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> there is a 'noise' threshold below which a probabilistic benefit will have no effect. [I]t simply will not have an effect no matter how many millions of gene

> there is a 'noise' threshold below which a probabilistic benefit will have no effect. [I]t simply will not have an effect no matter how many millions of generations go by We've arrived at a circle in this thread, considering the eyebrow example was initially offered to show how even small advantages will, over time, make some phenotype (and genotype) dominant. This is also mathematically true: given a coin with only the most minimal bias, cumulative results of coin tosses will eventually drift far away from 50%/50%. Concerning your empirical observation regarding the evolutionary usefulness of eyebrows: How many people have you seen being clearly impacted (in regards to their offspring) by missing toes, being born with only one kidney, having ears shaped sub-optimally for capturing sound etc...? Because extremely little regarding your body is left to chance. Unless you're one of less than a hundred with a given feature, be assured that it's a variation that, for a significant number of prior generations, has proven to be useful.

lurquer 9y ago
You wrote: This is also mathematically true: given a coin with only the most minimal bias, cumulative results of coin tosses will eventually drift far away from 50% This is what troubles me. I understand your point. But, if it takes a trillion years to 'drift away from 50/50' is it meaningful to describe the bias as something other than zero? That is, is there some Plank's Constant kinda-thing for probabilities? The reason this always comes to mind is the absurdly low probabilistic effect on fecundity of, say, a finch having a 4cm beak versus a 4.1cm beak. If the effect is some probability so low that it would take millions of generations to manifest itself, then, in light of the fact that finches were probably single-celled organisms a million generations back, the probability may as well be zero.

lurquer 9y ago

You wrote: This is also mathematically true: given a coin with only the most minimal bias, cumulative results of coin tosses will eventually drift far away from 50% This is what troubles me. I understand your point. But, if it takes a trillion years to 'drift away from 50/50' is it meaningful to describe the bias as something other than zero? That is, is there some Plank's Constant kinda-thing for probabilities? The reason this always comes to mind is the absurdly low probabilistic effect on fecundity of, say, a finch having a 4cm beak versus a 4.1cm beak. If the effect is some probability so low that it would take millions of generations to manifest itself, then, in light of the fact that finches were probably single-celled organisms a million generations back, the probability may as well be zero.