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Comment by tasn | Hacker News Reader

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.

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Good 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! :)

I 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.

Speaking 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.

Sorry, 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.

Maybe there's a "golf score" somewhere that rewards less expensive operations. The "Dirac hack" would run up a lot of points.

Really? 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?

Because 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.

If 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

Though 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.

The 2*2 also doesn't seem a general unwrap.

2^2 -> 2*2 -> 2+2

2^3 -> 2*2*2 -> (2+2)+(2+2)

It'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

N^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

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