

Slicing The Monoceros Overdensity with Suprime-Cam 

Blair C. Conn, Noelia E. D. Noël, Hans-Walter Rix, R. R. Lane, G. F. Lewis, M. J. Irwin, N. F. Martin, R. A. Ibata, A. Dolphin, S. Chapman

We derive distance, density and metallicity distribution of the stellar Monoceros Overdensity (MO) in the outer Milky Way, based on deep imaging with the Subaru Telescope. We applied CMD fitting techniques in three stripes at galactic longitudes: l=130 deg, 150 deg, 170 deg; and galactic latitudes: +15 < b [deg] < +25 . The MO appears as a wall of stars at a heliocentric distance of ~ 10.1\pm0.5 kpc across the observed longitude range with no distance change. The MO stars are more metal rich ([Fe/H] ~ -1.0) than the nearby stars at the same latitude. These data are used to test three different models for the origin of the MO: a perturbed disc model, which predicts a significant drop in density adjacent to the MO that is not seen; a basic flared disc model, which can give a good match to the density profile but the MO metallicity implies the disc is too metal rich to source the MO stars; and a tidal stream model, which bracket the distances and densities we derive for the MO, suggesting that a model can be found that would fully fit the MO data. Further data and modeling will be required to confirm or rule out the MO feature as a stream or as a flaring of the disc.

Tomorrow at 1 p.m. EST, accelerator physicists from four national laboratories will take to Twitter to discuss discovery science with the tweeting public. To take part in the event, dubbed Lab Breakthrough Office Hours, use the hashtag #labchat.

• Title: A New Sample of Candidate Intermediate-Mass Black Holes Selected By X-ray Variability
• Authors: Naoya Kamizasa, Yuichi Terashima, & Hisamitsu Awaki
• 1st Author’s Institution:  Department of Physics, Ehime University, Japan

Several previous astrobites have discussed the subject of intermediate-mass black holes – objects with masses somewhere in between those of stellar-mass black holes, the compact remnants of stars gone supernova, and supermassive black holes (SMBH), the monsters weighing in at several million to several billion (or more!) solar masses, which are  found at the center of every large galaxy. Intermediate-mass black holes would fill in the several-orders-of-magnitude gap between these two classes of objects, with masses somewhere between 1000 and 1,000,000 times that of the sun. While there are certainly theoretical grounds for intermediate-mass black holes to exist, finding them has proven something of a challenge. The authors of this paper seek to take on that challenge by using a clever technique, the X-ray variability of black holes, to try to scout out some of these elusive objects.

Some background on black holes…

Posted on behalf of Katherine Rowland.

Orbiting high above the Earth inside the International Space Station, an astronaut issued a grim report card on the state of the planet yesterday, describing current levels of resource consumption as 50% higher than the world can sustainably maintain.

In a recorded message, Andre Kuipers of the European Space Agency offered a unique view of the planet he circles 16 times a day. “From up here I can see humanity’s footprint, including forest fires, air pollution and erosion,” he said, launching the World Wildlife Fund (WWF) Living Planet Report for 2012.

The biennial audit, produced in collaboration with the Zoological Society of London and the Oakland, California-based Global Footprint Network, projects that by 2030 humanity will require the equivalent of two planets to sustain current levels of population growth and resource depletion. “We are living as if we have an extra planet at our disposal,” writes Jim Leape, director general of WWF International, in the report. “We are using 50% more resources than the Earth can provide, and unless we change course that number will grow very fast.”

The report monitored ecosystem health by tracking 9,000 populations of more than 2,600 species of mammals, birds, reptiles, amphibians and fish. The findings indicate that global biodiversity has decreased by nearly 30% since 1970, and by as much as 60% in the tropics.

According to the report, the precipitous losses in tropical regions point to a “potentially catastrophic” gap between the ecological footprint of rich and poor nations. By the study’s measures, if everyone on the planet lived like an average person in the United States, four Earths would be required to replenish the annual demand on natural resources. The United States ranks as the country with the fifth-largest per-capita resource footprint, trailing Qatar, Kuwait, the United Arab Emirates and Denmark.

And the disparity between rich and poor nations has been increasing, according to the report’s footprint index, which evaluates resource consumption in relation to biocapacity, or the ability to renew resources and absorb CO₂ emissions.

This trend is driven by high-income countries that subsidize their economic growth on the backs of developing nations, says Gemma Cranston, an engineer and lead scientist at the Global Footprint Network in Geneva. She argues that the consumption demands of rich nations encourage poor countries to plunder their resource wealth for export.

The report — the eighth of its kind — comes five weeks before the United Nations Conference on Sustainable Development in Rio de Janeiro. Cranston says that policy-makers there will have an opportunity to forge a new trajectory for economic growth. “High-income countries can help low-income countries set up systems that allow for gains in social well-being that don’t come at the expense of ecological harm.”

But Colin Butfield, head of campaigns at WWF UK, is doubtful that the summit will result in the level of international commitment necessary to halt “the alarming momentum of environmental damage”. Despite the international conventions signed since the original Rio summit in 1992, biodiversity losses and CO₂ emissions have accelerated. “Twenty years on and the overall direction of travel has gotten worse,” he says. “And that direction is pretty terrifying.”

No description available

Posted on behalf of Mico Tatalovic.

Members of Montenegro’s unofficial science academy, the Doclean Academy of Sciences and Arts (DANU), got a nasty surprise this week.

In March, the country’s parliament mandated that DANU should merge with the official academy, the Montenegrin Academy of Science and Arts (CANU), in an effort to unite the country’s scientific potential. The two academies have historically been divided along political and ideological lines.

But on 14 May, only 5 out of 29 DANU members were elected to CANU — and even those only as associate and foreign members.

DANU was established in 1998 as part of the Montenegrin national renaissances that led to its independence from Serbia in 2006. CANU was set up in 1971, when Montenegro was one of the republics in former Yugoslavia.

CANU members have opposed the merger — which effectively forces them to admit verified DANU members to their academy — arguing that it undermines their autonomy from government. CANU challenged the law in the constitutional court and also instituted a new procedure that puts members of DANU through a rigorous selection process instead of simply admitting them, as the law mandates.

Both DANU and the government’s science ministry have deemed this new procedure illegal, and this case is also being fought in the constitutional court. DANU members will probably have to wait for rulings from both of these cases to know whether or not they can join the country’s official academy.

“Decisions made at the CANU assembly on 14 May will not be valid, because their procedures do not call for verification of DANU members, but instead an election of new members,” Milena Milunović, an aide at the science ministry told Pobjeda newspaper earlier this month. The ministry declined to comment further until the court ruling is out.

DANU issued a statement calling CANU’s most recent decision “illegitimate and against the law”. Meanwhile, CANU spokesperson Marina Vukičević told Nature that the election of DANU members was done according to a procedure laid down in the new law, and not according to CANU’s disputed new procedure, and is therefore legitimate.

Every now again I get surprised by a photo, showing me something I didn’t know about. And I love it even more when that surprise is from an object I thought I knew!

So check out this incredible image of the nearby galaxy Centaurus A, a nearby galaxy harboring a whole slew of surprises:

[Click to galactinate, or get the 4000 x 4000 pixel version, or, if you're feeling frisky, cram this onto your hard drive: an image that's 8500 x 8400 pixels and 29 Mb in size! And trust me: you want to.]

Isn’t that stunning? This picture was taken by the MPG/ESO 2.2 meter telescope in Chile, and once you get over its beauty you’ll realize this galaxy is, frankly, seriously messed up.

Cen A is about 12 million light years away and has roughly the same mass as our Milky Way, containing a few hundred billion stars. The underlying glow of those stars is what makes that round background fuzz in the image, and takes on the familiar elliptical shape of many such galaxies. [Note: All the individual stars you see here are in our on galaxy, since we're inside ...

• n+1: Lions in Winter, Part One

  A very long and thorough history of the New York Public Library, how its current plans to gut the main research library came about, and what they mean for the idea of a public research library.

• Correcting the Record on College Graduates and Job Prospects by Joshua Tucker | Washington Monthly

  Using the same American Community Survey for 2009 and 2010 as Fogg and Harrington, but focussing on actual unemployment by major, Carnevale, Cheat and Strohl (Hard Times, Georgetown University, Center for Education and the Workforce, 2011) have similar findings (p. 7). Recent college graduates with a business major have a 7.4% unemployment rate, those with an arts degree have an 11.1% rate (with social science majors having an 8.9% rate and humanities/liberal arts students having a 9.4% rate). Combining these two studies, it is clear that being an arts major does not compel one to, at best, discussing supersizing with customers, nor does being a business major totally guard against that. Yes, business majors do better in the job market, and they make more money in their entry level positions than do arts majors ($39,000/yr vs. $$30,000/yr), but is this enough to tell everyone to flock into undergraduate business schools?

• Am I Mom Enough? A Motherhood Wish List - 24 Hour Workday - Boston.com

  The [infamous Time cover] story also made me think about what I wanted to teach Andrew--I mean really teach him. I'm not talking about the trendy must-dos that crop up each year about feeding and sleeping and discipline, insecurity porn concocted just in time to fill a fresh generation of parents with self-doubt. No, I'm talking about the things that I want to impart in average, totally inextreme moments, when my breasts are covered and my skinny jeans are in the wash. Here's my wish list.

Read the comments on this post...

I’m currently stuck in the office while my third year students are tackling an exam I set. I have to wait by the telephone in case there’s a problem with the paper that I have to sort out.

As a quick diversion I thought I’d give my blog readers a little test of their own. Try this little poser:

<noscript><a href="http://polldaddy.com/poll/6232931">Take Our Poll</a></noscript> Follow @telescoper

In beautiful agreement with the Standard Model, two new excited states (see below) of the Λ_b beauty particle have just been observed by the LHCb Collaboration. Similarly to protons and neutrons, Λ_b is composed of three quarks. In the Λ_b’s case, these are up, down and… beauty.

 

Although discovering new particles is increasingly looking like a routine exercise for the LHC experiments (see previous features), it is far from being an obvious performance, particularly when the mass of the particles is high. Created in the high-energy proton-proton collisions produced by the LHC, these new excited states of the Λ_b particle have been found to have a mass of, respectively, 5912 MeV/c² and 5920 MeV/c². In other words, they are over five times heavier than the proton or the neutron.

Physicists only declare a discovery when data significantly show the relevant signal. In order to do that, they often have to analyse large samples of data. To obtain its beautiful result, the LHCb Collaboration has analysed the information coming from about 60 million million (6x10¹³) proton-proton collisions collected during the 2011 data-taking period. In particular, since the excited states only survive for a very short time before decaying, physicists carefully studied the decay products and tracked the whole process back to the decay vertex. The analysis took scientists several months to complete but today they are able to present the discovery with very high statistical significance, namely 4.9 σ for the first excited state and 10.1 for the second one.

Although never observed before, the excited states of the Λ_b particle were expected to exist according to the Standard Model, the theory that tells us how quarks combine to build particles and matter. The LHCb result is therefore a new confirmation of the success of the theory itself.

 

EXCITED STATES OF MATTER

Read more about this result on the LHCb Public Webpage.

Proof-of-principle experiment shows how humanoid robots can co-operate on a large scale by copying the behavior of social insects and bacterial colonies.

In recent years, various companies and labs have developed impressive humanoid robots that walk, shuffle and even run. Some even dance in groups of up to 20, performing sophisticated choreographed routines. 

This kind of synchronisation is no easy task. One way to do it is have one robot as the leader, broadcasting details of its movement and position over a network that the other robots all follow. 

The trouble is that network dynamics are not as predictable as choreographers would like. Small delays of half a second or so are common while some messages can be delayed by several seconds. That's clearly not good enough for a dance routine or any other type of synchronised behaviour.

So the approach preferred by roboticists is to program each robot with the dance routine, synchronise their internal clocks at the start of the performance and then leave them to it. 

The advantage is that If the performance is reasonably short, the chances of the clocks becoming desynchronised can be made small.  The disadvantage is that if the robots become desynchronised--if one falls over, for example--there is no way to regain synchronisation.

So roboticists have been searching for a better form of synchronisation that is more robust to the various trials and tribulations that befall robotic dancers. Today, Patrick Bechon and Jean-Jacques Slotine at the Massachusetts Institute of Technology in Cambridge, reveal a new approach based on the biological phenomenon of quorum sensing.

Biologists have long puzzled over the ability of bacteria and social insects to sense not only the presence of compatriots but their number and to synchronise their behaviour.

It turns out that these creatures perform this synchronisation using a process called quorum sensing. This works by constantly releasing signalling molecules into the environment while at the same time measuring the local concentration of these molecules. 

This concentration rises as more creatures join the local population and so is an effective measure of population density. When the concentration rises over some threshold level, it triggers a different behaviour such cell division, pathogen production and nest building.  

Now Bechon and Slotine say a similar approach provides a robust way to synchronise humanoid robots. The ideal approach  to synchronisation is for each robot to have access to every other robot's position. Instead, the quorum sensing approach gives, each robot  access to a global variable such as the average position or average clock time. Each robot can also change this variable because it contributes to the average.

The idea is that if each robot attempts to synchronise with this global average, the swarm as whole should keep good time.

These guys test out their approach with a group of eight NAO robots built by the French robotics company Aldebaran. Each has an internal clock which attempts to synchronise with  a global average time maintained by a central server.

It's important to point out that the server is not acting as a master with the robots as slaves that simply follow its signal. If the connection to the central is lost, the robots simply continue with routine but without centralised synchrony. 

Instead, the central server is more like a a kind of environment that the robots can sense and interact with.

This arrangement has the significant advantage that if one robot falls over it can simply get back up and join in again when it has resynchronised its movements with the group (see video).

This work is part of a broader development in robotics. The advent of relatively cheap humanoid robots from Aldebaran and other companies means that the large-scale sychronisation of humanoid swarms is now possible.

That's interesting because while synchrony allows large numbers of robots to do the same thing at the same time--such as dancing or marching--it also allows large number so robots to do different but related tasks at the same time. 

In other words, synchrony is an enabling technology for large scale co-operation. And that opens the way to an entirely new set of tasks that robots could do--think manufacturing and construction. Perhaps even nest building.

Ref: arxiv.org/abs/1205.2952: Synchronization And Quorum Sensing In A Swarm Of Humanoid Robots 

Jordan Peacock has suggested interviewing me for Five Books, a website where people talk about five books they’ve read.

It’s probably going against the point of this site to read books especially for the purpose of getting interviewed about them. But I like the idea of talking about books that paint different visions of our future, and the issues we face. And I may need to read some more to carry out this plan.

So: what are you favorite books on this subject?

I’d like to pick books with different visions, preferably focused on the relatively near-term future, and preferably somewhat plausible—though I don’t expect every book to seem convincing to all reasonable people.

Here are some options that leap to mind.

Whole Earth Discipline

• Stewart Brand, Whole Earth Discipline: An Ecopragmatist Manifesto, Viking Penguin, 2009.

I’ve been meaning to write about this one for a long time! Brand argues that changes in this century will be dominated by global warming, urbanization and biotechnology. He advocates new thinking on topics that traditional environmentalists have rather set negative opinions about, like nuclear power, genetic engineering, and the advantages of urban life. This is on my list for sure.

Limits to Growth

• Donnella Meadows, Jørgen Randers, and Dennis Meadows, Limits to Growth: The 30-Year Update, Chelsea Green Publishing Company, 2004.

Sad to say, I’ve never read the original 1972 book The Limits to Growth—or the 1974 edition which among other things presented a simple computer model of world population, industrialization, pollution, food production and resource depletion. Both the book and the model (called World3) have been much criticized over the years. But recently some have argued its projections—which were intended to illustrate ideas, not predict the future—are not doing so badly:

• Graham Turner, A comparison of The Limits to Growth with thirty years of reality, Commonwealth Scientific and Industrial Research Organisation (CSIRO).

It would be interesting to delve into this highly controversial topic. By the way, the model is now available online:

• Brian Hayes, Limits to Growth.

with an engaging explanation here:

• Brian Hayes, World3, the public beta, Bit-Player: An Amateur’s Look at Computation and Mathematics, 15 April 2012.

It runs on your web-browser, and it’s easy to take a copy for yourself and play around with it.

The Ecotechnic Future

John Michael Greer believes that ‘peak oil’—or more precisely, the slow decline of fossil fuel production—will spell the end to our modern technological civilization. He spells this out here:

• John Michael Greer, The Long Descent, New Society Publishers, 2008.

I haven’t read this book, but I’ve read the sequel, which begins to imagine what comes afterwards:

• John Michael Greer, The Ecotechnic Future, New Society Publishers, 2009.

Here he argues that in the next century or three we will go through a transition through ‘scarcity economies’ to ‘salvage economies’ to sustainable economies that use much less energy than we do now.

Both these books seem to outrage everyone who envisages our future as a story of technological progress continuing more or less along the lines we’ve already staked out.

The Singularity is Near

In the opposite direction, we have:

• Ray Kurzweil, The Singularity is Near, Penguin Books, 2005.

I’ve only read bits of this. According to Wikipedia, the main premises of the book are:

• A technological-evolutionary point known as “the singularity” exists as an achievable goal for humanity. (What exactly does Kurzeil mean by the “the singularity”? I think I know what other people, like Vernor Vinge and Eliezer Yudkowsky, mean by it. But what does he mean?)

• Through a law of accelerating returns, technology is progressing toward the singularity at an exponential rate. (What does in the world does it mean to progress toward a singularity at an exponential rate? I know that Kurzweil provides evidence that lots of things are growing exponentially… but if they keep doing that, that’s not what I’d call a singularity.)

• The functionality of the human brain is quantifiable in terms of technology that we can build in the near future.

• Medical advances make it possible for a significant number of Kurzweil’s generation (Baby Boomers) to live long enough for the exponential growth of technology to intersect and surpass the processing of the human brain.

If you think you know a better book that advocates a roughly similar thesis, let me know.

A Prosperous Way Down

• Howard T. Odum and Elisabeth C. Odum, A Prosperous Way Down: Principles and Policies, Columbia University Press, 2001.

Howard T. Odum is the father of ‘systems ecology’, and developed an interesting graphical language for describing energy flows in ecosystems. According to George Mobus:

In this book he and Elisabeth take on the situation regarding social ecology under the conditions of diminishing energy flows. Taking principles from systems ecology involving systems suffering from the decline of energy (e.g. deciduous forests in fall), showing how such systems have adapted or respond to those conditions, they have applied these to the human social system. The Odums argued that if we humans were wise enough to apply these principles through policy decisions to ourselves, we might find similar ways to adapt with much less suffering than is potentially implied by sudden and drastic social collapse.

This seems to be a more scholarly approach to some of the same issues:

• Howard T. Odum, Environment, Power, and Society for the Twenty-First Century: The Hierarchy of Energy, Columbia U. Press, 2007.

More?

There are plenty of other candidates I know less about. These two seem to be free online:

• Lester Brown, World on the Edge: How to Prevent Environmental and Economic Collapse, W. W. Norton & Company, 2011.

• Richard Heinberg, The End of Growth: Adapting to Our New Economic Reality, New Society Publishers, 2009.

I would really like even more choices—especially books by thoughtful people who do think we can solve the problems confronting us… but do not think all problems will automatically be solved by human ingenuity and leave it to the rest of us to work out the, umm, details.

Europe has a plan. It's called Europe 2020 and it's "the EU's growth strategy for the coming decade." Part of that plan is an initiative called "Innovation Union" which "aims to improve conditions and access to finance for research and innovation in Europe". So many nice words.

In what I found to be a great idea for communicating science, part of this initiative is a collection of short science fiction stories based on actual research projects. The short stories, called "Tales from the Future," are written by Robert Billing, and while they seemed to me a little constructed towards their aim, they are not bad at all. You can read them online here. Enjoy!

Tell me a story. Tell me the story about the three hippopotamuses.

Ummm... OK.

Once upon a time, there were three hipopotamuses. And they lived in Africa, in a river.

Right, it was a great big long river, that had so much salt in it that they could float!

Well, salt does help things float, but rivers are usually fresh water. Anyway, hippos are pretty fat, so they can float in fresh water.

OK

And one day... What happened then?

Read the rest of this post... | Read the comments on this post...

As usual, reading the latest issue of Significance is quite pleasant and rewarding (although as usual I have to compete with my wife to get hold of the magazine!). This current issue is dedicated to the (London) Olympics. With articles on predictions of future records, on whether or not the 1988 records can be beaten (the Seoul Olympics were the last games before more severe anti-drug tests were introduced), on advices to Usain Bolt for running faster (!) and on the objective dangers of dying from running a marathon (answer: it is much more “dangerous” to train!).

However, a most puzzling (and least statistical) article is Stephanie Kovalchik’s proposal for a gender-neutral Olympics.  The author’s theme is that, in most sports (the exceptions being shooting, yachting, and horse riding, where competitions are mixed), raw performances of women are below those of men for physical and physiological reasons. Stephanie Kovalchik thus “question[s] whether a sex-stratified Olympics is the product of groundless stereotypes about male athletic superiority or could be justified by gender differences at the elite level of sport” (p.20). Unsurprisingly, she concludes that no amount of training seems capable to bring both sexes at the same level: indeed, for instance, Paula Radcliffe, the fastest female marathon runner (2:15:24), is still 11 minutes beyond Patrick Makau, the fastest male marathon runner (2:03:38). They are both super-terrific athletes, the top ones in their categories. Now, Paula runs half-marathon and marathon faster than the best male runners in my team (Insee Paris Club). Where’s the problem?! And why should we try to rank Paula against Patrick?!

A parenthesis: the author mentions a most bizarre (but eventually inappropriate) exception: in the Badwater Ultramarathon, a crazy race covering 135 miles and going from Badwater, Death Valley, at 280’ (85m) below sea level, to the Mt. Whitney Portals at nearly 8,300’ (2530m), with a total of 13,000’ (3962m) of cumulative vertical ascent, four women won over the 25 occurrences of the race. I found this phenomenon quite curious and went to check first the records of the comparable ultra-trail du Mont Blanc, another even crazier race (168km, 9,600 metres of positive height gain, at mostly higher altitudes, between 1000m and 2500m), and saw that last year the first woman in the race was 13th in total, with a difference of four and a half hours with the winner (20:36 hours, believe it or not..!). Going back to the Badwater Ultramarathon, checking the results showed that the race actually attracts a very limited number of runners, from 17 finishers the first year to 83 last year (where the first woman was 7th, about 5 hours from the winner), with a huge variation between runners and between years. So I would not draw so much of a conclusion from this example, certainly not that “in an event where sheer dogged endurance, guts and determination must count for almost everything, we may be there already”. It is rather a law of small numbers: such extreme events attract a very small number of participants with incredibly variable finishing times, e.g. two of the four winning women won out of…5 (1988) and 2 (1989) finishers, while the two other victories were achieved by Pamela Reed over 45 (2003) and 57 (2002) competitors, a much more remarkable feat. Meaning that one or two runners missing or giving up brings a huge change in the final time. The ultra-trail du Mont Blanc now involves a thousand runners and there, numbers count. End of the parenthesis (with total respect to all those runners, I wish I could do it!).

Going back to the paper proposal, Stephanie Kovalchik considers that “credit merit apart from hereditary luck will favour individuals who possess the best genes for sport. Thus, prejudice – in the true sense of pre-judging – at the Olympics runs deeper than gender lines. Geneticism more than sexism is to blame for making the possession of a Y chromosome an advantage at the Games” (p.21). She suggests to instead rank athletes by a “statistical adjustment [that would]  remove the confounding factor of genetic inheritance, to provide a standard of achievement that all could aim at, no matter what their hereditary luck” (p.22). In essence, the winner would be the one that had gained the most compared with a “demographically matched sample of untrained individuals” (p.24). If I may, this sounds perfectly ridiculous! First, the whole point of the Games and of any sporting competition is to determine the “best” athlete. This is not an egalitarian goal and can and does lead to poor outcomes such as cheating, drug enhanced performances, nationalistic recuperations, commercialisation, bribery, and so on. It is thus perfectly coherent to be against those competitions. (I am not a big fan of the Olympics myself for this reason. However, without competition, even at my very humble level, and with little hope of winning anything, I would certainly train much less than I currently do.) But to try to reward efforts to counteract physical differences sounds like political correctness pushed to the extreme!  Second, and this is why I find the paper so a-statistical!, the adjustment must be with respect to a reference population. If we carry the argument to its limit, the only relevant population is made of the athlete him/herself. Indeed, genetic, sociological, cultural, geographical, financial, you-name-it, elements should all be taken into account! Which obviously makes the computation just impossible because then everyone is competing against him/herself.

Filed under: Mountains, Running, Statistics, University life Tagged: Badwater Ultramarathon, London, marathon, Mont Blanc, Olympics, Pamela Reed, Paula Radcliffe, Significance, sport statistics, ultramarathon

Researchers deciding where to place the planned Neutrino Mediterranean Observatory, or NEMO, were measuring water currents and temperatures when they stumbled upon unexpected patterns in the water.

I was just going to let this go, but I couldn't. I can't stand how bad this report is, and it came from TIME, not some rinky-dink college paper!

Here's part of the original report:

Harry Potter and Star Trek fans, rejoice! Teleportation is real. Using powerful lasers and optics to manipulate photons, or units of light, researchers in China set a record for teleporting a photon more than 10 miles, TIME reported in 2010. Now, a different team of physicists at the University of Science and Technology of China in Shanghai say they have shattered that record, claiming to have sent a photon more than 60 miles.

Quantum teleportation, which has been around since 1997, is a little different than what you see in sci-fi movies. Considered “one of the holy grails of practical quantum communication,” as the scientists write in their abstract, teleportation is the ability to essentially move one object from one place to another without traversing the space in between. But, as Forbes explains, the actual object is not moving from point A to point B. Rather, the distant photon mirrors the information contained by the original photon, essentially becoming an identical twin.

What pissed me off is that they know what they're reporting isn't accurate, but they keep repeating that inaccurate information!

Let's examine this carefully. First, they mislead the reader into thinking that this is "teleportation" that we encounter in "Harry Porter" and "Star Trek":

Harry Potter and Star Trek fans, rejoice! Teleportation is real.

Then they make the first physics mistake:

Using powerful lasers and optics to manipulate photons, or units of light, researchers in China set a record for teleporting a photon more than 10 miles, TIME reported in 2010. Now, a different team of physicists at the University of Science and Technology of China in Shanghai say they have shattered that record, claiming to have sent a photon more than 60 miles.

No. As we shall see, the photo is not the one that is being "teleported", but rather, it is a particular STATE of the photon, or what the article later called "information contained by the original photon". The photons move in a "normal" manner here. Nothing is being teleported as far as the photon entity itself is concerned.

OK, so they already misled people into thinking that this is the Star Trek teleportation. But then, they corrected themselves by saying this:

Quantum teleportation, which has been around since 1997, is a little different than what you see in sci-fi movies.

You think everything should be fine from now on. Oh, but then, they resort back to the stupid Star Trek teleportation:

Considered “one of the holy grails of practical quantum communication,” as the scientists write in their abstract, teleportation is the ability to essentially move one object from one place to another without traversing the space in between.

Oh, so now we are back to moving objects, rather than a state or information, from one place to another. But wait, they then correct themselves back, and this is where the "information" part appears:

But, as Forbes explains, the actual object is not moving from point A to point B. Rather, the distant photon mirrors the information contained by the original photon, essentially becoming an identical twin.

So, how many twists and turns, and self-contradictions can one have in just 2 paragraphs? They know what the correct idea of quantum teleportation is, but they keep weaving this in and out with the Star Trek teleportation. And then we wonder how the general public may understand the wrong thing when they read about science reports in popular media!

TIME, for this report, you get a D-minus!

Zz.

I worked with Hubble Space Telescope data for about ten years, and one of the most amazing things about that was seeing the images fresh off the mirror. Knowing that no human on Earth had ever seen that particular object that sharply was a thrill.

Not every Hubble observation gets turned into a gorgeous image, though. A lot of them don’t need to be for scientific publications, for one thing, and for another not every observation is of a targeted object for a specific purpose. Because of that, there are probably hundreds and hundreds of amazing objects — galaxies, nebulae, star clusters — buried in the data, waiting to be found.

That’s where you come in: the folks at the European Space Agency’s Hubble HQ are holding a contest they call Hidden Treasures. You can look through the Hubble observation archive for images and tweak them using online tools they provide, or you can really roll up your sleeves and use professional astronomical software to prettify the images. They’ve made a video explaining the Hubble archive, which may help.

The contest has nice prizes (an iPod Touch, ...

Quantum tunneling had always been thought too complex to simulate on today's simple quantum computers. Now a new approach to quantum computing has changed that and opens the door to more complex simulations.

The exploitation of quantum weirdness for computing is one of the great goals of modern physics. It's promise is dramatic for a wide range of number-crunching tasks. 

But quantum computers have another trick up their sleeves which is sometimes forgotten--the ability to simulate other quantum systems. Physicists have already shown how quantum computers of various types can simulate phenomenon such as quantum phase transitions and the dynamics of entanglement--things that classical computers simply cannot handle. 

There is one quantum phenomenon, however, that has never been simulated--tunnelling. This is the ability of quantum particles to cross a barrier without seeming to have passed through it.

There's no reason in principle why quantum computers can't simulate tunnelling. The problem is the complexity of the task. 

The simulations performed so far have all involved so-called analogue processes which are relatively straightforward. The idea here is that the mathematical description of one system, its Hamiltonian, is exactly reproduced in another system. 

So watching one system tells you exactly how the other would behave. This is known as analogue quantum particle simulation and it works well provided you can find systems that match in required way. Watching quantum phase transitions is good example because many systems share the same mathematical description.

For more complex problems, physicists have recently been thinking about another approach. The idea here is to break the mathematical system into different parts and simulate them separately. This is known as digital quantum particle simulation and it has huge potential for events that involve more than one object, such as quantum chemistry and tunneling.

The problem is the sheer complexity of these calculations, which require numerous quantum logic gates processing dozens of qubits. That's always been beyond the state-of-the-art for quantum computing. 

Earlier this year, however, Andrew Sornborger at the University of Georgia in Athens showed how  the case of a single particle tunnelling through a barrier could be made simple enough to simulate on today's quantum computers. Such a demonstration would be the first example of a digital quantum simulation. 

And today Guan Ru Feng and pals at Tsinghua University in Beijing say they've done it. To simulate tunnelling, these guys used a quantum computer that relies on nuclear magnetic resonance to manipulate qubits in encoded in the carbon and hydrogen atoms that make up chloroform molecules. They say this  is the first demonstration of a quantum tunnelling simulation using an NMR quantum computer. 

That should open the floodgates for more digital quantum simulations in future. It's significant because this approach has the potential to simulate much more complex quantum phenomenon than is currently possible. Expect to see more of it.

Ref: arxiv.org/abs/1205.2421: Experimental Digital Simulation of Quantum Tunneling in a NMR Quantum Simulator

I woke up this morning to find via Twitter an interesting blog post about a demonstration in London against the policies of the Engineering and Physical Sciences Research Council (EPSRC).

For those of you not up with the ins and outs of the UK science funding regime, EPSRC is the agency that funds the more mainstream areas of physics (as well as chemistry, engineering and some mathematics) while the more exotic bits (particle physics, nuclear physics and astronomy) are the responsibility of the Science and Technology Facilities Council (STFC). The current protest seems to be lead by a number of eminent chemists, including Prof. Sir Harry Kroto, Prof. Sir John Cadogan and Prof. Anthony Barrett.

Almost five years ago – was it really so long? – owing to a mixture of funding cuts and incompetent management, STFC was born into a financial crisis that made many of us doing astronomy and particle physics wish that we also were protected by the friendly hands of EPSRC rather than left out in the cold as we felt we were at STFC. Things have slowly improved at STFC, which now has an executive team that actually seems to listen to its community as well as speaking the language that Whitehall wants to hear. Funding is still tight, but STFC is a noticeably happier ship now than it was it first launched.

In the meantime, any envy we might have had about our colleagues in, e.g., condensed matter physics being safer in the EPSRC stable has now well and truly evaporated. Their strategy, “Shaping Capability“, expressed in dreadful management-speak, involves the imposition of arbitrary priorities such as the restriction of fellowship applications to certain areas chosen by The Management. Worse, its new funding rules attempt to target funding at commercially-driven research. Dark clouds are gathering in the “blue skies” under which UK science has hitherto flourished.

The unresponsive top-down character of EPSRC has strengthened under the leadership of David Delpy who must have been made in the same factory as Keith Mason, former Chief Executive of STFC, whose diplomatic skills were similarly remarkable by their absence.

For some reason, this reminds me of the following quote from Smiley’s People

In my time, Peter Guillam, I’ve seen Whitehall skirts go up and come down again. I’ve listened to all the excellent argument for doing nothing, and reaped the consequent frightful harvest. I’ve watched people hop up and down and call it progress. I’ve seen good men go to the wall and the idiots get promoted with a dazzling regularity.

I’ve argued before that I think EPSRC’s approach is fundamentally wrong. When taxpayers’ money used is used to generate immediate commercial returns, it ends up in the pockets of entrepreneurs when the research succeeds and, if it doesn’t, the grant has effectively been wasted. Commercial Impact should not be a factor in awarding public funding, because it is perfectly suited as a criterion for attracting private funding. This is why we have a national fiscal policy: the only justification for levying taxation is to fund projects which will not yield short-term economic returns. There is no reason to spend public money on commercial projects: we need to justify pure research by a non-economic valuation.

This morning EPSRC have issued a press release calling upon scientists to work together ahead of the forthcoming comprehensive spending review. It doesn’t mention the demonstration, or other manifestations of unrest within the EPSRC community, but instead re-asserts the need for its so-called strategy, with a clear message not to rock the boat ahead of the next Comprehensive Spending Review.

I’ve heard that argument many times in the context of STFC during its crisis period. I firmly believe that rocking the boat in that case helped it get off the rocks. It remains to be seen whether the EPSRC protest, which is currently rather small, will gather enough momentum to make a difference. It all depends on what fraction of EPSRC scientists have actually signed up to the Delpy Agenda. Is the new campaign representative of the views of the EPSRC community? No doubt many research groups will be prospering under the new regime, at least in the short term. Time alone will tell what the long-term impact of short-termism will be.

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A recent arXiv posting of the paper “On the Generalized Ratio of Uniforms as a Combination of Transformed Rejection and Extended Inverse of Density Sampling” by Martino, Luengo, and Míguez from Madrid rekindled my interest in this rather peculiar simulation method. The ratio of uniforms samples uniformly on the subgraph

to produce simulations from p as the ratio v/u. The proof is straightforward first year calculus but I do not find the method intuitive as, say, accept/reject…. The paper gives a very detailed background on those methods, as well as on the “inverse of density method”, which is like looking at the uniform simulation over the subgraph, but with both axes inverted (slice sampling is the same on both). (A minor point of contention or at least misunderstanding: when using the inverse of density method, the authors claim that using the unormalised and the normalised versions of the target leads to the same outcome. While it is true for the direct method, I have trouble seeing the equivalent in the inverse case…) The paper also stresses that the optimal case for accept-reject is when the target is bounded because the uniform can then be used as a proposal. I agree this is a simpler solution but fail to see any optimality in the matter. The authors then study ways of transforming unbounded subgraphs into bounded domains (i.e. bounded pdfs and supports). This imposes conditions on the transform f, which must have finite limits for p(x)/f’(x) or p^-1(x)/f’(x) at the boundaries. (An optimal choice is when f is the cdf of p, since then the transform is uniform.)

The remainder (and more innovative) part of the paper is less clear in that I do not get a generic feeling on what it is about! The generalisation of the above is to consider uniform sampling from

for a generic increasing function g such that g(0)=0. And c a positive constant. (Any positive constant?!) But this is from a 1991 paper by Jon Wakefield, Alan Gelfand, and Adrian Smith. The extension is thus in finding g such that the above region is bounded and can be explored by uniform sampling over a box.. And in noticing that “the generalized Ratio-of-Uniform method is a combination of the transformed rejection method applied to the inverse density with the extended inverse-of-density method” (p.27).

I wonder at the applicability of the approach for costly target functions p. And at the extension to larger dimensions. And wish I had more time (or more graduate students) to look at possible adaptive constructions of the transform g. An interesting and fruitful read, nonetheless!

Filed under: R, Statistics, University life Tagged: accept-reject algorithm, inverse density algorithm, Madrid, ratio of uniform algorithm

I’m blogging from the site of CHARM-2012 conference, which has just started in Honolulu, Hawaii. This is a fantastic conference at a fantastic place! The conference will have four full-packed days filled with many aspects of physics related to charmed quark. As I reported earlier, many exciting recent results are associated with charm quark.

Why is the conference taking part in Hawaii? Besides being a nice place in general, it is almost exactly half way between Japan and the US. This meeting alternates between Asian, US and European locations, and last meeting, in 2009, was in Beijing — so it is US’ turn.  There will be many talks from KEK‘s Belle collaboration (which University of Hawaii is a member of), LHC experiments, as well as from Tevatron experiments. Besides, world’s only operating charm experiment (BES 3) is located in Beijing, China. Indeed, there would be many theory talks as well. It shapes to be a very nice conference — and I’ll be reporting about exciting results to be discussed here.

• Title: The Heliosphere’s Interstellar Interaction: No Bow Shock
• Authors: D.J. McComas et al.
• First Author’s Institution: Southwest Research Institute, San Antonio TX

What is the heliosphere?
A stream of charged and energetic particles continuously coming off the Sun, called the solar wind, extends outwards and essentially blows a bubble into the local interstellar medium (LISM) around us. This bubble of charged particles is what is known as the heliosphere.

The heliosphere has a layered structure (see Figure 1 for our previous understanding of what it looks like). The wind first passes through the termination shock, the point at which it is slowed to subsonic speeds. It then continues through a region called the heliosheath, before reaching the heliopause, which is the point at which the pressure from the wind balances the pressure from the LISM and the heliosphere officially terminates. Outside of that was hypothesized to be a bow shock (see Figure 2): a region wherein the LISM becomes shocked and turbulent as a result of its collision with the heliosphere as the sun moves through the LISM.

Our understanding of the structure of the heliosphere has changed fairly dramatically, however, since the launch of the Interstellar Boundary Explorer (IBEX, for short).

IBEX
The NASA satellite IBEX (see this astrobite for more on IBEX) was launched in 2008 with the goal of measuring the energetic neutral atom (ENA) emissions that result from collisions between the solar wind and LISM neutral atoms at the heliospheric boundary. The ENA measurements should help to illustrate the locations and shapes of the termination shock, heliopause, and bow shock.

So far, IBEX has done a very good job of challenging our models of the heliosphere. One of its first discoveries was a completely unexpected ribbon of ENA emission nearly encircling the heliosphere (see Figure 4), presumably ordered by the LISM magnetic field and indicating that this field has a much stronger influence on the heliosphere than anyone had originally thought.

The latest interpretation of IBEX data again leaves our understanding of the heliosphere in shambles: the authors of this paper show that, based on IBEX data, the heliosphere appears to have no bow shock after all.

No bow shock?
In this paper, the authors use IBEX measurements of ENA emission to recalculate the velocity of the LISM relative to the Sun. The resulting speed and direction are both slightly different from calculations based on previous measurements made by the older space probe Ulysses; IBEX’s speed is 23.2 km/s and Ulysses’ is 26.3 km/s. Though a small difference, this nonetheless produces a 22% decrease in the pressure of the LISM due to its motion at the interface between it and the solar wind, significantly increasing the importance of the LISM magnetic pressure. If magnetic pressure is more important, the speed needed to form a shock goes up, because magnetic fields tend to suppress shock formation. Thus higher values of the LISM magnetic field mean that it is less likely that a bow shock will form ahead of the heliosphere.

Using these new numbers, the authors then develop a simple analytical model of the heliosphere to determine the conditions under which a bow shock would now be able to form. By solving the Rankine-Hugoniot equations for shocks and taking into account effects such as local heating of ionized plasma, they calculate the likelihood of a bow shock forming given different values of the magnetic field within the LISM.

A combination of IBEX measurements from the ENA emission ribbon and data from Voyager 1 and 2 as they crossed the termination shock yields a predicted LISM magnetic field strength of significantly greater than 3 μG. In order to form a bow shock, however, the field strength would need to be less than roughly 2.2 μG (see Figure 3).

Conclusion
This study demonstrates that it’s extremely unlikely that the bow shock that has been predicted for decades to exist ahead of the heliosphere is actually able to form, given the parameters of the LISM as measured with IBEX. Our new understanding of the heliosphere’s structure, which replaces the bow shock with a bow “wave” of unshocked but slightly denser material, is illustrated in Figure 4. IBEX’s revelations suggest that we are due for a major reformulation of our understanding of the heliosphere and how it interacts with the interstellar medium. Luckily, we can expect significant new results from IBEX in the future, as well as new data from the Voyager satellites as they cross the heliopause in ~2015. With any luck, the data from these missions will help us to improve the picture of this bubble in which we live.

So there’s this thing invented by Anders Kock called a postulated colimit. It seems like I’ve read his note about them numerous times without really understanding it. I felt like there ought to be some relationship with my theory of exact completions, but I didn’t nail it down precisely in time for the posting of that preprint.

Now, however, I think I finally have a grasp on postulated colimits. They do turn out to be nicely related to exact completions, but to find out how, you’ll have to wait for me to update the exact completions paper (or figure it out yourself). Today, I just want to tell you what postulated colimits are, and talk about how they’re related to something else I like: absolute colimits.

An absolute colimit is a colimit that’s preserved by any functor whatsoever. The term is used in two slightly different ways, which can be confusing if you don’t watch out for it.

On the one hand, a particular colimit in a particular category $C$ is absolute if it is preserved by any functor with domain $C$. On the other hand, if $V$ is a nice category to enrich over, and $W$ is a weight for colimits in $V$-categories, then $W$ is absolute if all $W$-weighted colimits in all $V$-categories are preserved by all $V$-functors.

There is obviously a close relationship between the two meanings; the subtlest part is probably that an ordinary colimit can be preserved by all $V$-functors without being preserved by all unenriched functors. For instance, initial objects are never absolute in the first, unenriched, sense — but the weight for initial objects is an absolute weight when $V=$ pointed sets or abelian groups.

In this post I’m interested in the first meaning of absolute colimit; no enrichments today.

I would guess that I’m fairly typical in that my first exposure to absolute colimits was through Beck’s monadicity theorem, in which one uses split coequalizers, and remarks that they are a special sort of absolute coequalizer. An obvious question to ask after you first meet these notions is “are there absolute coequalizers that aren’t split?” If you’ve never thought about this question, then I encourage you to go away and work on it for a little while. Go on, I’ll wait.

---

Back? So you might have realized that there is a very trivial sort of absolute coequalizer that is not split: if $f:A\to B$ is a morphism that is not a split epi, then $1_B$ is a coequalizer of $f$ and $f$, which is not split. But there can also be other more interesting absolute coequalizers that are not split.

If you’re a seasoned category theorist who automatically reaches for the Yoneda lemma, then you might also have realized that there’s a very clever way to characterize all absolute coequalizers, and which is a generalization of the notion of split coequalizer. I believe this is originally a result of Bob Paré from 1969. The key is this: suppose we have an absolute coequalizer diagram

$$X\underset{f_1}{\overset{f_0}{\rightrightarrows }}Y\stackrel{e}{\to }Z.$$

Then this coequalizer must, in particular, be preserved by the representable functor $\mathrm{hom}(Z,-)$. Therefore, we have another coequalizer diagram

$$\mathrm{hom}(Z,X)\underset{f_1\circ -}{\overset{f_0\circ -}{\rightrightarrows }}\mathrm{hom}(Z,Y)\stackrel{e\circ -}{\to }\mathrm{hom}(Z,Z)$$

But this is a coequalizer in $\mathrm{Set}$, and we know what coequalizers in $\mathrm{Set}$ look like. In particular, coequalizers in $\mathrm{Set}$ are surjective, and so $(e\circ -):\mathrm{hom}(Z,Y)\to \mathrm{hom}(Z,Z)$ must be surjective. Thus, in even more particular, there must be something in $\mathrm{hom}(Z,Y)$ which maps onto $1_Z\in \mathrm{hom}(Z,Z)$. That just says that $e$ is split epic (just as it must be in a split coequalizer).

Now our coequalizer diagram must also be preserved by $\mathrm{hom}(Y,-)$, and from that and our knowledge of coequalizers in $\mathrm{Set}$, we can extract a generalization of the rest of the split coequalizer condition. See absolute coequalizer for details.

It turns out that this technique works in arbitrary generality. In fact, by abstract nonsense, a colimit is absolute if and only if it is preserved by the Yoneda embedding $C\to [C^{\mathrm{op}},\mathrm{Set}]$. And by looking at presenvation by particular hom-functors, we can extract a characterization of general absolute colimits. Bob Paré did this in 1971.

Specifically, let $\mu :F\to \Delta A$ be a cocone under a functor $F:I\to C$. Then the following are equivalent:

• $\mu$ is an absolute colimiting cocone.

• $\mu$ is a colimiting cocone and is preserved by the Yoneda embedding $C\to [C^{\mathrm{op}},\mathrm{Set}]$.

• There exists $i_0\in I$ and $d_0:A\to F(i_0)$ such that

  1. For every $i\in I$, $d_0\circ {\mu }_i$ and $1_{F(i)}$ are in the same connected component of the comma category $(F(i)/F)$.
  2. ${\mu }_{i_0}\circ d_0=1_A$.

In particular, there exists an $i_0$ such that ${\mu }_{i_0}$ is split epic, generalizing our above observation that absolute coequalizers are split epis. The rest of the characterization is likewise a generalization of the part of the characterization of absolute coequalizers that I didn’t mention.

---

So far, so good. Now what is a postulated colimit? Anders Kock introduces the notion as follows:

To say that a diagram

$$R\underset{b}{\overset{a}{\rightrightarrows }}X\stackrel{q}{\to }Q$$

in the category of sets is a coequalizer may be expressed in elementary terms by saying that $q\circ a=q\circ b$, and that the following two assertions hold

(1.1) $q$ is surjective

(1.2) for any $x$ and $y$ in $X$ with $q(x)=q(y)$, there exists a finite chain $z_1,\dots ,z_m$ of elements of $R$ with $x=a(z_1)$, $b(z_1)=a(z_2)$, … ,$b(z_m)=y$.

These assertions can be interpreted in any category where sheaf semantics is available; this means in any site…. If they hold for a given diagram in the site, we shall say that the diagram is a postulated coequalizer.

This already looks a bit familiar; those two characterizing facts about coequalizers in $\mathrm{Set}$ are exactly the same properties that we used, after applying some representable functors, in order to characterize absolute coequalizers. But then Kock goes in a seemingly different direction: he takes these two statements and interprets them in the internal logic of a category.

Recall (if you knew it) that the internal logic of a category $C$ is a way of “interpreting” or “compiling” mathematical statements which look like they are talking about sets into statements which talk about objects of $C$ instead. For instance, given a function $q:X\to Q$ between two sets, the statement “for all $y\in Q$, there exists an $x\in X$ with $q(x)=y$” expresses the surjectivity of $q$. In the internal logic of a topos, however, our function would be replaced by a morphism $q:X\to Q$ between objects, and the same statement “for all $y\in Q$, there exists an $x\in X$ with $q(x)=y$” would get compiled into one which turns out to express that $q$ is an epimorphism.

So Kock is saying that in a topos, we can take his conditions (1.1) and (1.2) and interpret them “internally”. As I said above, condition (1.1) will just become the assertion that $q$ is an epimorphism. Condition (1.2) will become something somewhat more mysterious. Regardless, a fork with these properties is called a postulated coequalizer — “postulated” I guess because the internal logic “postulates” that it is a colimit.

More generally, we can do something analogous for a cocone under any diagram and obtain a notion of postulated colimit. In that case the analogue of condition (1.1) will assert that the coprojections in the cocone are jointly epic.

Finally, generalizing in another direction, we have an “internal logic” in any site, which is basically just the restriction of the internal logic of its topos of sheaves. So we can define postulated colimits in any site. In that case, the analogue of condition (1.1) will assert that the coprojections of the cocone form a covering family.

Now a priori, it may not be obvious that a postulated colimit even is a colimit! We have these odd conditions about epimorphisms, but why should that imply a universal mapping property? However, Kock proves that if the site is subcanonical, then a postulated colimit is indeed a colimit.

You could say that this works because in a subcanonical site, the covering families themselves are already colimits (namely, they are universally effective-epimorphic), so that that colimit-ness can be extended to the postulated colimits which are defined in terms of the covering families. Alternatively, you could say that it works because a subcanonical site embeds fully-faithfully in its topos of sheaves, and a topos is sufficiently set-like that the “internal” characterization of colimits works there for the same reason that it does in $\mathrm{Set}$.

This leads us to another of Kock’s characterizations of postulated colimits: a cocone in a site $C$ is a postulated colimit if and only if it becomes a colimit in the topos of sheaves $\mathrm{Sh}(C)$. In particular, a colimit in $C$ is a postulated colimit if and only if it is preserved by the sheafified Yoneda embedding $C\to \mathrm{Sh}(C)$.

Now we can draw the loop closed. Recall that a colimit in $C$ is absolute if and only if it is preserved by the ordinary Yoneda embedding $C\to [C^{\mathrm{op}},\mathrm{Set}]$. But every category $C$ can be made into a site with a “trivial topology”, for which $\mathrm{Sh}(C)\simeq [C^{\mathrm{op}},\mathrm{Set}]$. Therefore, a colimit is absolute if and only if it is postulated by the trivial topology. (Note that since the trivial topology is subcanonical, every postulated colimit in a trivial site is in fact a colimit.)

The especially nice thing is that when we take the definition of postulated colimit and “$\beta$-reduce it” in the case of the trivial topology, we recover (as we must) Paré’s characterization of absolute colimits. The simple half of this is easy to see: in the trivial topology, the covering families are precisely those which contain a split epimorphism, so Kock’s condition (1.1) for the trivial topology reduces exactly to the part of Paré’s condition which says that some coprojection is split epi. The correspondence of the other two conditions is more tedious, but basically the same.

Let me end with the following suggestive remark. Since the notion of postulated colimit is defined entirely in terms of the topology of a site, it’s immediate that postulated colimits are preserved by any morphism of sites. And since the sheafified Yoneda embedding $C\to \mathrm{Sh}(C)$ is a morphism of sites, this property also characterizes postulated colimits.

However, this is reminiscent of the second type of absolute colimit I mentioned back at the beginning: the weights whose colimits are preserved by every enriched functor. Perhaps a topology on a category is something akin to an enrichment of it, and postulated colimits are the “absolute weights” for such an “enrichment”. Moreover, then the topos of sheaves, which is essentially a cocompletion under postulated colimits, would be the “Cauchy completion” relative to this “enrichment”. If you’ve read sections 6–8 of my exact completions paper, you may be able to guess what’s going on.

Gin a body meet a body
Flyin’ thro the air,
Gin a body hit a body,
Will it fly? And where?

Ilka impact has its measure
Ne’er a’ ane hae I
Yet a’ the lads they measure me,
Or, at least, they try.

Gin a body meet a body
Altogether free,
How they travel afterwards
We do not always see.

Ilka problem has its method
By analytics high;
For me, I ken na ane o’ them,
But what the waur am I?

by James Clerk Maxwell (1831-1879)

P.S. This poet is of course much better known as a physicist, but this is a nice little parody of Robert Burns’ Comin’ through the Rye in authentic Scots.

Follow @telescoper

Link to e-Bulletin Issue No. 20-21/2012Link to all articles in this issue No.

Latest simulation shows that the magnetic nozzles required for antimatter propulsion could be vastly more efficient than previously thought--and built with today's technologies

Smash a lump of matter into antimatter and it will release a thousand times more energy than the same mass of fuel in a nuclear fission reactor and some 2 billion times more than burning the equivalent in hydrocarbons. 

So it's no wonder that antimatter is the dream fuel for science fiction fans. 

The problem, of course, is that antimatter is in rather short supply making the prospect of ever building a rocket based on this technology somewhat remote. 

But from time to time physicists put aside these concerns and have a little fun working out how good antimatter rocket engines can be. Today it's the turn of Ronan Keane at Western Reserve Academy and Wei-Ming Zhang at Kent State University, both in Ohio, who take a new approach to the problem with some interesting results. 

First, some basic rocket science. The maximum speed of a rocket depends on its exhaust velocity, the fraction of mass devoted to fuel and the configuration of the rocket stages. "The latter two factors depend strongly on fine details of engineering and construction, and when considering space propulsion for the distant future, it seems appropriate to defer the study of such specifics," say Keane and Zhang.

So these guys focus on the exhaust velocity--the speed of the particles produced in matter-antimatter annihilations as they leave the rocket engine. 

The thrust from these annihilations comes largely from using a magnetic field to deflect charged particles created in the annihilation. These guys focus on the annihilation of protons and antiprotons to produce charged pions. 

So an important factor is how efficiently the magnetic field can channel these particles out of the nozzle. 

In fact, the exhaust velocity of these pions depends on two factors--their average initial velocity when they are created and the efficiency of the magnetic nozzle design. 

In the past, various physicists have calculated that the pions should travel at over 90 per cent the speed of light but that the nozzle would be only 36 per cent efficient. That translates into an average exhaust velocity of only a third of lightspeed, barely relativistic and somewhat of a disappointment for antimatter propulsion fans.   

All that is set to change now, however. Keane and Zhang have come up with a different set of figures with the help of software developed by CERN that simulates the interaction between particles, matter and fields of various kinds. 

CERN uses this software, called GEANT4 (short for Geometry and Tracking 4), to better understand how particles behave at the Large Hadron Collider, which itself collides beams of protons and antiprotons. So it's ideally suited to Keane and Zhang's task. 

The new work produces some good news and some bad news. First the bad. The new simulations indicate that pions produced in this way will be significantly slower than previously thought, travelling at only 80 per cent of light speed.

The good news is that the GEANT4 simulations indicate that a magnetic nozzle can be much more efficient than previously envisioned, reaching 85 per cent efficiency. That translates into an average exhaust velocity of about 70 per cent light speed. That's much more promising. "True relativistic speeds once more become a possibility," say Keane and Zhang.

These guys have another surprise up their sleeve. Their nozzle has a magnetic field strength of around 12 Tesla. "Such a field could be produced with today’s technology, whereas prior nozzle designs anticipated and required major advances in this area," they say.

That will bring a smile to the face of many science fiction fans.

There is, of course, the small problem of gathering enough antimatter for a journey of any decent length. The number of antiatoms made at CERN is small enough to be countable. By one estimate, at this rate it will take a thousand years to make a single microgram of antimatter. 

Keane and Zhang point out that all earlier estimates predate the PAMELA spacecraft's discovery last year that Earth is surrounded by a ring of antiprotons and suggest that this could mined for fuel. What they don't mention, however, is that PAMELA spotted only 28 antiprotons in two years--far less than the rate at which CERN makes them on a daily basis.

Keane and Zhang finish by noting that other fuel technologies have advanced at an exponential rate, liquid hydrogen production, for example. If antimatter manufacture turns out to follow a similar trajectory, who knows what could happen.  

Interesting, entertaining and wildly ambitious--all good fun.

Ref: arxiv.org/abs/1205.2281: Beamed Core Antimatter Propulsion: Engine Design and Optimisation

By Hamish Johnston
First predicted in 2005 and confirmed in the lab in 2007, topological insulators (TI) are perhaps the hottest material in condensed-matter physics these days. As well as constituting a new phase of quantum matter that should keep physicists busy for some time, the material has recently been shown to harbour quasiparticles resembling Majorana fermions. First predicted by the Italian physicist Ettore Majorana in 1937, such particles could be used to store and transmit quantum information without being perturbed by the outside world. As such, they could find use in the quantum computers of the future.

It's not surprising that scientists worldwide are working hard to discover and study new variants of TIs. However, researchers at Duke University in the US believe that, until now, discoveries have been based on trial and error.

To encourage a more systematic approach, Stefano Curtarolo (right) and colleagues have created a "master ingredient list" that describes the properties of more than 2000 compounds that could be combined to make TIs. The clever bit of the work is a mathematical formulation that helps database users search for potential TIs that are predicted to have certain desirable properties.

The system is based on Duke's Materials Genome Repository, which has already been used to develop both scintillating and thermoelectric materials.

According to Curtarolo, the system gives practical advice about the expected properties of a candidate material – for example, whether it will be extremely fragile or robust.

Commenting on the fragile materials, Curtarolo says "We can rule those combinations out because what good is a new type of crystal if it would be too difficult to grow, or if grown, would not likely survive?"

The research is also described in a paper published in Nature Nanotechnology.

First, a declaration. I'm NOT a theorist. I'm an experimentalist (and proud to be one, damn it!) :) So one can say that my take on this can easily be inaccurate and based on superficial observations. However, having looked at it for many, many years, and talking to many theorists for quite a while, I think I have a view that isn't too far off for someone who isn't one.

This thought came up because I keep coming across students just starting out (some even still in high school) wanting to be theoretical physicists. Neglecting the fact that many of them have a mistaken idea of what "theoretical physics" is, I think that most (if not all) of these kids do not realize just how difficult it is to not only graduate with a PhD in physics, but also having the chance to actually be employed as a theorist.

Let's start from the most obvious: there are more experimentalists than there are theorists working in physics. Regardless of the field of study (outside of string/etc, I mean), experimentalists tend to outnumber theorists, often by a lot (see, for example, condensed matter physics and accelerator physics). So already the "phase space" for employment does not look very appealing to theorists.

Experiments and experimentalists tend to bring in more funding to a particular institutions. Now granted that in many of these funding, both theorists and experimentalists are involved. But even in such situation, the funding proposal tends to have more experimentalists than theorists. This is also one reason why there are more employment for experimentalists than theorists.

A project may get by without a theorist, even if it requires theoretical work. More often than not, an experimentalist can pick up the task that a theorist does, but it is more daunting for a theorist to do an experimentalist job. I'm not saying that this is true all the time, but in my experience, I've seen experimentalists do theory (especially in high energy physics), or use tools such as packaged software to perform theoretical simulations (especially in accelerator physics) without officially needing a theorist. Now, they may consult a theorist on site, but such tasks are often done by experimentalists without needing to employ another theorist to do such jobs. I haven't seen the reverse yet in my experience, i.e. group of theorists taking on jobs done by experimentalists, without needing to hire or have the presence of experimentalists. In fact, last time a theorist got close to my vacuum components, he ruined it by touching a clean part with his bare hands!!

Finally, the competition for the few positions in theoretical physics, be it in Academia or other institutions, is fierce! I do not envy the theorists at in this aspect. Because of the small number of positions available, even the good ones will have a tough time finding a job in their respected fields. In fact, if you did not come from a top-tier school, and your mentor isn't a "brand-name, world famous theorist", there's a very good chance that you will not get accepted to such a position in a good institution in your field. I think that the "pedigree" factor is a lot more prominent for theorists than for experimentalists, mainly because of such limited job opportunities. There are just too many outstanding candidates. What this means is that newly-minted PhDs from less well-known schools or supervisors seldom have a chance for employment as a theorist in their fields, leading to many to go into other fields or even outside of physics completely.

I'm sure there are many exception to what I've just described. But I believe that, on average, this is what is going on based on my years of observation. So, are you a theorist? Did I get it right, or was I just blowing smoke?

Zz.

• Surviving the World - Lesson 1395 - Arguing

  And, once again, the internet has been explained in under 20 words.

• If Publishing Is Dead, What Happens to Non-Fiction? « Maureen Ogle

  Consider: I started working on the meat book in early 2007. I finished it in early 2012. You do the math. I spent five years researching and writing the beer book, and of that, a great deal of money and time was spent on traveling to specialized libraries. The Key West book took me two years to research and write. How did I pay for that? By entering into a partnership with a traditional publishing house that provided financial support. It works like this: My agent sells my book IDEA to a publishing house. The house pays an "advance": a sum of money upfront that I can live on while I research and write the book. It's not much money -- in fact it's an embarrassing amount of money and I also am fortunate enough to receive financial support from my spouse. Without that assistance, I couldn't do what I do. Period. Again, it's not much money, and it's the ONLY money I earn from my books.

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In this sorry age for Supersymmetry (SUSY) phenomenologists, it is quite easy to step on an aching toe while discussing the results of the Large Hadron Collider experiments, whose results have let these physicists down by excluding the presence of SUSY where most of them used to put their moneys until yesterday.

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The current situation of homotopy type theory reminds me a bit of the dot-com bubble at the turn of the millenium.

Back then a technology had appeared which was as powerful as it was new: while everybody had a sure feeling that the technology would have dramatically valuable impact, because it was so new nobody had an actual idea of what that would be. As opposed to other bubbles, that one did not burst because overly optimistic hopes had been unjustifed as such, but because it took a while to understand just how these hopes would be materialized in detail (for instance that today I would send a message as this here from a café via my webbook from my dropbox account).

With homotopy type theory the situation currently seems to be similar to me. On the one hand it is clear that some dramatic breakthrough right at the heart of mathematics has occured. One hears the sound of something big happening. But: what is the impact? It feels like after 1995 – when it was clear that the internet is going to be something big – but still before, say, 2003, when we started getting a good idea of how it changes our lives.

How will homotopy type theory change our lives?

Currently most research in homotopy type theory revolves around the fine-tuning of the formulation itself and completing the understanding of its relation to traditional homotopy theory. That’s necessary and good. (It’s great, I am enthusiastic about it!) But if the excitement about HoTT is not to be an illusion, then something will follow after that. The traditional homotopy theorist currently may complain (and some do) that much of what is happening is that facts already known are being re-formulated in a new language, not always yet to an effect a homotopy theorist would find noteworthy.

So I am wondering: how will the traditional homotopy theorist eventually benefit from homotopy type theory? How the researcher who uses homotopy theory for something else?

I am asking for personal reasons, too. Since, somewhat inadvertently, I have been investing some of my time into learning about it, I am naturally wondering: how will that time investment pay off for me? What does homotopy type theory do for my research?

I am not sure yet. But I have some first ideas. One of these I want to share here.

An example

My research, you may have noticed, is motivated from understanding basic structural phenomena in theoretical physics as incarnations of natural mathematical structures. What I will try to indicate in the following is a certain kind of problem that poses itself in the context of string theory, which – I think it is fair to say – was generally regarded to be among the more subtle problems in a field rich in subtle mathematical effects, and how it finds an elegant and simple solution once you regard it from the perspective of homotopy type theory.

What I say in the following I have said in different words before, together with my coauthors Domenico Fiorenza and Hisham Sati: in section 2 of an article titled The E8-moduli 3-stack of the C-field in M-theory. There we point out that the solution which we propose and study in the article, to some problem in string theory, can naturally be understood simply by reformulating a well-known equation – known as the flux quantization condition – first as a fiber product of sets of certain field configurations and then refining that to a homotopy fiber product of moduli ∞-stacks of certain field configurations.

Here I will just observe that if you come to this from homotopy type theory, then the solution looks even more elegant than this: one arrives there simply by taking verbatim the symbols denoting the solution set to the equation, but now interpreting these not in the ordinary logic of sets, but in the homotopy logic of homotopy types. It is then homotopy type theory which automatically produces the correct answer, the “$E_8$-moduli 3-stack of the supergravity C-field in M-theory”. A solution that looks subtle to the eye of classical logic becomes self-evident from the point of view of homotopy logic / homotopy type theory.

From these remarks everybody with just basic training in category theory and homotopy theory can already deduce what I will say below. And what I say next is not hard to see, once you see it. It is one of those cases where a simple change of perspective leads with great ease to a solution of what seemed to be a difficult technical problem. Nevertheless, or because of this, I thought I’d say this explicitly.

Formulation in ordinary logic

The situation studied in that article concerns a hypothetical physical system in which on spacetime $X$ three different species of fields propagate: 1. the field of gravity, 2. a gauge field for the gauge group E8, and 3. a higher gauge field called (part of) the supergravity C-field. It is not important for the following what exactly these fields are and why. Important are the following two aspects only.

1. Since all of them are gauge fields, there is no naive notion of equality between different field configurations. Instead, there is a sensible notion of equivalence of field configurations. (In physics this is called gauge equivalence.)

   Moreover, since these are higher gauge fields, there is no naive notion of equality even between the gauge equivalences themselves. Instead there are higher order equialences between them. (Physicists describe this state of affairs by saying that there are higher order ghosts.)

2. In the problem under consideration in the above article, there is a constraint equation that is required to be satisfied by the gauge equivalence classes of the three fields, the “flux quantization condition”.

The question is then: what is the right collection of field configurations that satisfy the constraint equation? What are the gauge equivalences between these? What is the mathematical model for the supergravity $C$-field?

Let’s formulate this a bit more in symbols. Naively, we would say that there is a set of configurations of the field of gravity. I’ll write that set “$[X,B{\mathrm{Spin}}_{\mathrm{conn}}]$”, but this is just notation which you need not care about for the following, if you don’t want to. (If you do, see the above article for details!) Similarly there is a set $[X,B{E}_8]$ of configurations of the gauge field. And a set, to be denoted, $[X,B^{3}U(1{)}_{\mathrm{conn}}]$, of configurations of (part of) the $C$-field. So we’d write

$$\begin{array}{rl}{\varphi }_{\mathrm{gr}}& \in [X,B{\mathrm{Spin}}_{\mathrm{conn}}]\\ {\varphi }_{\mathrm{ga}}& \in [X,B{E}_8]\\ {\varphi }_{\mathrm{hg}}& \in [X,B^{3}U(1{)}_{\mathrm{conn}}]\end{array}$$

to denote elements of these sets, representing configurations of each of these fields.

Now, each of these fields induces yet another field, much like the field of, say, electrons induces a magnetic field. We have functions that send the above field configurations to configurations of that induced field. These functions go by the following names (but again, these are just names, here we only need that there are three such functions):

$$\begin{array}{rl}\frac{1}{2}{p}_1& :[X,B{\mathrm{Spin}}_{\mathrm{conn}}]\to [X,B^{3}U(1)]\\ 2a& :[X,B{E}_8]\to [X,B^{3}U(1)]\\ 2G_4& :[X,B^{3}U(1{)}_{\mathrm{conn}}]\to [X,B^{3}U(1)]\end{array}.$$

In terms of this notation, that constraint equation to be satisfied by the three type of fields which I mentioned, the “flux quantization condition”, says that

$$\frac{1}{2}{p}_1({\varphi }_{\mathrm{gr}})+2a({\varphi }_{\mathrm{ga}})=2G_4({\varphi }_{\mathrm{hg}}).$$

This is just some equation in the set $[X,B^{3}U(1)]$ (which happens to come equipped with the structure of an abelian group,with respect to which the addition in the above equation is formed), for the present discussion it is not important what this means, as long as you can imagine that it may happen that three gauge fields are related by some such equation.

Given all this now, one might naïvely think that the collection of fields that satisfy the flux quantization condition is the set that in traditional ZFC logic one denotes by the right hand side of

$$\mathrm{CField}(X):=\{{\varphi }_{\mathrm{gr}},{\varphi }_{\mathrm{ga}},{\varphi }_{\mathrm{hg}}\mid \frac{1}{2}{p}_1({\varphi }_{\mathrm{gr}})+2a({\varphi }_{\mathrm{ga}})=2G_4({\varphi }_{\mathrm{hg}})\}.$$

However, this answer turns out to be physically wrong.

There are some evident deficiencies: this answer does not resolve the gauge transformations between fields and is hence unsuited for describing the actual quantum physics of the problem. But it is worse than that. In the correct answer there is yet one more field on $X$.

Formulation in $\mathrm{\infty }$-logic / homotopy type theory

Where is that extra field supposed to come from if we are imposing a constraint equation, thus seemingly reducing the degrees of freedom?

The answer is of course in the notion of homotopy or gauge transformation, which ordinary logic ignores. But this is precisely what homotopy type theory corrects. The same symbolic logical expressions are interpreted by homotopy type theory in a way that makes them correct for higher gauge theory. Automatically.

In that article we discuss how those “sets” of field configurations, $[X,B{\mathrm{Spin}}_{\mathrm{conn}}]$ etc., are in fact objects not of $\mathrm{Set}$, but of some (∞,1)-topos: they are smooth moduli ∞-stacks.

In the language of homotopy type theory the statement that there is a field configuration of, say, gravity

$${\varphi }_{\mathrm{gr}}\in [X,B{\mathrm{Spin}}_{\mathrm{conn}}]$$

becomes the statement that ${\varphi }_{\mathrm{gr}}$ is a term of type $[X,B{\mathrm{Spin}}_{\mathrm{conn}}]$. Of course that’s just terminology.

Now comes the key point: we form now the solution set to the flux quantization condition as we did before. But now we do so in homotopy type theory. This means we use precisely the same logical symbols as before, which I repeat for emphasis on the right of

$$\mathrm{CField}(X)≔\{{\varphi }_{\mathrm{gr}},{\varphi }_{\mathrm{ga}},{\varphi }_{\mathrm{hg}}\mid \frac{1}{2}{p}_1({\varphi }_{\mathrm{gr}})+2a({\varphi }_{\mathrm{ga}})=2G_4({\varphi }_{\mathrm{hg}})\},$$

where now the boldface on the left is to indicate that we take this expression no longer to evaluate to a set (a subset of $[X,B{\mathrm{Spin}}_{\mathrm{conn}}]\times [X,B{E}_8]\times [X,B^{3}U(1{)}_{\mathrm{conn}}]$), but now to a homotopy type. In fact, thus, to a smooth ∞-stack.

Taken apart, the above notation in homotopy type theory means

1. the dependent sum $\{\cdot \mid \cdots \}$

2. over the product type $[X,B{\mathrm{Spin}}_{\mathrm{conn}}]\times [X,B{E}_8]\times [X,B^{3}U(1{)}_{\mathrm{conn}}]$

3. of (and that’s the key) the dependent identity type ${\mathrm{Id}}_{[X,B^{3}U(1)]}$.

Here is where homotopy type theory automatically does some work for us that is quite non-trivial from the classical point of view: this type $\mathrm{CField}(X)$ automagically comes out as the homotopy pullback of $(\frac{1}{2}{p}_1+2a)$ along $2G_4$, the homotopy-universal way of completing the following diagram:

$$\begin{array}{ccc}\mathrm{CField}(X)& \stackrel{}{\to }& [X,B^{3}U(1{)}_{\mathrm{conn}}]\\ \downarrow & {⇙}_{\simeq }& {\downarrow }^{2G_4}\\ [X,B{\mathrm{Spin}}_{\mathrm{conn}}\times B{E}_8]& \underset{\frac{1}{2}{p}_1+2a}{\to }& [X,B^{3}U(1)]\end{array}$$

of smooth $\mathrm{\infty }$-stacks, up to that gauge transformation indicated as the double arrow filling the diagram.

That this is so, hence that in type theory with identity types dependent sums over identity types express in fact homotopy pullbacks, is not entirely obvious, a priori, and is one of the hallmarks of what makes homotopy type theory interesting. (For technical details see here.)

In our example, the claim is that this homotopy type $\mathrm{CField}(X)$ is the correct “type of $C$-field configurations”, being the answer to a subtle question in string theory. So in conclusion, amplifying the argument of our section 2 just a bit more with an emphasis on the homotopy-logic we find: formulating a higher gauge theoretic problem as one would naively, but then reading the result in the logic of homotopy type theory, automatically takes care of otherwise subtle phenomena.

Outlook

What do we learn from the existence of homotopy type theory?

There is the explicit lesson, which drives the whole interest, it says: with just a tiny little adjustment (allowing for identity types), traditional logic / type theory is a language that captures homotopy theory.

But inside this there might be another lesson of potentially more interest in common practice. That says: not only is there some formal language to capture homotopy theory. No, moreover: it’s a natural language, potentially more natural than the language you have been using so far, and speaking this language may help to make more transparent phenomena in homotopy theory that are less transparent otherwise.

Or so it feels. I would like to see this materialize in more detail. Therefore I close with a question:

Can you come up with more examples where thinking about situations in homotopy theory / in higher topos theory concretely profits from reformulating them from a homotopy-logical perspective? Some construction of natural interest involving various homotopies, homotopy pullbacks, homotopy pushouts, etc where you can step back and say: look, with homotopy type theory we can equivalently think of this as expressing the following logical formula, and this is much simpler than the original formulation?

Many of the basic definitions of Voevodsky’s in the foundation files of homotopy type theory are of the form that I am after here. For instance that the geometric procedure of giving a contracting homotopy of an $\mathrm{\infty }$-stack $X$ is equivalent to the homotopy-logical procedure of proving ${\exists }_{x\in X}{\forall }_{y\in X}(x=y)$ (see at contractible type for details) might be taken as an example.

Or consider the notion of free loop space objects (“derived loop spaces”) $ℒX$ of an $\mathrm{\infty }$-stack $X$. Often these are heuristically motivated as formalizing the idea that a point in them is given by “making two points in $X$ equal in two different ways” (such as to yield a loop). In terms of homotopy type theory, this heuristics becomes a theorem, which reads:

$$ℒX=\{x,y:X\mid (x=y)\mathrm{and}(x=y)\}.$$

These first simple examples seem to suggest that there is a whole universe of similar, but more interesting (even more interesting, if you wish), homotopy-logical reformulations of familiar phenomena in homotopy theory… and hopefully eventually of unfamiliar and previously unknown phenomena. Eventually I want to collect such examples at a page like HoTT methods for homotopy theorists.

If you know anything about Loop Quantum Gravity, you know that people working on it suffer from an inferiority complex because, when counting black hole microstates, they only get the Bekenstein-Hawking entropy of black holes up to a factor. This factor, known as the Barbero-Immirzi parameter, enters the theory through the quantization condition and then has to be fixed to match the correct semi-classical result.

Now there has been a recent paper on the arXiv by Eugenio Bianchi

Entropy of Non-Extremal Black Holes from Loop Gravity
By Eugenio Bianchi
arXiv:1204.5122 [gr-qc]

which addresses the issue, or at least that's what I thought when I first read the abstract. Bianchi derives the black hole entropy in a spin-foam formalism and finds the usual Bekenstein-Hawking entropy - without any additional factors.

I've been scratching my head over this paper for a while now. The purpose of this blogpost is twofold: First to draw your attention to what is potentially an important contribution in the field, check. And second, I want to offer you my interpretation of that finding, and hope some reader who knows more about LQG than I will correct me when I'm wrong.

The Bekenstein-Hawking entropy is not a quantum gravitational result. One finds that black holes have a temperature by considering a quantum field (usually a massless scalar field but that doesn't matter) in the classical background geometry of a black hole. If one has the mass of the black hole, one can identify it with the total energy and integrate dE = TdS to get the entropy. The validity of this argument breaks down at the Planck scale, but that's not the regime of interest here. One can also abuse the Unruh effect to argue that black holes have a temperature, same result.

If one has some candidate theory for quantum gravity, one can ideally go and compute the microstates of a black hole. In LQG, areas and volumes are quantized in multiples of the Barbero-Immirzi parameter. Even without knowing the details, this leads one to expect that the number of possible microstates depends on that parameter. Thus, the number of microstates will generically not reproduce the Bekenstein-Hawking entropy, unless the parameter is chosen suitably. Now what I would conclude at this point is that the Bekenstein-Hawking entropy is not a measure for the microstates of the black holes. Alas, most of my colleagues seem to believe it is, especially the string theorists, and there's then the origin of the loop quantized inferiority complex.

So, with that avant-propos, why does Bianchi get a result different from the previous LQG results, a result that reproduces the Bekenstein-Hawking entropy?

Well, it looks to me like that's because he doesn't count the black hole microstates to begin with. He considers an observer in the black hole background with a two-level detector and finds the temperature, then S=E/T, and no Barbero-Immirzi parameter ever appears because it's a kinetic effect that has nothing to do with the quantization of areas and volumes. I am greatly simplifying and omitting many details, but that is what it looks like to me.

It is good to see this can be done by constructing the worldline of the observer in the spin-network and express the acceleration and so on in the proper kinetic formalism; that is an interesting calculation in its own right. But does that solve the problem with the black hole entropy in LQG?

In my opinion, it doesn't. In fact, it only manifests the problem further. Now not only is the microstate counting inconsistent with the Bekenstein-Hawking entropy unless a free parameter of the model is fixed appropriately, but the kinetic result is inconsistent with the microstate counting within the same theory.

Truth be said, this paper has created more questions for me than it has answered. I am wondering now for example, what really is the observer fundamentally? It ought to be described by quantum fields. But these quantum fields have a quantization prescription. And that quantization prescription, not having anything to do with gravity, doesn't have an additional parameter in it. That after all is why the Bekenstein-Hawking result is reproduced, because it doesn't have anything to do with the quantization of gravity. But the fields interact with the geometry, so how can they have a different quantization prescription?

If somebody can point me into the direction of a helpful reference or a bottle of ibuprofen, please dump in the comments.

Flute recording. Source.

A decades old paper made me philosophical.

In 1975, Voss and Clarke, two physicist from Berkeley, studied noise in electronic devices. For the fun of it, they also analyzed the spectra of different types of music. They found that the fluctuations in loudness and pitch decrease with the inverse of the frequency; they have a 1/f spectrum. This finding was basically independent of the type of music; Western, Oriental, Blues, Jazz, Classic all showed the same pattern. Voss and Clarke’s musical power spectrum made it into Nature.

A Fourier-transformation of a 1/f power spectrum leads to a power-law decay in the autocorrelation time of the fluctuations, meaning there are correlations over all times, rather than over a characteristic decay time as is most often the case. Physicists like power-law autocorrelated fluctuations because systems show them on a critical point, ie if something cool is going on, you get a power law. The opposite is not necessarily true though; there are more mundane ways to get a power law, but that hasn’t deterred enthusiasts. The 1/f spectrum is scale-invariant, so it has – theoretically – no preferred time scale or frequency to it, as one might have expected to be present in music.

In the 70s and 80s everything power-law was chique, and not all of that power-law-finding was very meaningful. To some approximation, in some parameter range, everything is a power-law. If you put your data on a log-log plot, you can make a linear fit, at least over some range. Yet, strictly speaking nothing really is a power law. And of course music doesn’t really have a 1/f spectrum either. To begin with, because it doesn’t use the full frequency spectrum, most of which we couldn’t hear. Also, Mozart hasn’t been composing since the Big Bang.

Scale-invariance is a property also shared by fractals. When I first heard about Voss and Clarke’s study, I jokingly asked when we’ll be listening to fractal music. Needless to say, I learned that had been said and done when I was still wearing diapers. Google “fractal music” to see where this thought leads you.

I’m not sure what the power-law finding means for the origin of music, but intuitively what it means for what you hear is that music (at least the type we find appealing) lives on the edge between predictability and unpredictability. White noise has a constant spectral density and no autocorrelation. A random walk moving a melody along adjacent pitches has a strong correlation and a 1/f² spectrum. Somewhere in between are Bach and Adele.

When you turn on the radio, you want to be surprised – but not too much. Popular music today follows quite simple recipes. In most cases, you’ll be able to sing along when the chorus repeats. If you’ve heard a song a dozen times it gets dull though – it’s become too predictable. Symphonies are more complex, but they all have recurring motives and variations around that.

However, the musical edge must have a finite width. For some purposes, music can be more predictable than for others. What amount of predictability we find appealing doesn’t only depend on the occasion, it is also individually different. If you spend a lot of time analyzing pop songs, I suspect what’s in the charts today will sound very repetitive to you, though for the casual listener it arguably has an appeal.

It is tempting to extrapolate this to areas where autocorrelations are less easily measureable than pitch, for example to ideas in the written and spoken form. A scientific paper or a talk needs to strike a balance between the known and the unknown. Repeat too much common knowledge, and you’re obvious. Jump too far, and you’re crazy. The scientific pop stars are the ones on the edge. That also means the pop stars are the ones not too far ahead of their time.

It seems to me today the width of the scientific edge is very thin, maybe too thin. Sometimes, the obvious must be stated just so it remains in awareness. And sometimes the crazy starts making sense if you’ve listened to it often enough.

There’s another lesson. While fashions seem to come back, the cycle never is perfectly periodic, but always comes with a new twist. Thus, when the colors of the 70s will return to haunt us, maybe they’ll come with a metallic shine. And so, my impression that we’re having the same discussions over and over again must be wrong. They can’t be periodic, I am missing a change on longer time scales. History may be self-similar, but it’s not repeating. Though that's one of my all-time favorite songs.

I've got a lot of roses blooming in the garden, just in time for (US) Mother's day. Well, a week earlier, actually. This was good timing, allowing me to make a card (as I always do) to send over to the UK to my mum and my sister for their Mother's day greetings. I hope they got them in time... Happy Mother's Day to all! -cvj

If you want to fire up astronomers (and scientists in general), start discussing the topics of research impact and research metrics. These are the buzz words at the moment, as governments around the world are carrying out assessment of research done with public funds. Here in Australia we are in the current round of The Excellence in Research for Australia, where research in universities is scored on a scale which compares it to international standards.

(Warning: this post is pretty far outside of my usual bailiwick…)

I was reading today’s Guardian and came across Zoe Williams’ sketch (in UK newspapers, this is a short, often humorous, descriptive piece, usually about an event like a parliamentary debate or court proceedings), “Rebekah Brooks lays bare the secret of her success”, recounting the appearance of former News International CEO Rebekah Brooks at the Leveson Inquiry into “phone hacking” and the too-cozy relationship between the media and politicians.

The sketch was mostly remarkable for what it couldn’t say. Williams writes

But ultimately, this is a ridiculous person. You couldn’t live a life with this bad a memory. Never mind that you’d never be able to do a demanding job, you wouldn’t be able to pass your GCSEs.

And that makes the whole business grating to watch. “I can’t remember” is the defence of a person who wasn’t really concentrating, whose mind was somewhere else.

And this makes the whole business grating to read. I don’t think this is only an indulgence in some old-fashioned British circumlocution: Williams really means “I think Rebekah Brooks was lying”. But I assume she can’t write that, because that would be accusing Brooks of the crime of lying under oath, and Brooks would be free to sue for libel — and under UK libel law, the burden of proof is on the defendant to prove the statement true, impossible in this case. (I am not a lawyer, but this is my understanding.)

This is just one of the minor repercussions of the current state of UK libel law, which the government may be overhauling soon — it was discussed in last week’s Queen’s Speech (another amusing tradition in which the Monarch reads a speech written by the government recounting its plans for the next parliamentary session). Simon Singh, a science writer who was sued for liable by the [redacted] of the chiropractic industry, writes that the proposal still doesn’t go far enough, especially in its lack of distinction between individuals and corporations. (Americans may think this sounds familiar from a different context.)

Tags: libel

Or: ideal fluids—dry water?

guest post by Tim van Beek

Last time in this series, we set the stage by explaining infinite dimensional manifolds. Then we looked at a simple example: the inviscid Burgers equation. We saw this was the equation for geodesics in the diffeomorphism group of the circle.

Now let’s look at a more interesting example! It will still be a simplified model of fluid flow: it will describe an ideal fluid that is incompressible. I’ll start by explaining these concepts. We will then see how the equation of motion for ideal incompressible fluids can be interpreted as a geodesic equation.

En route I will also repeat some stuff from classical vector analysis, mostly for my own sake. The last time I seriously had to calculate with it was when I attended a class on “classical electrodynamics”, which was almost 15 years ago!

When we delve into differential geometry, it is always a good idea to look both at the “coordinate free” formulation using abstract concepts like differential forms, and also at the “classical vector analysis” part, that is best for calculating stuff once suitable coordinates have been chosen. Our fluid flows will take place in a smooth, orientable, compact, -dimensional Riemannian manifold possibly with a smooth boundary

I will frequently think of as an open set in or so I will use the globally defined coordinate chart of Euclidean coordinates on denoted by (and if needed) without further warning.

Before we continue: Last time our reader “nick” pointed out a blog post by Terence Tao about the same topic as ours, but—as could be expected—assuming a little bit more of a mathematical background: The Euler-Arnold equation. If you are into math, you might like to take a look at it.

So, let us start with the first important concept: the ‘ideal fluid’.

What is an ideal fluid?

When you are a small parcel in a fluid flow, you will feel two kinds of forces:

• external forces like gravity that are there whether or not your fellow fluid parcels surround you or are absent,

• internal forces that come from your interaction with the other fluid parcels.

If there is friction between you and other fluid parcels, for example, then there will be a force slowing down faster parcels and speeding up slower parcels. This is called viscosity. I already explained it back in the post Eddy Who? High viscosity means that there is a lot of friction: think of honey.

The presence of viscosity leads to shear stress whenever there are differences in the velocities of nearby fluid parcels. These lead to the formation of eddies and therefore to turbulence. This complicates matters considerably! For this reason, sometimes people like to simplify matters and to assume that the fluid flow that they consider has zero viscosity. This leads us to the physics definition of an ideal fluid:

An ideal fluid (as physicists say) is a fluid with zero viscosity.

As you can guess, I have also a mathematical definition in store for you:

An ideal fluid (as mathematicians say) is a fluid with the following property: For any motion of the fluid there is a (real valued) function called the pressure such that if is a surface in the fluid with a chosen unit normal the force of stress exerted across the surface per unit area at at time is

This implies that there is no force acting tangentially to the surface :

This picture is from

• Alexandre Chorin and Jerrold E. Marsden, A Mathematical Introduction to Fluid Mechanics, 3rd edition, Springer, New York 1993.

An ideal fluid cannot form eddies by itself without the help of external forces, nor can eddies vanish once they are present. So this simplification exclude a lot of very interesting phenomena, including everything that is usually associated with the term ‘turbulence’. But it is a necessary simplification for describing fluid flow using geodesic equations, because something moving along a geodesic doesn’t lose energy due to friction! So we will have to stick with it for now.

Historically, ideal fluids were almost exclusively studied during the 19th century, because the mathematics of viscous fluids seemed to be too hard—which it still is, although there has been a lot of progress. T his led to a schism of theoretical hydrodynamics and engineering hydrodynamics, because engineers had to handle effects like turbulence that ideal fluids cannot model. A very problematic aspect is that no body with a subsonic velocity feels any drag force in an ideal fluid. This is known as D’Alembert’s paradox. This means that one cannot find out anything about optimal design of ships or aircrafts or cars using ideal fluids as a model. This situation was overcome by the invention of ‘boundary layer techniques’ by the physicist Ludwig Prandtl at the beginning of the 20th century.

John von Neumann is cited by Richard Feynman in his physics lectures as having said that ideal fluids are like “dry water”, because they are so unlike real water. This is what the subtitle of this post alludes to. I don’t think this is quite fair to say. Along these lines one could say that quantum mechanics is the theory of stagnant light, because it does not include relativistic effects like quantum field theory does. Of course every mathematical model is always just an approximation to a Gedankenexperiment. And ideal fluids still have their role to play.

Maybe I will tell you more about this in a follow-up post, but before this one gets too long, let us move on to our second topic: incompressible fluids and ‘volume preserving’ diffeomorphisms.

What is an incompressible fluid flow?

If you are a parcel of an incompressible fluid, this means that your volume does not change over time. But your shape may, so if you start out as a sphere, after some time you may end up as an ellipsoid. Let’s make this mathematically precise.

But first note, that “incompressible” in the sense above means that the density of a given fluid parcel does not change over time. It does not mean that the density of the whole fluid is everywhere the same. A fluid like that is actually called homogeneous. So we have two different notions:

• incompressible means that the volume of an infinitesimal fluid parcel does not change as it moves along the fluid flow,

• homogeneous means that the density at a given time is everywhere the same, that is: constant in space.

This distinction is important, but for now we will study fluid flows that are both homogeneous and incompressible.

Let us see how we can make the notion of “incompressible” mathematically precise:

Remember from the last post: The flow of each fluid parcel is described by a path on parametrized by time, so that for every time there is a diffeomorphism

defined by the requirement that it maps the initial position of each fluid parcel to its position at time :

Now let’s assume our fluid flow is incompressible. What does that mean for the diffeomorphisms that describe the flow? Assuming that we have a volume form on these diffeomorphisms must conserve it:

For people who need a reminder of the concepts involved (which includes me), here it is:

Remember that is a smooth orientable Riemannian manifold of dimension A volume form is a -form that vanishes nowhere. In with Cartesian coordinates the canonical example would be

The dual basis of is denoted by in our example.

Given two manifolds and a differentiable map we can pull back a differential form on to one on via

For the übernerds out there: remember that we see the group of diffeomorpisms as a Fréchet Lie group modelled on the Fréchet space of vector fields on For those who would like to read more about this concept, try this:

• Karl-Hermann Neeb, Monastir Summer School: infinite-dimensional Lie groups.

is clearly a subgroup of It is less obvious, but true, that it is a closed subgroup and therefore itself a Lie group. What about its Lie algebra? For a vector field to give a flow that’s volume preserving, it must have zero divergence. So, the vector fields that form the tangent space consist of all smooth vector fields with zero divergence:

These vector fields form a vector space we denote by Remember stands for the tangent space at the identity element of the group which is the identity diffeomorphism of The tangent space at the identity of a Lie group is a Lie algebra, so is a Lie algebra.

I will need a little refresher about the definition of divergence. Then I will point you to a proof of the claim above, namely that zero-divergence vector fields form the Lie algebra of volume preserving diffeomorphism. This may seem obvious on an intuitive level, if you ever learned that the zero-divergence vector fields have ‘no sinks and no sources’, for example in a course on classical electromagnetism.

So, what is the divergence, again? You’ve probably seen it somewhere if you’ve survived reading this so far, but you may not have seen it in full generality.

The divergence of a vector field with respect to a volume form is the unique scalar function such that:

Here, is the contraction with Contraction means that you feed the vector in the first slot of the differential form and therefore reduce the function of vector fields to one of vector fields.

When we use our standard example we of course write a vector field as

where and are smooth real-valued functions. The divergence of is then

which we get if we plug in the expression for into the formula

So, how does one see that ‘zero divergence’ of a vector field is equivalent to ‘volume preserving’ for the flow it generates?

If we write

for the path of a fluid particle and $u$ for its velocity, then of course we have:

For a scalar function we get

Here is the inner product. The latter part is often written with the help of the nabla operator as

This is really just a handy short notation, there is no mystery behind it: it’s just like how we write the divergence as and the curl as

The operator

appears so often that it has its own name: it is called the material derivative.

Why ‘material’? Because if we follow a little bit of material—what we’re calling a parcel of fluid—something about it can change with time for two different reasons. First, this quantity can explicitly depend on time: that’s what the first term, is about. Second, this quantity can depend on where you are, so it changes as the parcel moves: that’s what is about.

Now suppose we have a little parcel of fluid. We’ve been talking about it intuitively, but mathematically we can describe it at time zero as an open set in our manifold. After a time it will be mapped by the fluid flow to

This describes how our parcel moves. We define the fluid to be incompressible if the volume of for all choices of is constant, that is:

If we write for the Jacobian determinant of then we have

So in a first step we get that a fluid flow is incompressible iff the Jacobian determinant is for all times, which is true iff is volume preserving.

It is not that hard to show by a direct calculation that

If you don’t want to do it yourself, you can look it up in a book that I already mentioned:

• Alexandre Chorin and Jerrold E. Marsden, A Mathematical Introduction to Fluid Mechanics, 3rd edition, Springer-Verlag, New York 1993.

This is the connection between ‘volume preserving’ and ‘zero divergence’! Inserting this into our equation of incompressibility, we finally get:

which is true for all open sets iff The equation of continuity for a fluid flow is:

This says that mass is conserved. Written with the material derivative it is:

So, since we’re assuming we get

which is what we intuitively expect, namely that the density is constant for a fluid parcel following the fluid flow.

Euler’s equation for the ideal incompressible fluid

The equation of motion for an ideal incompressible fluid is Euler’s equation:

is the pressure function mentioned in the mathematical definition of an ideal fluid above. As I already mentioned, to be precise I should say that we also assume that the fluid is homogeneous. This means that the density is constant both in space and time and therefore can be cancelled from the equation of motion.

If has a nonempty (smooth) boundary the equation is supplemented by the boundary condition that is tangential to

How can we turn this equation into a geodesic equation on ? Our strategy will be the same as last time when we handled the diffeomorphism group of the circle. We will define the necessary gadgets of differential geometry on using the already existing ones on First we define them on Then, for any diffeomorphism we use right translation by to define them on After that, we can use the version of the abstract version of the geodesic equation for right invariant metrics to calculate the explicit differential equation behind it.

Let us start with defining right invariant vector fields on A right invariant vector field is a vector field such that there is a such that In the following, we restrict ourselves to right invariant vector fields only.

We define the usual inner product of vector fields on just as last time:

The inner product used on the right is of course the one on

For two right invariant vector fields with and we define the inner product on by

This definition induces a right invariant metric on Note that it is right invariant because we are only considering volume preserving diffeomorphisms. It is not right invariant on the larger group of all diffeomorphims !

For an incompressible ideal fluid without external fields the only kind of energy one has to consider is the kinetic energy. The inner product that we use is actually proportional to the kinetic energy of the whole fluid flow at a fixed time. So geodesics with respect to the induced metric will correspond to Hamilton’s extremal principle. In fact it is possible to formulate all this in the language of Hamiltonian systems, but I will stop here and return to the quest of calculating the geodesic equation.

Last but not least, we define the following right invariant connection:

Here on the right is the connection on —sorry, this is not quite the same as the we’d been using earlier! But in or Euclidean space of any other dimension, is just another name for so don’t get scared.

Remember from last time that the geodesic equation says

where is the velocity vector of our geodesic, say

where is the curve describing our geodesic. We saw that for a right-invariant metric on a Lie group, this equation says

where the coadjoint operator is defined by

For simplicity, let us specialize to or an open set in there. What can we say about the right hand side of the above equation in this case? First, we have the vector identity

Since we are talking about divergence-free vector fields, we actually have

Also note that for a scalar function and the divergence-free vector field we have

The last term is zero because of our boundary condition that says that the velocity field is tangent to

So, now I am ready to formulate my claim that

for some yet undetermined scalar function This can be verified by a direct calculation:

What next? We can use the following 3 dimensional version of Green’s theorem for the curl operator:

That is, the curl operator is symmetric when acting on vector fields that have no component that is tangent to Note that I deliberately forgot to talk about function spaces that our vector fields need to belong to and the regularity assumptions on the domain and its boundary, because this is a blog post and not a math lecture. But the operators we use on vector fields obviously depend on such assumptions.

If you are interested in how to extend the symmetric curl operator to a self-adjoint operator, for example, you could look it up here:

• R. Hiptmair, P. R. Kotiuga, S. Tordeux, Self-adjoint curl operators.

Since our vector fields are supposed to be tangent to we have that the boundary term in our case is

because is normal, and therefore is tangent to so its inner product with the normal vector is zero.

So we can shift the curl operator from right to left like this:

In the last step we used the cyclicity of the relation of the vector product and the volume spanned by three vectors:

This verifies the claim, since the part does not contribute, as stated above.

And now, yet another vector identity comes to our rescue:

So, we finally end up with this:

for some function Why? Since the middle term is actually a gradient, we can absorb this summand and into one summand with a new function,

Thanks to this formula we derived, the abstract and elegant equation for a geodesic on any Lie group

becomes, in this special case

If we can convince ourselves that is the pressure of our fluid, we get Euler’s equation:

Wow! Starting with abstract stuff about infinite-dimensional Lie groups, we’ve almost managed to derive Euler’s equation as the geodesic equation on ! We’re not quite done: we still need to talk about the role of the function and why it’s minus the pressure. But that will have to wait for another post.

The best of the rest from the Physics arXiv this week

Three-Body Amplification Of Photon Heat Tunneling

Complexity and Information: Measuring Emergence, Self-organization, and Homeostasis at Multiple Scales

The Variability Of Tidewater-Glacier Calving: Origin Of Event-Size And Interval Distributions

Can Timeouts Change the Outcome of Basketball Games?

Parent-Offspring Conflict In Feral Dogs: A Bioassay

Is Eternal Inflation Past-Eternal? And What if It Is?

Richard Feynman was one of the most influential physicists of the twentieth century. Not only did he revolutionize quantum theory with his development of quantum electrodynamics, but he also revolutionized the way we think about physics and physicists. He spoke to people from all kinds of backgrounds about physics, from lecturing students destined to change the field themselves, to appearing on television to discuss physics and the philosophy of science, to meeting with the greatest minds of the time.

For me, Feyman’s great contribution was the way he thought about physics. His Lectures on Physics are world famous, and rightly so. (In fact, one of the first things I did after landing in San Francisco to work at SLAC was to buy a copy of his lectures from the Stanford bookstore. Shortly afterwards by bank froze my card, suspecting fraud. It was worth the inconvenience!)

As a jaded undergraduate they were a source of inspiration to me. A faint glimmer of hope turned into a roaring inferno after reading his lectures on electromagnetism, and I’ve never looked back since. Finally, here was someone who wanted to discuss the beauty of the subject, as well as the truth. He had no time for obscuring the underlying symmetry of a concept, nor for lying to students in order to make things easier. Inevitably having to unlearn and relearn ideas leaves people confused, disillusioned and unable to trust their tutors. In that spirit, this is how he started his course on electromagnetism:

“We begin now our detailed study of the theory of electromagnetism. All of electromagnetism is contained in the Maxwell equations.

Maxwell’s equations:

\[
\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}
\]
\[
\nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t}
\]
\[
c^2\nabla \times \vec{B} = \frac{\partial \vec{E}}{\partial t} + \frac{\vec{j}}{\varepsilon_0}
\]
\[
\nabla \cdot \vec{B} = 0
\]

Don’t worry about trying to understand these equations. The important thing here is that Feynman has given the students the complete truth about electromagnetism. With these four equations he can solve any problem about the shape and nature of electromagnetic fields for any configuration of charges and currents. The equations he provides are not some approximation of the theory, or some equations that only work some of the time, these are the equations that all physicists and engineers use and they are, as far as we know, complete and state of the art. Feynman has shown a level of honesty and respect for his students/readers that was not present when I sat through lectures. My lecturers taught me backwards, Feynman taught me forwards.

(Experts might notice that the Lorentz force law is missing here, but Feynman already mentioned it a few pages before Maxwell’s equations. With the Lorentz force law physicists can relate the electromagnetic fields to the forces on charged particles.)

Feynman continues:

The situations that are described by these equations can be very complicated. We will consider first relatively simple situations, and learn how to handle them before we take up more complicated. The easiest circumstance to treat is one in which nothing depends on time- called the static case. All charges are permanently fixed in space, or if they do move, they move as a steady flow in a circuit (so \(\rho\) and \(\vec{j}\) are constant in time). In these circumstances, all of the terms in the Maxwell equations which are time derivatives of the field are zero. In this case Maxwell’s equations become:

Electrostatics:
\[
\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}
\]
\[
\nabla \times \vec{E} = \vec{0}
\]

magnetostatics:
\[
c^2\nabla \times \vec{B} = \frac{\vec{j}}{\varepsilon_0}
\]
\[
\nabla \cdot \vec{B} = 0
\]

You will notice an interesting thing about this set of four equations. It can be separated into two pairs. The electric field \(\vec{E}\) appears only in the first two, and the magnetic field \(\vec{B}\) appears only in the second two. The two fields are not interconnected. This means that electricity and magnetism are distinct phenomena so long as charges and currents are static.

And he goes on. Immediately at the start of the course he’s pointed out one of the most important and beautiful symmetries in electromagnetism. He also lets us know how the course is going to proceed, with static cases first and the full treatment later. This leaves the student with a wonderful surprise later in the course, when the two fields finally get united again. When this happens Feynman goes on to show us how electromagnetism comes about as a result of special relativity, and if done properly that is one of the most breathtaking moments in physics! This is the way physics should be taught, and I wish I could have been in that lecture hall to see it happen!

The rest of the lectures are a fascinating journey, full of neat little asides, teasers, paradoxes, and it’s all handled with refreshing clarity. He even pokes fun at physics itself from time to time, showing how our mathematical notation is just a trick to make complicated things look simple and how different problems appear to have similar solutions only because we choose to use the same kinds of methods to solve them. Towards the end of his electromagnetism course he even goes out of his way to show how electromagnetism fails in an epic way. The problem of the infinite energy of the field, and the intractable problem of the mass of the electron are two major failings of the classical theory, and he dedicates a lecture to showing us just many questions were left unanswered by the subject.

Feynman gave us a lot to digest, from Nobel prize worthy discoveries, to a view of scientists that was anything but a crusty old professor, and for me what I value most is the lectures he gave, packed with inspiration and clarity. If you have a chance, go read some of the lectures and find out what made this man get out of bed in the morning. You won’t be disappointed. His other books are also excellent (Six Easy Pieces, Six Not So Easy Pieces, QED and Surely You’re Joking, Mr Feynman!) and well worth a read. Put them on your Christmas wish list!

Feynman’s birthday should be a national day of celebration, not just for physics, but for getting people hooked on physics! (I’m just sorry I’m a bit late to the party here, have a great weekend.)

If you want to find out a bit more about Richard Feynman check out this lecture about Feynman from Lawrence Krauss, one of today’s most eloquent speakers and best advocates for physics.

(Quotes taken from “The Feyman Lectures on Physics, The Definitive Edition Volume II”, Feynman Leighton and Sands, ISBN 0-8053-9047-2)

This essay was motivated by a question from an engineering colleague. It would be presumptuous to say “friend,” as scientist and engineers are in a state of “friendly” rivalry, however, not to the extent as with arts. I once saw a sign in an engineering department hallway that read: Friends do not let friends study arts. Be that as it may, my colleague’s question was why scientists do not show the same order in all their work as they show in writing papers. That question I will attempt to answer in this essay.

Engineering is far older than science, being perhaps the second oldest profession, dating back at least to the building of the pyramids (Imhotep from the 27^th century BCE is the oldest named engineer) and Stonehenge and probably back to when the first club was engineered.  Stonehenge is amazing as it was probably built without the documentation that is the hallmark of modern engineering practice. Unfortunately, that means we do not know what the initial requirements[1] were and this has led to much futile speculation as to its purpose.

Science and engineering are sibling disciplines, frequently mentioned together and have much in common. The main similarity is that they both deal with the observable universe and are judged by their ability to make correct predictions regarding its behaviour. For example, that the Higgs boson will be found at the Large Hadron Collider (LHC) or that the building will not collapse in an earthquake. Secondarily they use similar techniques, placing high importance on analytic reasoning, to the extent that Asperger’s syndrome is sometimes called the engineer’s disease. The relation between Asperger’s syndrome and engineers or scientists may be an urban myth but it does indicate the relation of extreme analytic thought to both science and engineering. The solution to problems in both relies on the same problem solving skills, analytic thinking and mathematics. Do not let anyone tell you that either does not require a high degree of intellectual activity.

Science and engineering rely on each other. Behind every engineering project is a great deal of science, from the basic understanding of Newtonian mechanics in the building of a bridge to the advanced materials science in the construction of a cell phone. Actually, the cell phone is a good example of all the science needed: it depends on Newtonian mechanics (the construction of the cell phone towers), quantum mechanics (the operation of the transistors), classical electromagnetism i.e. Maxwell’s equations (the propagation of the signal from the tower to the cell phone), materials science (almost all the cell phone itself), and general and special relativity (the GPS timing that is necessary in some cell phone technologies).

Equally, science is beholden to engineering. From simple things like the buildings that house scientific equipment to complicated things like the ATLAS detector at the Large Hadron Collider (LHC). Making a building may seem simple but, as I see with the new ARIEL building at TRIUMF, nothing is simple and even something as basic as a laboratory building relies on engineering expertise. The ATLAS detector is another story. Its size and complexity are a marvel of engineering virtuosity. Back to TRIUMF, the IEEE has recognized the TRIUMF cyclotron, commissioned in 1974 and the main driver for much of TRIUMF’s science program, as an Engineering Milestone. Even the slide rule I used back in ancient history as an undergraduate[2] was an engineering achievement.

Despite the close relationship between science and engineering the two are different. The difference can be summarized in this statement: “In engineering you do not start a project unless you know the answer while in science you do not start a project if you know the answer.” Engineering is based on everything being predictable; you do not start building a bridge unless you know you can complete it. In science, the purpose of a project is to answer a question to which the answer is currently unknown. For example, if the properties of the Higgs boson were known, it would not have been necessary to build the LHC. Good engineering practice is based on order but at the center of science is chaos. We are exploring the unknown; great discoveries can come from serendipity. In science, something not working as expected can lead to the next big breakthrough. In engineering, something not working as expected can lead to the bridge collapsing. Advances in science are frequently due to creativity, not following rules.

This difference in perspective leads to very different cultures in the two disciplines. The engineer is much more concerned with process and following procedure. The scientist with following up his most recent hunch—after all, it could lead to a Nobel Prize.  Engineering versus science: order versus creative chaos. This is clearly an oversimplification as there is no clean separation between engineering and science, but it is a good indication of the divergence between the two mindsets. Thus, although engineering and science are closely related and indeed intertwined, the two, in their heart of hearts, are very different; engineering uses science in order to build and science uses engineering in order to explore.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod.

Posts are limited this week and next — partly because a draft of a document about “exotic” Higgs particle decays (which I wrote about here,  here,  here,  here and  here), relevant to how the Large Hadron Collider experiments ATLAS and CMS might collect their data in 2012 (in particular, how they might trigger on such decays), needs to get done right away. (Data’s already coming in! we’re later than I’d like.)   And it really has to get done now since I’m traveling next week with limited internet.

Meantime, a reminder in case you missed it: For those of you in the New York City area: I’ll be joined by the wonderfully talented singer-songwriter-pianist Andrea Wittgens in giving a physics/music joint performance/presentation at the storied Cornelia Street Cafe, Sunday May 13th at 6 p.m., as part of their Entertaining Science series.  It’s entitled Rhapsody for Piano and Universe, and intended for the general public.  The place is pretty small, so get reservations in advance by calling 212.989.9319.

One more heads-up: again in NYC, June 16th, I’ll be giving a lecture:

THE EINSTEIN OBSESSION: SCIENCE, MYTH AND PUBLIC PERCEPTION

June 16th, 2pm

Jefferson Market Library, 425 6th Ave. West Village, NYC

Free and open to the public!

Who hasn’t heard of Einstein? We all know Einstein failed eighth grade math. (Although he didn’t.)  We know he showed energy is the same thing as mass (or was it “matter”?), that he’s the father of the atomic bomb, that he was an old man with frizzy hair, and that he was a patent clerk whose theory was that everything is relative and that nothing can move faster than light.  This messy assortment of half-truths and misconceptions permeates our culture and affects public perceptions of science, at many different levels.  In this talk we’ll consider how our culture’s obsession with Einstein impacts efforts to convey science to the public.

Filed under: LHC News, Public Outreach Tagged: ExoticDecays, Higgs, LHC, PublicTalks

During the three months that I worked as a visitor in the “Commissioning and Science Verification” group at ALMA, I had the opportunity to spend four week-long “turnos” (shifts) in northern Chile at the ALMA Operations Support Facility (OSF), where the antennas are operated.  If you’re interested to learn more about ALMA, you can check out the webpage, or my two previous posts about my experiences during turnos at ALMA.  For some of the early science results from ALMA, check out these astrobites.

Scientifically and personally, ALMA is an interesting and inspiring place to work.  Making observations and then analyzing data, I worked with a number of people with a variety of positions and expertise.  At the end of a recent turno I asked them a few simple questions to get a better idea of what a job at ALMA entails.  Below are their responses (to the questions in bold), which represent just one sample of perspectives, but to me are sufficiently interesting and demonstrate the diversity and complexity of this project.

1. How long have you worked at ALMA?  What is your position/title here?

At any given time at the OSF, a team of ALMA staff work together to tackle all aspects of the system.  Job titles (for those interviewed here) at ALMA include commissioning scientist, data analyst and system astronomer.  ALMA is an international partnership of Europe, North America and East Asia in cooperation with the Republic of Chile, so the control room is nearly always staffed with a very diverse group of people from around the world.  Many organizations contribute funding and personnel for the project.

One of the scientists whom I met on my last turno is a member of Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), and will be in Chile for several months to participate in commissioning and science verification on behalf of the East Asia partner.  Others with whom I worked bring nearly 6 years of experience with the ALMA project, beginning with testing the ALMA system and antenna prototypes at the National Radio Astronomy Observatory (NRAO) in Charlottesville (VA) and Socorro (NM).  The Joint ALMA Observatory (JAO) in Chile provides the unified leadership and management of the construction, commissioning and operation of ALMA, and coordinates the diverse group of people who arrive from around the world to develop the project in Northern Chile.

2. What did you study, and where have you worked before coming to ALMA?

One astronomer told me that one of his favorite parts of ALMA is “getting to work with so many experts and people from all over the world. One gets to learn a lot, not only from radio interferometry but also from the different cultural backgrounds. Since my undergrad, I always knew I wanted to work for ALMA, so I feel very grateful to be here.”

So you think that you might be interested to one day work at an observatory like ALMA?  What type of education and training will help you land a job at an observatory?  From my small sample, I gathered that a bachelor degree in astronomy and astrophysics, physics and/or mathematics is a useful first step.

One data analyst at ALMA has previously worked as observatory coordinator at a university in Chile, and is also involved as research assistant in one of the European Southern Observatory (ESO) large public surveys currently being carried out with the VISTA telescope at Cerro Paranal.

Those with astronomer positions have PhDs in (you guessed it) astronomy.  One interesting note is that among four people, these degrees and jobs have been held in five distinct countries (in fact, five distinct continents).  After the PhD, these scientists sought post-doc positions with direct involvement in observatory development and/or operations, mostly (but not all) which observe at mm- and sub-mm frequencies.

 

3. What is your favorite part of working at ALMA?

“It’s right at the cutting edge – the only place to be if you like millimeter astronomy. Also the Atacama is always an amazing place to work. And you can’t beat seeing Aconcagua out of the window on the Monday morning commute.”

Talking with others working in the control room, I’m inspired by the passion that accompanies this job, for both the science and the diverse work environment.  One colleague told me, “Since my childhood I had always dreamed of working at one of the big observatories in Chile; for me this [data analyst at ALMA] is an ideal job. And my favorite part is that I can actually help to increase our knowledge of the universe.”

Working at the Operations Support Facility (OSF), one gains experience with both the scientific and technical aspects of the observatory, as well as the observational data which need to be analyzed.  Combining all aspects gives a clearer, first-hand view of what (and how) ALMA is doing.

Granted, there are many challenges to ensure the observatory is operating as planned.  Even these challenges are considered some of the favorite aspects of working at ALMA, in part because with new challenges come new advances.  Some of the technologies for ALMA have existed before, but the size (66 antennas, over distances spanning 16 km) and frequency coverage (30 GHz to 950 GHz, corresponding to “mm and sub-mm” wavelengths of 0.003 to 0.0003 meters) of the array are unprecedented.

4. What is the most challenging part of working at ALMA?

Of course, an important part of the job at ALMA is dealing with the new challenges which make the project exciting.  Many technical issues arise which require knowledge of some combination of instrumentation and programming, and even becoming familiar with the terminology takes time and experience.

Some of the scientists and data analysts have experience with millimeter interferometry, but for those who previously worked with other types of astronomy, including optical and near-IR observations, it has been important to learn some of the finer aspects of radio/mm/sub-mm astronomy at the heart of ALMA.

Add to these challenges the elevation (the OSF is at an elevation of about 3000 meters, or 10,000 feet, while the AOS is at 5000 meters, or 16,000 feet), some isolation and strange work schedule, and even human interactions can become a bit more difficult.  Keeping a clear head when things don’t work properly, debugging problems, or simply working with colleagues from different cultures challenges the ALMA staff to grow into better, more tolerant people.

While it can be hard to get enough quality sleep during a turno due to the altitude, the dry climate, and sun peeking through the dorm windows while you try to sleep during the day, one scientist even cites the excitement of her work as keeping her in the control room for longer hours than the assigned shift.  Indeed, ALMA operates 24 hours per day, and many of those who work at ALMA are motivated to be a part of the operations nearly around the clock.

5. What do you hope will be the greatest accomplishment of ALMA?

It’s the hope and belief at ALMA that many great accomplishments will come from all of this hard work.  ALMA has already accomplished the feat of becoming the largest astronomy project in the world, a huge array of 66 antennae working together to mimic a telescope with diameter of 16 kilometers, with a goal to explore the universe with incredible resolution (being able to resolve details of size 0.004 arcseconds, or the apparent size of a truck at the distance of the Moon).

ALMA will help increase understanding of (among other things) possible scenarios for star formation, how life emerged on Earth, and how life might have formed/form elsewhere in the Universe.  Hopefully, some of you who read this post will use ALMA to make many more discoveries beyond those even imaginable during the construction phase of the project.  These goals motivate the ALMA team to develop and perfect its capabilities, which will become a facility available to radio and non-radio astronomers alike.

Disclaimer: The personal opinions and views expressed here are mine (and my understanding of those who responded to my questions), and do not necessarily represent those of ALMA or Fulbright.

James Dacey

"What is dark matter?...you've got up to 100 seconds to answer...your time starts...NOW!"

This was the challenge facing Luke Davies (above) during a day of filming at the University of Bristol, where academics were asked to give super-condensed lectures on some of the biggest questions in physics. Participants at this UK university were armed with nothing more than a whiteboard and a couple of marker pens. And just to make the experience that bit more thrilling/nerve-racking, speakers were faced with a countdown alarm that sounded once their time was up.

The idea is to compile a series of short films for physicsworld.com that will provide introductions to topics across the whole spectrum of physics and its related disciplines. Films are presented by various physicists and cover everything from antimatter to fracking to black holes. Oh, and I almost forgot to mention the presentation about recognizing penguins in a crowd. From behind the camera, I certainly learned an awful lot about an awful lot!

The scientists appeared to get a lot from the day too. Several of them commented about what a vast departure it was from their usual experiences of presenting: standing in front of students and lecturing for an hour or so. Clearly 100 seconds is not very much time to explain topics as complex and detailed as dark energy or the Higgs boson, but everybody rose to the challenge and it was fascinating to observe the different styles that people adopted.

These films will be appearing on physicsworld.com over the coming weeks.

As mentioned previously, the crack technical team at ScienceBlogs HQ is working on shifting us from our creaky Movable Type system to a shiny new WordPress system. Part of that process involves moving all the old posts over, which has been done... sort of. At present, any post since April 18 has not been moved, and will need to be shifted by me, by hand. Worse yet, the comments to posts between April 18 and whenever the switch finally happens are currently going to be lost forever.

This is, obviously, highly sub-optimal, and efforts are being made to find a better solution. Until and unless some way is found to move the comments along with the posts, I don't think there's much sense in posting anything new and having people comment on it. Which works out well in one sense, as I have a lot of other things I ought to spend time working on, so freeing up the time I usually spend blogging (less whatever it will take to move the old posts over) will be a good thing. (And we're heading out of town for the weekend, anyway, so the timing's good in that sense...)

I may still post the occasional Links Dump entry, because those tend not to generate much comment, anyway. And I may or may not continue working on the Ten Years Before the Blog series-- right at the moment, it looks like the transition may break all inbound links to ScienceBlogs, in which case it doesn't make any sense to generate new posts with 50-odd links in them. I'm fairly certain that particular problem will be fixed, but until I know that it will work out, I'm not posting anything.

Read the comments on this post...

The University of Minnesota is launching an peer-reviewed open textbook catalog. It contains basic courses for math and physics many originating from the Rice University Openbooks initiative, but one also finds rare gems like the Introduction to Physical Oceanography, which makes for an excellent weekend read involving all the physics of our oceans. Plus it is available in pdf for any screen reader without costs.

Hum... I don't think I've ever seen this type of data/survey before. This is a report on a recent survey of graduate students in science and how their career preference change over time as they go through their graduate program.

Here's the result that has gotten the most press: Academic research careers were less popular with the late cohorts than the early ones in all disciplines, suggesting, perhaps, that graduate students are disillusioned by exposure to the lives and careers of their faculty advisers.

There's a breakdown of the study into various subject areas, and you may read that for yourself.

But the implication to such a shift is interesting, and something that I've tried to instill into students who are interested in majoring in physics.

Instead, we should all be worrying about the difficulty Ph.D. graduates often have locating jobs in, and making transitions into, some of those other work sectors that they appear to view favorably. We also need to worry about whether science careers in any sector are sufficiently rewarding, remunerative, and stable to justify the long time investment, the frustrations of training, and the forgone earnings; if they're not, we can't expect the most capable young people to choose careers in science. Instead, they'll choose other careers with better prospects, like finance or figuring out how to make people click on banner ads on Facebook.

We should also worry about whether those students are receiving the training they need to compete for jobs in sectors beyond academia. Our graduate programs already do the most important thing extremely well: The best way to convey strong analytical skills is to teach students to be outstanding researchers. But there is plenty of room for improvement when it comes to even the most basic professional skills.

Definitely! It is a FACT that there aren't that many tenure-track faculty positions in most fields, and this includes physics. Students going into such fields with the sole aim to obtain such a position need to have a reality check so that they can best prepare for other possible careers.

Zz.