Wei, I need to find enough time to go over the math with a fine-toothed comb, both in Worden’s paper and MacKay’s. Worden says his result holds for sexual reproduction and I’m not sure the simulation disproves that; in my own experiments, sustainable information did go as log(children). Rather than Worden being wrong, it may be that one bit of mathematical information per generation, suffices to cancel out an amount of mutation at equilibrium which goes as the square root of the number of mutations—for reasons similar to the ones you gave above. One death, many mutations, as some previous commenter remarked. In other words the only math mistake would have been, neither in Worden’s paper nor MacKay’s, but the single calculation I tried to do myself—which seems plausible, as they underwent peer review and I didn’t. (Actually, I guess I just did, sort of.)
When I’m sure I’ve got the math right this time, and worked out which commenters get the credit for correcting me, I can do another post. Meanwhile I inserted a quickie warning so that no additional readers would be misled.
Wei, I need to find enough time to go over the math with a fine-toothed comb, both in Worden’s paper and MacKay’s. Worden says his result holds for sexual reproduction and I’m not sure the simulation disproves that; in my own experiments, sustainable information did go as log(children). Rather than Worden being wrong, it may be that one bit of mathematical information per generation, suffices to cancel out an amount of mutation at equilibrium which goes as the square root of the number of mutations—for reasons similar to the ones you gave above. One death, many mutations, as some previous commenter remarked. In other words the only math mistake would have been, neither in Worden’s paper nor MacKay’s, but the single calculation I tried to do myself—which seems plausible, as they underwent peer review and I didn’t. (Actually, I guess I just did, sort of.)
When I’m sure I’ve got the math right this time, and worked out which commenters get the credit for correcting me, I can do another post. Meanwhile I inserted a quickie warning so that no additional readers would be misled.