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!

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