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Contest: An Alien Message

Your interlocutor in the other thread seemed to suggest that they were busy until mid-July or so.  Perhaps you could take this into account when posting.

I agree that IEEE754 doubles was quite an unrealistic choice, and too easy.  However, the other extreme of having a binary blob with no structure at all being manifest seems like it would not make for an interesting challenge.  Ideally, there should be several layers of structure to be understood, like in the example of a "picture of an apple", where understanding the file encoding is not the only thing one can do.

Contest: An Alien Message

These simple ratios are "always" , see my comment for a proposal that 0.73 is close to  (which I am not completely convinced by).

Contest: An Alien Message

If you calculate the entropy  of each of the 64 bit positions (where  and  are the proportion of bits 0 and 1 among 2095 at that position), then you'll see that the entropy depends much more smoothly on position if we convert from little endian to big endian, namely if we sort the bits as 57,58,...,64, then 49,50,...,56, then 41,42,...,48 and so on until 1,...,8.  That doesn't sound like a very natural boundary behaviour of an automaton, unless it is then encoded as little endian for some reason.

Contest: An Alien Message

Do you see how such an iteration can produce the long-distance correlations I mention in a message below, between floats at positions that differ by a factor of ?  It seems that this would require some explicit dependence on the index.

Contest: An Alien Message

This observation is clearer when treating the 64-bit chunks simply as double-precision IEEE754 floating points.  Then the set of pairs  for which  is  for some  clearly draws lines with slopes close to powers of .  But they don't seem quite straight, so the slope is not so clear.  In any case there is some pretty big long-distance correlation between  and  with rather different indices.  (Note that if we explain the first line  then the other powers are clearly consequences.)

Contest: An Alien Message

Here is a rather clear sign that it is IEEE754 64 bit floats indeed.  (Up to correctly setting the endianness of 8-byte chunks,) if we remove the first n bits from each chunk and count how many distinct values that takes, we find a clear phase transition at n=12, which corresponds to removing the sign bit and the 11 exponent bits.

These first 12 bits take 22 different values, which (in binary) clearly cluster around 1024 and 3072, suggesting that the first bit is special.  So without knowing about IEEE754 we could have in principle figured out the splitting into 1+11+52 bits.  The few quadratic patterns we found have enough examples with each exponent to help understand the transitions between exponents and completely fix the format (including the implicit 1 in the significand?).

Contest: An Alien Message

Whenever , this quantity is at most 4.

I'm finding also around 50 instances of  (namely ), with again .

Contest: An Alien Message

I'm treating the message as a list of 2095 chunks of 64 bits.  Let d(i,j) be the Hamming distance between the i-th and j-th chunk.  The pairs (i,j) that have low Hamming distance (namely differ by few bits) cluster around straight lines with ratios j/i very close to integer powers of 2/e (I see features at least from (2/e)^-8 to (2/e)^8).

My Fear Heuristic

Yes, heuristic means a method to estimate things without too much effort.

"If I were properly calibrated then [...] correct choice 50% of the time." points out that if lsusr was correct to be undecided about something, then it should be the case that both options were roughly equally good, so there should be a 50% chance that the first or second is the best.  If that were the case, we could say that he is calibrated, like a measurement device that has been adjusted to give results as close to reality as possible.

"I didn't lose the signal. I had just recalibrated myself." means that lsusr has not lost the fear "signal", but has adjusted the perception of fear to only occur when it is more appropriate (such as jumping off buildings).  In that sense lsusr's fear occurs at the right time, it is better calibrated.

Playing with DALL·E 2

It would be very interesting to see how much it understand space, for instance by making it draw maps. Perhaps "A map of New York City, with Central Park highlighted"? (I'm not sure if this is specific enough, but I fear that adding too many details will push Dall-E to join together various images.)

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