*Summing It Up*is the latest of the three, but it’s also the most elementary. It’s an introduction to the subject of modular forms, starting at the very beginning. The first half of the book covers in detail some basic ideas about number theory that can be understood in elementary terms, including things like the problems of counting the ways an integer can be a sum of squares or higher powers, or partitioned as a sum of smaller integers. The second half of the book tries to explain in as simple and concrete terms as possible what a “modular form” is, and what some of the properties of such objects are.I’ve just finished teaching a graduate course on representation theory, and ended up the course with a short discussion of the representations of the group SL(2,

**R**) (two by two real matrices of determinant one), and what this had to do with modular forms. The relation of modular forms to representation theory (not discussed in the book) is roughly the following. The action of SL(2,**R**) on itself by left multiplication induces an action on functions on the quotient space SL(2,R)/SL(2,**Z**) (elements of SL(2,**Z**) are matrices with integer entries) and one can ask how this representation decomposes into irreducible representations, with modular forms providing part of the answer. How this works is quite basic to our modern understanding of how representation theory and number theory are related.In the last few chapters the authors try to explain how modular forms answer concrete counting questions raised in the first half of the book. A problem with trying to do this kind of thing is that while the questions may be straightforward to state, and the basic definitions of modular forms relatively accessible, connecting the two requires invoking some subtleties (half-integral modular forms). The authors several times apologize for not being able to explain exactly what is going on. I’ve always been quite fascinated by these particular subtleties, since they appear in the basic relationship of representation theory and quantum mechanics. The half-integrality here is related to the half-integer that appears in the ground-state energy of the harmonic oscillator. For quite a bit about how this is related to representation theory, see the book I’ve been working on. I’d love some day to write about the relationship of the ideas that appear in quantum mechanics to the ones that appear in modular forms, but first of all I need to understand myself much better what is going on.

- The first of the three books by Ash and Gross was Fearless Symmetry: Exposing the Hidden Patterns of Numbers, published in 2006. It’s perhaps the best place to start for a popular introduction to the Langlands program and what it says about the relationship of number theory and representation theory. Modular forms make a brief appearance in that book, where an explanation of them had to be skipped over due to a lack of space. The newest book makes up for that omission.
- The second of the three books was the 2012 Elliptic Tales: Curves, Counting, and Number Theory. It covers in detail the topic of elliptic curves and their role in number theory, aiming at a description of one of the main open problems of the subject, the conjecture due to Birch and Swinnerton-Dyer. This is a very active subject of current research, with significant progress being made. If one had to guess which of the Millenium Problems will be the next to fall, this might be a good bet.

While there’s a long tradition of popular books about number theory, these typically emphasize elementary methods for solving problems, ones that can be understood without a lot of the modern machinery. The first two Ash-Gross books do a good job of trying to give some insight into this modern machinery, even though a popular book can only do this in a very limited way (just as popular physics books can only give a very limited explanation of quantum field theory). The new one is different in that it makes a serious effort to explain exactly what is really going on, although following this path means that the book can only cover the first steps in the direction of modern techniques for understanding number theory.

]]>I confess I’ve never worried much about killer asteroids, but am glad that someone is doing this. Nathan has always pursued a wide range of different interests, and killer asteroids has evidently been one of them. I first heard from him a year or two ago about how he had gotten interested in the question of how to model the observability of such objects. Such modeling affects choices to be made about how to optimally search for these things (space-based or earth-based telescopes? what kind?). He wrote a paper last year about this, which was published in March.

What Nathan told me when I saw him was that he had found significant problems with the modeling done by the NEOWISE/WISE group at NASA, and you can now judge for yourself by reading his paper. I’m very far from being able to understand the details of this story well enough to judge who’s right here. I do know Nathan well enough to know that his work on this deserves to be taken very seriously, and would bet that he has identified real problems. As noted in the comments there, the reaction from one of the ~~NASA~~ WISE people quoted at the end of the Science article wasn’t exactly confidence inspiring.

**Update**: There’s a press release about this out from NASA today, pretty much devoted to attacking Nathan’s work.

**Update**: For some specific criticisms of Nathan’s work, see the comment thread here. For a response to some of this from Nathan, see here.

**Update**: Scientific American has an article about this here.

- For those fascinated by the arguments over string theory, you might want to look at a document sent to me by Ilyas Khan, The People vs. String Theory. It’s also available in a free Kindle version, here. Some claim characters in this are recognizable to those well-versed in the subject.
- One thing that has always annoyed me about popular accounts of string theory is that they often claim that known particles are just like vibrational modes of a physical string, bringing music into it, as an argument for the beauty of string theory. No one ever mentions that the analogs of physical string vibrational modes have nothing to do with observed particles. If they exist at all, they’re some sort of Planck-scale states. Known particles are modeled typically by zero modes, with the classical analog not playing your guitar strings, but picking up the guitar and carrying it around, a much less musical activity.
I don’t remember ever bothering to make that argument publicly, because it seemed likely to lead nowhere but to silly arguments from string theorists. I’m now glad to see that 4gravitons has taken up the issue with a blog entry Particles Aren’t Vibrations. And, yes, check the comments for the expected response.

- Kudos to John Horgan for his talk at a recent Science and Skepticism conference here in New York. I’ve never quite understood why conferences like this seem devoted to a defense of ideas about science that are pretty much mainstream, especially in a place like New York, while ignoring pseudo-science when it comes from people considered members of the pro-science tribe. Horgan has some discussion of reaction to the talk here.
- Maybe this should have its own entry for This Week’s Hype, but I’ll just mention here that the June Scientific American has The Collider That Could Save Physics. It seems that SUSY is needed to “save physics”. Way back when it was LEP that was going to “save physics” by finding SUSY, then it was to be the LHC. This year’s LHC run should put the final nails in that coffin (data is now starting to be collected, see for instance here). Unfortunately the reaction of many SUSY partisans is not to follow the usual norms for how science is supposed to work and give up on the idea, but instead to claim that the LHC results aren’t conclusive, and a new machine is needed. In the SciAm article the ILC is advertised for this task. This electron-positron machine would have a much lower center of mass energy than the LHC, but one can find obscure SUSY models specially designed to have states that would be hard to see at the LHC, but could be seen at the ILC. I hope this isn’t the best argument for the $10 billion ILC…
- The L-functions and Modular Form Database is up and running now, providing a wealth of data about a central part of modern mathematics. Persiflage has an expert’s take on the significance of the project, including some criticism of the hype surrounding its launch (non-zero, but quite small on any scale used to measure theoretical physics hype). Other experts weigh in in the comment section, so don’t miss that.

**Update**: One more I forgot to add. Some people at Rutgers have decided to show what can go wrong when you have the Templeton Foundation funding “philosophy of physics”. They’ve scheduled a two-day Rutgers Mini-Conference on Multiverse, Theodicy, and Fine-Tuning, during which the speakers will consider the following two topics:

**Everettian Quantum Mechanics and Evil**The problem of evil has been around for a long time: How can an all-powerful and all-good God allow evil of the sorts we see in the world? If the Everettian interpretation of quantum mechanics is correct, though, then there is a lot more evil in the world than what we see. This suggest a second problem of evil: If Everettianism is true, how can an all-powerful and all-good God allow evil of the sort we don’t see?

**A Probability Problem in the Fine-Tuning Argument**

According to the fine-tuning argument: (i) the probability of a life-permitting universe, conditional on the non-existence of God, is low; and (ii) the probability of a life-permitting universe, conditional on the existence of God, is high. I demonstrate that these two claims cannot be simultaneously justified.

**Update**: One more, from CERN-TH, Is theoretical physics in crisis?. Nothing really new, but don’t miss the photo of John Ellis’s office…

A little while ago I bought a copy of Sean Carroll’s new book The Big Picture, which is now reaching the bookstores. This posting is not really a review of the substance of the book, but more a reaction to its basic conception. The first point to make is that I mostly agree with what Carroll has to say, to the extent that one reason for not writing a more usual sort of review is that I didn’t bother to do more than skim a lot of the chapters, since the theme seemed both so familiar and so unobjectionable. One exception would be a small number of pages about the multiverse, which he contrasts with religion, ending with (referring to religion)

This is the problem with theories that are not well-defined.

He’s got the problem right, but doesn’t notice that it applies equally well to this particularly dubious bit of “science”.

The largest part of the book (from my rather quick read) is a very conventional argument for science as opposed to religion, of a sort that has existed for centuries, been common since the 19th century, and very common in recent years as part of the “New Atheism”. One reason I can’t focus on this is that I just don’t see any evidence that science needs this sort of defense against religion, it seems to me to be doing extremely well without it. Our culture valorizes science and scientists very highly these days (much more so than ministers or theologians), and I just don’t see what some other people see as a need for books arguing the case for science.

The really striking thing about this particular book though is that Carroll has a much more unusual and ambitious goal than just arguing for science. He wants to promote what he calls “poetic naturalism“, which as far as I can tell is a term of his own invention (“naturalism” by itself is now a conventional term for the “science, not religion” viewpoint). Beyond the “science instead of religion” idea though, “poetic naturalism” seems to me to simultaneously lack any real content, while claiming to address the deepest human questions of meaning and morality. Asked in this interview the question

**Your book, The Big Picture, roams far beyond cosmology and physics, into consciousness, philosophy and the meaning of life. What do you hope to achieve?**

he answers

*Well, this is the book that should accompany the Gideons Bible in all hotel rooms in the world – that would be a nice achievement!*

I’m not sure what Carroll might have had to do with this, but poetic naturalism is now listed on Facebook as a possible choice for one’s religion.

Perhaps the strangest thing in the book is a chapter devoted to Carroll’s replacement for the Ten Commandments, which he calls the “Ten Considerations”, since they’re not commandments. They are:

- Life Isn’t Forever.
- Desire Is Built Into Life.
- What Matters Is What Matters To People.
- We Can Always Do Better.
- It Pays to Listen.
- There Is No Natural Way to Be.
- It Takes All Kinds.
- The Universe Is in Our Hands.
- We Can Do Better Than Happiness.
- Reality Guides Us.

It’s hard to argue with such sentiments, but also hard to understand what they have to do with the author’s expertise as a theoretical physicist.

The last chapter of the book begins with a description of Carroll’s early experiences in the Episcopal church, which he was quite fond of. I also had such experiences (I was an altar boy for several years at an Episcopal church, the American Cathedral in Paris). Unlike Carroll, I was never a believer, but just figured this was one of quite a few mystifying things that adults got up to, and that it seemed I had to go along with it until I got older. Thinking back to those days, I was struck by the realization that I recognized the tone and a lot of the content of Carroll’s writing. It very much sounds like a sermon, one evangelizing the good news not of Jesus, but of science, and is aiming for much the same effect: “I want to shiver with awe and wonder at the universe”.

My own point of view on all of this is that I just don’t think theoretical physicists have anything useful to tell the average person about meaning and morality, other than that it’s a mistake to search for it in our discoveries about physics. I don’t understand why we’re increasingly seeing texts promoting physics as inspiration for how to live (for another recent example among many see here). I’m with Steven Weinberg, and his famous line

The more the universe seems comprehensible, the more it also seems pointless.

Given that, the best advice to people who come to physicists looking for the meaning of life seems to me to politely tell them that they’re looking in the wrong place and asking the wrong person.

While I deeply value and respect my many friends and colleagues among physicists and mathematicians, I can’t imagine why anyone would think they have any unusual insight into the great questions of meaning and morality. I’m afraid that to some extent the opposite is true. My background, career and circumstances are quite similar to Carroll’s, and when I think about them my main thought these days is that I lead an extremely lucky and privileged (and not just in the white/Anglo/male/hetero sense) life, well-isolated from many of the challenges that most people have to deal with. There are a lot of beautiful, wonderful, and useful things one can learn from physicists and mathematicians, but our expertise is in something very far-removed from the question of how to live a good life in the face of significant challenges.

It seems likely that one motivation for books with this defensive attitude about science is the current ugly environment of our politics and culture. This ugliness I believe is driven by the economic disaster that has been inflicted on a significant fraction of our citizenry over the last few decades by the privileged and well-educated, both Democrats and Republicans. While Carroll and I were enjoying our respective times at Harvard and similar places, and have ended up turning our upbringing and Ivy League experiences into a very pleasant and cosseted lifestyle in the wealthy enclaves along either coast, things have not been going so well for many others. They’re now in bitter rebellion against what has happened to them, with an anger sadly turned against other racial groups, but even more so against self-satisfied elites. I don’t think a book like this has much hope of speaking to such people, to their view of science or their experience of religion. Scientists who want more respect should stick to what they know, and avoid the temptation of “science-splaining” to the public. In particular they should avoid preaching about meaning, morality, and other issues that they know no more about than anyone else.

**Update**: Robert Crease has a review of the book in Nature. He also finds odd the “greeting-card-like homilies” that appear in the book.

I had added this as an update to the last posting, but just looked at it more carefully and realized that it’s squarely in the “string theory predictions” tradition covered by editions of “This Week’s Hype”. In particular, the article claims:

The upcoming Evolved Laser Interferometer Space Antenna could help verify string theory’s predictions of gravity waves. Three spacecraft will orbit around the sun and measure tiny ripples in space-time via sensitive lasers.

The article starts off by explaining the history of string theory this way:

String theory was once the hottest thing in physics…

Strominger knew, even in the euphoric ’80s, that such assertions were overblown. And, sure enough, skepticism has seeped in over the years. No one has yet conceived of an experiment that could definitively verify or refute string theory. The backlash may have peaked in 2006, when several high-profile books and articles attacked the theory. But while string theory has receded from the spotlight, it has not gone away. “The theory is still evolving and getting better — and better understood,” maintains Juan Maldacena of the Institute for Advanced Study at Princeton University….

Emerging from this diverse work is a new consensus: String theory may not be the fabled theory of everything, Strominger says, “but it is definitely a theory of something.”

The article’s main selling point for string theory is that it led Strominger to think about something else, ideas about the conformal symmetry of black hole solutions.

Strominger subsequently realized that the presence of this symmetry, which hadn’t been recognized before, could be used to support a range of predictions. For example, he and his collaborators are currently trying to calculate the intensity of electromagnetic radiation emanating from the vicinity of a black hole. In a few years, Strominger says, once the worldwide network known as the Event Horizon Telescope comes online, astronomers can test those radiation estimates through direct measurements.

Using similar techniques originally inspired by string theory, Strominger’s group has computed the spectrum of gravitational waves emitted when compact objects like stars fall into giant black holes — predictions that could be verified by the future Evolved Laser Interferometer Space Antenna, planned to launch in two decades (or maybe sooner). Strominger also believes that evidence of conformal symmetry might emerge from the Laser Interferometer Gravitational-Wave Observatory, which spotted gravitational waves for the first time earlier this year. Soon, he says, astronomers may be drowning in data that they cannot fully interpret. “We’d like to use ideas from string theory to shed some light on corners of this.”

From now on, I guess use of conformal symmetry in physics now likely to be sold as a “prediction of string theory”.

The article goes on to a different area of string theory hype, that of AdS/CMT. According to Andrew Green of University College, London, string theory is “the new calculus”, and according to the piece’s author “Strominger agrees.” It’s hard to come up with appropriate words to characterize this level of hype.

]]>- Things had been going quite well at the LHC, they were ahead of schedule, starting to ramp up intensity for the new run. Then at 5:30 this morning a weasel decided to visit a 66kV transformer, which did not end well either for the weasel or for the LHC power grid. The machine and a lot of its cryogenics lost power, and recovery is going to take a week or so.
- For some commentary on the excitement about the new run building up (pre-weasel), see Tommaso Dorigo (at least I’m guessing he’s the author) here. He points to the twitter #MoarCollisions hashtag.
- In various Breakthrough Prize related news, first there’s an announcement from Terry Tao about the new IMU Graduate Breakout Fellowships, funded by him and some of the other math prize winners.
On the physics front, Caltech has Glitz and Qubits, about Alexei Kitaev and John Schwarz’s experience with the prize. Schwarz still hopes for vindication of his string theory prize by a discovery of SUSY at the LHC, assigning a much higher probability to this than I think most other people would these days:

I would say the probability is on the order of 50 percent or so that it will show up.

As for the glitz:

At the 2014 award ceremony, Schwarz says, he and his wife, Patricia, were “both struck by the fact that the Hollywood types showed no interest in mingling with scientists.” And the media coverage also seemed to focus on the movie stars rather than the award winners.

Kitaev points out a major positive effect of the $3 million: more respect from one’s family:

But for Kitaev, the biggest impact of awards like the Breakthrough Prize in Fundamental Physics is on his family. “They don’t really understand what I’m working on,” he says. But thanks to these awards, they at least realize his research is a pretty big deal. “It helps me do more work because they have more respect for it,” he says. “My wife is really proud of me.”

- In other big money news the Perimeter Institute and the Stavros Niarchos Foundation have announced a new professorship for Asimina Arvanitaki, funded by $8 million. More about her here.
- At Nautilus you can read an interview with IAS director, theoretical physicist Robbert Dijkgraaf.
- At Edge, there’s a conversation with Frank Wilczek. I’m quite curious what the following is about, have no idea:

What I’ve been thinking about today specifically is something of a potential breakthrough in understanding our fundamental theories of physics. We have something called a standard model, but its foundations are kind of scandalous. We have not known how to define an important part of it mathematically rigorously, but I think I have figured out how to do that, and it’s very pretty. I’m in the middle of calculations to check it out.

**
Update**: Two more:

- Jim Baggott has a post on Status Anxiety, with more thoughts about the Munich conference and the use of the term “theory”.
- Discover magazine has an article in the upcoming June issue on The Fall and Rise of String Theory. The story seems to be that String theory for some reason ran into a little trouble in 2006, but now it’s back, because Strominger has done some “string-inspired” black hole calculations, and some people are claiming inspiration from AdS/CFT for an approximate calculational method in some condensed matter models. The idea now seems to be that, starting from this, string theory is on its way to again finding a theory of everything. No comment on its hype problem.

**Update**: A special 2016 physics Breakthrough Prize has been awarded to the LIGO people. $1 million split by Drever, Thorne and Weiss, $2 million for the rest of the collaboration.

The new book on group theory has a length much better matched to the amount of material (it’s longer than the QFT book, and the material covered is much less complicated). The level of detail for most topics should be a good amount for students encountering the subject for the first time. The main topics covered are:

- Finite groups and their representations.
- Unitary and orthogonal groups, their representations, and applications to quantum mechanics.
- Classification of simple Lie algebras.
- The Lorentz and Poincare groups and their representations, with a discussion of the Dirac equation and Weyl and Majorana spinors.
- A grab-bag of some other topics, including a little bit about conformal symmetry and grand unified theories.

While for each of these topics there are other good textbooks out there, this is a great selection for an advanced undergraduate/graduate physics course. I expect this to justifiably become a popular choice for such courses.

While I liked a lot about the book, I have to confess that there were things about it that did put me off. Some of this likely has to do with the fact that I’ve been working for the last few years on a book (see here) that covers some of the same topics, so I’m hyper-aware of both the technicalities involved, and the issues that arise of how best to approach these subjects. In addition, much of these topics is standard core mathematics, but Zee seems to have consulted few if any mathematicians (at least I didn’t recognize any in his acknowledgements). Unlike some others, this is a subject where mathematicians and physicists really can communicate and teach each other a lot.

Some of the choices Zee makes that I don’t think are good ones are things that input from mathematicians probably would have helped with. Maybe the most egregious is his decision to use the same notation for a Lie group and its Lie algebra, on the grounds that physicists sometimes do this, and to notationally distinguish the two in the usual way (upper vs. lowercase letters) is “rather fussy looking”. Using the same notation for two very different things is just asking for confusion, and I remember struggling with this as a student. Zee is well aware of the problem, on page 79 having his interlocutor “Confusio” say:

When I first studied group theory I did not clearly distinguish between Lie group and Lie algebra. That they allow totally different operations did not sink in. I was multiplying the Js together and couldn’t make sense of what I got.

Please, if you’re using this book to teach students about this subject, discourage them from following Zee in this choice.

~~There are places in the text where Zee gets things wrong in a way that just about any mathematician could likely have saved him from~~. ~~One minor example is a footnote saying “Mathematicians have listed all possible finite groups up to impressively large values of n” (actually, they’re classified for ALL values of n)~~ *(my mistake, I misread and wasn’t looking at the finite group chapters carefully enough. Zee does get this right)*.

One place Zee gets things wrong is when he writes down the Heisenberg commutation relations, and says this is an “other type of algebra”, off-topic “since this is a textbook on group theory, I talk mostly about Lie algebras”. Actually those are the commutation relations of a Lie algebra, the Heisenberg Lie algebra, and there’s a group too, the Heisenberg group.

This gets into my own prejudices about the subject, with the story of the Heisenberg group to me (and I think to most mathematicians), a central part of the story of quantum mechanics, something little appreciated by most physicists. Another place where I think Zee goes wrong due to current physics prejudices is in ignoring Hamiltonian mechanics in favor of Lagrangian mechanics. As a result, instead of being able to tell the beautiful story of the Lie algebra of functions on phase space and what it has to do with conservation laws, he just mentions that Noether’s theorem leads to conservation laws and refers elsewhere for a discussion. The connection between symmetry and conservation laws is one of the central parts of the connection between Lie groups and physics, and deserves a lot more attention in the context of a course like this.

So, in summary, the book is highly recommended, with the caveats that you absolutely shouldn’t use the same notation for Lie groups and Lie algebras, and you should supplement Zee’s treatment with that of a certain more mathematically-minded blogger…

]]>- I’m very excited to see an article at Smithsonian Magazine with the title Can Physicists Ever Prove the Multiverse is Real? (remember, answers always no to headlines). Unlike just about every other effort of this kind, the author (Sarah Scoles) brings up the obvious problems, quoting Carlo Rovelli:

Some theoretical physicists say their field needs more cold, hard evidence and worry about where the lack of proof leads. “It is easy to write theories,” says Carlo Rovelli of the Center for Theoretical Physics in Luminy, France. Here, Rovelli is using the word colloquially, to talk about hypothetical explanations of how the universe, fundamentally, works. “It is hard to write theories that survive the proof of reality,” he continues. “Few survive. By means of this filter, we have been able to develop modern science, a technological society, to cure illness, to feed billions. All this works thanks to a simple idea: Do not trust your fancies. Keep only the ideas that can be tested. If we stop doing so, we go back to the style of thinking of the Middle Ages.”

- John Horgan has a wonderful, very long, interview with Scott Aaronson. Highly recommended as a way to avoid work and learn all sort of interesting things from and about Scott, whose blog you should be reading anyway. If you want to discuss this, you likely can do so with the man himself here.
- If you just can’t get enough of the multiverse, there’s something else quite long available, a podcast of Sam Harris in conversation with Max Tegmark.

String theory is leading to a revolutionary revision of many fundamental and long held principles of physics

despite a lack of any connection to experiment, either now or in the future.

In the local bookstore I took a look at Christophe Galfard’s The Universe in Your Hand, which builds up to a final chapter with some sort of rather incomprehensible voyage with a robot to the string theory multiverse. Nothing anywhere to be seen there about whether this might be science or fantasy. Jennifer Ouellette has a review in the New York Times here.

While mulling over these thoughts about the new prediction-free environment for string theory, I noticed that an article has just appeared that seemed to contradict such thoughts, Natalie Wolchover’s Physicists Hunt for the Big Bang’s Triangles, with a headline claiming that “evidence for string theory” could be found in the sky. It’s by far the best popular piece I’ve seen about “string cosmology”, giving an excellent idea of what people in that field are up to these days (which includes large amounts of hype, coming from the scientists, not the journalist).

In summary, here’s what we learn about current string cosmology. One of the main targets is a “prediction” of the level of non-gaussianity in the CMB, something which all observations so far have shown to be unobservably small:

- Matthew Kleban and Eva Silverstein are described as “cosmological clocksmiths”, working out the non-Gaussianity “predictions” of a large range of string cosmology models. It seems that you can get any number you want this way by an appropriately complicated model. Kleban likes unwinding inflation and we’re told:

“I think it’s pretty plausible that some version of this happens,” he said.

Though Kleban acknowledges that it’s too soon to tell whether he or anyone else is on to something, plans are under way to find out.

Silverstein has “many string inflationary models” of all sorts, so can get you one with any amount of non-gaussianity you might want. As far as she is concerned, having plenty of complicated models with zero evidence for any of them, such that, no matter what you see or don’t see, there’s always lots more and more “predictions”, is a perfectly traditional kind of science. Her reaction to people pointing out the problems with this?

I find it surreal, because we are currently doing some traditional science with string theory.

- Her Stanford colleagues Andre Linde and Renate Kallosh are taking a different approach, promoting theories with no observable non-gaussianity, and, it seems, no observable effects at all:

Linde isn’t bothered by this. In supporting the alpha-attractor models, he and Kallosh are staking a position in favor of simplicity and theoretical beauty, at the expense of ever knowing for sure whether their cosmological origin story is correct. An alpha-attractor universe, Linde said, is like one of the happy families in the famous opening line of Anna Karenina. As he paraphrased Tolstoy: “Any happy family, well, they look in a sense alike. But all unhappy families — they’re unhappy for different reasons.”

- On the East Coast, there’s Arkani-Hamed and Maldacena, with a paper last year on Cosmological Collider Physics. It described observable signatures of new physics at the inflationary scale, but the only comment I could find about how you would actually observe such things was

In terms of measurability, if the couplings are Planck suppressed, then it seems impossible to measure this through the CMB or large scale structure. (See e.g. [58, 59, 60, 61] for a discussion of measuring these effects via large scale structure.) But it might be possible using the 21cm tomography [50].

Arkani-Hamed explains to Wolchover that there’s a “cosmic variance” problem making things inherently unobservable, but he removed most discussion of this from the paper, hoping to get around it by changing the laws of quantum mechanics:

In his paper with Maldacena, Arkani-Hamed initially included a discussion of this issue, but he removed most of it. He finds the possibility of a limit to knowledge “tremendously disturbing” and sees it as evidence that quantum mechanics must be extended. One possible way to do this is suggested by his work on the amplituhedron, which casts quantum mechanical probabilities (and with them, unitarity) as emergent consequences of an underlying geometry. He plans to discuss this possibility in a forthcoming paper that will relate an analogue of the amplituhedron to non-Gaussianities in the sky.

There has been further work on this by Kamionkowski and collaborators, and we’re told:

Observing the signals predicted by Arkani-Hamed, Maldacena and Kamionkowski would be like striking gold, but the gold is buried deep: Their strength is probably near the gravitational floor and will require at least 1,000 times the sensitivity of current equipment to detect.

No word on prospects for more than 1,000 times more sensitive experiments.

For about as long as I can remember, string cosmologists have been promising that their ideas would be tested by the Planck experiment. Now that negative results are in from that, we’re told to instead look forward to a new generation of experiments. The ones mentioned in the article are SPHEREx and the LSST, with results next decade. SPHEREx claims that they may be able to push down bounds on non-gaussianity by a factor of 10, which would be an impressive result. This would rule out lots of string cosmology models, but of course there would still be plenty more.

The next experiment all involved are talking about is looking for signals in the 21cm hydrogen line, see Sabine Hossenfelder here for more about that. No time estimates on that one. As far as I can tell, the plan for this starts off with “First, build a base on the other side of the moon…”

]]>The story of Ramanujan is one of the great romantic stories of mathematics, with a large part played in it by the Cambridge mathematician G. H. Hardy. The filmmaker was inspired by Robert Kanigel’s excellent 1991 biography of the same name (he says his mother gave it to him to read, she had it through her book club). The book is an excellent source for the story of Ramanujan’s life, and Hardy’s A Mathematician’s Apology is something everyone should read (for one thing, it’s short). For some more about the film from an expert on Ramanujan’s work, the AMS Notices have this from George Andrews.

Some dramatic license was taken, for instance in having Jeremy Irons play Hardy as a much older man than he actually was when he met Ramanujan. After the film there was a panel discussion, with filmmaker and screenwriter Matt Brown explaining that it took 10 years to get the film made, largely because of the difficulty of financing it. He claimed that he could have gotten the financing much earlier if he had been willing to go along with certain plot changes the financiers wanted: in particular they wanted the story to revolve around a love affair of Ramanujan with a (white) nurse, to be played by a high-profile starlet.

Also at the panel discussion were two mathematicians: Princeton’s Manjul Bhargava and my Columbia colleague Ina Petkova. One reason the film is so true to the real story of the mathematics and mathematicians involved in it is the involvement of Ken Ono and Bhargava. Ono was heavily involved in the filming (and he has a memoir from Springer, My Search for Ramanujan, about to appear). Bhargava was involved in the editing, in particular in helping choose among the many takes of the actors acting out a mathematical discussion those which seemed true to life.

The film is supposed to be released here in the US on April 29, I can’t recommend it enough.

**Update**: Scott Aaronson has a far better review of the film than mine here.