lookingforoctober: (Default)
[personal profile] lookingforoctober
Apparently, some mathematicians have discovered an "envy-free" algorithm for dividing up cake between any number of people. (https://www.quantamagazine.org/20161006-new-algorithm-solves-cake-cutting-problem/)

The difference between mathematics and reality is that when I'm cutting cake, even if it's just into two pieces, I inevitably survey the results when I'm done and then go "Oops, this one is bigger and this one is smaller." What I don't do is try to cut little bits off the cake or smear the icing all over the place to try to make it more even, because that would just be messy, and the people for whom I'm generally cutting cake appreciate nice slices that don't look like someone has taken a chainsaw to them over exact equivalence of cake slices.

I just resign myself to having a slightly smaller piece if I'm the one who has to cut it. (Unless it's my birthday cake, because in the past on my birthday I have been generously granted the big piece even though I messed up and made a big piece. But then, it's not like anyone else is reliably exact either, cake-cutting is just like that.)

This outlook, I suppose, is why I'm not a mathematician.

(Truthfully, though, I thought that the cut it and then let the other person chose was because you couldn't complain, not because it was "envy-free". But it's really sort of amusing to image a group of people all gathering around with their cake knives, and doing n-squared steps in order to get it perfect... and then sitting down to eat their collection crumbs...)

Date: 2016-10-07 08:20 pm (UTC)
yhlee: icosahedron (d20) (d20 (credit: bag_fu on LJ))
From: [personal profile] yhlee
I think the key here from a mathematical standpoint is this bit:

Cake-cutting is a metaphor for a wide range of real-world problems that involve dividing some continuous object

The object being divided need not be a literal cake, despite the name of the algorithm--the nice thing about how abstract mathematics is is that it can be applied to a range of things, rather than applying very specifically to cake.

But yeah, in real life, I just deal with my imperfect cake divisions. :)

Nevertheless, this is very cool; I used to have a book on cake-cutting algorithms and participated in a workshop on the problem once (at a very basic level), and it's neat hearing more about it!

Date: 2016-10-08 12:29 am (UTC)
yhlee: icosahedron (d20) (d20 (credit: bag_fu on LJ))
From: [personal profile] yhlee
Fair enough! I mean, part of the attraction of math for me was bunches of pretty without having to worry about applications, but then I very much identified with the whackadoodle "pure math" thing, if not as extreme as the pure math people who think math is ~forever sullied~ if it finds an application. (I wish I were joking, but...)

Date: 2016-10-08 12:45 am (UTC)
yhlee: icosahedron (d20) (d20 (credit: bag_fu on LJ))
From: [personal profile] yhlee
Hee! Yeah, I switched majors in undergrad from history to CS (I wanted to eat) then to math when I realized that (a) I sucked at debugging and (b) I enjoyed the math courses I was taking for CS more than I was enjoying the CS courses and (c) I liked pure math more than applications (except crypto; I have a soft spot for crypto, and even then math-side crypto is way abstracted from how it's implemented and used IRL).

It has always tickled me that the mathematician who invented binary numbers thought it was a pretty little bit of math with no possible application.

Date: 2016-10-08 03:14 am (UTC)
yhlee: icosahedron (d20) (d20 (credit: bag_fu on LJ))
From: [personal profile] yhlee
You're probably right about writing proofs vs. writing computer programs? But the kind of math they wanted for computer programs was the kind of math that I was desperately slow at (discrete math, algorithms, combinatorics, etc.), and I was even more desperately slow at debugging my stuff when it went wrong. I just could not keep up with the people who were actively good at CS. I was kind of a late bloomer in math, too, and still feel like an incredible impostor about it. I always started my problem sets the day I got them so that my backbrain had time to chew on the problems, which saved my ass once we got to upper-division math and the problems were proofs instead of computations. I can do computations on short notice if I absolutely have to. I can't hurry a proof. :] Anyway, thank God I am done with undergrad and don't have to go back...

There are all sorts of math things that were once believed to be of no possible practical use that...turned out to have practical uses. It's adorable. =) Heck, when I was introduced to quadratic residues, it was in the context of a crypto class--it's my understanding that they were originally just random abstract number theory!

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