physics | Chris Aldrich

Arun Debray (web.ma.utexas.edu)

I LATEXed up lecture notes for many of the classes I have taken; feel free to read through them or use them to review. If you find a mistake or typo, please let me know. If you want to look over the .tex source for any of these notes, please send me an email.

A great set of LaTeXed notes from a variety of coursework.

via Rama Kunapuli.

Bookmarked At the Interface of Algebra and Statistics by Tai-Danae Bradley (arXiv.org)

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.

Read Freeman Dyson, Math Genius Turned Technological Visionary, Dies at 96 (nytimes.com)

After an early breakthrough on light and matter, he became a writer who challenged climate science and pondered space exploration and nuclear warfare.

How did I miss this when it came out?

Bookmarked on March 21, 2020 at 02:39PM

Listened to Mindscape 72 | César Hidalgo on Information in Societies, Economies, and the Universe by

Sean Carroll from preposterousuniverse.com

Maxwell’s Demon is a famous thought experiment in which a mischievous imp uses knowledge of the velocities of gas molecules in a box to decrease the entropy of the gas, which could then be used to do useful work such as pushing a piston. This is a classic example of converting information (what the gas molecules are doing) into work. But of course that kind of phenomenon is much more widespread — it happens any time a company or organization hires someone in order to take advantage of their know-how. César Hidalgo has become an expert in this relationship between information and work, both at the level of physics and how it bubbles up into economies and societies. Looking at the world through the lens of information brings new insights into how we learn things, how economies are structured, and how novel uses of data will transform how we live.

César Hidalgo received his Ph.D. in physics from the University of Notre Dame. He currently holds an ANITI Chair at the University of Toulouse, an Honorary Professorship at the University of Manchester, and a Visiting Professorship at Harvard’s School of Engineering and Applied Sciences. From 2010 to 2019, he led MIT’s Collective Learning group. He is the author of Why Information Grows and co-author of The Atlas of Economic Complexity. He is a co-founder of Datawheel, a data visualization company whose products include the Observatory of Economic Complexity.

It was interesting to hear Cesar Hidalgo use the concept of “big history” a few times in this episode. I’m not 100% sure he meant it in the David Christian sense of the words, but it at least felt right.

I was also piqued at the mention of Lynne Kelly’s work, which I’m now knee deep into. I suspect it could dramatically expand on what we think of as the capacity of a personbyte, though the limit of knowledge there still exists. The idea of mnemotechniques within indigenous cultures certainly expands on the way knowledge worked in prehistory and what we classically think of and frame collective knowledge or collective learning.

I also think there are some interesting connections with Dr. Kelly’s mentions of social equity in prehistorical cultures and the work that Hidalgo mentions in the middle of the episode.

There are a small handful of references I’ll want to delve into after hearing this, though it may take time to pull them up unless they’re linked in the show notes.

hat-tip: Complexity Digest for the reminder that this is in my podcatcher. 🔖 November 22, 2019 at 03:28PM

👓 The Jaguar and the Fox | The Atlantic

Read The Jaguar and the Fox (The Atlantic)

Hard as he tried, Murray Gell-Mann could never make himself into a legend like his rakish colleague and collaborator, Richard Feynman -- even if he was probably the greater physicist

Great story of two physicists. There has to be some interesting study one could do here on scientific communication to compare these two.