Randomness and quotations — I like this meme

I picked this meme up from Chad.

The four quotes below showed up at the bottom of the list when I used the random quote generator that Chad references.

They seem to apply aptly to my life at the moment, as I am sure I would find if I generated another set of random quotes some other day in the future. Another little piece of anecdotal evidence in my theory about statistical mechanics and stories. Randomness, as always, delivers.

Dreaming permits each and every one of us to be quietly and safely insane every night of our lives. William Dement

If a cluttered desk is the sign of a cluttered mind, what is the significance of a clean desk? Laurence J. Peter

We do not know what we want and yet we are responsible for what we are – that is the fact. Jean-Paul Sartre

A conservative is a man with two perfectly good legs who, however, has never learned to walk forward.Franklin D. Roosevelt , radio address, Oct. 26, 1939

The memory of persistence

Now that my school year is winding down somewhat, I have been turning back to research issues. One project that has been moving slowly for me is on so-called “persistent patterns”.

These arise in situations where you’ve got chaotic dynamics interacting with some sort of noise or diffusive behavior, with applications ranging from chemical reactors to ocean modeling. Think about putting cream in coffee: As you stir, you get tendrils growing out of the original blob, and combined with the diffusion, this results in a homogeneous mixture very soon. You would think that if the stirring dynamics was chaotic, the mixing would go even more efficiently and quickly — and this is often true.

However,  work over the last decade or so, both theoretical and experimental (see the superb work by Jerry Gollub’s group, for example), shows that it is not always true: In certain incompressible time-periodic fluid flows long-lived patterns emerge. Once these patterns emerge, the mixing process is completely determined by the rates imposed by the slowest decaying structures. Basically, these patterns show up that hang around effectively forever.

Getting a little technical, these persistent regions of high concentration of the passive scalar have been shown to be associated with the stable and unstable manifolds of the underlying chaotic dynamics. But we are far from figuring out the conditions for their emergence and other details about their properties.

I’ve been trying to understand this on and off for years, and there’s a current preprint with my friends Bala Sundaram and Drew Poje where I think we’ve nailed down some critical issues. Almost. Sigh.

Why would someone interested in quantum mechanics and the quantum-classical transition and decoherence care about fluid mixing? It turns out that the behavior of these fluids in real space is identical to that of the phase-space behavior of classical probability densities in Hamiltonian systems with added noise. So understanding the behavior of these fluid dynamics systems is a way of building intuition about the classical limit of the quantum systems I have been thinking about for years. Which is how I got into this problem. And it’s an excellent mathematical physics problem in its own right — with experimental tests of claims available through ‘table-top’ experiments. Wonderful.

Now if we could only finish the last couple of things we need to …

How many hours does it take?

I had a recent conversation with Christopher, who is from the part of campus that figures out where the money is for academics to use, and helps us get it. We were talking about a bunch of things, and in the middle of all this came up the notion of trying to figure out the number of hours it takes to ‘produce’ results in my line of work, whether student hours, or my own hours.  That is, if we insist on being all corporate, what’s your guess for the billable hours for a research ‘product’?

I threw out a ballpark guess of about 1000 hours to ‘results’ and probably another couple of hundred to manuscript. (See, that works out to about 4 months of focused non-stop work on one project for the results and a few more weeks on the manuscript. There have been stages in my life where that kind of work yielded absolutely nothing, and others where I got a bunch of papers out suddenly, so I am seriously smoothing the fluctuations, but that does seem in the right ballpark).

So let’s say 1000 hours of my work. How about student work, say on a project supervised by me, but where I am not doing any of the ‘calculations’? What’s the multiplier? 2, 3, 4 ? Hard to tell. Summer research is about 400 hours worth of pay to students. I ask all of them to spend time with me before the summer and say that I expect them to return after the summer because that increases the chances that we’ll actually finish the project. Painful experience tells me that this is still too little — I would barely get 500 or so student work hours out of that arrangement, so I have to put the rest of the time in myself, or else distribute the project over multiple students and multiple years.

Looking back on my recent papers, including those with students, I would say I have the order of magnitude about right.

So. What’s the point?

Well, sigh. I guess this blog post is basically a reminder to self to be patient. Results take time. Papers take time. Publishing takes time. Referees are guaranteed to raise objections you thought you’d cleverly anticipated and responded to in the very first paragraph of your paper. Two steps forward and one step back is standard operating procedure. Getting stuck just as you thought you were done is typical. And not to reiterate the obvious, but the way to keep going is not because of the results but because you enjoy the process itself (well, most of it ).

Procedural, analytical, relational, innovative

Spring pause today, and I’m enjoying reading and writing while skilfully procrastinating dealing with grading today. An article that caught my eye, and that I almost put in the comments section to my previous post on lessons learned/things to remember for my write-up on my attempt to re-vamp intro mechanics, triggered this particular post.

This is from the New York Times, and it’s about learning new habits. It’s a short article, so I won’t bother summarizing here, but a couple of interesting points:

“Researchers in the late 1960s discovered that humans are born with the capacity to approach challenges in four primary ways: analytically, procedurally, relationally (or collaboratively) and innovatively. At puberty, however, the brain shuts down half of that capacity, preserving only those modes of thought that have seemed most valuable during the first decade or so of life.

The current emphasis on standardized testing highlights analysis and procedure, meaning that few of us inherently use our innovative and collaborative modes of thought.”

Hah. No kidding. I think the students in intro physics/intro mechanics have a hard time getting from procedural to analytical in the first place. That is, they expect physics to be about a certain set of equations, and also expect that I will tell them which equations to use. When confronted by the fact that a typical physics assignment requires analytical AND procedural abilities, they get slightly shaken. But these are Carleton students, so they get over that. However, when confronted by the need for relational work (‘group’ problem-solving) and innovation (‘ask a question, and answer it’ — part of my instructions for the last lab they did) they are palpably out of their comfort zone.

The articles goes on to say that in new experiences, there are “three zones of existence: comfort, stretch and stress. Comfort is the realm of existing habit. Stress occurs when a challenge is so far beyond current experience as to be overwhelming. It’s that stretch zone in the middle — activities that feel a bit awkward and unfamiliar — where true change occurs.”

The trick, therefore, is to stretch these minds without stressing them. Sigh.

Where did the weirdness go?

Nature just featured an excellent article on “one of the great conundrums of modern physics: the quantum–classical transition” by Philip Ball, at the semi-popular level, talking about the mystery of where and how weird quantum mechanical effects go — that is, why we know they exist, but don’t see them in daily life.

Most of my work is concerned with some aspects of this, and when I try to explain this to my research students, I talk about it as follows: If atoms are quantal, and we are made of atoms, why don’t we behave quantum mechanically? And if it’s a matter of size or complexity (nonlinearity of the system concerned) or temperature and influence of the environment on the system (as is believed) then how and when does the change from quantum mechanics to classical mechanics happen as a function of these properties? Is the change smooth or abrupt — that is, do we go from very quantal to somewhat quantal (and what does that look like?) to classical, or does it go from quantum-classical immediately? Is the transition monotonic — that is, do we only go from quantum to less quantum as we change parameters in one direction, or do you have regions of more quantum-ness and less quantum-ness? How does the quantum dynamics reflect behavior in the classical dynamics? Etc. (Some more discussion of these issues is on my research web-page.)

These are entirely fascinating questions as fundamental physics, but quantum effects are not only cool, they are impressively powerful, and very useful sometimes, so the practical question is: where can we find them?

As a theorist, I wonder about right measure of quantum-ness: How quantum is a given state? How do you measure the difference between a classical distribution and a quantum distribution? I’d like to be able to discuss all this in some sort of abstract way so I can understand the topology, the geography, really, of the quantum-classical boundary. And of course, if I do find an effect, how do I translate this into something an experimentalist might measure?

As the school year heads into the home stretch, I’m getting excited again about getting some uninterrupted (well, relatively uninterrupted, let’s be honest) time to make some progress on these questions again. It’s been a long and complicated year, and I’m looking forward to the comfort and joy (and pain, yes, and pain) of grappling with some of these intriguing questions with more focus soon.

Computational modeling

The ‘other’ class (that is, other than intro) that I’ve been teaching this term, is an interdisciplinary elective called ‘Computational modeling’; I am co-teaching it with my colleague Cindy Blaha, who is a galactic astronomer.

This is the second time I’ve taught this course. The first time was last year, with my fellow-theorist Bill Titus. This course grew out of funding from the last HHMI grant cycle, and is directed at students in geology or biology (preferably) to address the idea that (a) the typical biologist or geologist tends to be less comfortable/less prepared with mathematics than, say, the typical physicist and (b) there are a lot of cool problems in their fields amenable to quantitative analysis if only people in their fields would use some sort of modeling and that (c) current computational technology allows you to ‘code’ and model systems without being extremely mathematically or computationally adept necessarily.

I like teaching this course, and even more when I am not drowning in intro. I get to convey what I regard as the distillation of *my* scientific research attitude: Take a system you’d like to study, find a decent set of equations that capture the essence of the behavior, and then study the heck out of that system of equations. That is, ‘solve’ the equations using whatever tools you can deploy, and make predictions about the behavior of the system, and in the process generalize your study as much as possible — preferably capturing the dynamics in some broad intuitive explanations.

That I am ‘modeling’ nature in my studies was not entirely obvious to me until I spent some time collaborating with Randy Hulet as well as with Barry Dunning when I was at Rice. Let me explain what I mean by what might sound like a very silly comment: As a ‘typical’ theorist, I had gone through my thesis and my post-doc with an implicit attitude where I believed in the meaning and validity of the equations I was using as the absolute truth, and thought of an ‘experiment’ as a place where the equations were approximately realized. This shifted slowly during my time at Rice. The shift started when I finally visited Randy’s lab a few months after I started talking with him about a strange phenomenon in his Lithium 7 Bose-Einstein condensates (more on this elsewhere, if requested or if I get around to it). I spent an hour or so with his post-doc and grad students being walked through the ‘atom-trapping’ equipment — the optics and the magnets, and what not — the entire complicated process needed to cool the Lithium gas down to nano-kelvin temperatures before it condensed, and the way a signal was extracted from the system. The place was stuffed to the gills with tons of expensive equipment, all beautifully arranged and tuned to produce the effects needed. I walked out of there with a better understanding of what was going on in the experiment, but also feeling a little stunned that I had only one equation to describe all of this! (For the curious, this is the the Gross-Pitaevskii equation, a nonlinear Schrodinger equation, which is a mean-field description of the condensed atoms). Sure, this was a pretty mean and nasty equation, but it felt … inadequate.

And I would argue back and forth with Randy about what exactly he and his students were doing in their lab, and how we were trying to take care of that in the equations, steadily improving my hold on the exact correspondence between the theory and the experiment. Despite the tenuous connections, in general theorists AND experimentalists have a lot of trust in this equation, particularly because the predictions did so well. Something similar happened in my discussions with Barry Dunning’s group, though since he was working on a Rydberg atom in an almost classical state, as opposed to Randy’s condensate, the interpretation issues were a little less confusing.

These interactions with experimentalists were a wonderful education, and that’s when I got a better feel for the elaborate dance between theory and experiment — experimenters trying hard to reproduce the ‘idealized’ conditions of the theory, theorists trying to extract their best models for the experimental situation, and both negotiating on the interpretation of the correspondence.

And it is this sense that I am trying to convey to my students (all of whom are biologists or geologists, except for one physicist who is a pre-med, so he’s pretty up on the biology). The equations in physics are so much more reliable, the correspondence between reality and the math so much cleaner, than those describing the messy messy messy real world systems of biology and geology, so we really do have a head-start when we ‘model’ in physics. But surely some of that attitude can pay off elsewhere? That’s what’s the effort is with this class.