LookingForOctober (

**lookingforoctober**) wrote2016-10-07 05:23 pm### The difference between mathematics and reality

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

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...)
## no subject

yhlee2016-10-07 08:20 pm (UTC)(link)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

isthat 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!

## no subject

lookingforoctober2016-10-08 12:10 am (UTC)(link)And trimming seems sort of integral to the algorithm. Even if they can get the amount of trimming down, it's still...*shrug* Not so much about reality?

But I had no idea this was a class of algorithms, or that mathematical algorithms had ideas about being envy-free (or having anything to do with emotions), so that was interesting. I'm actually amazed there's enough material on this one thing for a whole book, too!

## no subject

yhlee2016-10-08 12:29 am (UTC)(link)## no subject

lookingforoctober2016-10-08 12:42 am (UTC)(link)I suspect those pure math people are in some ways drivers of innovation, because of the other people who come along and see their fun stuff that hasn't been used yet, and try to figure out how to use it. Which means the pure math people have to go find new stuff to be pure about...

## no subject

yhlee2016-10-08 12:45 am (UTC)(link)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.

## no subject

lookingforoctober2016-10-08 12:53 am (UTC)(link)myapproach than the tasks themselves.Oh, wow, really? That is very funny.

## no subject

yhlee2016-10-08 03:14 am (UTC)(link)wereproofs 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!