Tales from the ArXiv: The "Chicken McNugget Monoid"

Yes, there really is a mathematical object called the "Chicken McNugget Monoid", and here is a screenshot from page one of the paper.

Apparently, this comes from the standard nugget counts in boxes of Chicken McNuggets. Here is one line from the paper: Under regular integer addition, ⟨6,9,20⟩ forms a monoid, meaning the sum of any two McNugget numbers is again a McNugget number. And if this sounds like something out of The Onion, you may be interested in this recent article.

Also, in case you were wondering: Using [17, Proposition 1 and Table 1], it follows that the Frobenius number of 🐤 is 43. This is the largest number of Chicken McNuggets that cannot be ordered using whole boxes of sizes 6, 9, or 20.

Tales from the ArXiv: "Tautological Algebra"

I feel like tautological algebra is what we get from many of our students.

Extra Special Mathematics Terminology

One of my favorite terminology fails in mathematics is the notion of an "extra special group" (which has the added bonus that my undergraduate abstract-algebra professor was unable to say it without also giggling): https://t.co/BsW1dgDYaC

So inspired!#terminologyfail

— Mason Porter (@masonporter) November 27, 2018

Mathematician Wins 2017 Dance Your Ph.D. Contest!

That's right: The top overall video in the 2017 Dance Your Ph.D. contest was for an explanation of braid groups! Awesome!

Groups of Fire

Johnny Cash sang about a "Ring of Fire".

Big Country sang about "Fields of Fire".

Clearly, somebody has to record a song about Groups of Fire. It would provide a sense of completion.

This is what I think about when I am dazed, and I am seeing rings and other algebraic structures show up in a talk. It also reminds me of comments I made as an undergrad about Killing fields.

Update: Also, "ring of functions" naturally makes my mind blurt "ring of fire".

The Derivator

Algebraist: "You don't want the full definition of derivator. It would take five journal pages."

Me [after conversation about this continues among others for a bit]: "I think it would be fine to have a five-page article for the definition as long as it includes a picture of The Terminator."

Name a Symmetry for Charity!

Come on. Name a symmetry for charity! You know you want to!

Mine is called "Mason's Spectacular Narcisstic Group". Part of the inspiration for my name was the "extraspecial group", whose name would also be accompanied by giggling whenever my Math 5 prof mentioned it. [He also invariably giggled whenever he added "with 1" to "commutative ring".]

Group Theory in the Bedroom

But it's not what you think (and anyway I blatantly stole that title from Brian Hayes)...

Instead, it's just that group theory is the subject of Steve Strogatz's latest article in the New York Times. And group theory in the bedroom plays an important role in that article. (However, group actions were not mentioned.)

The Joy of $x$

Here is Steve Strogatz's latest opinion piece on mathematics in The New York Times.

This one wasn't as engaging for me as the previous ones.

Tales from the arXiv: Categories are just like animals

Here is a new abstract that just showed up on the arXiv:

arXiv:0808.1032
Date: Thu, 7 Aug 2008 14:15:28 GMT (2695kb)

Title: Introducing categories to the practicing physicist
Authors: Bob Coecke
Categories: quant-ph math-ph math.CT math.MP
Comments: 30 pages and 19 pictures
Journal-ref: What is category theory? Advanced Studies in Mathematics and
Logic, volume 30, pages 45-74, Polimetrica Publishing, 2006
\\
We argue that category theory should become a part of the daily practice of
the physicist, and more specific, the quantum physicist and/or informatician.
The reason for this is not that category theory is a better way of doing
mathematics, but that monoidal categories constitute the actual algebra of
practicing physics. We will not provide rigorous definitions or anything
resembling a coherent mathematical theory, but we will take the reader for a
journey introducing concepts which are part of category theory in a manner that
the physicist will recognize them.
\\ ( http://arxiv.org/abs/0808.1032 , 2695kb)


The reason I am including this entry is that it reminds me of a certain incident in the graduate abstract algebra course I took at Cornell. The professor was introducing the idea of 'category' and decided he wanted to do it without a precise definition. None of us were really following him, so we asked him kindly if he'd give him a definition and he said something along the lines of 'You're going to learn what a category is the way you learned what an animal is: by seeing examples of them.' He then gave another one or two non-illuminating (at least without the definition) examples to us, at which point a brave student (not me) asked him "What is a category?" The professor went slightly ballistic at that question given the prior exchange.

To this day, all I remember about categories is that they're important in abstract algebra and that they're apparently like animals. (I suppose if I tried reading the above article, I could fix that, but I don't really care enough to do so.) That was one of my more memorable classroom experiences.