Magic Ingredients Exist!

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I’m a baker, as you probably know. I’ve regularly made bread, cakes, pies, and all sorts of things for friends and family. About a year ago, someone in the family was diagnosed with a severe allergy to gluten, and within days we removed all gluten products from the kitchen, began to be very selective about restaurants we ate at, and generally had to rethink a number of aspects of our lives as a family.

This had a big impact on my baking, to put it mildly. With the aid of some excellent gluten-free general purpose flours (mostly the ones made by Bob’s Red Mill) certain kinds of things could be readily made the way I used to make them (more or less – you quickly notice you have to increase moisture content a bit because such flours are more absorptive), such as scones, biscuits (American), and basic pastry, but other things really needed to be seriously re-thought, or abandoned altogether rather than make a terrible facsimile of it (particularly yeast breads, especially light fluffy loaves or buns, light cakes, anything that needs the structure gluten provides to rise and form a crumb, etc…)

For almost a year I just removed a lot of the baking I do from regular rotation, and resigned myself to not making certain kinds of things any more. It was a very painful goodbye (I’ve been baking breads and cakes for many decades), but I was fine with it, given the life-threatening health issues I’d seen gluten cause, up close.

At the same time, I began to be increasingly stunned by the situation concerning gluten-free bread and bread-like products you can find on sale. While some good breads can be found (with persistence), so very much of it is entirely, in the eating, devoid of joy, much of it is sometimes like eating solidified ash. But still they charge you huge amounts of money for it. I’ve seen all kinds of mediocre loaves of bread up or near (sometimes beyond!) the $20 price point, and people buy it without (it seems) batting an eyelid. Why? Because it is hard to find, and (I thought!) hard to make.

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Hope

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The delicious chaos that (almost always) eventually tames into a tasty flaky pastry crust… it’s always a worrying mess to start out, but you trust to your experience, and you carry on, with hope. #thanksgiving

Rolling out gluten-free flaky pastry dough…

Decoding the Universe!

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I realised just now that I entirely forgot (it seems) to post about an episode of PBS’ show Nova called “Decoding the Universe: Cosmos” which aired back in the Spring. I thought they did a good job of talking about some of the advances in our understanding that have happened over the last 50 years (the idea is that it is the 50th anniversary of the show) in areas of astrophysics and cosmology. I was a contributor, filmed at the top of Mount Wilson at the Observatory where Hubble made his famous discoveries about the size of the universe, and its expansion. I talk about some of those discoveries and other ideas in the show. Here’s a link to the “Decoding the Universe” site. (You can also find it on YouTube.)

If you follow the link you’ll notice another episode up there: “Decoding the Universe: Quantum”. That’s a companion they made, and it focuses on understanding in quantum physics, connecting it to things in the everyday world. and also back to black holes and things astrophysical and cosmological. It also does a good job of shining a light on many concepts.

I was also a contributor to this episode, and it was a real delight to work with them in a special role: I got to unpack many of the foundational quantum mechanical concepts (transitions in atoms, stimulated emission, tunnelling, etc) to camera by doing line drawings while I explained – and kudos Click to continue reading this post →

Bluesky!

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For those of you who keep up with my social media posts, you’ve probably been expecting that I’d eventually announce that I’m transitioning from Twitter to something else… and it is Bluesky. I’ll stay on Twitter for a bit longer while I settle in (and while I wait for people to see the change, etc.), but consider following @asymptotia.bsky.social asap. (I’ll continue posting at the Facebook and Instagram accounts for now.)

This change fits nicely with the fact that I have plans to somewhat increase my post frequency here on the blog – as time allows – and so I’ll post links to them on the new social media platform, and maybe welcome some new communities too. Truth be told, for the longest while I’ve been very tied up with too many projects (some of which I can’t tell you about yet!) to be as frequent a poster as I’d like to be, but I’ll do what I can.

-cvj

Westminster Wonders

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Never toured the inside of the Houses of Parliament before, seeing all the red and green colour coded areas (lords and commons – look at the benches next time you see debates in either place) and busts and statues of some of the shapers, for better or worse, of much of the fabric of UK democracy. (Thanks to my sister for this wonderful opportunity on Friday!) BTW, most of the interesting stuff I saw was off limits to photos, sorry!

–cvj

Running London

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During the pandemic shutdown I regularly ran these london streets and bridges -virtually- on a treadmill watching a YouTube video of such a run.

This morning (actually 8 days ago since I see now I forgot to hit “publish”) was the first time I did it for real! I wonder if any of the many other runners I saw were on the video?

(Do have a look, if you wish, on my social media accounts for other posts from this London visit.)

–cvj

Tumble Science Podcast Episode

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tumble_episode_logoFor some weekend listening, there’s a fun and informative podcast for youngsters called Tumble Science Podcast. I learned of it recently because they asked to interview me for an episode, and it is now available! It is all about time travel, and I hope you (and/or yours) have fun listening to it. The link is here.

There’s an accompanying blog post here.

More generally, listen to more episode on Tumble’s website, or at the pod link here.

Enjoy!

–cvj

When Worlds Collide…

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This morning I had a really fantastic meeting with some filmmakers about scientific aspects of the visuals (and other content) for a film to appear on your screens one day, and also discussed finding time to chat with one of the leads in order to help them get familiar with aspects of the world (and perhaps mindset) of a theoretical physicist. (It was part of a long series of very productive meetings about which I can really say nothing more at the current time, but I’m quite sure you’ll hear about this film in the fullness of time.)

Then a bit later I had a chat with my wife about logistical aspects of the day so that she can make time to go down to Los Angeles and do an audition for a role in something. So far, so routine, and I carried on with some computations I was doing (some lovely clarity had arrived earlier and various piece of a puzzle fell together marvellously)…

But then, a bit later in the morning while doing a search, I stumbled upon some mention of the recent Breakthrough Prize ceremony, and found the video below (one of several). It’s as though I fell asleep at my desk and was having one of those strange dreams where two parts of your life that have little to do with each other get intertwined: Robert Downey Jr (RDJ) and Da’Vine Joy Randolph (DJR) doing a “bit” about statistical physics, quantum field theory, and symmetries, and then John Cardy and Alexander Zamolodchikov come on stage…

-cvj

Catching Up

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KITP UCSB by cvj
Since you asked, I should indeed say a few words about how things have been going since I left my previous position and moved to being faculty at the Santa Barbara Department of Physics.

It’s Simply Wonderful!

(Well, that’s really four I suppose, depending upon whether you count the contraction as one or two.)

Really though, I’ve been having a great time. It is such a wonderful department with welcoming colleagues doing fantastic work in so many areas of physics. There’s overall a real feeling of community, and of looking out for the best for each other, and there’s a sense that the department is highly valued (and listened to) across the wider campus. From the moment I arrived I’ve had any number of excellent students, postdocs, and faculty knocking on my door, interested in finding out what I’m working on, looking for projects, someone to bounce an idea off, to collaborate, and more.

We’ve restarted the habit of regular (several times a week) lunch gatherings within the group, chatting about physics ideas we’re working on, things we’ve heard about, papers we’re reading, classes we’re teaching and so forth. This has been a true delight, since that connectivity with colleagues has been absent in my physics life for very many years now and I’ve sorely missed it. Moreover, there’s a nostalgic aspect to it as well: This is the very routine (often with the same places and some of the same people) that I had as a postdoc back in the mid 1990s, and it really helped shape the physicist I was to become, so it is a delight to continue the tradition.

And I have not even got to mentioning the Kavli Institute for Theoretical Physics (KITP) Click to continue reading this post →

Recurrence Relations

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(A more technical post follows.)

By the way, in both sets of talks that I mentioned in the previous post, early on I started talking about orthogonal polynomials P_n(\lambda)=\lambda^n+\mbox{lower powers}, and how they generically satisfy a three-term recurrence relation (or recursion relation):

\lambda P_n(\lambda) = P_{n+1}(\lambda) +S_n P_n(\lambda) +R_n P_{n-1}(\lambda) \ .

Someone raised their hand and ask why it truncates to three terms and on the spot I said that I’d forgotten the detailed proof (it has been many years since I thought about it) but recall that it follows straightforwardly from orthogonality. Lack of time meant that I did not want to try to reconstruct the proof on the board in real time, but it is a standard thing that we all use a lot because it is true for all the commonly used families of polynomials in lots of physics, whether it be Hermite, Legendre, Laguerre, Chebyshev, etc. Anyway, I finally got around to reminding myself of it and thought I’d record it here. Now all I have to do in future is point people here as a handy place to look it up. ([Although you can find equivalent discussions in several sources, for example this nice YouTube lecture here, which is part of a lovely series of lectures on polynomial approximation of functions, which is a fascinating topic in its own right.]

Ok, I should quickly remind what the setup is. The polynomials are normalised so that the nth one is P_n(\lambda)=\lambda^n+\mbox{lower powers} (they’re “monic”) and they are orthogonal with respect to the measure w(\lambda)d\lambda where w(\lambda) is called the “weight function” (it has some suitable properties we won’t worry about here). In the case of random matrix models we have w(\lambda) = \exp\{-N V(\lambda)\} for some potential V(\lambda) (here N is the size of the matrix; in this problem it is just a normalisation choice – you can just as well absorb it into the potential).

So we have the inner product:

\langle P_n, P_m\rangle\equiv \int w(\lambda) P_m(\lambda) P_n(\lambda) d\lambda = h_n\delta_{mn}\ ,

defining the orthogonality, where the h_n are some positive non-vanishing normalisation constants. Ok now we are ready for the proof.

Imagine there are terms in the recursion beyond the three terms. Let’s write these “remainder” terms as a linear combination of all lower polynomials up to degree n-2, so the recursion is tentatively:

\lambda P_n = P_{n+1} +S_n P_n +R_n P_{n-1} + \sum_{k=0}^{n-2} T_kP_k.

Taking the inner product \langle P_m, \lambda P_n\rangle for m=n-1, n or n+1 just tells you the definition of the recursion coefficients S_n and R_n in terms of ratios of inner products for those m, and for m any higher you get zero since the polynomial is then of too high order to give anything non-zero.

So S_n = \frac{\langle \lambda P_n,P_n\rangle}{\langle P_n,P_n\rangle} and R_n = \frac{\langle \lambda P_n,P_{n-1}\rangle}{\langle P_{n-1},P_{n-1}\rangle} .

Then you take the inner product \langle P_m, \lambda P_n\rangle for the cases m < n-2.

But this is also (by definition; I can let the lambda act in the opposite direction inside the integral) \langle\lambda P_m, P_n\rangle, which vanishes since the degree of the first entry, m+1, is less than n, and so it can only contain polynomials of degree less than n which are orthogonal to P_n. Therefore the inner product says T_m \langle P_m,P_m\rangle=0 in all those cases, which means that T_k=0 for k=0, 1,...n-2.

That’s it. All done. Except for the remark that given the expression for S_n above, when the weight function is even, the S_n vanish. (This is the case for even potentials in the case of random matrix models.)

Ok, one more useful thing: It is clear from the definition of the inner product integral that h_{n+1}=\langle P_{n+1},\lambda P_n\rangle. But you can also write this as h_{n+1}=\langle \lambda P_{n+1}, P_n\rangle and use the recursion relation \lambda P_{n+1} = P_{n+2}+S_nP_{n+1}+R_{n+1}P_n, and all these terms vanish in the integral except the last, and so we get h_{n+1}= R_{n+1}\langle P_n,P_n\rangle = R_{n+1}h_n.

Hence we’re derived an important relation: R_n=\frac{h_n}{h_{n-1}}\ .

(We essentially got this already in the earlier equation for R_n; just rearrange the action of \lambda up there again.)

–cvj

Multicritical Matrix Model Miracles

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Well, that was my title for my seminar last Thursday at the KITP. My plan was to explain more the techniques behind some of the work I’ve been doing over the last few years, in particular the business of treating multicritical matrix models as building blocks for making more complicated theories of gravity.

chalkboard from KITP seminar

The seminar ended up being a bit scattered in places as I realised that I had to re-adjust my ambitions to match limitations of time, and so ended up improvising here and there to explain certain computational details more, partly in response to questions. This always happens of course, and I sort of knew it would at the outset (as was clear from my opening remarks of the talk). The point is that I work on a set of techniques that are very powerful at what they do, and most people of a certain generation don’t know those techniques as they fell out of vogue a long time ago. In the last few years I’ve resurrected them and developed them to a point where they can now do some marvellous things. But when I give talks about them it means I have a choice: I can quickly summarise and then get to the new results, in which case people think I’m performing magic tricks since they don’t know the methods, or I can try to unpack and review the methods, in which case I never get to the new results. Either way, you’re not likely to get people to dive in and help move the research program forward, which should be the main point of explaining your results. (The same problem occurs to some extent when I write papers on this stuff: short paper getting swiftly to the point, or long paper laying out all the methods first? The last time I did the latter, tons of new results got missed inside what people thought was largely just a review paper, so I’m not doing that any more.)

Anyway, so I ended up trying at least to explain what (basic) multicritical matrix models were, since it turns out that most people don’t know these days what the (often invoked) double scaling limit of a matrix model really is, in detail. This ended up taking most of the hour, so I at least managed to get that across, and whet the appetite of the younger people in the audience to learn more about how this stuff works and appreciate how very approachable these techniques are. I spent a good amount of time trying to show how to compute everything from scratch – part of the demystifying process.

I did mention (and worked out detailed notes on) briefly a different class of Click to continue reading this post →

Living in the Matrix – Recent Advances in Understanding Quantum Spacetime

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ribbon diagram that can be drawn on a torusIt has been extremely busy in the ten months or so since I last wrote something here. It’s perhaps the longest break I’ve taken from blogging for 20 years (gosh!) but I think it was a healthy thing to do. Many readers have been following some of my ocassional scribblings on social media (see sidebar), and will guess from those that the main news to report is that I’ve been getting on with the usual practices of my job (research, teaching and mentorship, science communication, etc) and life, including getting settled into a new city and a new working environment. The latter has all been rather fantastic, I’m happy to say! I hope to say a bit more about all these things at more-than-social-media length.

Let me end this little update with something juicy to dig into: Last week I gave a public lecture at the Kavli Institute for Theoretical Physics (KITP) here at UCSB. Its title was “Living in the Matrix – Recent Advances in Understanding Quantum Spacetime” and you can see a recording of it here. It is a little bit of an update on some aspects of research into understanding black holes at the quantum level using random matrix model methods to perform the gravitational path integral.

I put a lot of preparation into it, trying to motivate the research and give some ideas about how and why it proceeded the way it has. I was trying to do a bit more than just show a lot of pretty pictures and talk over them. I wanted to convey to the audience member a little bit of the sense of what it is like to think about some of the issues involved, and how a theoretical physicist tackles them. So you get to look over the shoulder of physicist as they write in their notebook.

I learned afterwards that people seemed to enjoy the talk, and so maybe you will too.

Enjoy.

–cvj

And so it begins…

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cvj sitting with mountain view
There’s not much in this post, but I wanted to mark a significant date. It is the first day of the rest of 2023, but in addition, it is the beginning of a new chapter for me. Yesterday was my last day as an employee of the University of Southern California, after 20 years (!) and today is my first day as an employee of the University of California, Santa Barbara. (I mentioned this was coming up in a previous post, and some of its significance is explained there.)

Of course, since I’m still on a research retreat at the Aspen Center for Physics, none of this seems entirely real just yet. Electronic signatures winging back and forth over the web don’t really substitute for the physical business of changing where you show up for work, who you meet there, and so forth, and so that will have to wait for little while. That having been said, lots of electronic welcomes and so forth did help a lot with that “new job smell”, if that’s a thing. But I’ll be showing up in person soon enough, and it’ll be fun to begin to construct a new routine.

Sadly I’ve not had a lot of time to properly sit and contemplate and let this all sink in, to be honest, so I’ll have to find time to do it later. (That photo, above, of me at the top of Aspen mountain is nice, but I was in that spot for about 5 minutes!) Right now, there’s travel, and then sorting and packing and more packing to do, along with family matters, and all that entails. I’ll have to leave the contemplation for a bit later.

Perhaps during a nice long run along the beach…!

-cvj

Rattle and Hum

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A lot of us have been waiting for a long time to hear this news! The NANOGrav collaboration has announced strong evidence of a background of low frequency gravitational waves emitted from supermassive black hole mergers. Their detection methods are pulsar timing arrays (still one of those fantastically simple, cool ideas I still wish I’d thought of). There’s a New York Times article by Katrina Miller here (“The Cosmos is Thrumming with Gravitational Waves…”), and here’s Yale’s Chiara Mingarelli (one of the team) describing some of what this means in simple terms:

-cvj