Re: [math-fun] Five-fingered hands
Re: redundancy True, but then why not have 6,7 or 8? There must be a steep marginal cost associated with having 1 more finger, so that evolution calls a halt to digit inflation. According to some theories, every square inch of skin is mapped to a distinct area of the brain, where the fingertips get a much larger portion of the brain than would the back of the arm, for instance. Since brain area is very valuable, additional digits wouldn't be able to get their fair share of this area & would be at even greater risk for damage due to less feeling. I can't come up with a theory that explains why evolution places such a huge value on exactly 5 fingers, not 4 or 6. Evolution is happy to make huge mistakes about all kinds of endocrine & mitochondrial diseases, but not about the # of digits. There is a huge variation in body size & amount of body hair, but not in the # of digits. A conundrum. At 08:17 AM 12/20/2010, Torgerson, Mark D wrote:
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)
Henry Baker:
There must be a steep marginal cost associated with having 1 more finger, so that evolution calls a halt to digit inflation.
Michael Coates, professor in the department of Organismal Biology and Anatomy at the University of Chicago, might have addressed this a few years ago by positing that, on a genetic level, "the mechanisms involved in patterning the tips of our limbs include those involved in our reproductive success". http://www.scientificamerican.com/article.cfm?id=why-do-most-species-have
My cat has almost fully functional extra paws and claws on the front, about half the size of the "regular" paw. It gives him a sort of "wide grip" look. Apparently it's a fairly common variant, and its a simple dominant trait. -- so just wait a few thousand years, and see if all feral cats have it.
Taken to the extreme, there is even someone with 27 digits: http://www.mid-day.com/news/2010/sep/030910-Varalakshmi-Sadenahalli-Layout-V... Sincerely, Adam P. Goucher ----- Original Message ----- From: "Dave Dyer" <ddyer@real-me.net> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Monday, December 20, 2010 6:39 PM Subject: Re: [math-fun] Five-fingered hands
My cat has almost fully functional extra paws and claws on the front, about half the size of the "regular" paw. It gives him a sort of "wide grip" look. Apparently it's a fairly common variant, and its a simple dominant trait.
-- so just wait a few thousand years, and see if all feral cats have it.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
This reference is fascinating. I'd love to learn more about the connection with the genito urinary tract. --- The argument that 5 is merely a holdover from 60 million years ago is not a good argument, because 50 million years is plenty of time to move up or down from 5 if it were important enough. A good argument why exactly 5 is that within the past 100,000 years (order of magnitude), there was a "bottleneck", where the number of humans was reduced to fewer than 1,000, and every human today is descended from that small group which presumably was pretty homogeneous. So there hasn't been enough time since that bottleneck for evolution to experiment with more or fewer digits. However, 5 digits must have been appropriate for the conditions during the bottleneck, because these individuals survived & reproduced & the others didn't. So we should look for "human" remains older than 100k years that have more or fewer than 5 digits/hand. One theory I've heard proposed is that the bottleneck was caused by massive flooding, in which case the ability to swim would become paramount. More fingers does seem to help with swimming, as even w/o webbing between the fingers, the turbulence around the fingers supplies enough resistance to be useful. At least one researcher has decided that the diaspora of humans around the Earth at some points required swimming in order to get across rivers, so even though swimming may not be used by very many humans very often, it appears to be a critical capability for the species as a whole. At 10:08 AM 12/20/2010, Hans Havermann wrote:
Henry Baker:
There must be a steep marginal cost associated with having 1 more finger, so that evolution calls a halt to digit inflation.
Michael Coates, professor in the department of Organismal Biology and Anatomy at the University of Chicago, might have addressed this a few years ago by positing that, on a genetic level, "the mechanisms involved in patterning the tips of our limbs include those involved in our reproductive success".
http://www.scientificamerican.com/article.cfm?id=why-do-most-species-have
Perhaps this sheds some light: http://www.straightdope.com/columns/read/1879/why-do-we-have-five-digits-on-... Note that having 5 digits is really ancient, and probably predates digits. --ms On Monday 20 December 2010 12:48:26 Henry Baker wrote:
Re: redundancy
True, but then why not have 6,7 or 8? There must be a steep marginal cost associated with having 1 more finger, so that evolution calls a halt to digit inflation.
According to some theories, every square inch of skin is mapped to a distinct area of the brain, where the fingertips get a much larger portion of the brain than would the back of the arm, for instance. Since brain area is very valuable, additional digits wouldn't be able to get their fair share of this area & would be at even greater risk for damage due to less feeling.
I can't come up with a theory that explains why evolution places such a huge value on exactly 5 fingers, not 4 or 6. Evolution is happy to make huge mistakes about all kinds of endocrine & mitochondrial diseases, but not about the # of digits. There is a huge variation in body size & amount of body hair, but not in the # of digits.
A conundrum.
At 08:17 AM 12/20/2010, Torgerson, Mark D wrote:
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
Hey folks, Can we stop with the anthro-centric evolutionary arguments? Please look at this image [1]: http://upload.wikimedia.org/wikipedia/commons/5/5b/Evolution_pl.png Five digits is clearly NOT optimal for some of these mammals. The mole needs more, the anteater and horse need fewer. Any argument that is based on just one function, like grasping a tool, is missing a lot of the issues. I suggest that we are limited to 5 fingers only because the common ancestor had 5, and it might have been stuck with something inherited from earlier in the synapsid[2] or general reptile lineage. - Robert [1] apparently from http://ncse.com/image/homologous-limbs -- a popular image; a different but equivalent image is at http://www.zoology.ubc.ca/~bio336/Bio336/Lectures/Lecture5/Overheads.html [2] bridge between reptiles and mammals, see http://en.wikipedia.org/wiki/Synapsid On Mon, Dec 20, 2010 at 12:48, Henry Baker <hbaker1@pipeline.com> wrote:
Re: redundancy
True, but then why not have 6,7 or 8? There must be a steep marginal cost associated with having 1 more finger, so that evolution calls a halt to digit inflation.
According to some theories, every square inch of skin is mapped to a distinct area of the brain, [...]
12/20/2010, Torgerson, Mark D wrote:
Maybe the issue is about redundancy. [...]
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?" [...]
-----Original Message----- From: Henry Baker
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. [...]
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. [...]
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)
-- Robert Munafo -- mrob.com Follow me at: mrob27.wordpress.com - twitter.com/mrob_27 - youtube.com/user/mrob143 - rilybot.blogspot.com
Evolution is happy to make huge mistakes about all kinds of endocrine & mitochondrial diseases, but not about the # of digits.
What about polydactyly (wow, a word with three 'y's!), where people are born with 6 digits on each limb? http://en.wikipedia.org/wiki/Polydactyly Sincerely, Adam P. Goucher
Thanks! It took me a while, but I finally found that "oligodactyly" is the word for too few digits. You can now dazzle on your next crossword puzzle, scrabble game, or spelling bee! http://en.wikipedia.org/wiki/Oligodactyly This small, isolated tribe in Africa has the middle 3 toes missing, apparently without functional handicap. http://en.wikipedia.org/wiki/Vadoma The 1 in 500 incidence for polydactyly is higher than I would have guessed, but it is indicative of the ongoing evolutionary pressures. The article for oligodactyly doesn't indicate incidence, so I would guess it is much lower than 1 in 500. At 10:23 AM 12/20/2010, Adam P. Goucher wrote:
Evolution is happy to make huge mistakes about all kinds of endocrine & mitochondrial diseases, but not about the # of digits.
What about polydactyly (wow, a word with three 'y's!), where people are born with 6 digits on each limb?
http://en.wikipedia.org/wiki/Polydactyly
Sincerely,
Adam P. Goucher
I wonder if the fact that 5 is a Fibonacci number is somehow relevant. Things that grow have a predilection for Fibonacci numbers. Pine cones, sunflowers and...er...human hands? And those pesky animals with non-Fib numbered digits are the exceptions that prove the rule... On 20 Dec 2010, at 19:06, Henry Baker wrote:
Thanks! It took me a while, but I finally found that "oligodactyly" is the word for too few digits. You can now dazzle on your next crossword puzzle, scrabble game, or spelling bee!
http://en.wikipedia.org/wiki/Oligodactyly
This small, isolated tribe in Africa has the middle 3 toes missing, apparently without functional handicap.
http://en.wikipedia.org/wiki/Vadoma
The 1 in 500 incidence for polydactyly is higher than I would have guessed, but it is indicative of the ongoing evolutionary pressures. The article for oligodactyly doesn't indicate incidence, so I would guess it is much lower than 1 in 500.
At 10:23 AM 12/20/2010, Adam P. Goucher wrote:
Evolution is happy to make huge mistakes about all kinds of endocrine & mitochondrial diseases, but not about the # of digits.
What about polydactyly (wow, a word with three 'y's!), where people are born with 6 digits on each limb?
http://en.wikipedia.org/wiki/Polydactyly
Sincerely,
Adam P. Goucher
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On the topic of sunflowers, the Vogel model has an elegant description in the complex plane: z = sqrt(n)*w^n, where w = e^(2*pi*i/phi), for all naturals n. I thought about encoding raster graphics in this way, instead of going from left-to-right in horizontal rows. It should be less pixelated, and thus more aesthetically appealing, even at low resolutions. (Indeed, I considered that, to send image data to an alien race, this may be the most natural way to do so. With ordinary bitmaps, the aliens will have to guess the dimensions to visualise the image, as was the case for the Aricebo message.) Sincerely, Adam P. Goucher
I wonder if the fact that 5 is a Fibonacci number is somehow relevant.
Things that grow have a predilection for Fibonacci numbers. Pine cones, sunflowers and...er...human hands?
And those pesky animals with non-Fib numbered digits are the exceptions that prove the rule...
On 20 Dec 2010, at 19:06, Henry Baker wrote:
Thanks! It took me a while, but I finally found that "oligodactyly" is the word for too few digits. You can now dazzle on your next crossword puzzle, scrabble game, or spelling bee!
http://en.wikipedia.org/wiki/Oligodactyly
This small, isolated tribe in Africa has the middle 3 toes missing, apparently without functional handicap.
http://en.wikipedia.org/wiki/Vadoma
The 1 in 500 incidence for polydactyly is higher than I would have guessed, but it is indicative of the ongoing evolutionary pressures. The article for oligodactyly doesn't indicate incidence, so I would guess it is much lower than 1 in 500.
At 10:23 AM 12/20/2010, Adam P. Goucher wrote:
Evolution is happy to make huge mistakes about all kinds of endocrine & mitochondrial diseases, but not about the # of digits.
What about polydactyly (wow, a word with three 'y's!), where people are born with 6 digits on each limb?
http://en.wikipedia.org/wiki/Polydactyly
Sincerely,
Adam P. Goucher
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 12/20/10, Adam P. Goucher <apgoucher@gmx.com> wrote:
... (Indeed, I considered that, to send image data to an alien race, this may be the most natural way to do so. With ordinary bitmaps, the aliens will have to guess the dimensions to visualise the image, as was the case for the Aricebo message.)
Of course, this would not be (much of a ) a problem if the raster were instead p x q, for p,q prime ... WFL
Indeed, that's why the Aricebo message used a semiprime for the area. It would be even better if the area were instead p², for prime p, in which case there are only three possibilities (rather than four) for the dimensions. Amazingly, Felix Klein's date of birth consists entirely of squares of primes: 1849-04-25 Sincerely, Adam P. Goucher
On 12/20/10, Adam P. Goucher <apgoucher@gmx.com> wrote:
... (Indeed, I considered that, to send image data to an alien race, this may be the most natural way to do so. With ordinary bitmaps, the aliens will have to guess the dimensions to visualise the image, as was the case for the Aricebo message.)
Of course, this would not be (much of a ) a problem if the raster were instead p x q, for p,q prime ... WFL
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (8)
-
Adam P. Goucher -
Alex Bellos -
Dave Dyer -
Fred lunnon -
Hans Havermann -
Henry Baker -
Mike Speciner -
Robert Munafo