Betz limit for sailboats?

In the study of sustainable energy, there is a nice result on windmills, called the Betz limit: There is a finite limit to the fraction of the kinetic energy of the wind that a windmill can absorb or exploit. The reason is often stated as: If the windmill took all of the power in the wind, the wind would stop, and then there would be no flow of energy over the windmill. I'm not sure I exactly agree with that explanation, but let's leave that here.

On my travel home today I worked on the possibility that there is an equivalent to the Betz limit for sailboats. Is there an energetic way of looking at sailing that is useful?

One paradox is that a sailboat is sailing steadily when the net force on the boat is zero (just like when a windmill is turning at constant angular velocity). In the Betz limit, the windmill is thought of as having two different torques on it, one from the wind, and one from the turbine. Sailing has no turbine. So this problem has a conceptual component to it.


Happy birthday, Rix

Today was an all-day event at MPIA to celebrate the 60th birthday (and 25th year as Director) of Hans-Walter Rix (MPIA). There were many remarkable presentations and stories; he has left a trail of goodwill wherever he has gone! I decided to use the opportunity to talk about measurement, which is something that Rix and I have discussed for the last 18 years. My slides are here.

I've been very lucky with the opportunities I've had to work with wonderful people.


divide by your selection function, or multiply by it?

With Kate Storey-Fisher (San Sebastián), Abby Williams (Caltech) is working on a paper about large-angular-scale power, or anisotropy, in the distribution of quasars. It is a great subject; we need to estimate this power in the context of a very non-trivial all-sky selection function. The tradition in cosmology is to divide the data by this selection function. But of course you shouldn't manipulate your data. Instead, you could multiply your model by the selection function. You can guess which one I prefer! In fact you can do either, as long as you weight the data in the right way in the fit. I promised to write up a few words and equations about this for Williams.


why study astrophysics?

I spent the day with Neige Frankel (CITA), working on various projects. One of the things we discussed was her slides for an upcoming talk. I made the following blanket statement; is it true? There are only two ways to ultimately justify a subject of study in astrophysics. Either it will tell us something important about fundamental physics (think: dark matter, initial conditions of the Universe, or nucleosynthesis, say), or else it will tell us something about our origins (formation of our Galaxy, occurrence of rocky, habitable planets, origin of life, say). I am not entirely sure this is right, but I can't currently think of much in the way of counter-examples. I guess one other justification might be that we are developing technologies that will help people in other areas (CCDs, spacecraft attitude management, or machine learning, say).


Galactic cartography

Neige Frankel (CITA) and I discussed measurements of the age and metallicity gradients in the Milky Way today. In my machine-learning world, I am working on biases that come in when you use the outputs of regressions (label transfer) to perform population inferences (like mean age as a function of actions or radius). We are gearing up to do a fake but end-to-end simulation of how the Milky Way gets observed, to see if the observed Galaxy looks anything like (what we know in this fake world to be) the truth.


auto-encoder for calibration data

Connor Hainje (NYU) is looking at whether we could build a hierarchical or generative model of SDSS-V BOSS spectrograph calibration data, such that we could reduce the survey's per-visit calibration overheads. He started by building an auto-encoder, which is a simple, self-supervised generative model. It works really well! We discussed how to judge performance (held-out data) and how performance should depend on the size of the latent space (I predict that it won't want a large latent space). We also decided that we should announce an SDSS-V project and send out a call for collaboration.

[Note added later: Contardo (SISSA) points out that an autoencoder is not a generative model. That's right, but there are multiple definitions of generative model; only one of which is that you can sample from it. Another is that it is a parameterized model that can predict the data. Another is that it is a likelihood function for the parameters. But she's right: We are going to punk parts of the auto-encoder into a generative model in the sense of a likelihood function.]


what book am I going to write?

One possible new year's resolution this year is for me to decide which book am I going to write? I don't love this, because it is the hallmark of a scientist at the end of the career that they switch to writing books! I guess maybe I'm at the end of my career? But that said, I have (maybe like many scientists at the end of their careers?) a lot to say. Okay anyway, I had a long conversation this morning with Greg McDonald (Rum&Code) about all this, and he strongly encouraged me to make some content for the project code-named ”The Practice of Astrophysics“.


wind power

I met up with Matt Kleban (NYU) to discuss our dormant project on the physics of sailing. Our conversation ranged around many different things related to sustainable power. In particular, we discussed whether it was possible to take a energy or power point of view on sailing, which has to do with the work that the sailboat is doing on the water and on the air. I feel like there will be some symmetries in play there. We also discussed power generation with wind farms, including the Betz limit (which is a limit on how much power you can get out of the wind). Is there an equivalent of the Betz limit for a sailboat? Finally, Kleban made a remark that is simultaneously obvious and deep: If you have a propeller turning in a fluid (like air), it might be a turbine (generating power from the wind) or a fan (using power to make wind). The question of turbine or fan has a frame-independent (relativistically scalar) answer.


informal scientific communication

I have been sending out my draft manuscript on machine learning in the natural sciences to various people I know who have opinions on this. I've been getting great feedback, and it reminds me that there is a lot of important scientific communication that is on informal channels. One thing that interests me: Is there a way to make such conversation more public and viewable and research-able?