4 ms·
Maybe it's just me, but writing sqrt(2+2) instead of sqrt(2*2) or sqrt(2^2) was such an odd choice. It obfuscates the reason why 2=sqrt(2+2), and unnecessarily
by tasn 2y ago
Maybe it's just me, but writing sqrt(2+2) instead of sqrt(2*2) or sqrt(2^2) was such an odd choice. It obfuscates the reason why 2=sqrt(2+2), and unnecessarily so.
- mmooss 2y agoGood point and feedback, but an odd choice by the author? It could be the phenomenon of the author's cognitive bandwidth being consumed by everything in the article, including each argument, the overall argument, the writing, the formatting, etc. etc., and with time pressures. The critic can focus at their leisure on one point, with bandwidth to spare - and so it's obvious! :)
- tasn 2y agoI agree it potentially wasn't a conscious choice, but it's still interesting nonetheless. I wasn't criticizing him for this, but rather fascinated that this is the variant that was chosen.
- hinkley 2y agoSpeaking of odd choices: 12 = 2 * (2+2+2) Is a hell or a lot simpler than using complex numbers. Might be a different example for that would have been better.
- eliben 2y agoSorry, the intention was just to show a cool use of complex numbers, not claim this is the simplest method to generate 12 which is pretty simple, as you demonstrate.
- axus 2y agoMaybe there's a "golf score" somewhere that rewards less expensive operations. The "Dirac hack" would run up a lot of points.
- eliben 2y agoReally? But why? All of 2+2, 2*2 2^2 are trivially 4, and sqrt(4)=2 so why is the + more odd than others?
- tasn 2y agoBecause sqrt is the reverse of 2^2 and 2*2 (which is 2^2 unwrapped). Though there's no direct relationship between sqrt and 2+2 other than that it happens to be equal to 2*2. Or put differently: N = sqrt(N^2) or sqrt(N * N) for every positive N, but x = sqrt(x + x) or sqrt(x + 2) is only true for x = 2 for both or x = 0 for the first representation.
- gpm 2y agoIf 2*2 is 2^2 unwrapped, then surely 2+2 is 2*2 unwrapped, thus 2+2 is 2^2 unwrapped^2 and is also natural via transitivity? :P
- tasn 2y agoThough as I said in the rest of my comment, the 2+2 unwrap only works for N=2. So it's not a general unwrap, but rather a specific example that happens to work for N=2.
- Tistron 2y agoThe 2*2 also doesn't seem a general unwrap. 2^2 -> 2*2 -> 2+2 2^3 -> 2*2*2 -> (2+2)+(2+2)
- tasn 2y agoIt's not N^Y, it's N^2 as we are talking about the reverse of sqrt which is N^(1/2). N^2 == N*N != N+N
- gpm 2y agoN^2 = N*N = Sum_i=1 to N of N. More generally "unwrap" is being used as inlining the recursive hyper operation once more: https://en.wikipedia.org/wiki/Hyperoperation https://en.wikipedia.org/wiki/Hyperoperation