Maybe the issue is about redundancy. Back when folks were using rocks and sticks to pound stuff, the loss of a digit or two had to be common. Up until even a few hundred years ago, when a finger got broke it had a good chance of being essentially useless thereafter. There was no chance of recovery of the digit if it were severed. So maybe the question isn't "Is X digits optimal for the tasks at hand?" But rather "How far off from optimal is X-1 or X-2?" Looking at it this way 5 digits makes some sense. 5 may be more than is needed and life can continue on just fine if we suddenly have 4. If we start with 4 and lose 2... Though, I know a guy who was born with just a thumb and a single other digit on each hand. He gets along just fine, but he does admit that having another digit or two would be nice. -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Henry Baker Sent: Sunday, December 19, 2010 3:51 PM To: Fred lunnon Cc: math-fun Subject: Re: [math-fun] Five-fingered hands I keep asking my friends in the evo-devo (evolutionary development) community why 5-fingered hands and 5-toed feet in humans are so resistant to variation -- particularly relative to the variation found in many other traits. From time to time, there are a minute fraction of people who are born with extra fingers and/or toes, but this seems far less common than many other not-so-rare traits which are incredibly debilitating. Given the effort required during development to enforce this 5-digit constraint, there must be extremely powerful evolutionary factors involved. Darwin's Theory of Sexual Selection provides one possibility: that having exactly 5 digits/hand/foot is extremely sexy, but this is a cop-out. For some reason, humans tend to think that cartoon figures with only 4 digits (thumb + 3 fingers) are extremely cute. There must be some extremely important tasks for which are impossible with only 4 digits/hand, as well as other extremely important tasks which are impossible with more than 5 digits/hand. Even if the evolutionarily important tasks involved counting, what on earth is so important that 5 or 10 is just the right number? Are the digits used for counting the months during gestation? Perhaps the husband has to be back in 10 months from his latest war? If he comes back too soon or too late, terrible things happen? Perhaps certain important foods only achieve ripeness after 10 days, but become rotten in 11 days? At 09:33 AM 12/19/2010, Fred lunnon wrote:
Jon Selig tells me that the theory is familiar among the robotics community, having been developed 20+ years ago in the somewhat different context of the number of fingers required by a mechanical hand --- imagine trying to grasp securely a light, slippery ball, without it touching the palm. With one hand --- could be a good game for party forfeits in there!
The reference he gives is B. Mishra, J. T. Schwartz and M. Sharir, "On the existence and synthesis of multifinger positive grips", Algorithmica, Volume 2, Numbers 4, 541-558 (1987)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun