Including thumbs that is. Having said that, not everyone has those:
I can only imagine how difficult not having thumbs must be. This is of course literally a five-fingered hand, meaning that it’s impossible for the first digit to touch the others fingerpad to fingerpad, which is crucial to tool use. Primates generally do have thumbs of course, although their opposability isn’t always like ours. This is a squirrel monkey’s hand:
Squirrel monkeys are from the other half of the monkey clade and have pseudo-opposable thumbs, meaning that they operate like hinges but can’t swivel to touch the other fingertips. Tarsiers, which are nocturnal versions of our direct ancestors the omomyids, have completely non-opposable thumbs:
By Jasper Greek Golangco – http://www.sxc.hu/photo/490925, Copyrighted free use, https://commons.wikimedia.org/w/index.php?curid=646723
Clearly tarsiers elicit a cuteness response in humans, probably because they’re proportioned like babies, which is therefore presumably ideal for a small primate, or at least one option.
An oddity about hands and feet, which I mentioned yesterday, is that whereas there are many species with fewer than five digits per limb, for instance horses and many lissamphibians, there never seem to be any animals which usually have more than five actual digits. There are animals with an extra dew claw, such as cats and dogs, but this is a wrist bone rather than a real digit. Even odder is the fact that whereas there are no species with more than five digits as standard, there are many cases of individuals in certain species born with more than five, including humans:
As a healthcare professional I have come across a few patients with more than the usual number of digits per hand, and because we generally have two types of digit there are two ways in which this can happen – two thumbs or five fingers, or more. Also, they tend to be branched from other digits rather than simply come off the hand as such. I could go on about Robinow Syndrome at this point but that really belongs on another blog, as does Kennedy’s Syndrome incidentally, which I mention because its social construction is similar.
The issue of functional extra digits, each with their own nails, bones, muscles, blood vessels, nerves and part of the brain onto which their sensory and motor functions are mapped, illustrates an oddity about the nature of genes and DNA. My own fifth digits are bent, a trait known as clinodactyly which can be associated with various other genetic rarities such as the chromosomal Turner and Down syndromes. Both these involve one fewer chromosomes than usual, but different ones, yet one possible result of both is clinodactyly, meaning that it can occur due to completely different sets of genes being absent. Similarly, although it’s tempting to think of there being genes for specific features of different digits and their associated muscles, nerves and other organs, the fact that people can have fully functional extra fingers is strong evidence against the idea that genes work that way. What there seems to be instead is a set of inherited traits for the ends of one’s limbs to become “frayed” as an embryo, and the tendency to have extra digits is about something else, meaning also that the tendency not to have them is as well.
So why five? If it isn’t completely genetic – there’s not a separate gene or set of genes for each finger – then where does the fiveness come from? Why five also when having more than five can happen too without any disadvantages? I personally think the answer lies in the Fibonacci Series.
At this point you’re going to have to indulge me because I have no idea whether the Fibonacci Series is well-known or not. It’s a sequence of numbers each of which is the previous two added together, so it goes 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… ad infinitum. The other thing about it is that if you divide a Fibonacci number by its predecessor you get a number close to its own reciprocal plus one, and the higher the two numbers are the closer that number is to that value, which is called φ. To illustrate this, the number φ, which like π goes on forever, is roughly equal to 1.61803399. 5/3 is 1.4, 144/89 is 1.61797753 and so on, and of course the reciprocal, which is one divided by that number, is 0.618055555 in that case. This is known as the Golden Ratio.
I think nearly everybody knows all that but I’m not sure, so I’m just mentioning it in case there are people who don’t know it.
Something I’ve never understood about either the Fibonacci Series or the Golden Ratio is why they turn up so much in nature, but they do. For instance, here’s a picture of an ox-eye daisy with a crab spider:
The florets in the centre of the inflorescence (what people generally refer to incorrectly as a flower when in fact like all plants in that family a daisy’s “flower” is in fact a bouquet of many flowers) occur in spirals of 21 in one direction and 34 in the other. These kinds of numbers also turn up in the spirals of pine cones, pineapples and cauliflowers. However, they needn’t be directly governed by genes alone, as this picture of the M51 galaxy shows:
The spiral arms of the galaxy, like many others possibly including the Milky Way, pass through the rectangles, each of which is a golden rectangle with the sides in proportion of around 1.618. The same applies to the shell of a nautilus and the cloud swirls in hurricanes:
By Chris 73 / Wikimedia Commons, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=19711
These are all logarithmic spirals and the hurricane and galaxy have nothing to do with genetic inheritance in their form. The spiral and its association with the Golden Ratio just represent a path of least resistance.
As for the actual numbers of the Fibonacci sequence itself, these turn up as well. For instance, the crab spider has eight legs, a starfish has five arms and so on. However, when the numbers get that small the chances of coindences increase dramatically because smaller Fibonacci numbers are more frequent than larger ones. Also, it starts to look a bit like numerology because whereas an octopus or a spider might have eight appendages, the actual reason for that might be that it has four on each side multiplied by two due to its bilateral symmetry, and whereas that symmetry itself is in the Fibonacci series – two sides – it starts to feel to me like I’m seeing patterns everywhere which aren’t really there.
Nonetheless, I do consider five to be an important number. There are only a few different forms of symmetry among animals. An animal may be completely asymmetrical, for instance some sponges are:
By Peng – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=113733
(By the way, although this isn’t really symmetrical it does have a fractal kind of pattern to it), they may be radially symmetrical like jellyfish:
By Alexander Vasenin – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=32753304
They can also be bilaterally symmetrical, like humans, insects and many other species. Or, they can be pentamerously symmetrical, like a star, as found of course in starfish:
By Nhobgood Nick Hobgood – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=6279893
In the distant past there were also life forms with threefold – triplanar – symmetry. However, there are no animals with sixfold or sevenfold symmetry, and this to me is significant. The reason starfish and their relatives evolved fivefold symmetry seems to have been that it makes them tougher. This isn’t immediately apparent with starfish but with a sand dollar it’s a different matter:
These animals are tough. Although their shells are made up of five plates joining at corners, the weak lines of the cracks between these plates are compensated for by the fact that the opposite point is the middle of a plate, meaning that every weak point is accompanied by a strong one. This would also be true, however, of a heptagonal animal:
The seven-sided fifty pence piece is, incidentally, designed so as to have the same diameter in all directions so it can work in slot machines. So I’ve heard anyway. The point being that there is no real reason why a sand dollar shouldn’t be a sand fifty pence piece, were it not for the sole fact that seven is not in the Fibonnaci series. I don’t know this for sure, but I suspect that’s the reason echinoderms have five sides rather than seven. Having said that, I find the Fibonacci series mysterious and I don’t know why it turns up all the time.
Of course, what I’m working up to is the claim that limbs have a maximum of five digits because the number five is in the sequence. I suspect that if there is vertebrate-like life elsewhere in the Universe it will turn out to have something like three, five or eight digits rather than six or seven. I think also that there’s a way of testing this hypothesis, although I haven’t done it.
Limbs evolved from the fins of fish, particularly their pectoral fins. If I’m right, a prediction which could be made would be that pectoral and pelvic fins will tend to have a number of rays in the Fibonacci sequence. This would confirm the fact because fins have much larger numbers of rays than hands and feet have digits, thereby reducing the chances of coincidence. However, I haven’t checked. If that turns out not to be true, though, it may not mean I’m wrong.
So basically I can’t tell if I’m being a mathematician or a numerologist about this. Or indeed a palm-reader.