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42 is found to be the sum of three cubes

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Re: 42 is found to be the sum of three cubes

#241

Post by MertsA »

chrisau wrote: post #237
nserrino wrote: post #230

Earlier quoted context omitted.

For a^3 + b^3 + c^3 = 42, You can enumerate a,b pairs and then you need to check whether the "locked in" value of c^3 is a cube. However imagine it takes 1ns to validate a given pair [a,b]. The eventual solution was [-80538738812075974, 80435758145817515, 12602123297335631]. Since no combination of 3 positive (and therefore small) numbers has worked, we know that one of a,b,c are negative. Let's assume at least one o…

> I am interested to learn more about how they solved it if not brute force. "Professors Booker and Sutherland's solution for 42 would be found by using Charity Engine; a 'worldwide computer' that harnesses idle, unused computing power from over 500,000 home PCs to create a crowd-sourced, super-green platform made entirely from otherwise wasted capacity." https://phys.org/news/2019-09-sum-cubes-solvedusing-real-lif..…

>SUSTAINABLE, ULTRA-LOW CARBON - using PCs that already exist but are just underused

Wow, do they honestly believe their own marketing nonsense? There's no way the PUE and power efficiency of a bunch of old random desktop computers is going to come close to beating a modern Amazon, Google, or Microsoft datacenter. Cost wise, yeah sure, I'd bet it would be cheaper even with the lower efficiency and increased power usage but as far as "super-green" and low emissions this is just absurd. I think they might honestly not know that idle power usage is a small fraction of full load usage for any modern processor.

Re: 42 is found to be the sum of three cubes

#242

Post by MertsA »

jjtheblunt wrote: post #220
ColanR wrote: post #178

Earlier quoted context omitted.

It is enumerable, but I think what you may have missed is that negative numbers are included. i.e., > 42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3

With negative numbers, it's still enumerable, as if it were a six-tuple of natural numbers, I figured.

Maybe I'm looking at this the wrong way, but I'd handle enumerating this just like enumerating a set of three numbers. For an integer i just do (1-2(i%2)) * (i/2) using integer division. If it's recursively enumerable with natural numbers then it has to be trivially extendable to all integers just by that method alone.

Re: 42 is found to be the sum of three cubes

#243

Post by [deleted] »

apaprocki wrote: post #235
FreeFull wrote: post #194

Earlier quoted context omitted.

Google and Duckduckgo use floating point rather than arbitrary precision integers. Wolfram Alpha's solver is significantly more advanced (including arbitrary precision for integers and floating point numbers)

I’m actually surprised someone at Google hasn’t switched to BigInt yet in JS if the browser supports it? Googlers, front page OKR time! :)

[deleted]

Re: 42 is found to be the sum of three cubes

#244

Post by pvinis »

Florin_Andrei wrote: post #225
hbosch wrote: post #218

Earlier quoted context omitted.

I think this falls under the mathematical category of "fun things you can do with numbers", and not much else. Just cool.

Unless in the future someone finds a useful application for this. It's happened before.

Interesting. Like what?

Re: 42 is found to be the sum of three cubes

#245

Post by ChrisLomont »

robrenaud wrote: post #179
ChrisLomont wrote: post #162

Earlier quoted context omitted.

It is not computationally tractable to enumerate all triples of integers up to the size required to find the values for 42. So certainly any integer N either is or is not the sum of three cubes. Deciding which is the case computationally can be intractable. Each of the integers in the solution are ~53 bits in length. To enumerate all triples of integers (with plus and minus) requires testing around 2^(53+53+53+1+1+1)…

You only need to enumerate pairs of integers, the 3rd is then forced (quickly check if it's a cube).

You’re assuming a fixed target. I was enumerating which targets get hit to solve the problem for all cubes up to some fixed size.

If you’re assuming a fixed target, you don’t know how large you need to check to find an answer. That 53 bit numbers sufficed for 42 was not known in advance, and is not the bound for other targets.

Re: 42 is found to be the sum of three cubes

#246

Post by xelxebar »

emergie wrote: post #208
erikig wrote: post #186

Earlier quoted context omitted.

Strangely, typing this into Google does NOT result in 42 ((-80538738812075974)^3)+(80435758145817515^3)+(12602123297335631^3)

for big numbers you can use bc (infix) or dc (rpn) calculator: echo '((-80538738812075974)^3)+(80435758145817515^3)+(12602123297335631^3)' | bc echo '_80538738812075974 3 ^ 80435758145817515 3 ^ 12602123297335631 3 ^ + + p' | dc

Nice! My go to calc is dc. If you're like me at all, then you might like to know that we can avoid the pipe usng the -e switch

    $ dc -e '_80538738812075974 3^ 80435758145817515 3^+ 12602123297335631 3^+p'

Re: 42 is found to be the sum of three cubes

#247

Post by crobertsbmw »

pvinis wrote: post #244
Florin_Andrei wrote: post #225

Earlier quoted context omitted.

Unless in the future someone finds a useful application for this. It's happened before.

Interesting. Like what?

Pretty much all of mathematics was founded on "fun things to do with numbers", and then later we came up with using prime numbers for cryptography and finding Fibonacci sequences in nature, etc.

Re: 42 is found to be the sum of three cubes

#249

Post by nqzero »

Svip wrote: post #228
nqzero wrote: post #148

Earlier quoted context omitted.

why did you switch from the mit site to twitter ? (i'm currently blocked on twitter - they want a phone number and are blocking all content till i provide one)

Can't you just log out? Or are you IP blocked?

given that they blocked me for "rules violations" (which i clearly didn't do, as it was a brand new account that had taken zero actions and my previous account was fine when i closed it) i didn't want to circumvent the block (which might have actually been against the rules) so i didn't use technical measures (which certainly would have worked). i ended up just giving them my phone number, but it's a sad reality that we've accepted all these walled gardens
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