Rob
Posts: 154
Joined: July 2007
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It looks like they're now acknowledging that their numbers apply to a much easier target than the one in Schneider's paper. (A target of all positives is a cakewalk -- all it takes is a very low threshold value.)
Their numbers are still all wrong, since they're based on a misunderstanding of ev. They think that the search space is 2^131, but it's really 2^256. Had they stepped through a a few generations of an ev run, they would have known this.
But their biggest problem is still that their framework is nothing more than an obfuscatory semantic game. For instance, they say that endogenous information is "a numerical measure of the inherent difficulty of the problem to be solved," but it would be more accurate to say that it's the inherent difficulty of a different problem with different probabilities.
Here's an example: What is the inherent difficulty of rolling a 7 with a pair of dice? We might naively think that the answer is based the number 1/6, which is the probability of rolling a 7. Wrong, say D&M, the actual probability doesn't matter -- all that matters is the size of the search space. D&M would presumably say that the inherent difficulty of rolling a 7 is based on a probability of 1/11, which is not the probability of the problem in question.
And how do we non-arbitrarily define the search space? D&M seem to define it as the set of outcomes accessible to the algorithm in question. But for non-trivial problems, we don't know what outcomes are accessible unless the algorithm's starting point is chosen randomly from a well-defined set. But the java version of ev starts at the same point every time (it doesn't randomly seed the random number generator), so its set of accessible outcomes is much smaller than the set of all n-bit sequences. So even if 131 were the correct number for n, the search space of ev would be much less than 2^131.
To see further see why D&M's notion of "inherent difficulty" isn't very meaningful, consider a problem that involves an infinite set possible outcomes. Take, for instance, a Poisson distribution, which occurs commonly in nature. For lambda=1, all non-negative numbers have a non-zero probability, but the outcome is virtually guaranteed to be 0, 1, 2, or maybe 3. But according to D&M, the inherent difficulty of finding any of these very likely outcomes is infinite! D&M's terminology simply doesn't mean what it seems to mean.
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-- Rob, the fartist formerly known as 2ndclass
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