For hundreds of years, x has been the go-to symbol for the unknown quantity in mathematical equations. So who started this practice?
Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.
An interesting story in that physicists found the connection first and mathematicians are tying the two areas together after the fact. More often it’s the case that mathematicians come up with the theory and then physicists are applying it to something. I’m not sure I like some of the naming conventions laid out, but it’ll be another decade or two after it’s all settled before things have more logical sounding names. I’m a bit curious if any category theorists are playing around in either of these areas.
After having spent the last couple of months working through some of the “rigidity” (not the best descriptor in the article as it shows some inherent bias in my opinion) of algebraic geometry, now I’m feeling like symplectic geometry could be fun.
Cox-Zucker machine. What sounds like a high-tech device for oral sex is actually an algorithm used in the study of certain curves, including those that arise in cryptography. The story goes that David A. Cox co-authored a paper with fellow mathematician Steven Zucker, just so that the dirty-sounding term would enter the lexicon.
I always thought he was cool before (many of his students didn’t “get” him), but I’m now even more proud to have had Steven Zucker as my first math professor in college.
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed. [.pdf]
This is the textbook that John Carlos Baez is going to use for his online course in Applied Category Theory.Syndicated copies to:
Some awesome news just as I’ve wrapped up a class on Algebraic Geometry and was actively looking to delve into some category theory over the summer. John Carlos Baez announced that he’s going to offer an online course in applied category theory. He’s also already posted some videos and details!Syndicated copies to:
G. W. Peck is a pseudonymous attribution used as the author or co-author of a number of published mathematics academic papers. Peck is sometimes humorously identified with George Wilbur Peck, a former governor of the US state of Wisconsin. Peck first appeared as the official author of a 1979 paper entitled "Maximum antichains of rectangular arrays". The name "G. W. Peck" is derived from the initials of the actual writers of this paper: Ronald Graham, Douglas West, George B. Purdy, Paul Erdős, Fan Chung, and Daniel Kleitman. The paper initially listed Peck's affiliation as Xanadu, but the editor of the journal objected, so Ron Graham gave him a job at Bell Labs. Since then, Peck's name has appeared on some sixteen publications, primarily as a pseudonym of Daniel Kleitman.
I’d known about Bourbaki, but this one is a new one on me.Syndicated copies to:
Three new books on the challenge of drawing confident conclusions from an uncertain world.
Not sure how I missed this when it came out two weeks ago, but glad it popped up in my reader today.
This has some nice overview material for the general public on probability theory and science, but given the state of research, I’d even recommend this and some of the references to working scientists.
I remember bookmarking one of the texts back in November. This is a good reminder to circle back and read it.
📖 Read pages 163-194, Part 4: Fat-Based Sauces, of Ratio: The Simple Codes Behind the Craft of Everyday Cooking by (Scribner, , ISBN: 978-1-4165-661-3)
Mayonnaise: 20 parts oil: 1 part liquid: 1 part yolk
Hollandaise: 5 parts butter: 1 part liquid: 1 part yolk
Vinaigrette: 3 parts oil: 1 part vinegar
Rule of thumb: You probably don’t need as much yolk as you thought you did.
I like that he provides the simple ratios with some general advice up front and then includes some ideas about variations before throwing in a smattering of specific recipes that one could use. For my own part, most of these chapters could be cut down to two pages and then perhaps even then cut the book down to a single sheet for actual use in the kitchen.
But what greatly helps the oil and water to remain separate is, among other things, a molecule in the yolk called lecithin, which, McGee explains, is part water soluble and part fat soluble.
Added on Sunday, February 4, 2018
The traditional ratio, not by weight, is excellent and works beautifully: Hollandaise = 1 pound butter: 6 yolks. This ratio seems to have originated with Escoffier. Some cookbooks call for considerably less butter per yok, as little as 3 and some even closer to 2 to 1, but then you’re creeping into sabayon territory; whats more, I believe it’s a cook’s moral obligation to add more butter given the chance.
more butter given the chance! Reminiscent of the Paula Deen phrase: “Mo’e butta is mo’e betta.”
Added on Sunday, February 4, 2018
How do nonsensical counting-out rhymes like these enter the lexicon?
I’d read this a year or two ago for a specific purpose and revisited it again today just for entertainment. There’s some interesting history hiding in this sort of exercise.
I also considered these rhymes as simple counting games, but the’re not really used to count up as if they were ordinals. Most people couldn’t even come close to saying how many things they’d have counted if they sang such a song. I also find that while watching children sing these while “counting” they typically do so with a choice for each syllable, but this often fails in the very young so that they can make their own “mental” choice known while still making things seem random. For older kids, with a little forethought and some basic division one can make something seemingly random and turn it into a specific choice as well.
So what are these really and what purpose did they originally serve?
It’s not specifically femme yet does involve tea, but I’ve noticed something informal like this at the Starbucks just two blocks West of CalTech in Pasadena.
Separately but related, “adults” looking for a varied advanced math outlet in the Los Angeles area are welcome to join Dr. Mike Miller’s classes at UCLA Extension on Tuesday nights from 7-10pm. We’re working on Algebraic Geometry this quarter. For those who might need notes to play catch up, I’ve got copies, with full audio recordings, that I’m happy to share.Syndicated copies to: