At Scientific American’s blog network, Ashutosh Jogalekar muses about the “greatest American physicist”, eventually voting for Josiah Willard Gibbs, one of the pioneers of statistical mechanics. As both times I took StatMech (as an undergrad and in grad school), it was at 8:30 in the morning, I retain almost no memory of the subject, and will bow to greater experience in assessing Gibbs’s importance.

I do, however, want to take issue with one thing in the post. When assessing the historical place of American physics, he writes:

Here’s my personal list for the title of greatest American physicist in history, in no particular order: Joseph Henry, J. Willard Gibbs, Albert Michelson, Robert Millikan, Robert Oppenheimer, Richard Feynman, Murray Gell-Mann, Julian Schwinger, Ernest Lawrence, Edward Witten, John Bardeen, John Slater, John Wheeler and Steven Weinberg. I am sure I am leaving someone out but I suspect other lists would be similar in length. It’s pretty obvious that this list pales in comparison with an equivalent list of European physicists which would include names like Einstein, Dirac, Rutherford, Bohr, Pauli and Heisenberg; and this is just if we include twentieth-century physicists. Not only are the European physicists greater in number but their ideas are also more foundational; as brilliant as the American physicists are, almost none of them made a contribution comparable in importance to the exclusion principle or general relativity. [...]

More importantly though, the sparse list of great homegrown American physicists makes two things clear. Firstly, that America is truly a land of immigrants; it’s only by including foreign-born physicists like Fermi, Bethe, Einstein, Chandrasekhar, Wigner, Yang and Ulam can the list of American physicists even start to compete with the European list. Secondly and even more importantly, the selection demonstrates that even in 2013, physics in America is a very young science compared to European physics. Consider that even into the 1920s or so, the Physical Review which is now regarded as the top physics journal in the world was considered a backwater publication, if not a joke in Europe (Rhodes, 1987). Until the 1930s American physicists had to go to Cambridge, Gottingen and Copenhagen to study at the frontiers of physics.

I would argue that there’s a word missing near the end of that last sentence, namely “theoretical.” It’s absolutely true that American theorists like Oppenheimer studied in Europe in order to learn from the quantum pioneers, but I would say that even by the 1930′s, American experimental physics was nearly equal to that in Europe. Michelson, Millikan, Lawrence are a trio to put up against anyone Europe has to offer in that same time period (Thomson and Rutherford are the big names on that side of the pond), and you can throw in people like Compton and Davisson and Germer as well. Depending on whether you count cosmology as part of physics, you could probably get Hubble into the mix on the American side, as well.

Now, it’s true that they didn’t contribute “foundational” ideas to physics, which tends to see them pushed somewhat down the list of “greats,” but I think that’s a mistake. Yeah, the exclusion principle and general relativity are great ideas, but big ideas are meaningless unless you can measure them, and Americans were essential to that process. Einstein famously proposed a revolutionary particle theory of light to explain the photoelectric effect, but it was Millikan’s measurements (which grudgingly confirmed the photon model) that forced people to take it seriously, and Compton’s gamma-ray scattering experiments helped seal the deal.

This is, of course, a personal obsession with me, but I think it’s essential to remember that theory and experiment go hand in hand. Revolutionary theories arise because they’re needed to explain experimental results, and they’re ultimately accepted because they’re found to agree with further measurement. Experiments get downplayed because they’re full of fiddly technical details and harder to explain and interpret, but they’re absolutely essential, and the US was pulling its weight in experimental physics even before top theorists started fleeing fascist regimes. (This is prompted in part by a bunch of recent reading on the history of 20th century physics, where even some big European names grudgingly admit that the Americans were good experimenters…)

So, while Europe is still ahead, I think it’s a somewhat closer thing than Jogalekar suggests, when you properly weight the two facets.

As for the general question of who was the greatest American physicist, I’d probably cast my vote for John Bardeen, who is, after all, the only person to share two Nobel Prizes in Physics. He’s the “B” in the “BCS” theory of superconductivity, but more importantly helped invent the transistor. It’s hard to think of anyone whose contributions to physics had a bigger influence on the way we live today, and if that’s not greatness, I’m not sure what is.

Lee Smolin has a new book out, Time Reborn: From the Crisis in Physics to the Future of the Universe. His previous subtitle lamented “the fall of a science,” while this one warns of a crisis in physics, so you know things must be pretty dire out there.

I’m not going to do a full-fledged review of the book, which gives Lee’s argument for why “time” needs to be something more than just a label on spacetime or a parameter in an evolution equation, but a distinct fundamental piece of reality with respect to which the laws of physics and space of states can change. (Sabine Hossenfelder does offer a review.) There are also suggestions as to how this paradigm-changing viewpoint gives us new ways to talk about economics and social problems.

Over at Edge, John Brockman has posted an interview with Lee, and is accumulating responses from various interested parties. I did contribute a few words to that, which I’m reproducing here.

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Time and the Universe

Cosmology and fundamental physics find themselves in an unusual position. There are, as in any area of science, some looming issues of unquestioned importance: how to reconcile quantum mechanics and gravity, and the nature of dark matter and dark energy, to name two obvious ones. But the reality is that particle physicists, gravitational physicists, and cosmologists all have basic theories that work extraordinarily well in the regimes to which we have direct access. As a result, it is very hard to make progress; we know our theories are not absolutely final, but without direct experimental contradictions to them it’s hard to know how to do better.

What we have, instead, are problems of naturalness and fine-tuning. Dark energy is no mystery at all, if we are simply willing to accept a cosmological constant that is 120 orders of magnitude smaller than its natural value. We take fine-tunings to be clues that something deeper is going on, and try to make progress on that basis. Sadly, these are subtle clues indeed.

“Time” is something that physicists understand quite well. Quantum gravity remains mysterious, of course, so it’s possible that the true status of time in the fundamental ontology of the world is something that remains to be discovered. But as far as how time works at the level of observable reality, we’re in good shape. Relativity has taught us how to deal with time that is non-universal, and it turns out that’s not such a big deal. The arrow of time—the manifold differences between the past and future – is also well-understood, as long as one swallows one giant fine-tuning: the extreme low entropy of the early universe. Given that posit, we know of nothing in physics or cosmology or biology or psychology that doesn’t fit into our basic understanding of time.

But the early universe is a real puzzle. Is it puzzling enough, as Smolin suggests, to demand a radical re-thinking of how we conceive of time? He summarizes his view by saying “time is real,” but by “time” he really means “the arrow of time” or “an intrinsic directedness of physical evolution,” and by “real” he really means “fundamental rather than emergent.” (Opposing “real” to “emergent” is an extremely unfortunate vocabulary choice, but so be it.)

This is contrary to everything we think we understand about physics, everything we think we have learned about the operation of the universe, and every experiment and observation we have ever performed. But it could be true! It’s always a good idea to push against the boundaries, try something different, and see what happens.

I have two worries. One is that Smolin seems to be pushing hard against a door that is standing wide open. With the (undeniably important) exceptions of the initial-conditions problem and quantum gravity, our understanding of time is quite good. But he doesn’t cast his work as an attempt to (merely) understand the early universe, but as a dramatic response to a crisis in physics. It comes across as a bit of overkill.

The other worry is the frequent appearance of statements like “it seems to me a necessary hypothesis.” Smolin seems quite content to draw sweeping conclusions from essentially philosophical arguments, which is not how science traditionally works. There are no necessary hypotheses; there are only those that work, and those that fail. Maybe laws change with time, maybe they don’t. Maybe time is fundamental, maybe it’s emergent. Maybe the universe is eternal, maybe it had a beginning. We’ll make progress by considering all the hypotheses, and working hard to bring them into confrontation with the data. Use philosophical considerations all you want to inspire you to come up with new and better ideas; but it’s reality that ultimately judges them.

Guest post by Emily Riehl

Whether we grow up to become category theorists or applied mathematicians, one thing that I suspect unites us all is that we were once enchanted by prime numbers. It comes as no surprise then that a seminar given yesterday afternoon at Harvard by Yitang Zhang of the University of New Hampshire reporting on his new paper “Bounded gaps between primes” attracted a diverse audience. I don’t believe the paper is publicly available yet, but word on the street is that the referees at the Annals say it all checks out.

What follows is a summary of his presentation. Any errors should be ascribed to the ignorance of the transcriber (a category theorist, not an analytic number theorist) rather than to the author or his talk, which was lovely.

Prime gaps

Let us write $p_1,p_2,\dots$ for the primes in increasing cardinal order. We know of course that this list is countably infinite. A prime gap is an integer $p_{n+1}-p_n$. The Prime Number Theorem tells us that $p_{n+1}-p_n$ is approximately $\log (p_n)$ as $n$ approaches infinity.

The twin primes conjecture, on the other hand asserts that

$$\underset{n\to \mathrm{\infty }}{\mathrm{liminf}}(p_{n+1}-p_n)=2$$

i.e., that there are infinitely many pairs of twin primes for which the prime gap is just two. A generalization, attributed to Alphonse de Polignac, states that for any positive even integer, there are infinitely many prime gaps of that size. This conjecture has been neither proven nor disproven in any case. These conjectures are related to the Hardy-Littlewood conjecture about the distribution of prime constellations.

The strategy

The basic question is whether there exists some constant $C$ so that $p_{n+1}-p_n<C$ infinitely often. Now, for the first time, we know that the answer is yes…when $C=7\times {10}^7$.

Here is the basic proof strategy, supposedly familiar in analytic number theory. A subset $H=\{h_1,\dots ,h_k\}$ of distinct natural numbers is admissible if for all primes $p$ the number of distinct residue classes modulo $p$ occupied by these numbers is less than $p$. (For instance, taking $p=2$, we see that the gaps between the $h_j$ must all be even.) If this condition were not satisfied, then it would not be possible for each element in a collection $\{n+h_1,\dots ,n+h_k\}$ to be prime. Conversely, the Hardy-Littlewood conjecture contains the statement that for every admissible $H$, there are infinitely many $n$ so that every element of the set $\{n+h_1,\dots ,n+h_k\}$ is prime.

Let $\theta (n)$ denote the function that is $\log (n)$ when $n$ is prime and 0 otherwise. Fixing a large integer $x$, let us write $n\sim x$ to mean $x$ ≤ $n<2x$. Suppose we have a positive real valued function $f$—to be specified later—and consider two sums:

$$S_1=\sum _{n\sim x}f(n)$$ $$S_2=\sum _{n\sim x}(\sum _{j=1}^k\theta (n+h_j))f(n)$$

Then if $S_2>(\log 3x)S_1$ for some function $f$ it follows that ${\sum }_{j=1}^k\theta (n+h_j)>\log 3x$ for some $n\sim x$ (for any $x$ sufficiently large) which means that at least two terms in this sum are non-zero, i.e., that there are two indices $i$ and $j$ so that $n+h_i$ and $n+h_j$ are both prime. In this way we can identify bounded prime gaps.

Some details

The trick is to find an appropriate function $f$. Previous work of Daniel Goldston, János Pintz, and Cem Yildirim suggests define $f(n)=\lambda (n{)}^2$ where

$$\lambda (n)=\sum _{d\mid P(n),d<D}\mu (d)\left(\log \right(\frac{D}{d}){)}^{k+\ell }P(n)=\prod _{j=1}^k(n+h_j)$$

where $\ell >0$ and $D$ is a power of $x$.

Now think of the sum $S_2-(\log 3x)S_1$ as a main term plus an error term. Taking $D=x^{\vartheta }$ with $\vartheta <\frac{1}{4}$, the main term is negative, which won’t do. When $\vartheta =\frac{1}{4}+\omega$ the main term is okay but the question remains how to bound the error term.

Zhang’s work

Zhang’s idea is related to work of Enrico Bombieri, John Friedlander, and Henryk Iwaniec. Let $\vartheta =\frac{1}{4}+\omega$ where $\omega =\frac{1}{1168}$ (which is “small but bigger than $ϵ$”). Then define $\lambda (n)$ using the same formula as before but with an additional condition on the index $d$, namely that $d$ divides the product of the primes less that $x^{\omega }$. In other words, we only sum over square-free $d$ with small prime factors.

The point is that when $d$ is not too small (say $d>x^{1/3}$) then $d$ has lots of factors. If $d=p_1\cdots p_b$ and $R<d$ there is some $a$ so that $r=p_1\cdots p_a<R$ and $p_1\cdots p_{a+1}>R$. This gives a factorization $d=rq$ with $R/x^{\omega }<r<R$ which we can use to break the sum over $d$ into two sums (over $r$ and over $q$) which are then handled using techniques whose names I didn’t recognize.

On the size of the bound

You might be wondering where the number 70 million comes from. This is related to the $k$ in the admissible set. (My notes say $k=3.5\times {10}^6$ but maybe it should be $k=3.5\times {10}^7$.) The point is that $k$ needs to be large enough so that the change brought about by the extra condition that $d$ is square free with small prime factors is negligible. But Zhang believes that his techniques have not yet been optimized and that smaller bounds will soon be possible.

Okay, so there hasn’t been an official IceCube press release on this, not until the paper finishes collaboration review and is posted on the Arxiv, but there have been some talks showing neutrino events observed by IceCube which are almost certainly astrophysical in origin. Short version, neutrino astronomy is now a real thing. We are observing the universe in photons (ever since we looked up at the night sky, and starting with Galileo with increasingly sophisticated instruments) and also in neutrinos (which travel undisturbed from deep within the astrophysical objects, reflecting the nuclear interactions deep within).

There’s a nice Gizmodo article with interesting comments.

University of Wisconsin news item.

Phys.org coverage of the news item.

The BBC news article.

Nature blog entry.

New Scientist entry written by our friend Anil who got to visit IceCube during construction.

Since the middle of last week, the news are spread around and there are Russian, Spanish, and French language versions (at a minimum!) of the news. Previously, only the neutrinos from Supernova 1987A had been seen from beyond the sun and the Earth’s atmosphere. Analysis is still ongoing, so this isn’t a final result by any means, but it is a proof-of-functionality of the IceCube detector and of neutrino astronomy.

Addition:

Scientific American’s article includes good quotes from the three Wisconsin-Madison postdocs who led the analysis, Nathan, Claudio, and Naoko.

 

Completing an action-packed trilogy that began with quantum mechanics and picked up speed with the Higgs boson, here I am talking with Brady Haran of Sixty Symbols about the arrow of time. If you’d like something more in-depth, I can recommend a good book.

Will there be more? You never know! The Hitchhiker’s Guide to the Galaxy started out as a trilogy, and look what happened to that. (But I promise no prequels.)

The final session in the online discussion of the NASA Astrobiology Roadmap is today from 4-5 pm eastern.

Go to Astrobiology Future to sign in to the live web chat. Questions and comments will be taken both from call-ins and from written questions.

The online discussion will be moderated by Dr Francis McCubbin from UNM, Dr Sean Raymond from Laboratoire d’Astrophysique de Bordeaux, and yours truly…

The live session will, as with the other Roadmap sessions, be followed by a week long opportunity to input questions, ideas and topics for discussion at The Astrobiology Future Forum.

The four questions identified to kick-off the discussion are:
• Is life a chemical consequence of thermodynamics or did it emerge in spite of thermodynamics?
• Will we ever be able to uniquely identify fossils of microorganisms in the rock record of another planet given the absence of biologically exclusive chemical and morphologic signatures?
• Organic molecules can be produced a wide variety of inorganic chemical processes, what geologic conditions are needed to promote the concentration and complexification of organics towards abiogenesis?



• What factors determine the amount of water delivered to planets in a star’s habitable zone and the availability of that water for participation in chemical reactions?


Water delivery to the inner planets for different planetary system configurations: Raymond, Mandell & Sigurdsson

As I have noted before, it is critically important that the community in general, and junior researchers in particular, provide input, questions and ideas.
If you don’t, I’ll decide your research priorities for you.
So there!

Astrobiology Future

The NASA online discussion session on the Astrobiology Roadmap continues this week.

This morning there was a web chat on “Early Evolution of Life and the Biosphere”, which is being followed up by an ongoing online discussion on the questions posed and soliciting ideas for priorities in research direction.

The questions being discussed are:

• How has the exponential growth in our discovery and understanding of exoplanets impacted the kinds of questions and information we extract from the early Earth record?
• Are there problems you think are vital to understanding the early evolution of life and the biosphere that have not yet been articulated by NASA?
• What types of approaches are needed to answer mechanistic questions about the early evolution of life and the biosphere, and which specific approaches are most helpful for particular types of questions?

It is critical that there be community input to these discussions.
The questions posed and ideas suggested will be factored into the current and immediate discussion on the future priorities for research in Astrobiology.
It is particularly important the junior researchers provide their perspective on what are the interesting and important questions do explore.

[Howard Burton, founding director of Perimeter Institute, has a new project, Ideas Roadshow, a weekly magazine dedicated to ideas of all types and shapes. Rather than having the declared aim of spreading fractured pieces with little content, the Ideas Roadshow is for those who are looking for content, and who want to know more than the catchy phrases. The magazine will be published in text and as video (streaming and downloadable).]

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A fairly common reaction when I tell people what I’m doing now with Ideas Roadshow is a quizzical raising of the eyebrows followed by a wry little smile.

“Well, good luck,” they say sceptically. “I certainly think that’s needed right now. But you know Howard, the internet is not exactly about substance. We live in a sound bite world. How do you think you’re going to make money from this? Who is going to watch it?”

So one of the few benefits about careening into advanced middle age is that I’ve witnessed enough by now to recognize that any references to recent golden ages are wildly exaggerated. I don’t remember being brought up in a world awash in substantive, measured discussions of the latest issues in neuroscience or public policy. My high school experience didn’t consist of teachers having to forcibly detach kids from their iPhones, but there was no shortage of ways for us to waste our hours and avoid doing what we were supposed to: Donkey Kong manages to kill time just as well as Angry Birds.

That’s not to say that, by some objective measure, things aren’t getting worse. In some ways they certainly are.

It’s true that newspapers almost everywhere are in deep financial trouble and those that have managed to stay afloat are devoting increasingly less of their time and resources towards long-form analysis and more for mindless knee-jerk responses to the ever-increasing amount of “breaking news”.

But it’s also true that there are now far more effective and salubrious ways for a young ambitious musician to gain a popular audience than by being forced to cavort with sleazy record executives.

Technology, of course, is but a tool. That is so obvious as to border on the cliché. But that doesn’t mean that the message doesn’t sometimes get overlooked.

The notion that, somehow as a result of our developing technology, virtually nobody on planet Earth actually cares anymore about engaging in the world of ideas, is, of course, simply ludicrous. It can’t be true. And it bloody well isn’t.

What technology has done, however, is change the way that those who are interested interact with the world of ideas. In particular, one decidedly ironic effect of the internet has been to intellectually ghettoize people. So while it’s now trivial to meaningfully interact with like-minded people living on the other side of the world, it’s also the case that one is much less likely to be confronted with interesting and stimulating ideas outside of one’s own self-selected area of interest.

Often the most illuminating and stimulating experiences happen when we are forced to encounter people who hold radically different approaches or interests to our own. But the more we spend time with our like-minded friends, the less likelier such encounters are going to be.

This is the core issue. It has, of course, been commented on before. But somehow I don’t think it’s as appreciated as much as it should be.

Conventional newspapers are not collapsing because nobody cares about general ideas. Conventional newspapers are collapsing because their principal revenue stream – print advertising revenue – has dried up. Advertisers are naturally much keener to ensure that their message is being delivered to their particular target audience, which naturally argues for a segmented, specialized approach to sponsorship. Now that technology allows for detailed methods to precisely deliver content and measure its impact, advertisers are increasingly unwilling to participate in scattershot approaches that will clearly be hugely less efficient and effective.

All quite reasonable. But the solution for those who seek a general level of stimulation, for those who are keen to be at play in the world of ideas, is not to bemoan the logic of the marketplace or fall back on dreamy reminiscences of some mythical golden age, but to simply capitalize on the opportunities afforded.

Twenty years ago, or even ten, it would have been completely inconceivable to imagine creating a program where one travels the world and records substantial conversations with a diverse range of fascinating people. Camera technology would have made it prohibitively expensive to develop a professional-quality product; and even had that been somehow circumvented, it would have been virtually impossible to disseminate the results with anywhere near the range necessary to make it profitable.

People interested in ideas have always been a small minority, so to make it work one has to scale globally, or at least nationally. How could a private start-up even attempt such a thing? We’d have had to effectively take over a TV station. Inconceivable.

Recent technology has allowed both of these fundamental obstacles to be overcome. We can not only film for a fraction of the cost of ten years ago, we can also fit all of our cameras, lights and gear into two travelling cases that we can easily travel with anywhere. And once we’ve made our videos and eBooks, we can easily market them to ideas-oriented consumers worldwide.

Of course, just because structural impediments are eliminated, success is hardly guaranteed. One still has to make a product that people actually like. And then one has to establish a new brand and market it successfully.

But let’s be very clear: those are the issues. Not that we are all too superficial now. Or that nobody cares about ideas. That’s just silly.

Starting something new is always a challenge. But there are challenges and then there are challenges.

Being at the front end of a new wave of global niche market digital media products is one thing. But it’s not like some unknown guy trying to build a theoretical physics institute in the middle of nowhere from scratch.

Now that, surely, is impossible.

My 20th Harvard reunion book is in hand, offering a social snapshot of a certain educationally (and mostly financially) elite slice of the US population.

Here is what Harvard alums name their kids.  These are chosen by alphabetical order of surname from one segment of the book.  Most of these children are born between 2003 and the present.  They are grouped by family.

Molly, Danielle

Zachary, Zoe, Alex

Elias, Ella, Irena

Sawyer, Luke

Peyton, Aiden

Richard, Sonya

Grayson, Parker, Saya

Yoomi, Dae-il

Io, Pico, Daphne

Lucine, Mayri

Matthew, Christopher

Richard, Annalise, Ryan

Jackson

Christopher, Sarah, Zachary, Claire

Shaiann, Zaccary

Alexandra, Victoria, Arianna, Madeline

Samara

Grace, Luke, Anna

William, Cecilia, Maya

Bode, Tyler

Daniel, Catherine

Alex, Gretchen

Nathan, Spencer, Benjamin

Ezekiel, Jesse

Matthew, Lauren, Ava, Nathan

Samuel, Katherine, Peter, Sophia

Ameri, Charles

Sebastian

Andrew, Zachary, Nathan

Alexander, Gabriella

Liam

Andrew, Nadia

Caroline, Elizabeth

Paul, Andrew

Shania, Tell, Delia

Saxon, Beatrix

Benjamin

Nathan, Lukas, Jacob

Noah, Haydn, Ellyson

Freddie

Leonidas, Cyrus

Isabelle, Emma

Joseph, Theodore

Asha, Sophie, Tejas

Gabriela, Carlos, Sebastian

Brendan, Katherine

Rayne

James, Seeger, Arden

Helena, Freya

Alexandra, Matthew

George

If you saw these names, would you be able to guess roughly what part of the culture they were drawn from?  Are there ways in which the distribution is plainly different from “standard” US naming practice?

 

Best intentions (put nose to the grindstone, get these papers finished) notwithstanding, I do have a few more public lectures and whatnot coming up over the next few weeks. Would love to see you there! And if not, I recently did an episode of the Rationally Speaking podcast with Massimo Pigliucci and Julia Galef, where we talked about naturalism, science, philosophy, and other things I’m marginally qualified to speak on.

Wednesday May 22: I’m giving a public talk on the arrow of time at UC Davis. This is in the midst of a conference on the early universe, which should also be fun.

Wednesday May 29: I’ll be talking with Jim Holt, author of Why Does the World Exist?, at the LA Public Library. It’s possible this is will be sold out, but I think they’re going to tape it.

Sunday June 2: I’m the keynote speaker at the American Humanist Society annual conference in San Diego. 10:30 a.m. on a Sunday, so this one might be easier to get into! In fact you can get in for free even if you didn’t register for the conference, by following these simple steps:

1. Go to the website here: http://ahacon13.eventbrite.com/#
2. Click the orange “Enter Promotional Code” link.
3. Enter FREECON in the field that appears and click Apply.
4. The list of items should then include the free “Free to the Public: Matt Harding & Sean Carroll” option.
5. Choose that one (and any others) and then complete the registration.

Thursday June 6: Opening night at the Seattle Science Festival features Brian Greene, Adam Frank, and me, under the stern but fair moderation of Jennifer Ouellette. Adam and I will give short talks, and Brian will show us the West Coast premiere of the multimedia performance Icarus at the Edge of Time.

Wednesday June 12: I’m giving a public lecture at Fermilab on particles, fields, and the future of physics. It’s part of the Fermilab Users’s Meeting, as well as a workshop on the International Linear Collider. Not sure if I’ve ever given a public talk that will have so many people ready to correct my mistakes.

After a couple more trips in July, my calendar actually does clear up, and I can look forward to uninterrupted vistas of productivity. Watch out!

During our weekly trip to the Schenectady Greenmarket, we took refuge from the rain in the Open door bookstore, where a short while later I saw the following scenes at opposite ends of the kids-book aisle (also the “Featured Image” for this post, but I’ll reproduce it to save the RSS folks from having to click through):

So, clearly, they take after me and Kate…

(We ended up buying the “How to Make Paper Airplanes” book SteelyKid is looking at, because paper airplanes are awesome. The music-playing book about an orchestra that The Pip is looking at went back on the shelf over his protests, though, because we don’t really need any more noisy toys in the house.)

I was just in Chicago for a conference, and, having always meant to go to a highly touted experimental restaurant in the Chicago style, made a reservation — sorry, I mean “got tickets” — for EL Ideas.

To get this out of the way first — yes, the food was good.  Very, very good.  But I don’t actually want to talk about the food!  Lots of restaurants have good food.  What’s really interesting about EL Ideas is the way it merges the idea of “restaurant” with the idea of “theater.”

There’s no menu — each of the 24 diners eats the same thing at the same time, so that, as in a play, everyone in the room is having the same experience.  Before the meal begins, the chef/impresario/director/producer pops out from the kitchen to tell you that this isn’t going to be the usual stuffy expensive restaurant deal — he wants you to wander into the kitchen and ask what’s going on, he wants you to really get into it.  He warns that you should summon an Uber car rather than trying to walk home through the somewhat desolate neighborhood because if you did the latter “you might die.”  In other words:  we are the ones hip enough to be in this neighborhood, to feel a  little frisson of danger, though nothing you can’t dispel with an app!  (In fact, I cannot say the crowd looked notably hip — my dinner companions were younger than me, but most other people looked old and rich, one more thing EL Ideas has in common with the theater.)

Before each dish is presented, the chef gives a little introduction, during which you are supposed to be quiet — if you talk while the he’s talking, the chef warns, you might get thrown out.  Just like the theater.

You don’t exactly get a reservation here; you purchase the meal in advance, as with a ticket to a show.

And at the end everyone claps!

When I was younger, I used to go to plays a lot.  OK, not a lot.  But I probably saw three to five plays a year, and even then I think most people I knew weren’t going.  Now I never go to plays; for all I know, I may never see a play again.

But EL Ideas makes me think that there are things people want from plays, and these are things that people who never go to plays sense, consciously or not, that they still want, and so something wonderful happens — the theater, seemingly made extinct by other, nimbler forms of entertainment, spores out into the atmosphere and embeds itself in another cultural host.

 

 

 

 

 

 

The Pan-Andromeda Survey (PAndAS) continues to be a gold-mine for science. We're squeezing it hard to get out key results, but next year, the data will become public and everyone can have a looksie and write their own paper.

Here we have another paper by ANU astronomer, Dougal Mackey. Dougal's expertise is understanding the globular clusters orbiting the Andromeda galaxy, especially the distant clusters. He published a really nice piece of work recently which showed that these distant globulars are not just scattered randomly about Andromeda, but are more likely to be sitting on the stellar substructure we see. This substructure is the tidal debris from smaller galaxies that have fallen in and been shredded, meaning that the globulars are immigrants, having been born outside Andromeda, but joining the halo when their parent galaxy is destroyed; this is galactic cannibalism in action.

This new paper is about a particular cluster of stars orbiting Andromeda, named PAndAS-48 (who says astronomers aren't imaginative when it comes to naming things!). While this cluster was initially observed with the Canada-France-Hawaii Telescope (CFHT) as part of PAndAS, this paper presents new observations with the Hubble Space Telescope.

While the CFHT, at 3.6m, is larger than Hubble (2.5m), the lack of an atmosphere means we get much sharper images, and hence can see a lot fainter. Here's images from CFHT (left) compared to Hubble (right).
Nice! We actually observed the cluster in a couple of photometric bands with Hubble, which allowed us to make a colour-magnitude diagram; as you know, stars are not randomly scattered in such a picture, but sit on sequences that are driven by stellar evolution. What do we see?
For those in the know, yes, the faintest stars in there are around 28^th magnitude!

In there, we can see the Red Giant Branch and Horizontal Branch, and that allows us to understand lots of things about the globular, such as how far away it is and what stage it is at in terms of its evolution.

We can also measure the distribution of stars, and measure the shape of the clusters.
So, what is this cluster of stars? Is it a dwarf galaxy, dominated by dark matter? or a globular cluster, which are thought not to contain dark matter? It's actually very hard to tell. This piccy illustrates the issue.
The picture is pretty self-explanatory; size is along the bottom in parsecs, and brightness is up the side. The dots are colour-coded in terms of how elliptical they are.  The squares on the right are dwarf galaxies; they tend to be big and elliptical. The dots on the left are globular clusters, which tend to be small and circular (but notice that they can be of the same brightness as the dwarfs).

Where's PAndAS-48? It's the point with a circle around it, stubbornly right between the two populations! In fact, the ultimate conclusion is that we don't know what it is. If it is one or the other, then there are problems. But that's cool too!

 It is worth noting that PAndAS-48 appears to sit on the vast thin plane of satellites orbiting Andromeda, which makes it even more intriguing, but we haven't got it's velocity so can't confirm if it is orbiting in the same sense. But if it is, it will be extra cool.

As ever, the more we learn, the more questions we have. Yay!!

Well done Dougal!

I've lived in Australia for thirteen years, but in the way that Sting was an English Man in New York, I have never quite felt "Australian", rather, I am a Welsh Man in Sydney. Anyway, I still feel very British, and am a fan of British TV (apart from a few highlights, Australian TV is generally bilge).

Anyway, I've always loved a good murder mystery, and I like Midsomer Murders, even though they have changed the lead character (and the new chief inspector was actually a criminal in a previous episode). The premise of Midsomer's is simple; a cop in the quite fictional county of Midsomer solves murders. However, the show has been running for 15 years, and there seems to have been an awful lot of murders (although the murder rate is considerably lower than Honduras!). To keep the stories going, murders are set in, quite often, bizzarre circumstances.

A recent episode, Written in the Stars, focused on the intrigue and mystery at a research observatory at Midsomer University (up until this point, I don't think there had been mention of a university in the county). With usual stereotypical fashion, we have a mean professor, who is ready to steam-roller anybody to build his reputation, and a young genius who is writing her thesis (on the Heisenberg uncertainty principle) and threatens to dethrone the evil professor.

As part of her research, she needs to look at an eclipse (go figure) and the murder mayhem ensues. That's not the bad physics (but doesn't help).

Here's the young genius at work, presenting her work in the dome of a telescope (not sure why she is not in an office or lecture room).
Someone has gone to great effort to fill the board with lots of scientific squiggles. It's not, however, gibberish. I'm not sure if they used a text book, or wikipedia, but there are some correct things there.

However,  something annoyed me. Zooming in on the board, what do we see?
Plank's constant! Argh!! You'd think that our young genius who has written a thesis on quantum mechanics and is presenting her research to evil and nasty professor could spell Planck's name correctly. But there is more! Whoever wrote the squiggles got the symbol, h, correct, and even the value, 1.054 x 10^-27, correct, but they completely screwed up the units (that's too painful to go into) and what this number actually is is ħ ,which is Planck's constant divided by 2π.

Why would they bother going to the effort of writing something semi-correct, but pay so little attention that they make a mess of it? Why not just do it right? Don't they realise that professors of astrophysics might be watching?

One other thing that annoyed me is that they did the "astronomers only do their work inside telescope domes" thing
We don't. We have offices like everyone else. And even when we are at the telescope, we are in the control room, not freezing our bottoms off in the dome.

Before finishing, I think it's worth noting that the observatory actually used in the show is actually a university observatory. It is the University of London Observatory at Mill Hill
Even though I was a student at the University of London, I never used this observatory, although I did visit there when I was looking for a PhD position. However, the observatory is not in the picturesque county of Midsomer, but is next to the A1 in North West London.
Like a lot of observatories around the world, it was build outside of a city, but the cities have grown around them.

Anyway, the murderer was not the evil astrophysicist..... It was actually the friendly professor of Quantum Physics! I'm sure his knowledge of the uncertainty principle will help him in prison.

There’s going to be a “thematic trimester” in Paris starting next spring:

• Semantics of proofs and certified mathematics, Institut Henri Poincaré, April 22nd - July 11th, 2014, organized by Pierre-Louis Curien, Hugo Herbelin, Paul-André Melliès.

If you like applications of category theory to logic and computer science, there should be a lot for you here!

The basic layout is this:

• Week 1 — Kick-off: Formalisation in mathematics and in computer science
• Week 3 — Workshop 1: Formalization of mathematics in proof assistants, organized by Georges Gonthier and Vladimir Voevodsky.
• Week 6 — Workshop 2: Constructive mathematics and models of type theory, organized by Thierry Coquand and Thomas Streicher.
• Week 8 — Workshop 3: Semantics of proofs and programs, organized by Thomas Ehrhard and Alex Simpson.
• Week 10 — Workshop 4: Abstraction and verification in semantics, organized by Paul-André Melliès and Luke Ong.
• Week 12 — Workshop 5, Certification of high-level and low-level programs organized by Christine Paulin and Zhong Shao.

A lot of people I know will attend parts of this, such as Jean Benabou, Marcelo Fiore, Dan Ghica, André Joyal, Samuel Mimram, and Bas Spitters. And that makes me happy, because Paul-André Melliès has invited me to spend up to a month attending this series of workshops, perhaps in two 2-week stretches. With a little luck I’ll be able to actually do this.

(My wife Lisa Raphals has gotten invited to Erlangen for the spring of 2014, meaning roughly April 1 - June 1. If she and I succeed in getting leaves of absence, I’ll go with her, and then take some trips to nearby places. Since I split my time between the Wild West and the Far East, Paris seems nearby to Erlangen to me. I also have vague invitations to IHES, Prague and Berlin which I might try to take advantage of. And if you have a luxurious villa in northern Italy or the French Riviera, let me know.)

I was sent or came across a few interesting links that relate to things covered on this blog and/or of general scientific interest.

It was announced yesterday that the European Physical Society 2013 High Energy Physics Prize was awarded to the collaboration of experimental physicists that operate the ATLAS and CMS experiments that discovered a type of Higgs particle, with special mention to Michel Della Negra, Peter Jenni, and Tejinder Virdee, for their pioneering role in the development of ATLAS and CMS.  Jenni and Virdee are both at the LHCP conference in Barcelona, which I’m also attending, and it has been a great pleasure for all of us here to be able to congratulate them in person .

One thing that came up a couple of times regarding weather forecasting (for instance, in forecasting the path of Hurricane Sandy) is that the European weather forecasters are doing a much better job of predicting storms a week in advance than U.S. forecasters are.  And I was surprised to learn that one of the the main reasons is simple: U.S. forecasters have less computing power than their European counterparts, which sounds (and is) ridiculous.  The new director of the U.S. National Weather Service, Louis Uccellini, has been successful in his goal of improving this situation, as reported here.  [Thanks to two readers for pointing me to this article.]

One of the possible interpretations of the new class of high-energy neutrinos reported by IceCube (see yesterday’s post) is that they come from the slow decay of a small fraction of the universe’s dark matter particles, assuming those particles have a mass of a couple of million GeV/c². [That's much heavier than the types of dark matter particles that most people are currently looking for, in searches that I discussed in a recent article.]  I didn’t immediately mention this possibility (which is rather obvious to an expert) because I wanted a couple of days to think about it before generating a stampede or press articles.  But, not surprisingly, people who were paying more attention to what IceCube has been up to had recently written a paper on this subject.  [Here's an older, related paper, but at much lower energy; maybe there are other similar papers that I don't know about?]  At the time these authors wrote this paper, only the two highest energy neutrinos — which have energies that, within the uncertainties of the measurements, might be equal (see Figure 2 of yesterday’s post) — were publicly known.  In their paper, they predicted that (just as any expert would guess) in addition to a spike of neutrinos, all at about 1.1 million GeV, one would also find a population of lower-energy neutrinos, similar to those new neutrinos that IceCube has just announced. So yes, among many possibilities, it appears that it is possible that the new neutrinos are from decaying dark matter.  If more data reveals that there really is a spike of neutrinos with energy around 1.1 million GeV, and the currently-observed gap between the million-GeV neutrinos and the lower-energy ones barely fills in at all, then this will be extremely strong evidence in favor of this idea… though it will be another few years before the evidence could become convincing.  Conversely, if IceCube observes any neutrinos near but significantly above 1.1 million GeV, that would show there isn’t really a spike, disfavoring this particular version of the idea.

Regarding yesterday’s post, it was pointed out to me that when I wrote “The only previous example of neutrinos being used in astrophysics occurred with the discovery of neutrinos from the relatively nearby supernova, visible with the naked eye, that occurred in 1987,” I should also have noted that neutrinos were and are used to understand the interior of the sun (and vice versa).  And you could even perhaps say that atmospheric neutrinos have been used to understand cosmic rays (and vice versa.)

In sad news, in the “all-good-things-must-come-to-an-end” category, the Kepler spacecraft, which has brought us an unprecedented slew of discoveries of planets orbiting other stars, may have reached the end of the line (see for example here), at least as far as its main goals.  It’s been known for some time that its ability to orient itself precisely was in increasing peril, and it appears that it has now been lost.  Though this has occurred earlier than hoped, Kepler survived longer than its core mission was scheduled to do, and its pioneering achievements, in convincing scientists that small rocky planets not unlike our own are very common, will remain in the history books forever.  Simultaneous congratulations and condolences to the Kepler team, and good luck in getting as much as possible out of a more limited Kepler.

Filed under: Astronomy, LHC News, Particle Physics, Science and Modern Society Tagged: astronomy, cms, DarkMatter, Higgs, LHC, neutrinos, weather

Garry Gutting's recent post What Do Scientific Studies Show? at the NYT blogs is utterly unremarkable. Or so I thought, being clearly biased because the guy is a professor of philosophy, and I - I'm at the other end of the circle. But then he puts forward a proposal I think is brilliant: A labeling system for scientific news "that made clear a given study’s place in the scientific process", ranging from the speculative idea and preliminary results all the way to established scientific theory.

I like the idea because it would be an easy way to solve a tension in science news, which is that what's new and exciting, and therefore likely to make headlines, is also often controversial and likely to be refuted later. The solution can't be to not report what's new and exciting, but to find a good way to make clear that, while interesting and promising, this isn't (yet) established scientific consensus.

23andMe has a star rating to indicate how reliable a correlation between a genetic sequence and certain traits/diseases is, based on what has been reported in the scientific literature. (See my earlier blogpost for screenshots showing how that looks like.) They have a white paper laying out the criteria for assessing the scientific status of these correlations. The 23andMe rating serves a similar purpose as the proposed rating for science news. It is handy as a quick orientation, and it is a guide for those who can't or don't want to dig into the scientific literature themselves. It doesn't tell you to disregard results with few stars, just to keep in mind that this might turn out to be a data glitch, and to enjoy or worry with caution.

I think that such a label indicating how established a scientific result or idea is would be easy to use. Writers could just assign it themselves with help from the researchers they have been in contact with while working on a piece. That might not always be very accurate, but undoubtedly bloggers would add their voice. There would most likely be a service popping up to aggregate all ratings on a given topic/press release (probably weighted by the source). I am guessing it would be pretty much self-organized because we're all so very used to these ratings for other purposes.

Do you think such a labeling would be helpful? If so, what criteria would you require for zero to five stars?

Dimensionally reduced scientist.

“Science is the only news,” Steward Brand wrote. My reading of this sentence is that science, the exploration of nature and natural law, is the ultimate source of inspiration. Developing a model and studying its properties can be like discovering a new world, and the discoveries that are the most fascinating are the ones that are surprising and unintuitive.

Probability amplitudes and wavefunctions are examples of such surprising and unintuitive properties, examples that are now a century old and that have changed the way we think about the world. Holography is a more recent example. And, gathering momentum in the quantum gravity community right now, is dimensional reduction.

Dimensional reduction means that on short distances the dimension of space-time decreases. To quantify what this means one has to be very careful with defining “dimension.”

The way we normally think about the dimension of space is to picture how lines spread out from a point. How quickly the lines dilute into their environment tells us something about the spheres we can draw around the point. The dimension of these spheres can be used to define the “Hausdorff dimension” of a space. The faster the lines dilute with distance, the larger the Hausdorff dimension.

The notion of dimension that is relevant for the effect of dimensional reduction is not the Hausdorff dimension, but instead the “spectral dimension.” The spectral dimension can be found by first getting rid of the Lorentzian signature and going to Euclidean space. And then to watch a random walker who starts at one point, and measure the probability for him to return to that point. The smaller the average return probability, the higher the probability he’ll get lost, and the higher the number of dimensions. One can define the spectral dimension from the average return probability.

Normally, for a flat, classical space, both notions of dimension are identical. However, there have been several approaches toward quantum geometry that found that the spectral dimension at short distances goes down from four to two. The return probability for short walks is larger than expected. One says that the spectral dimension “runs”, meaning it depends on the distance at which space-time is probed.

Surprising. Unintuitive.

This strange behavior was first found in Causal Dynamical Triangulations (hep-th/0505113), where one does a numerical simulation of an actual random walk in Euclidean space. But in other approaches one does not need a numerical simulation; it is possible to study the spectral dimension analytically as follows.

The behavior of the random walk is governed by a differential equation, the diffusion equation, in which there enters the metric of the background space-time. In approaches to quantum gravity in which the metric is quantized, it is then the expectation value of the operator that the metric has become which enters the diffusion equation. From the diffusion equation one calculates the return probability for the random walk.

This way, one can then infer the spectral dimension also in Asymptotically Safe Gravity (hep-th/0508202). Interestingly, one finds the same drop from four to two spectral dimensions. Yet another indication comes from Loop Quantum Gravity, where the scaling of the area operator with length changes at short distances. It is somewhat questionable whether the notion of a metric makes sense at all in this regime, but if one nevertheless constructs the diffusion equation from this scaling, one again finds that the spectral dimension drops from four to two (0812.2214). And Horava-Lifshitz gravity is maybe the best studied case where one finds dimensional reduction (0902.3657).

Surprising. Unintuitive. It is difficult to interpret this behavior. Maybe a good way to picture it, as Calcagni, Eichhorn and Saueressig suggested, is to think of the quantum fluctuations of space-time hindering a particle’s random walk and slowing it down. It wouldn’t have to be that way. Quantum fluctuations could also be kicking the particle around wildly, thus increasing the spectral dimension rather than decreasing it. But that’s not what the theory tells us. One shouldn’t take this picture too seriously though, because we’re talking about a random walk in Euclidean space, so it’s not an actual physical process.

It seems strange that such entirely different approaches to quantum gravity would share a behavior like this. Maybe our theories are trying to teach us a lesson about a very general property of quantum space-time. But then again, the spectral dimension does not say all that much about the theory. There are many different types of random walks that give rise to the same spectral dimension. And while these different approaches to quantum gravity share the same scaling behavior for the spectral dimension, they differ in the type of random walk that produces this scaling (1304.7247).

So far, this is an entirely theoretical observation. It is interesting to speculate whether one can find experimental evidence for this scaling behavior. In fact, this recent paper by Amelino-Camelia et al aims to “explore the cosmological implications” of running spectral dimensions. At least that is what the first sentence of the abstract says. If you read the second sentence though you’ll notice that what they actually explore are modified dispersion relations. And while modified dispersion relations lead to a running spectral dimension, the opposite is not necessarily the case. But is there any better indication for a topic being hot than that people use it in the first sentence of an abstract to draw the readers interest?

Suppose $X$ is a topological space and $U\subseteq X$ is an open subset, with closed complement $K=X\setminus U$. Then $U$ and $K$ are, of course, topological spaces in their own right, and we have $X=U\bigsqcup K$ as a set. What additional information beyond the topologies of $U$ and $K$ is necessary to enable us to recover the topology of $X$ on their disjoint union?

Recall that the subspace topologies of $U$ and $K$ say that for each open $V\subseteq X$, the intersections $V\cap U$ and $V\cap K$ are open in $U$ and $K$, respectively. Thus, if a subset of $X$ is to be open, it must yield open subsets of $U$ and $K$ when intersected with them. However, this condition is not in general sufficient for a subset of $X$ to be open — it does define a topology on $X$, but it’s the coproduct topology, which may not be the original one.

One way we could start is by asking what sort of structure relating $U$ and $K$ we can deduce from the fact that both are embedded in $X$. For instance, suppose $A\subseteq U$ is open. Then there is some open $V\subseteq X$ such that $V\cap U=A$. But we could also consider $V\cap K$, and ask whether this defines something interesting as a function of $A$.

Of course, it’s not clear that $V\cap K$ is a function of $A$ at all, since it depends on our choice of $V$ such that $V\cap U=A$. Is there a canonical choice of such $V$? Well, yes, there’s one obvious canonical choice: since $U$ is open in $X$, $A$ is also open as a subset of $X$, and we have $A\cap U=A$. However, $A\cap K=\varnothing$, so choosing $V=A$ wouldn’t be very interesting.

The choice $V=A$ is the smallest possible $V$ such that $V\cap U=A$. But there’s also a largest such $V$, namely the union of all such $V$. This set is open in $X$, of course, since open sets are closed under arbitrary unions, and since intersections distribute over arbitrary unions, its intersection with $U$ is still $A$.

Let’s call this set $i_{*}(A)$. In fact, it’s part of a triple of adjoint functors $i_{!}⊣i^{*}⊣i_{*}$ between the posets $O(U)$ and $O(X)$ of open sets in $U$ and $X$, where $i^{*}:O(X)\to O(U)$ is defined by $i^{*}(V)=V\cap U$, and $i_{!}:O(U)\to O(X)$ is defined by $i_{!}(A)=A$. Here $i$ denotes the continuous inclusion $U\hookrightarrow X$.

Now we can consider the intersection $i_{*}(A)\cap K$, which I’ll also denote $j^{*}{i}_{*}(A)$, where $j:K\hookrightarrow X$ is the inclusion. It turns out that this is interesting! Consider the following example, which is easy to visualize:

• $X={ℝ}^2$.
• $U=\{(x,y)\mid x<0\}$, the open left half-plane.
• $K=\{(x,y)\mid x\ge 0\}$, the closed right half-plane.

If an open subset $A\subseteq U$ “doesn’t approach the boundary” between $U$ and $K$, such as the open disc of radius $1$ centered at $(-2,0)$, then it’s fairly easy to see that $i_{*}(A)=A\cup \{(x,y)\mid x>0\}$, and therefore $j^{*}{i}_{*}(A)=\{(x,y)\mid x>0\}$ is the open right half-plane.

On the other hand, consider some open subset $A\subseteq U$ which does approach the boundary, such as

$$A=\{(x,y)\mid x^2+y^2<1\text{and}x<0\}$$

the intersection with $U$ of the open disc of radius $1$ centered at $(0,0)$. A little thought should convince you that in this case, $i_{*}(A)$ is the union of the open right half-plane with the whole open disc of radius $1$ centered at $(0,0)$. Therefore, $j^{*}{i}_{*}(A)$ is the open right half-plane together with the strip $\{(0,y)\mid -1<y<1\}$.

This example suggests that in general, $j^{*}{i}_{*}(A)$ measures how much of the “boundary” between $U$ and $K$ is “adjacent” to $A$. I leave it to some enterprising reader to try to make that precise. Here’s another nice exercise: what can you say about $i^{*}{j}_{*}(B)$ for an open subset $B\subseteq K$?

Let us however go back to our original question of recovering the topology of $X$. Suppose $A\subseteq U$ and $B\subseteq K$ are open such that $A\cup B$ is open in $X$; how does this latter fact manifest as a property of $A$ and $B$? Note first that $(A\cup B)\cap U=A$. Thus, since $i_{*}(A)$ is the largest $V$ such that $V\cap U=A$, we have $A\cup B\subseteq i_{*}(A)$, and therefore $B=j^{*}(A\cup B)\subseteq j^{*}{i}_{*}(A)$. Let me say that again:

$$B\subseteq j^{*}{i}_{*}(A).$$

This is a relationship between $A$ and $B$ which is expressed purely in terms of the topological spaces $U$ and $K$ and the function $j^{*}{i}_{*}:O(U)\to O(K)$, which we have just shown is necessary for $A\cup B$ to be open in $X$.

In fact, it is also sufficient! For suppose this to be true. Since $B$ is open in $K$, there is some open $C\subseteq X$ such that $C\cap K=B$. Given such a $C$, the union $C\cup U$ also has this property, since $U\cap K=\varnothing$. Note that in fact $C\cup U=B\cup U$, and also $B\cup U=j_{*}(B)$, the largest open subset of $X$ whose intersection with $K$ is $B$. (Since $K$, unlike $U$, is not open, there may not be a smallest such, but there is always a largest such.) Now I claim we have

$$A\cup B=j_{*}(B)\cap i_{*}(A)$$

To show this, it suffices to show that the two sides become equal after intersecting with $U$ and with $K$. For the first, we have

$$(j_{*}(B)\cap i_{*}(A))\cap U=j_{*}(B)\cap (i_{*}(A)\cap U)=j_{*}(B)\cap A=A=(A\cup B)\cap U$$

and for the second we have

$$(j_{*}(B)\cap i_{*}(A))\cap K=(j_{*}(B)\cap K)\cap i_{*}(A)=B\cap i_{*}(A)=B=(A\cup B)\cap K$$

using the assumption at the step $B\cap i_{*}(A)=B$.

In conclusion, the topology of $X$ is entirely determined by

• the induced topology of an open subspace $U\subseteq X$,
• the induced topology on its closed complement $K=X\setminus U$, and
• the induced function $j^{*}{i}_{*}:O(U)\to O(K)$.

Specifically, the open subsets of $X$ are those of the form $A\cup B$ — or equivalently, by the above argument, $i_{*}(A)\cap j_{*}(B)$ — where $A\subseteq U$ is open in $U$, $B\subseteq K$ is open in $K$, and $B\subseteq j^{*}{i}_{*}(A)$.

An obvious question to ask now is, suppose given two arbitrary topological spaces $U$ and $K$ and a function $f:O(U)\to O(K)$; what conditions on $f$ ensure that we can define a topology on $X≔U\bigsqcup K$ in this way, which restricts to the given topologies on $U$ and $K$ and induces $f$ as $j^{*}{i}_{*}$? We may start by asking what properties $j^{*}{i}_{*}$ has. Well, it preserves inclusion of open sets (i.e. $A\subseteq A\prime \Rightarrow j^{*}{i}_{*}(A)\subseteq j^{*}{i}_{*}(A\prime )$) and also finite intersections ($j^{*}{i}_{*}(A\cap A\prime )=j^{*}{i}_{*}(A)\cap j^{*}{i}_{*}(A\prime )$), including the empty intersection ($j^{*}{i}_{*}(U)=K$). In other words, it is a finite-limit-preserving functor between posets. Perhaps surprisingly, it turns out that this is also sufficient: any finite-limit-preserving $f:O(U)\to O(K)$ allows us to glue $U$ and $K$ in this way; I’ll leave that as an exercise too.

Okay, that was some fun point-set topology. Now let’s categorify it. Open subsets of $X$ are the same as 0-sheaves on it, i.e. sheaves of truth values, or of subsingleton sets, and the poset $O(X)$ is the (0,1)-topos of 0-sheaves on $X$. So a certain sort of person immediately asks, what about $n$-sheaves for $n>0$?

In other words, suppose we have $X$, $U$, and $K$ as above; what additional data on the toposes $\mathrm{Sh}(U)$ and $\mathrm{Sh}(K)$ of sheaves (of sets, or groupoids, or homotopy types, etc.) allows us to recover the topos $\mathrm{Sh}(X)$? As in the posetal case, we have adjunctions $i_{!}⊣i^{*}⊣i_{*}$ and $j^{*}⊣j_{*}$ relating these toposes, and we may consider the composite $j^{*}{i}_{*}:\mathrm{Sh}(U)\to \mathrm{Sh}(K)$.

The corresponding theorem is then that $\mathrm{Sh}(X)$ is equivalent to the comma category of ${\mathrm{Id}}_{\mathrm{Sh}(K)}$ over $j^{*}{i}_{*}$, i.e. the category of triples $(A,B,\varphi )$ where $A\in Sh(U)$, $B\in \mathrm{Sh}(K)$, and $\varphi :B\to j^{*}{i}^{*}(A)$. This is true for 1-sheaves, $n$-sheaves, $\mathrm{\infty }$-sheaves, etc. Moreover, the condition on a functor $f:\mathrm{Sh}(U)\to \mathrm{Sh}(K)$ ensuring that its comma category is a topos is again precisely that it preserves finite limits. Finally, this all works for arbitrary toposes, not just sheaves on topological spaces. I mentioned in my last post some applications of gluing for non-sheaf toposes (namely, syntactic categories).

One new-looking thing does happen at dimension 1, though, relating to what exactly the equivalence

$$\mathrm{Sh}(X)\simeq ({\mathrm{Id}}_{\mathrm{Sh}(K)}\downarrow j^{*}{i}_{*})$$

looks like. The left-to-right direction is easy: we send $C\in \mathrm{Sh}(X)$ to $(i^{*}C,j^{*}C,\varphi )$ where $\varphi :j^{*}C\to j^{*}{i}_{*}{i}^{*}C$ is $j^{*}$ applied to the unit of the adjunction $i^{*}⊣i_{*}$. But in the other direction, suppose given $(A,B,\varphi )$; how can we reconstruct an object of $\mathrm{Sh}(X)$?

In the case of open subsets, we obtained the corresponding object (an open subset of $X$) as $A\cup B$, but now we no longer have an ambient “set of points” in which to take such a union. However, we also had the equivalent characterization of the open subset of $X$ as $i_{*}(A)\cap j_{*}(B)$, and in the categorified case we do have objects $i_{*}(A)$ and $j_{*}(B)$ of $\mathrm{Sh}(X)$. We might initially try their cartesian product, but this is obviously wrong because it doesn’t incorporate the additional datum $\varphi$. It turns out that the right generalization is actually the pullback of $j_{*}(\varphi )$ and the unit of the adjunction $j^{*}⊣j_{*}$ at $i_{*}(A)$:

$$\begin{array}{ccc}C& \to & j_{*}(B)\\ \downarrow & & {\downarrow }^{j^{*}(\varphi )}\\ i_{*}(A)& \to & j_{*}{j}^{*}{i}_{*}(A)\end{array}$$

In particular, any object $C\in \mathrm{Sh}(X)$ can be recovered from $i^{*}C$ and $j^{*}C$ by this pullback:

$$\begin{array}{ccc}C& \to & j_{*}{j}^{*}C\\ \downarrow & & \downarrow \\ i_{*}{i}^{*}C& \to & j_{*}{j}^{*}{i}_{*}{i}^{*}C\end{array}$$

Now let’s shift perspective a bit, and ask what all this looks like in the internal language of the topos $\mathrm{Sh}(X)$. Inside $\mathrm{Sh}(X)$, the subtoposes $\mathrm{Sh}(U)$ and $\mathrm{Sh}(K)$ are visible through the left-exact idempotent monads $i_{*}{i}^{*}$ and $j_{*}{j}^{*}$, whose corresponding reflective subcategories are equivalent to $\mathrm{Sh}(U)$ and $\mathrm{Sh}(K)$ respectively. In the internal type theory of $\mathrm{Sh}(X)$, $i_{*}{i}^{*}$ and $j_{*}{j}^{*}$ are modalities, which I will denote $I_U$ and $J_U$ respectively. Thus, inside $\mathrm{Sh}(X)$ we can talk about “sheaves on $U$” and “sheaves on $K$” by talking about $I_U$-modal and $J_U$-modal types (or sets).

Moreover, these particular modalities are actually definable in the internal language of $\mathrm{Sh}(X)$. Open subsets $U\subseteq X$ can be identified with subterminal objects of $\mathrm{Sh}(X)$, a.k.a. h-propositions or “truth values” in the internal logic. Thus, $U$ is such a proposition. Now $I_U$ is definable in terms of $U$ by

$$I_U(C)=(U\to C)$$

I’m using type-theorists’ notation here, so $U\to C$ is the exponential $C^U$ in $\mathrm{Sh}(X)$. The other modality $J_U$ is also definable internally, though a bit less simply: it’s the following pushout:

$$\begin{array}{ccc}U\times C& \to & C\\ \downarrow & & \downarrow \\ U& \to & J_U(C)\end{array}.$$

In homotopy-theoretic language, $J_U(C)$ is the join of $C$ and $U$, written $U*C$. And if we identify $\mathrm{Sh}(U)$ and $\mathrm{Sh}(K)$ with their images under $i_{*}$ and $j_{*}$, then the functor $j^{*}{i}_{*}:\mathrm{Sh}(U)\to \mathrm{Sh}(K)$ is just the modality $J_U$ applied to $I_U$-modal types.

Finally, the fact that $\mathrm{Sh}(X)$ is the gluing of $\mathrm{Sh}(U)$ with $\mathrm{Sh}(K)$ means internally that any type $C$ can be recovered from $I_U(C)$, $J_U(C)$, and the induced map $J_U(C)\to J_U(I_U(C))$ as a pullback:

$$\begin{array}{ccc}C& \to & J_U(C)\\ \downarrow & & \downarrow \\ I_U(C)& \to & J_U(I_U(C))\end{array}$$

Now recall that internally, $U$ is a proposition: something which might be true or false. Logically, $I_U(C)=(U\to C)$ has a clear meaning: its elements are ways to construct an element of $C$ under the assumption that $U$ is true.

The logical meaning of $J_U$ is somewhat murkier, but there is one case in which it is crystal clear. Suppose $U$ is decidable, i.e. that it is true internally that “$U$ or not $U$”. If the law of excluded middle holds, then all propositions are decidable — but of course, internally to a topos, the LEM may fail to hold in general. If $U$ is decidable, then we have $U+\neg U=1$, where $\neg U=(U\to 0)$ is its internal complement. It’s a nice exercise to show that under this assumption we have $J_U(C)=(\neg U\to C)$.

In other words, if $U$ is decidable, then the elements of $J_U(C)$ are ways to construct an element of $C$ under the assumption that $U$ is false. In the decidable case, we also have $J_U(I_U(C))=1$, so that $C=I_U(C)\times J_U(C)$ — and this is just the usual way to construct an element of $C$ by case analysis, doing one thing if $U$ is true and another if it is false.

This suggests that we might regard internal gluing as a “generalized sort of case analysis” which applies even to non-decidable propositions. Instead of ordinary case analysis, where we have to do two things:

• assuming $U$, construct an element of $C$; and
• assuming not $U$, construct an element of $C$

in the non-decidable case we have to do three things:

• assuming $U$, construct an element of $C$;
• construct an element of the join $U*C$; and
• check that the two constructions agree in $U*(U\to C)$.

I have no idea whether this sort of generalized case analysis is useful for anything. I kind of suspect it isn’t, since otherwise people would have discovered it, and be using it, and I would have heard about it. But you never know, maybe it has some application. In any case, I find it a neat way to think about gluing.

Let me end with a tantalizing remark (at least, tantalizing to me). People who calculate things in algebraic topology like to work by “localizing” or “completing” their topological spaces at primes, since it makes lots of things simpler. Then they have to try to put this “prime-by-prime” information back together into information about the original space. One important class of tools for this “putting back together” is called fracture theorems. A simple fracture theorem says that if $X$ is a $p$-local space (meaning that all primes other than $p$ are inverted) and some technical conditions hold, then there is a pullback square:

$$\begin{array}{ccc}X& \to & X_p^{\wedge }\\ \downarrow & & \downarrow \\ X_{\mathbb{Q}}& \to & (X_p^{\wedge }{)}_{\mathbb{Q}}\end{array}$$

where $(-{)}_p^{\wedge }$ denotes $p$-completion and $(-{)}_{\mathbb{Q}}$ denotes “rationalization” (inverting all primes). A similar theorem applies to any space $X$ (with technical conditions), yielding a pullback square

$$\begin{array}{ccc}X& \to & \prod _p{X}_{(p)}\\ \downarrow & & \downarrow \\ X_{\mathbb{Q}}& \to & (\prod _p{X}_{(p)}{)}_{\mathbb{Q}}\end{array}$$

where $(-{)}_{(p)}$ denotes localization at $p$.

Clearly, there is a formal resemblance to the pullback square involved in the gluing theorem. At this point I feel like I should be saying something about $\mathrm{Spec}(\mathbb{Z})$. Unfortunately, I don’t know what to say! Maybe some passing expert will enlighten us.

A few days ago our Ghost Pontiff Dave Bacon wondered how Toom’s noisy but highly fault-tolerant 2-state classical cellular automaton  can get away with violating the Gibbs phase rule, according to which a finite-dimensional locally interacting system, at generic points in its phase diagram, can have only only one thermodynamically stable phase.  The Gibbs rule is well illustrated by the low-temperature ferromagnetic phases of the classical Ising model in two or more dimensions:  both phases are stable at zero magnetic field, but an arbitrarily small field breaks the degeneracy between their free energies, making one phase metastable with respect to nucleation and growth of islands of the other.  In the Toom model, by contrast, the two analogous phases are absolutely stable over a finite area of the phase diagram, despite biased noise that would seem to favor one phase over the other.  Of course Toom’s rule is not microscopically reversible,  so it is not bound by laws of equilibrium thermodynamics.

Nevertheless, as Dave points out, the distribution of histories of any locally interacting d-dimensional system, whether microscopically reversible or not, can be viewed  as an equilibrium Gibbs distribution of a d+1 dimensional system, whose local Hamiltonian is chosen so that the d dimensional system’s transition probabilities are given by Boltzmann exponentials of interaction energies between consecutive time slices.  So it might seem, looking at it from the d+1 dimensional viewpoint, that the Toom model ought to obey the Gibbs phase rule too.

The resolution of this paradox, described in my 1985 paper with Geoff Grinstein,  lies in the fact that the d to d+1 dimensional mapping is not surjective.  Rather it is subject to the normalization constraint that for every configuration X(t) at time t, the sum over configurations X(t+1) at time t+1 of transition probabilities P(X(t+1)|X(t)) is exactly 1.    This in turn forces the d+1 dimensional free energy to be identically zero, regardless of how the d dimensional system’s transition probabilities are varied.  The Toom model is able to evade the Gibbs phase rule because

• being irreversible, its d dimensional free energy is ill-defined, and
• the normalization constraint allows two phases to have exactly equal  d+1 dimensional free energy despite noise locally favoring one phase or the other.

Just outside the Toom model’s bistable region is a region of metastability (roughly within the dashed lines in the above phase diagram) which can be given an interesting interpretation in terms of the  d+1 dimensional free energy.  According to this interpretation, a metastable phase’s free energy is no longer zero, but rather -ln(1-Γ)≈Γ, where Γ is the nucleation rate for transitions leading out of the metastable phase.  This reflects the fact that the transition probabilities no longer sum to one, if one excludes transitions causing breakdown of the metastable phase.  Such transitions, whether the underlying d-dimensional model is reversible (e.g. Ising) or not (e.g. Toom), involve critical fluctuations forming an island of the favored phase just big enough to avoid being collapsed by surface tension.  Such critical fluctuations occur at a rate

Γ≈ exp(-const/s^(d-1))

where s>0 is the distance in parameter space from the bistable region (or in the Ising example, the bistable line).  This expression, from classical homogeneous nucleation theory, makes the d+1 dimensional free energy a smooth but non-analytic function of s, identically zero wherever a phase is stable, but lifting off very smoothly from zero as one enters the region of metastability.

 

 

Below, we compare  the d and d+1 dimensional free energies of the Ising model with the d+1 dimensional free energy of the Toom model on sections through the bistable line or region of the phase diagram.

We have been speaking so far only of classical models.  In the world of quantum phase transitions another kind of d to d+1 dimensional mapping is much more familiar, the quantum Monte Carlo method, nicely described in these lecture notes, whereby a d dimensional zero-temperature quantum system is mapped to a d+1 dimensional finite-temperature classical Monte Carlo problem.   Here the extra dimension, representing imaginary time, is used to perform a path integral, and unlike the classical-to-classical mapping considered above, the mapping is bijective, so that features of the d+1 dimensional classical system can be directly identified with corresponding ones of the d dimensional quantum one.

 

 

There’s a famous story about Richard Feynman at Cornell suffering from the science equivalent of writer’s block, after WWII. He was depressed and feeling like everything he did was pointless, until one day he spotted a student throwing a plate up in the air in the cafeteria. As the plate spun, it wobbled, and the wobble seemed to go faster than the spin. Intrigued, he sat down and calculated the physics involved, finding that, indeed, the wobble should go at twice the rate of spin. This basically reignited his interest in physics, and shortly after that, began his legendarily productive period when he invented his version of QED.

I mention this not to put myself in Feynman’s category, but just as a reminder of the universal tenddency of physicists to get caught up in looking at silly, simple problems in more detail than is really required. Such as, for example, the several hours I spent this week simulating the motion of a pendulum in VPython.

Like a lot of things these days, this came out of a passing mention on Twitter: Andrew Morrison was asking about using a pendulum in a lab as a demonstration of conservation of energy, and I got brought into the conversation. This, in turn, got me thinking about simulating a pendulum, something I’ve wondered about in the past, particularly when I was doing a seminar on timekeeping.

I had toyed with the idea of using a simulation to demonstrate the physics of a pendulum, and how its period depends on the angle, as this is a big issue for making accurate pendulum-based clocks. If you use a really wide swing for a pendulum, it takes longer to complete an oscillation than you would expect from a simple model. You can calculate approximately how much it varies, but the math is kind of hairy, and a simulation is probably more engaging, anyway.

I ended up not doing it because when I started thinking about it, the obvious way to do it was to just stick in the necessary force, which I can easily calculate– the “string” of the pendulum needs to pull on the bob with a force equal to to outward component of gravity plus the centripetal force needed to keep it on the right arc. The problem is, that seems like a cheat– I’ve calculated the force needed before doing the simulation, which defeats the purpose of the simulation, and brings in a bunch of physics that goes beyond what I wanted to deal with.

As usual, I was being an idiot, and when the Twitter conversation got me thinking about this again, I realized that the Matter and Interactions textbook that got me into simulating things in VPython in the first place also provides an explanation for how to calculate the motion of a pendulum without putting the force in by hand. The book spends a whole bunch of time on a microscopic model of material objects as balls (atoms) connected by springs (chemical bonds). So, the solution is simple: treat the string of the simulated pendulum as a spring. The idealized version of a pendulum, after all, that provides whatever force it needs to to keep the ball on a set path, is just a spring with an infinite spring constant, giving a finite force for an infinitesimal stretch.

Once you do that, it’s easy to code up, and doesn’t require any prior knowledge of the path. Of course, you need some idea of what to use for a spring constant, but then the beauty of this method is that you can just stick in any value you like, and see what happens. The screen shot at the top is for a spring constant of 100 N/m (not all that strong) and a starting angle of 37 degrees (which is close to the small angle of a 3-4-5 triangle). The program assumes the spring-string is at its relaxed length to start, so providing no force, and the red trace in that image shows the resulting path, which makes a cool pattern.

That motion can be broken down into two pieces: there’s a mass-on-a-spring oscillation in and out, as the spring-string stretches and compresses; the period of that is pretty much exactly what you expect for the spring constant and mass in the simulation. Then there’s the back-and-forth oscillation of the pendulum on a mostly circular arc. For this particular choice of parameters, these periods are close to commensurate, so the pendulum more or less retraces its own path, giving a nifty pattern. For a different choice of angle, the path sort of smears out into a broad band after several oscillations.

Of course, the interesting thing to do with this is to look at how the period depends on angle, as I toyed with doing back when I taught about timekeeping. Measuring the period for a bunch of different angles gives the following graph:

The red points here represent the simulation for a spring constant of 100 N/m, as in the above screen shot. You can see that, as you expect, the period increases slightly as you go to larger angles. The theoretical value for an ideal pendulum is 2.0071s, and all of these points are higher than that, presumably because the stretching of the pendulum increases the effective length as it swings.

There are three other sets plotted here, as well, though it’s hard to see them. There are black circles, labeled “cheat” for the simulation where I put in the formula for the right force by hand. These are almost impossible to see, because they’re under the yellow triangles from the simulation for a spring constant of 10,000 N/m; almost all of these are within 0.0001s of the “cheat” values. There are also green triangles, for a spring constant of 1,000 N/m (half as many, because I got tired of copying down values), which are very slightly higher than the 10,000 N/m points, but not by all that much.

So, this does exactly what you would expect: as you increase the spring constant, the period value approaches the “ideal” case of a string that doesn’t stretch at all. Physics works, hooray!

It’s sort of interesting to look at how that approach happens, so here’s another graph:

This shows the period for a single starting angle– 37 degrees– for a bunch of different spring constants. Note that the horizontal scale is logarithmic, so this spans a range from 10 N/m to 100,000 N/m. The dashed horizontal line is the “cheat” value of 2.0610s. This is a few hundredths of a percent from the approximate theoretical value for that angle, so again: physics works, hooray! I don’t have a particular expectation for what the approach to the ideal value should look like, mathematically, or I’d fit a function to those points. This looks pretty reasonable, though.

So, the upshot here is that it is, in fact, possible to simulate the motion of a simple pendulum very well without knowing the right answer in advance. This also produces a slightly surprising result, namely that the force on the string oscillates rapidly during the whole swing, as the spring-string stretches and compresses. At any given instant, the force can be substantially less or substantially more than the theoretical value for the “cheat” version. This isn’t something you’d necessarily anticipate, but it does make sense when you think about the underlying physics. I didn’t make graphs of this, but did look at the ratio of the maximum force measured through the swing and the “theoretical” maximum that you expect from the “cheat” model. These numbers were very consistent across the different spring constants, and varied with the angle in a kind of interesting way: the larger the starting angle, the smaller the ratio of the two.

Again, this makes some sense if you think about the underlying physics: the initial condition of the model is that the spring-string is unstretched, and thus exerting zero force at the starting point. This is a good fit at large angles– the “cheat” model would give zero force for an angle of 90 degrees. At smaller angles, though, this is a very bad approximation, so you would expect the simulation to deviate from the ideal by a larger amount. At 85 degrees, the maximum force is about 3% more than the “cheat” version, while at 5 degrees it’s close to a factor of two larger.

You can also do a time-average of the force over one of the radial oscillations (basically adding up the force for each time step between reversals of the velocity along the string, then dividing by the number of time steps), and look at that. As you might well expect, this tracks the “cheat” value reasonably well, coming within a few percent for most of the oscillation. It tends to come in a little low, which might just be a numerical artifact due to the fact that I’m a lousy programmer.

The obvious extension of this is to correct the zero-force assumption at the starting point– in reality, if you start a pendulum, you stretch the spring so it’s under a slight tension, so the string is taut. In principle, I think there should be a position where the spring-string ought to smoothly stretch to always be exactly the length it needs to be to supply the necessary centripetal force. It’s not obvious how to calculate the right starting position, though, and I’ve spent enough time futzing around with this is it is, so let’s just leave that as a homework exercise for the interested reader. (If I get bored enough in the near future, I may try to trial-and-error my way to the right value…)

So, anyway, there’s the latest in my open-ended series of overthinking the physics of simple systems. I’m not sure this will actually be any use in a class, unless I end up teaching our intermediate mechanics course– the issues involved in this end up going well beyond the content of our introductory courses (even though it was Matter and Interactions that kicked the whole thing off…). But it was fun to work up, and good enough for a blog post…

IceCube, the big high-energy neutrino experiment cleverly embedded into the ice at the South Pole, announced a very interesting result yesterday, following on an already interesting result from a few weeks ago, one that I failed to cover properly. They have seen the highest-energy neutrinos ever observed, ones that, unlike previously observed high-energy neutrinos, appear not to be generated by cosmic rays hitting the top of the atmosphere. Instead, they apparently come from new sources far out in space. And as such, it tentatively appears that they’ve opened up, as long anticipated, a new era in neutrino astronomy, in which high-energy neutrinos will be used to understand astrophysical phenomena!

[The only previous example of neutrinos being used in astrophysics occurred with the discovery of neutrinos from the relatively nearby supernova, visible with the naked eye, that occurred in 1987. But those neutrinos had energies millions of times smaller than the ones discussed here.  And there was hope that IceCube might see neutrinos specifically from gamma-ray bursts, including the one that occurred just two weeks ago; but that appears not to have happened.]

I don’t understand certain details well enough yet to give you a careful explanation — that will probably come next week — but here’s an early description (and expert readers are strongly encouraged to correct any errors.)

—

At present, there are various sources, one known and others suspected, of high-energy neutrinos (and anti-neutrinos) coming from the sky, as illustrated in Figure 1, taken from the IceCube talk that announced the result.

1. When cosmic rays (mostly high-energy protons and some atomic nuclei created in natural particle accelerators in outer space) hit atoms in the atmosphere, they produce showers of hadrons, some of which are pions and kaons.  Some of these in turn decay to muons (and anti-muons) and neutrinos (and anti-neutrinos). These “atmospheric neutrinos” take a wide range of energies, and (just like the cosmic rays that make them) become increasingly rare the higher-energy you go, the number falling like 1/(energy)^3.7. They should be detectable by IceCube out to energies of a million GeV or so (the black curve in Figure 1), and in the early days of IceCube were already detected out to about 300,000 GeV (the blue dots in Figure 1).
2. The cosmic rays give a second source of neutrinos that may be observable around a hundred thousand to a million GeV, from the production of charm quarks, which can create a small number of neutrinos that fall off more slowly with energy than do the neutrinos from other hadrons. One prediction for how many “prompt atmospheric” or “charm atmospheric” neutrinos should be present is the red curve in Figure 1.
   

   Fig. 1: The number of neutrinos (and anti-neutrinos), multiplied by their energy-squared (to make the plot easier to read but harder to interpret), per unit angular area on the sky, versus the energy of those neutrinos. Older data from IceCube is the blue dots. Predictions for four different sources of neutrinos (see text) are given by the four curves. Note the green line for astrophysical neutrinos could in fact be lower than shown. 1 TeV = 1000 GeV.  Plot taken from the IceCube talk.

3. Neutrinos produced when the very highest-energy cosmic rays, which, above a certain energy, collide with photons from the cosmic microwave background, and (mainly through the process proton + photon –> “Delta” [an excited version of the proton] –> neutrino + pion, followed by pion –> anti-muon + neutrino, and also by anti-muon –> anti-electron + neutrino + anti-neutrino). These are called “GZK neutrinos” or “cosmogenic neutrinos”. Since the number and energy of high-energy cosmic rays is roughly measured, the number and energy of these GZK neutrinos can be roughly predicted.
4. High-energy “astrophysical neutrinos” produced directly inside extremely energetic astrophysical objects, perhaps including the objects that make gamma-ray bursts. Since little is known about what objects are out there and how they work, the only clear thing that can be said about these neutrinos is that there can’t be too many of them (or we’d see more high-energy cosmic rays than we do). It is expected that the number of neutrinos from such sources will decrease as 1/(energy)²; since the plot in Figure 1 shows not the number of neutrinos but the number of neutrinos times their energy-squared, the (very rough) prediction from astrophysical sources is a flat green line in Figure 1.  We don’t know how many of these neutrinos to expect, so the location of that line, though it cannot be higher than shown, but could well be lower.

Recently, in their data from 2010-2012, IceCube reported, in a pre-publication paper that appeared a few weeks ago, that they observed two neutrinos with energies of about one million GeV. [For some reason I don't know, they amusingly decided to call these neutrinos Bert and Ernie.] These are unusually energetic for atmospheric neutrinos, yet not energetic enough to be GZK neutrinos. This makes it likely (but not certain) that they are from new astronomical sources! But with just two events, it’s hard to say anything else about them.  Until yesterday.

Yesterday, IceCube reported that, by using a technique that reduces the number of atmospheric neutrinos in their data, they were able to look for neutrinos from other sources at somewhat lower energies. They expected something like 10 (more precisely 10.6+4.5-3.9, or, including the charm atmospheric neutrinos in some model [??] 12.1±3.4 ) — about 5 from atmospheric neutrinos and 6 from muons from cosmic rays that give fake signals of neutrinos. But, as shown in Figure 2, they observed 28, including the two I mentioned in the previous paragraph. (To be clear, this means that 10 to 20 of them are probably neither atmospheric neutrinos nor fakes.) This is strong evidence (4.3 standard deviations) that IceCube is observing neutrinos that are not from atmospheric neutrinos… but they aren’t GZK neutrinos either.

What are these things? Are they astrophysical neutrinos, from some new, unknown class of sources? Well, it’s hard to say with so few of these neutrinos observed so far. On the one hand,

• They have some features expected from astrophysical neutrinos… they are consistent with coming uniformly across the sky (though with so few neutrinos it’s hard to tell), and their numbers appear to decrease with energy more slowly than atmospheric neutrinos do across the range of 20,000 – 1,200,000 GeV.
• There’s no sign that these neutrinos are associated with other particles simultaneously coming out of the sky, as would be expected for overhead cosmic rays that make atmospheric neutrinos.
• And, unlike the atmospheric neutrinos which are more often muon-neutrinos and muon-antineutrinos, these neutrinos seem to be more evenly distributed among the three types of neutrinos and antineutrinos.

But on the other hand, there are some possible challenges for this interpretation.

• If their numbers really decrease with as 1/(energy)², as naively expected for most astrophysical sources, then IceCube should also have seen some additional neutrinos (something like five to ten of them) well above 1,000,000 GeV.
• Moreover, these neutrinos (which should have traveled straight across space from their source) don’t point back toward any known object (such as an active galaxy or a recent gamma-ray burst) so we don’t have any way to know what type of object may be producing them.

In short, these neutrinos appear to be from a new, unidentified, and perhaps unexpected type of source!

We must remain somewhat cautious about any new result that comes from a single experiment and involves so few neutrinos.  But if IceCube’s result continues to hold up with more data and is confirmed by other similar neutrino experiments, or if in future this class of neutrinos can be linked with specific astrophysical objects, I suspect it will be seen as a major discovery — one that opens up the era of neutrino astronomy, and whose implications can today only be guessed at.

Filed under: Astronomy, Particle Physics Tagged: astronomy, neutrinos

“Settle thy studies.”

Alone in his workroom, a student contemplates his future. Piles of books teeter next to him. Boxes line the walls; and glass vials, the boxes. Sunbeams that struggle through the stained-glass window illuminate dust.

The student’s name is Faust. I met him during my last winter in college, while complementing Physics 42: Introductory Quantum Mechanics with German 44: The Faust Tradition. A medieval German alchemist, Faust has inspired plays, novels, operas, the short story “The Devil and Daniel Webster” about an American Congressman, and the film “Bedazzled” starring Brendan Frasier.

As I wondered what to pursue a PhD in, so (roughly speaking) did Faust. In plays by Christopher Marlowe and Johann Wolfgang von Goethe, Faust wavers among law, theology, philosophy, and medicine. You’ve probably heard what happens next: Faust chooses sorcery, conjures a demon, and bargains away his soul. Hardly the role model for a college student. I preferred to keep my soul, though Maxwell’s demon had stolen my heart.

A few decades after Goethe penned Faust, English physicist James Maxwell proposed a thought experiment. Consider a box divided into two rooms, he wrote, and a demon controlling the door between the rooms. Since others have explained Maxwell’s paradox, I won’t parrot them. Suffice to say, the demon helps clarify why time flows, what knowledge is, and how information relates to matter. Quantum-information physicists, I learned in a seminar after German 44, study Maxwell’s demon. Via the demon, experiment, and math, QI physicists study the whole world. I wanted to contemplate the whole world, like Goethe’s Faust. By studying QI, I might approximate my goal. Faust, almost as much as my QI seminar, convinced me to pursue a PhD in physics.

Fast forward two years. Someone must have misread my application, because Caltech let me sign my soul to its PhD program. I am the newest Preskillite. Or Preskillnik. Whichever term, if either, irks my supervisor more.

For five years, I will haunt this blog. (Spiros will haunt me if I don’t haunt it.) I’ll try to post one article per month. Pure quantum information occupies me usually: abstract math that encodes physical effects, like entropy (a key to why time flows), decoherence (a system’s transformation from quantum to ordinary), and entanglement (one particle’s ability to affect another, instantaneously, from across a room).

In case I wax poetic about algebra, I apologize in advance. Apologies if I write too many stories about particles in boxes. In addition to training a scientist’s lens on atoms, I enjoy training it on science, culture, and communities. Tune in for scientists’ uses (and abuses) of language, why physics captivates us, and the bittersweetness of representing half our species in a roomful of male physicists (advantage: I rarely wait in line to use a physics department’s bathroom).

As I prepare to move to Caltech, a Faust line keeps replaying in my mind. It encapsulates my impression of a PhD, though written 200 years ago: “Nothing I had; and yet, enough for youth—/ delight in fiction, and the thirst for truth.”

Pleasure to meet you, Quantum Frontiers. Drink with me.

I come to praise Kepler, not to bury it…

The Kepler Mission is one of the little NASA spacecraft that so frequently comes along, exceeds all expectations and changes our perspective of the universe.

There is a good Quick History of the transit method and Kepler Mission concept on the website.

Otto Struve noted in his seminal 1952 note that planetary “eclipses” of their parent stars ought to be detectable by photoelectric methods, a proposal that some two decades later was quantified by Rosenblatt, and then explored in detail (including development research) by Borucki and collaborators at NASA Ames.

A space based transit mission was first proposed more than 20 years ago, and was highly rated, IF the detector technology could get to the point where very low transit amplitudes could be measured and small radii planets detected. The review also noted that there would be significant secondary astrophysical science accomplished by any such mission.

A decade later, Kepler was finally selected, the fourth time it was proposed to the Discover class medium size NASA mission. By that point the detector technology was mature, a testbed demonstrator had been built, and the concept of transit observations of exoplanets had been demonstrated both from the ground, and from space, using the Hubble Space Telescope. The latter demonstrated that very high precision relative photometry was in fact achievable from space.

Kepler launched in March 2009, just over 4 years ago.
It had a nominal mission life of three years, and a main mission goal to find earth size planets in the habitable zone of solar like stars.

After the nominal mission, Kepler was given a three year mission extension to 2016, to continue the continuous monitoring of the 150,000 or so stars in the Kepler field.

Kepler has discovered almost 3,000 planetary candidates, of which about 100 have been confirmed through a variety of techniques, and, statistically, most of the rest are likely to be real planets.

Kepler has not quite found earth like planets in the habitable zone, yet.
It is heartbreakingly close to doing so.
More time for observations is needed, primarily because the stars being observed are a little bit noisier than expected. The periodic signal from the planetary transits can be dug out of the noise, but more observations of repeated transits are needed to get the signals out as you approach the limit of detectability.
Six years of observations ought to get Kepler to its goal of detecting earth size planets orbiting stars similar to the Sun at a distance where liquid water can persist on the planet’s surface.

To operate, Kepler’s orientation has to be held very stably to view the stars it is looking at. To do that it uses reaction wheels:

Kepler needs three reaction wheels to stay on target.
Any less and the spacecraft drifts, losing lock on the stars.
It has thrusters but cannot use those to stay on target for any length of time before they run out fuel.
Kepler carries 4 reaction wheels. They are heavy and expensive.
That is one spare.

One reaction wheel, wheel #2, failed in 2012.
A second reaction wheel started to show symptoms of degradation a few months ago. Twice in the last few weeks the spacecraft has safed, gone to a rest pointing, while the reaction wheels were despun with the thrusters, and diagnosis tests runs.
Reaction wheels are moving parts, they wear and tear, and have finite life expectancies.
Since the reaction wheels are all the same, they are vulnerable to common mode failure.

Then, last night Kepler went into a safe mode, again.
Switching back to reaction wheel mode the diagnosis showed reaction wheel #4 had seized.

That is the end of Kepler’s primary science mission.
The data is in the archives available for analysis. There will be no more.
It is just short of finding the other Earth.
So very very close..

Kepler can do some stuff with only three reaction wheels, basically driftscan observing. It is a wide band wide field optical telescope with a 1 m mirror.
Whether it is worth doing so to keep the spacecraft going will be an interesting decision.

I’m still seeing articles in the news media (here’s one) that say that the majority of Americans think the recent sequester in the US federal budget isn’t affecting them. These articles implicitly suggest that maybe the sequester’s across-the-board cuts aren’t really doing any serious damage.

Well, talk to scientists, and to research universities and government laboratories, if you want to hear about damage.

I haven’t yet got the stomach to write about the gut-wrenching destruction I’m hearing about across my own field of particle physics — essential grants being cut by a quarter, a third, or altogether; researchers being forced to lay off long-standing scientific staff whose expertise, of international importance, is irreplaceable; the very best postdoctoral researchers considering leaving the field because hard-hit universities across the country won’t be hiring many faculty anytime soon… There’s so much happening simultaneously that I’m not sure how I can get my head around it all, much less convey it to you.

But meanwhile, I would like to point you to a strong and strongly-worded article by Eric Klemetti, a well-known blogger and professor who writes at WIRED about volcanoes.  Please read what he wrote, and consider passing it on to those you know.  Everyone needs to understand that the damage that’s being done now across the U.S. scientific landscape, following a period of neglect that extends back many years before the recession, will last a generation or more, if it’s not addressed.

These deep, broad and sudden cuts are a short-sighted way of saving money.  Not only do they waste a lot of money already spent, the long-term cost of the permanent loss of expertise, and of future science and technology, is likely to exceed what we’ll save.  It’s not a good approach to reducing a budget.  So tell your representatives in Congress, and anyone who will listen: Scientific research isn’t excess fat to be chopped off crudely with a cleaver; it’s fuel for the nation’s future, and it needs wiser management than it’s receiving.

Filed under: Science and Modern Society Tagged: press, ScienceAndSociety

Greetings from Barcelona, where the LHCP 2013 conference is underway. I wanted to mention a couple of the opening remarks made by CERN’s Sergio Bertolucci and Mirko Pojer, both of whom spoke about the near-term and medium-term future of the Large Hadron Collider [LHC].

It’s worth taking a moment to review what happened in the LHC’s first run. During its first few years, the LHC was initially intended to run at around 14 TeV of energy in each proton-proton collision, and at a moderate collision rate. But shortly after beams were turned on, and before there were any collisions, there occurred the famous accident of September 19, 2008. The ensuing investigation of the cause revealed flaws in the connections between the superconducting magnets, as well as in the system that protects the machine against the effect of a magnet losing its superconductivity (called a “quench”; quenches are expected to happen occasionally, but they have to be controlled.) To keep the machine safe from further problems, it was decided to run the machine at 7 TeV per collision, and make up (in part) for the lower energy by running at a higher collision rate. Then:

• Late 2009: beams were restarted at 2.2 TeV per collision.
• 2010: a small number of collisions and a few new experimental results were obtained at 7 TeV per collision
• 2011: a large number of collisions (corresponding to nearly 100,000 Higgs particles per experiment [i.e. in ATLAS and CMS]) were obtained at 7 TeV per collision
• 2012: an even larger number of collisions (corresponding to over 400,000 Higgs particles per experiment) were obtained at 8 TeV per collision.

All in all, this “Run 1” of the LHC is widely viewed as enormously successful. For one thing, it showed that (excepting only the flawed but fixable magnet connections) the LHC is an excellent machine and works beautifully.  A high collision rate was indeed achieved, and this, combined with the quality of the experimental detectors and the cleverness of the experimental physicists, was sufficient for discovery of and initial study of what is now referred to as a “Standard Model-like Higgs particle”, as well as for ruling out a wide range of variants of certain speculative ideas [here are a couple of examples.]

Currently, the LHC is shut down for repairs and upgrades, in preparation for Run 2, which will begin in 2015. The machine has been warmed up to room temperature (normally its magnets have to be kept at 1.9 Kelvin, i.e 1.9 degrees Celsius above absolute zero), and, among many adjustments, all of those potentially problematic connections between magnets are being improved, to make it safer for the machine to run at higher energy per collision.

So here’s the update — I hesitate to call this “news”, since none of this very surprising to those who’ve been following events in detail. The plan, according to Bertolucci and to Pojer, includes the following

• When Run 2 starts in 2015, the energy per collision will probably be 13 TeV, with the possibility of increasing this toward the design energy of 14 TeV later in Run 2. This was more or less expected, given what was learned about the LHC’s superconducting magnets a few years ago: some of these crucial magnets may have quenches too often when operating at 14 TeV conditions, making the accelerator too inefficient at that energy.
• A big question that is still not decided (and may not be decided until direct experience is gained in 2015) is whether it is better to run with collisions every 50 nanoseconds [billionths of a second], as in 2011-2012, or every 25 nanoseconds, as was the original design for the LHC.  The latter is better for the operation of the experimental detectors and the analysis of the data, but poses more challenges for operating the LHC, and may cause the proton beams to be less stable. Studies on this question may be ongoing  throughout a good part of 2015.
• Run 2 is currently planned for 2015-2017, but as Pojer reminded us, 2015 will involve starting up the machine at a new energy and collision rate, and so a lot of time in 2015 will be spent on making the machine work properly and efficiently. Somewhat as in 2010, which was a year of pilot running before large amounts of data were obtained in 2011-2012, it is likely that 2015 will also be a year of relatively low data rate. Most of the data in the next run will appear in 2016-2017.  The bottom line is that although there will be new data in 2015, one should remember not to expect overly much news in that first year.

Of course the precise dates and plans may shift.  Life being what it is, it would not be surprising if some of the challenges are a bit worse than expected; this could delay the start of Run 2 by a few months, or require a slightly lower energy at the start. Nor would it be surprising if Run 2 extends into 2018.  But if Run 1 (and the experience at other accelerators) is any guide, then even though some things won’t go as well as hoped, others will go better than expected.

Filed under: Higgs, LHC News Tagged: atlas, cms, Higgs, LHC

This is at least thought-provoking.  Lamar Smith (R-Texas, chair of the US House science committee, famous for things like this) and Zoe Lofgren (D-CA, about as far from Lamar Smith as I can imagine with the possible exception of Nancy Pelosi) are co-sponsoring a bill that would create a position called Scientist Laureate of the United States.  This person would be appointed by the President following nomination by the National Academy of Sciences, and would be meant to act as an inspirational figure, making public appearances and furthering the cause of science.  This could be a good thing, provided (1) an actual accomplished scientist is chosen, not someone who has to satisfy a political agenda; and (2) the person chosen is charismatic and able to use the bully pulpit effectively.  The Science Laureate should do more than show up at middle schools - they should get major exposure (e.g., late night talk shows; hosting a science program on a major network with actual resources to make it good; having the ear of Congress, perhaps even the limited ability to insist on speaking at a hearing of the House or Senate science-related committees).  (Halftime at the Superbowl is probably out of line.)

While I applaud scientists with great public outreach track records (Neil deGrasse Tyson just spoke at our commencement), that should not be the sole criterion.  If this passes, hopefully Congress will keep in the bit about the NAS making the choice.  Suggestions are invited in the comments.

Some time ago I blogged about the Australian National Broadband Network (NBN), the centrepiece infrastructure policy of the current Labor government. I’d like to follow up on this issue from a different perspective. In the meantime, both the government and opposition have dedicated themselves to a national broadband policy. So I’d like to analyse the issue in this new context. In this post I will no longer ask the question “should the government build a national broadband network?”, but rather “given that both sides of the House have committed themselves to a national broadband scheme, which is the superior model?”. I’m firmly of the opinion that the Government’s NBN policy is by far the superior model.

First let’s compare the Government’s and the Coalition’s models. The Government’s NBN policy will roll out optical fibre to almost every premise in the country (93% fibre coverage, with various other technologies, such as satellites or wireless, reaching the remainder that are remote and inaccessible). This is the so-called ‘fibre to the home’ (FTTH) approach. It will guarantee 100Mbps downstream bandwidths to all areas covered by fibre, and is easily upgradeable in the future to 1Gbps speeds (indeed optical fibre is capable of far more than this). The Coalition’s scheme on the other hand relies on ‘fibre to the node’ (FTTN) technology, whereby fibre is rolled out to cabinets on the street corner, which are subsequently connected to individual premises using existing copper cables. The Coalition claims this will guarantee 25Mbps downstream speeds, but will be much cheaper than FTTH.

Let’s begin by considering the cost issue. The Coalition criticises the NBN as being too costly, claiming that their FTTN approach is vastly less expensive (the Coalition claims $17b less). If we work off the assumption that the copper infrastructure ‘comes for free’ then this might be a reasonable claim. But it doesn’t. The reality is that the Australian copper network is nearing the end of its lifetime and will be in need of complete replacement in the near future followed by ongoing maintenance. To my knowledge, this cost has not been factored into the Coalition’s estimates, which significantly underestimates the total long-term cost of the network. Fibre has a very long lifespan – on the order of at least half a century. This is not the case for copper, which deteriorates very rapidly, requiring constant maintenance or downright replacement. I suspect that once this is factored into the pricing, the Coalition’s plan will not be quite as cheap as touted. Telstra currently spends $1b per year maintaining their copper network. Accumulate that over the life expectancy of the NBN and you’ve got a hell of an expense on the order of $50b for maintenance alone. Then there’s the energy consumption cost. Powering optical fibre is very cheap – light doesn’t take much energy to produce and transmit. Copper on the other hand uses electrical signals, which, when deployed across the entire country, adds up to a very hefty electricity bill (according to one estimate I read, such a copper network would require the equivalent of at least a whole coal-fired power plant to drive). To my knowledge, this has also not been factored into the Coalition’s estimates. In summary, it’s highly debatable whether, all things considered, the Coalition’s plan will actually be cheaper in the long term. But let’s for a second give Abbott the benefit of the doubt and assume that he’s spot on in estimating that his FTTN scheme is $17b cheaper than Labor’s FTTH. With a population of roughly 22 million, and amortised over a life expectancy of around half a century, this amounts to $15 per person per year in net savings (admittedly not accounting for compound interest or return). This is a pretty small additional price to pay for an immensely better network, which almost certainly has economic multiplier effects worth well in excess of $15/person/year. The economic arguments being touted by Abbott and Turnbull seem like lunacy.

Next there’s the bandwidth issue. The Coalition themselves admit that their FTTN scheme guarantees vastly inferior bandwidths compared to FTTH. In the case of FTTN they guarantee 25Mbps downstream (which can only be guaranteed if you’re living right next to a node, and deteriorates exponentially with distance from the node). This is barely more than what lots of existing broadband customers can access with today’s infrastructure. Furthermore, it’s not upgradeable, as the 25Mbps figure all but saturates what’s possible with copper technology. The Government’s FTTH scheme on the other hand will guarantee 100Mbps downstream, which, as mentioned earlier, is easily upgradeable tenfold (and probably more) in the future. There are fundamental physical reasons why copper will never achieve these kinds of speeds (electrical channels are subject to capacitive coupling, interference and resistive loss – light isn’t). Thus, if one of the objectives of a national broadband policy is to be future-proof then the Coalition’s plan is dead in the water.

The Coalition’s broadband policy seems incredibly shortsighted. We need to factor in Moore’s Law – the exponential growth in demand for computing power and bandwidth. Tony Abbott and Malcolm Turnbull have stated that their alternative caters to today’s demands (Turnbull: “The Coalition plan would meet current demand for broadband services”). While a couple of tens of megabits (at best) may satisfy today’s needs, it most certainly doesn’t satisfy tomorrow’s, and it strikes me as myopic to base a major technological infrastructure project worth tens of billions of dollars purely on today’s needs. The advent of ultra-high-def (4K) video will already saturate the bandwidths being promised by the Coalition, not to mention applications in 10 or 20 years time (e.g. future developments in cloud computing or higher-def, multi-channel video). By the time the Coalition’s infrastructure is complete, it is likely to already be obsolete technology. If we’re going to spend tens of billions of dollars on such an infrastructure project, then the most pressing requirement should be that it caters for tomorrow’s needs, since this infrastructure, being as expensive as it is, should last us decades, not months.

If we’re going to invest this kind of money in such infrastructure, then we should only pay for the infrastructure once. The coalition’s plan will require paying for it over and over again as the copper network deteriorates, until, ultimately, people realise that it can’t provide the bandwidths we need, at which point we’re going to have to reinvest in the infrastructure from scratch and roll out FTTH anyway. So why not just do it right in the first place?

The final issue I’d like to touch upon is that of competition. The Coalition consistently criticises the NBN for being an uncompetitive monopoly. I heavily dispute this. Inevitably such infrastructure will be a natural monopoly. It makes zero sense to have half a dozen fibre lines running into each household, each owned by a different provider, to compete with one another. It would be hugely economically inefficient since the majority of it would be unused (of course, if secondary providers do decide they wish to run additional cables into people’s households, they shouldn’t be legislatively prevented from from doing so, but I can’t see this happening). So the best we can hope to achieve is to maximise competition within the context of this natural monopoly. The way the Government intends to achieve this is by structurally separating the wholesale and retail divisions of the NBN, such that the infrastructure is owned by NBN Co., but they don’t have the right to sell it to individual consumers. Rather, there is a level playing field in which third-party retailers can purchase bandwidth wholesale from NBN Co. and resell it to the consumer. This is exactly what’s being proposed by the Government. Under the proposed scheme, there will be no barrier to market participants purchasing bandwidth wholesale, so that even small competitors will be able to enter the broadband market. This will create the closest to a competitive market that we can realistically hope to achieve with such a project. A broadband market with a level playing field in which even small competitors can compete is a pretty decent deal.

Laughably, Tony Abbott recently said it’s a mistake to put all our eggs in the one basket (i.e. spend all our money on fibre as opposed to spreading the investment across a diverse range of technologies). This is an absolute joke. When it comes to traditional investment and portfolio management theory, certainly the ethos “don’t put all your eggs in the one basket” is a very wise philosophy. But when it comes to technological infrastructure, this doesn’t make any sense whatsoever. Surely it makes sense to choose the superior technology (fibre) and use it universally rather than investing in a mix of inferior technologies (copper) just in the name of “not putting all your eggs into one basket”. Should we equip school computer laboratories with a mix of cutting edge PCs and 1990′s 386 computers, just because we don’t want to put all our eggs into the one basket? No, we should just choose the best technology and employ it universally. Should we equip half of our defence forces with Soviet MiG fighter jets for the sake of diversity, or should we just universally adopt the latest NATO fighters? It’s a no brainer.

Given that both sides of politics have committed themselves to investing in such infrastructure using public money, it makes zero sense to choose the technology to cater only for today’s needs, which has to be continually replaced and upgraded, and which doesn’t cater for tomorrow’s needs.

The NBN is inevitably going to be one of the big policy issues determining the upcoming federal election in September, and the fact of the matter is that the Coalition’s policy is a joke – it’s much (much) slower, it’s almost certainly not cheaper, it’s not at all upgradeable (unless we abandon the copper and switch to fibre), and it doesn’t accommodate for tomorrow’s needs. Why waste the money?

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This essay makes a point that is only implicit in most of my other essays–namely that scientists are arro—oops that is for another post. The point here is that science is defined not by how it goes about acquiring knowledge but rather by how it defines knowledge. The underlying claim is that the definitions of knowledge as used, for example, in philosophy are not useful and that science has the one definition that has so far proven fruitful. No, not arrogant at all.

The classical concept of knowledge was described by Plato (428/427 BCE – 348/347 BCE) as having to meet three criteria: it must be justified, true, and believed. That description does seem reasonable. After all, can something be considered knowledge if it is false? Similarly, would we consider a correct guess knowledge? Guess right three times in a row and you are considered an expert –but do you have knowledge? Believed, I have more trouble with that: believed by whom? Certainly, something that no one believes is not knowledge even if true and justified.

The above criteria for knowledge seem like common sense and the ancient Greek philosophers had a real knack for encapsulating the common sense view of the world in their philosophy. But common sense is frequently wrong, so let us look at those criteria with a more jaundiced eye. Let us start with the first criteria: it must be justified. How do we justify a belief? From the sophists of ancient Greece, to the post-modernists and the-anything-goes hippies of the 1960s, and all their ilk in between it has been demonstrated that what can be known for certain is vanishingly small.

Renee Descartes (1596 – 1960) argues in the beginning of his Discourse on the Method that all knowledge is subject to doubt: a process called methodological skepticism. To a large extend, he is correct. Then to get to something that is certain he came up with his famous statement: I think, therefore I am.  For a long time this seemed to me like a sure argument. Hence, “I exist” seemed an incontrovertible fact. I then made the mistake of reading Nietzsche[1] (1844—1900). He criticizes the argument as presupposing the existence of “I” and “thinking” among other things. It has also been criticized by a number of other philosophers including Bertrand Russell (1872 – 1970). To quote the latter: Some care is needed in using Descartes’ argument. “I think, therefore I am” says rather more than is strictly certain. It might seem as though we are quite sure of being the same person to-day as we were yesterday, and this is no doubt true in some sense. But the real Self is as hard to arrive at as the real table, and does not seem to have that absolute, convincing certainty that belongs to particular experiences. Oh, well back to the drawing board.  

The criteria for knowledge, as postulated by Plato, lead to knowledge either not existing or being of the most trivial kind. No belief can be absolutely justified and there is no way to tell for certain if any proposed truth is an incontrovertible fact.  So where are we? If there are no incontrovertible facts we must deal with uncertainty. In science we make a virtue of this necessity. We start with observations, but unlike the logical positivists we do not assume they are reality or correspond to any ultimate reality. Thus following Immanuel Kant (1724 – 1804) we distinguish the thing-in-itself from its appearances. All we have access to are the appearances. The thing-in-itself is forever hidden.

But all is not lost. We make models to describe past observations. This is relatively easy to do. We then test our models by making testable predictions for future observations. Models are judged by their track record in making correct predictions–the more striking the prediction the better. The standard model of particle physics prediction of the Higgs[2] boson is a prime example of science at its best. The standard model did not become a fact when the Higgs was discovered, rather its standing as a useful model was enhanced.  It is the reliance on the track record of successful predictions that is the demarcation criteria for science and I would suggest the hallmark for defining knowledge. The scientific models and the observations they are based on are our only true knowledge. However, to mistake them for descriptions of the ultimate reality or the thing-in-itself would be folly, not knowledge.

 

Matthew Hankins and others on Twitter are making fun of scientists who twist themselves up lexically in order to report results that fail the significance test, using phrases like “approached but did not quite achieve significance” and “only just insignificant” and “tantalisingly close to significance.”

But I think this fun-making is somewhat misplaced!  We should instead be jeering at the conventional dichotomy that a result significant at p < .05 is “a real effect” and one that scores at p = .06 is “no effect.”

The lexically twisted scientists are on the side of the angels here, insisting that a statistically insignificant finding is usually much better described as “not enough evidence” than “no evidence,” and should be mentioned, in whatever language the journal allows, not mulched.

 

 

 

 

Not much more to say about the Templeton Foundation, but in the interest of open discussion it seems fair to point to a couple of alternative viewpoints. My original post was republished at Slate, where there are over 3300 comments thus far, so apparently people like to talk about this stuff?

For a more pro-Templeton point of view, here’s Jason Wright, explaining why he didn’t think it was wrong to take money from JTF. While he is a self-described atheist, he thinks that “questions like the ultimate origin of the Universe and Natural Law may be beyond scientific inquiry,” and correspondingly in favor of dialogue between science and religion. To be as clear as possible, I have no objections at all to dialogue between scientists and religious believers, having participated in such and planning on continuing to do so. I just want to eliminate any possibility that my own contribution to such a dialogue will favor any position other than “religion is incorrect.” (Obviously that depends on one’s definition of “religion,” so if you want to indulge in a boring discussion of what the proper definition should be — be my guest.)

From an anti-Templeton perspective, here’s Jerry Coyne, who doesn’t accept that it’s okay to draw a line between JTF itself and distinct organizations that take money from them. (Jerry’s post is perfectly reasonable, even if I disagree with it — but a short trip down to the comment section will give you a peer into the mind of the more fervently committed.) That’s fine — I admit from the start that this is a complicated issue, and people will draw the line in different places. But let’s admit that it is a complicated issue, and not pretend that there are any straightforward and easy answers.

One thing that seems to bother some people is that I agreed to be on the Board of Advisors for Nautilus, a new science magazine that takes funding from Templeton. It’s instructive to have a look at the Board of Advisors for the World Science Festival, another organization that takes funding from Templeton. It’s a long and distinguished list, and here are some of the names included: Richard Dawkins, Daniel Dennett, Lawrence Krauss, Steven Pinker, Steven Weinberg. Are these folks insufficiently sincere in their atheistic worldview? Alternatively, would the world be a better place if they all resigned? I would argue not, for the simple reason that the WSF does enormous good for the world, and is an organization well worth supporting, even if I don’t agree with all of their decisions.

Refusing to have anything to do with an organization that takes money from a foundation we don’t like is easier said than done. What about, say, the University of Chicago? Here they’re taking $3.7 million from Templeton for something called Expanding Spiritual Knowledge Through Science: Chicago Multidisciplinary Research Network. And here’s $5.6 million from Templeton for a program labeled New Frontiers in Astronomy and Cosmology, celebrating “a unique opportunity to honor the extraordinary vision of Sir John Templeton.” And here’s $2.2 million for a program on Understanding Human Nature to Harness Human Potential. Not to mention that the UofC has quite a prominent Divinity School (home of the best coffee shop on campus) and Seminary. (They also denied me tenure, which doubtless set the cause of reason and rationality back centuries.)

There’s no question that the University of Chicago has done much more to promote the cause of religion in the world than Nautilus has — which has been, to date, precisely nothing. One could say, with some justification, that some parts of the UofC have promoted religion, while other parts have not, and it’s okay to be involved with those other parts. But we begin to see how fuzzy the line is. Big grants like those above generally put a fraction of their funds toward “overhead,” which goes into general upkeep of the institution as a whole. Can we really be sure that, as we walk across the lawn, the groundskeeping was not partially paid for by the pernicious Templeton Foundation?

But that doesn’t mean that self-respecting atheists employed by the UofC should instantly resign. I’m sure you could play the same game with most big universities. The world would not be improved by having thousands of atheist professors abandon their posts out of principle.

It’s much more sensible to be a consequentialist rather than a deontologist when it comes to these ethical questions. I’m not going to stay away from Nautilus, or the World Science Festival, or the Foundational Questions Institute, out of some fruit-of-the-poisonous-tree doctrine according to which they have become forever tainted by accepting money from Templeton. Rather, I’m going to try to judge whether these organizations provide a net good for the world; I will complain when I think they are making a mistake; and if I think they’ve gone too far in a direction I don’t personally like, I will disengage. That’s the best I think I can do, according to my own conscience. Others will doubtless feel differently.