It has been computed for at least 10^16 steps, and it sure does look drunk, but sadly that does not constitute a proof.
Re:The Riemann Hypothesis
by emilgouliev on Sunday September 08, 2019 @09:04PM
(#20914396)
They meant 3^2 = 9.
what does "look drunk" actually mean tho? it's a bit of a weird property...
The drunken man is moving away from where he started (any point in time can be labelled as "start") at a speed of about the square root of his linear speed (speed from his point of view). And the direction is random. This can also be 1D motion. Actually in 1 and 2D it is likely that the drunken man hits his starting point again at some point, it goes to 0 fast in 3D.
For 1D It's trivial to see that a side scroller with side-strafing controls (Space Invaders not Asteroids) will always return to the center if L and R appear with equal probability, in euclidean geometry
Re:The Riemann Hypothesis
by wodenokoto on Monday September 09, 2019 @04:03AM
(#20916100)
As the parent poster quotes, drunk looks like:
> if the sequence was of n steps, almost surely its distance from the starting point would be close to √n.
Of course that raises the question "What is close?"
Did they mean 3x3x2 instead of 32? There is no way 18 is divisible by 32 in any common sense of divisible.
> This explicit sequence of instructions, which is determined by the prime numbers, causes a robot to look drunk, if and only if the Riemann Hypothesis is true!
So, do they look drunk for large walks? That sounds like something that is easily computed for tens of thousands of steps.