People who know math: Are questions like this as logically unsound as I think they are?
1, 2, 4, 8, 16, __ What comes next in this sequence?*
I always feel like I could construct a set of rules where “1, 2, 4, 8, 16, 875″ is a correct answer, and the preference to take the simple route and complete the sequence with “32″ is more of a cognitive bias than an actually mathematically preferred answer.
Am I way off here?
(Don’t even get me started on “which one doesn’t belong?” questions.)
What if you looked at it like, “what does the shortest computer program that outputs these numbers output next?”
That actually helps a lot!
…even if the shithead part of my brain wants to respond with:
print(‘1, 2, 4, 8, 16, 875’);
I love this question because I wondered about it myself when I was little!
Someone already namedropped Kolmogorov complexity, so I don’t have too much to add. 😦 But it case it wasn’t clear, the Wikipedia article has a lot of detail:
https://en.wikipedia.org/wiki/Kolmogorov_complexity
Okay, I guess the Wikipedia article isn’t particularly easy to understand if you don’t already know a ton of computer science. One of these might be better:
https://jeremykun.com/2012/04/21/kolmogorov-complexity-a-primer/
http://c2.com/cgi/wiki?KolmogorovComplexity
So the idea is that, yes, print(‘1, 2, 4, 8, 16, 875’); works for any string, but if something has low Kolmogorov complexity, there’s an even shorter algorithm than just printing it outright.
For instance, [2^n for n = 0…6] is shorter than [1, 2, 4, 8, 16, 875].
Obviously, this depends on what programming language you choose, but there exists an optimal description language (for which I think any Turing machine qualifies) for which any computable algorithm in any description language can be represented with constant overhead, so, like, your choice of language doesn’t matter that much in the long run.
Okay, now I think this is the really correct answer. Children, please complete the string with minimum Kolmogorov complexity!
Published
Kimchi and Justice 