Will the Sun not not .... not explode on April 15, 2023, where the number of "not"s is equal to Σ(5)?
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30
8.6k
2061
4%
chance

Σ is the busy beaver function.

This resolves as soon as we find out what both the question and the answer are.

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Seems that this market might actually be able to resolve within a year or two! Apparently, there is an avenue towards a proof that the remaining candidates don't halt.

Ok people have really overvalued NO here now. This bing-chat answer states only that it's AROUND 4098, and if it is even ± 1 difference it could be as well odd as even.

@Swordfish42 Might be wrong, but I thought that 4098 was the best known machine, and all the other ones are suspected to not halt (and have been run for a gazillion iterations), but it’s technically unproven - meaning it’s highly likely that it’s 4098, but the hard part is a proof. But it won’t be like 4099, the 4098 number is exact.

predicts NO

@Conflux (by “the other ones” I mean those that could beat the 4098 one)

@Conflux That is correct according to Wikipedia:

The current (as of 2023) 5-state busy beaver champion produces 4098 1s, using 47176870 steps (discovered by Heiner Marxen and Jürgen Buntrock in 1989), but there remain many machines with non-regular behavior which are believed to never halt, but which have not been proven to run infinitely.

@Swordfish42 Bing Chat isn't exactly correct there. The value is known to be at least 4098, not around 4098. If it's not exactly 4098, it could be almost anything and is probably much larger than 4098.

Thus, if the current "champion" machine isn't a busy beaver, there is basically a 50/50 shot of Σ(5) being even. So, if we let P be our degree of confidence that Σ(5)=4098, the "probability" (in the sense of our degree on confidence based on the information we have, not a strict mathematical sense) that Σ(5) is even is P+(1-P)/2=(1+P)/2. This market currently estimates a probability of 78% that Σ(5) is even (assuming a 100% probability that the Sun won't explode on April 15th). That means that P is estimated to be 56%.

predicts NO

@JosephNoonan Well, you also have to factor in discount rates, since there’s a good chance Busy Beaver 5 isn’t solved anytime soon. I think there’s probably a >90% chance that 4098 is correct.

3% is so low that I'd be uncomfortable buying it down this low unless I studied the topic