Eric Holloway: Algorithmic Specified Complexity

[swamidass (S. Joshua Swamidass)]

@swamidass

If you have a general method of determining what the correct P is, I’d like to put that to the test. I can produce a a few sets of sequences, and you determine which set has the highest CSI. If you have an objective strategy, without knowing how I generate these sequences (till the end), you should be able to determine which one has the highest CSI. I do not think this is possible. In fact, I think it can prove its impossible, but we can see if you can prove me wrong.

@EricMH

So, in regard to your challenge, it is certainly interesting and I would like to participate, but my failure will not indicate that Marks et. al. are wrong about ASC. The key property of ASC is mathematically proven, and so empirical counter evidence can only mean we have erred in our construction of OASC, possibly in our selection of P_{est.}.

The Puzzle Rules

If you can’t solve this puzzle with an objective metric, it means you can’t objectively determine the CSI of objects. I do not think this is a solvable puzzle, but because I generated the sequences I know the right answer. For each of the following sequences, I know the correct CSI. I can give a few hints, and a promise:

1. Each sequence has a different CSI, either 5, 10, 100, 150 or 200 bits of CSI to be precise.

2. Each sequence was constructed with about five lines of python code.

3. I’m saving the code used to generate this, and the answer key, and can produce it when you are done trying.

Remember, it is not enough to just permute these 5 numbers and try all combinations. You have to produce an implementation of ASC that produces results (1) consistent with these numbers and (2) able to identify which ones have high CSI. Of course, you could submit a function that always emits zero. It would be less than CSI in all cases, but it would be unable to determine which sequences were high or low.

If you cannot solve this puzzle (and I think it is impossible to solve), then it seems we have demonstrated that ASC cannot practically identify high CSI.

The Sequences

98d50ad729eb9af79bedc1eb64d555083513057ddfa6e86892fc6360d843e168

ce98c8f3aaddcac18d724c93ccde9b5af87f1967fe4481700d0832c5b003f4a2

451834bb93b6de3e8f87255f14789b728b544304027343000e57eabba0573318

1319730bc751757d7ae1b1f21f81978b9a2ee6d96685f03afc93d257c7d21d66

19385699c280f99b6825aa165c38191b9d7b6f150cf504f25b9934e96b90261d