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I agree with monkeys+typewriters, but look at how compact the quadratic formula is. It's not a work of shakespeare. it's maybe 12 to 20 "tokens" , using a loose

I agree with monkeys+typewriters, but look at how compact the quadratic formula is. It's not a work of shakespeare. it's maybe 12 to 20 "tokens" , using a loose definition of a token. To me, it's totally within the realm of a 1-10 billion search space, isn't it? I'm just thinking aloud, but suppose a random-math-syntax shuffler eventually produced the quadratic formula, how would you even check it? You would have to input many permutations of quadratic equation inputs and check them against the randomly-produced one. You'd quickly hit imaginary numbers, which could (falsely) signal that the QF is invalid. Compare that to monkey-typing fizzbuzz. That seemingly could be done in a few billion iterations, no? (assume you could exclude monkeys from typing syntax errors, and only produce valid C++/java whatever). IDK, I'm just mesmerized by the fact that the QF is so compact, yet there isn't an easily-discoverable way to derive it by brute force. (and I'm deliberately excluding AI because of how tiring the questions of the form "why can't AI do _____" are. I don't care that much about AI).

Pet_Ant 3y ago
The Pythagorean theorem is even more compact, and even more impactful. But the low hanging fruit has been already picked for centuries and how would you detect a meaningful formula if you were give a 10GB text file of various ones?
tromp 3y ago
> To me, it's totally within the realm of a 1-10 billion search space, isn't it? A proof of the theorem is going to be at least a few hundred bits, which is totally out of reach of brute force search. A 10 billion search space only covers 34 bits (less than 5 ASCII symbols) in which you'll struggle to even state the theorem.
Someone 3y ago
> It's not a work of shakespeare. it's maybe 12 to 20 "tokens" , using a loose definition of a token. To me, it's totally within the realm of a 1-10 billion search space, isn't it? Even 12 tokens with only 10 different token values gives you 10¹² different candidate ‘proofs’. That already is a thousand times 10 billion. In reality, there easily are 100 possible token values (lower and upper case alphabet, punctuation, Greek lower and upper case, dozens of symbols, a bit of Hebrew, etc), taking that number to 10²⁴. Also, I think even just express the two solutions to ax²+bx+c=0 without any hint of a proof in twelve tokens is an insurmountable challenge.

Pet_Ant 3y ago

The Pythagorean theorem is even more compact, and even more impactful. But the low hanging fruit has been already picked for centuries and how would you detect a meaningful formula if you were give a 10GB text file of various ones?

tromp 3y ago

> To me, it's totally within the realm of a 1-10 billion search space, isn't it? A proof of the theorem is going to be at least a few hundred bits, which is totally out of reach of brute force search. A 10 billion search space only covers 34 bits (less than 5 ASCII symbols) in which you'll struggle to even state the theorem.

Someone 3y ago

> It's not a work of shakespeare. it's maybe 12 to 20 "tokens" , using a loose definition of a token. To me, it's totally within the realm of a 1-10 billion search space, isn't it? Even 12 tokens with only 10 different token values gives you 10¹² different candidate ‘proofs’. That already is a thousand times 10 billion. In reality, there easily are 100 possible token values (lower and upper case alphabet, punctuation, Greek lower and upper case, dozens of symbols, a bit of Hebrew, etc), taking that number to 10²⁴. Also, I think even just express the two solutions to ax²+bx+c=0 without any hint of a proof in twelve tokens is an insurmountable challenge.