other kinds of sailing

In finishing up the first draft (yay!) of my paper on sailing, I thought about other kinds of sailing (for the discussion). One is solar sails: In principle if a spacecraft has a sufficiently large solar sail, of which it can change the size and shape, the spacecraft can navigate in arbitrary directions and perform arbitrary three-axis attitude adjustments, by working on a combination of radiation pressure and gravity. It's really very flexible. It makes me want to design a spacecraft!

I also thought about ice boats. An ice boat is like a sailboat with an extremely large keel and almost no water drag. That is, it sails like a sailboat in the limit that the keel gets large but the water drag gets small. This should make ice boats extremely fast at upwind sailing. Maybe I'll try to find an opportunity to sail on ice this winter?

emulators

Right now, in cosmology, emulators are all the rage: Cosmological simulations are slow and expensive, and we need to speed them up! But I'm concerned: What if we use emulators in all our Euclid and LSST pipelines, and then we find something very surprising? What then? Do we check it all using full-blown simulations? But then, if so, why not do full-blown from the outset? Or do our standards of care depend on our results? They aren't supposed to, but maybe they do?

Worried about all this, I have been thinking about how to make emulators better, and give them provably better properties. It's why I've been working on building methods that exactly obey symmetries. But from an epistemological perspective, emulators might be the Worst Idea Ever^TM.

In detail, I'm working out how we might build emulators that are trained on one simulation suite but can be tested on another, made with a different cosmology and at a different mass resolution. I think work I've been doing with Villar (JHU) on the exact symmetries imposed by geometry and units might make this possible. I'm trying to figure out the scope of an achievable paper on this.

sailing upwind; lift ratios; sail-to-keel ratio

In writing up a description of some of my physics-of-sailing results, I realized some things about sailboat design. For deep reasons you want the ratio of the area of the sail to the area of the keel to be roughly the ratio of the density of water to the density of air, or 700. That flows from the point that the sail and the keel have symmetric roles in sailing. But if you set this ratio to 700, you can only sail upwind if the sail lift ratio (the ratio of useful sail force to drag force) is very high. Since it is hard to make this lift ratio high on a commercial boat, the alternative is to make the sail smaller (relative to the keel). Looking at the data I can find on real sailboats, most have okay lift ratios but small sail-to-keel ratios (smaller than 700 anyway), so that they can sail quickly upwind. The cost of these design choices is that you can't go downwind faster than the wind. If you want to be able to sail both downwind faster than the wind—and also upwind—you have to have amazing sail and keel lift ratios.

steerable machine learning

Inspired by the hope of mashing up our paper on scalars and vectors in machine learning with work like this on steerable neural networks, I worked with Soledad Villar (JHU) today on writing down all possible linear convolutional kernels in a 3x3x3 block of a 3-d image that satisfy the geometric symmetries of scalar, vector, and second-order tensor forms. I feel like recent work on machine-learning in cosmology like this could be vastly improved by these geometric methods.

modeling arid ecologies?

[This blog died for a few months. I apologize. I am back now, and hope to continue.]

Today I worked with Soledad Villar (JHU) on our project to execute regressions (and other machine-learning methods) that are constrained to be exactly symmetric (or equivariant) with respect to units and dimensions. Our target problem is a regression involving ecologies of arid regions. There are differential-equation models for this, and all the inputs to the equations have interesting units (such as water volume per area, and grams of vegitation, and so on). It was fun to do some real coding again, after days of grading final exams!