Probably, if we had a different number of fingers, our world would look somewhat different. For example, we use the decimal number system precisely because we have five fingers and toes. What if there were six fingers?
Some experts believe that a mathematical system based on the number "12" will be more efficient than the existing one. What would an extra finger give us?
The thumb and forefinger are the most important on the hands, the thumbs on the feet. They carry out the main manipulations. If we had an extra finger next to our little finger (by the way, six-fingered sometimes occurs), then we could play more complex musical instruments, type faster on the keyboard and grip objects more tightly. But there is an opinion that we need an extra thumb rather than an extra little finger.
"A wider arm would make it easier to play basketball," said Cliff Tabin of Harvard Medical School. “But the fine motor skills of our hand are mainly the thumb and forefinger. An extra little finger wouldn’t have played a big role. ” According to the scientist, it is likely that an extra thumb could develop from the wrist.
True, his colleague, head of the laboratory for the study of the properties of human perception at a research institute in Idaho (USA), Mark Shangizi, is convinced that an extra thumb could not appear in humans. He called his theory, explaining why people have only five fingers, "the law of finiteness."
This mathematical formula provides for the optimal number of limbs that the body needs to interact with the outside world, taking into account its size. For example, if the limbs are very long relative to the body, there should be six of them (like some insects). The shorter they are, the more there should be (for example, centipedes). A person needs exactly five fingers to clasp a palm - no more and no less. "If we needed one more finger to perform newfangled tasks (typing, surgery, fanning, etc.), this would be a significant deviation from the optimal morphology for which our hands have evolved, namely, grasping various objects." - states Shangizi.
Although a number of neurologists believe that we have too many fingers. In modern developments, robotic limbs usually have two, three or four fingers, and this number is quite enough for the necessary manipulations.
A man has five fingers on his hands and feet, because that is how many fingers were in the monkeys from which we descended, and the monkeys inherited five-fingered limbs from their ancestors, and so on, up to the ancient amphibians, who lived more than 300 million years ago. Apparently, the common ancestor of all modern terrestrial vertebrates had five-toed limbs. In other words, the five-toed limb is a primitive, original limb structure for all terrestrial vertebrates. In most species, including humans, this structure has been preserved to this day.
Some vertebrates have a decrease in the number of fingers or even their complete loss, sometimes together with the limbs themselves. Usually this happened in those animals, which, for some reason, some fingers began to interfere, became "superfluous". For example, the ancestors of horses developed a large hoof on the middle toe, the toe itself increased greatly, and the rest of the fingers became unnecessary, they only interfered with the growth of the middle toe, and gradually disappeared. The ancestors of man, apparently, did not have such situations that some fingers became "superfluous". Therefore, they all survived.
The question, therefore, boils down to why the common ancestor of all modern terrestrial vertebrates had a five-toed limb. Scientists today believe that there was no special reason for this. The five-toed limb does not have any fundamental design advantages over the four- or six-fingered. Apparently, five-fingeredness was fixed in the evolution of vertebrates purely by chance.
Among the most ancient fossils of tetrapods, as paleontologists have found out, there were forms with a different number of toes: for example, ichthyosteg had seven toes on its hind legs (the front ones were not preserved), acanthosteg had eight toes on its front legs and at least the same number on its hind legs. ... The legs evolved from the fins of fish, the fingers from the rays of these fins, and the number of fin rays in those fish from which terrestrial vertebrates evolved was variable.
Apparently, in the most ancient terrestrial tetrapods, the number of toes also varied. It happened by chance that it was the five-toed forms that gave rise to the whole variety of modern tetrapods, and animals with a different number of fingers became extinct. But they died out, most likely, not because they had an unsuccessful number of fingers, but for some completely different reasons, in connection with some other, more significant "shortcomings" of their structure. In principle, it could well have been "lucky" not with five-fingered, but, say, seven-fingered ancient amphibians. And then, perhaps, people would now have seven fingers on their hands.
A person has five fingers on his hands and feet, because that is how many fingers were in the monkeys from which we descended, and the monkeys inherited five-fingered limbs from their ancestors, and so on, up to the ancient amphibians who lived more than 300 million years ago. Apparently, the common ancestor of all modern terrestrial vertebrates had five-toed limbs. In other words, the five-toed limb is a primitive, original limb structure for all terrestrial vertebrates. In most species, including humans, this structure has been preserved to this day.
In some vertebrates there was a decrease in the number of fingers or even their complete loss, sometimes together with the limbs themselves. Usually this happened in those animals, which, for some reason, some fingers began to interfere, became "superfluous". For example, the ancestors of horses developed a large hoof on the middle toe, the toe itself increased greatly, and the rest of the fingers became unnecessary, they only interfered with the growth of the middle toe, and gradually disappeared. The ancestors of man, apparently, did not have such situations that some fingers became "superfluous". Therefore, they all survived.
The question, therefore, boils down to why the common ancestor of all modern terrestrial vertebrates had a five-toed limb. Scientists today believe that there was no special reason for this. The five-toed limb does not have any fundamental design advantages over the four- or six-fingered. Apparently, five-fingeredness was fixed in the evolution of vertebrates purely by chance.
Among the most ancient fossils of tetrapods, as paleontologists have found out, there were forms with a different number of toes: for example, ichthyosteg had seven toes on its hind legs (the front ones were not preserved), acanthosteg had eight toes on its front legs and at least the same number on its hind legs. ... The legs evolved from the fins of fish, the fingers from the rays of these fins, and the number of fin rays in those fish from which terrestrial vertebrates evolved was variable.
Apparently, in the most ancient terrestrial tetrapods, the number of toes also varied. It happened by chance that it was the five-toed forms that gave rise to the whole variety of modern tetrapods, and animals with a different number of fingers became extinct. But they died out, most likely, not because they had an unsuccessful number of fingers, but for some completely different reasons, in connection with some other, more significant "shortcomings" of their structure. In principle, it could well have been "lucky" not with five-fingered, but, say, seven-fingered ancient amphibians. And then, perhaps, people would now have seven fingers on their hands.
"And subsection" "by article" ". This is an interesting question, since all mammals have five toes in one form or another. Why not six, not three, but five? We talked about a number of features of the human body in the article "The Lost Link in the Evolution of the Body." And here - a question that concerns not only people, but very, very many animals.
The fact that not everyone needs five fingers is no secret. Some animals turn their toes into hooves (three toes). Some splices them together, and it turns out four fingers (for example, an anteater). But, nevertheless, there are five fingers on the hand. Some of which are simplified and do not participate in the work.
What's the riddle?
The mathematical substantiation of five-fingeredness was suggested to us by G.P. Vetchinnikov, whose article "Why are there five fingers on the hand?" we publish.
Learning to find bliss in truth
A.S. Pushkin
Let's hear what the second grader Vanya has to say. Let's number the fingers of the hand. The thumb is number 1, then the little finger is number 5. What do you need to multiply 1 to get 5? That's right, five. And the number 2 to get 4? That's right, by 2. Multiply 3 by 1 to get the middle finger number 3.
This cannot be done for seven numbers. There is no factor to get 5 out of 3. And for three numbers you can. Checked out a few more odd numbers. Does not work. Other natural numbers greater than 5 do not have this property.
Vanya did not know and therefore did not notice a part of the series of Fibonacci numbers composed of factors 1,1,2,3,5.
We remind (under the article "Numbers and formulas in nature") that a series of Fibonacci numbers is a series, the next number in which is the sum of the two previous ones: 1 + 1 = 2; 1 + 2 = 3; 2 + 3 = 5 and so on. The golden ratio and golden spiral are built on the laws of Fibonacci numbers.
So, just like many other patterns in nature, five-fingeredness is based on Fibonacci numbers and the golden ratio.
The fact that there are no other numbers for which you can do the same as for the five fingers from the description above can be proved mathematically.
Petya, a ninth-grader, will begin the proof of this statement. Let's write a finite natural series of numbers as follows:
1, 2, 3,…, n, n + 1, n + 1, n + 2,…, 2n + 1.
We argue similarly: multiply the number 1 by k 1 to get 2n + 1.
1 * k 1 = (2n + 1) - 0,
2 * k 2 = (2n + 1) - 1,
3 * k 3 = (2n + 1) - 2,
………………………………
n * k n = (2n + 1) - (n-1) = n + 2,
(n + 1) k n + 1 = (2n + 1) - n = n + 1.
Hence we have n (k n-1) = 2 and (n + 1) k n + 1 = n + 1.
Case one: n = 1, k 1 = 3, k 2 = 1. Case two: n = 2, k 2 = 2, k 3 = 1, k 1 = 2 * 2 + 1 = 5.
So we got 1-2-2-3 and 1-2-3-3-4-5 .
Let's help Petya finish solving the problem. Let's introduce the concept of a symmetric number:
f (x) = x + x 2 + x = (x + 1) 2 -1 = x (x + 2) = 0,3,8,15,24,35,48,63,80,99,120,143,168,195,224,255,288,323,360,399,440, ...
Let's find the sum and product of the numbers that the children received.
1+2+2+3=8 , 1*2*2*3=12 ,
1+2+3+3+4+5=18 , 1*2*3*3*4*5=360 .
Now let's check the symmetry of the numbers 12 and 360: f ( 8 )=80>12 , f ( 18 )= 360 .
So, in natural conditions, there can be five fingers on the hand.
Is the property of the number 5 and the number of fingers a coincidence? Even here the reader may notice more than one "coincidence". There are too many of them, if the solution to this problem is associated with an important mathematical regularity.
About deviations. Six-fingered are found, as well as two-headed. Experimenters in experiments on animals received up to 13 fingers, inclusive. Apparently it didn't work any further.
On the hand of the phalanges of the fingers we have 14, and the bones in the foot of the foot are exactly 28. The stick is taken between the thumb and forefinger. Inside the palm we see, as it were, the number 14, and outside 41.
The mysterious Euler polynomial x 2 + x + 41 with 40 prime numbers emerges.
Let us put in correspondence with the natural series of numbers prime numbers, starting from 1.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20… 26 27…
1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67… 97 101…
There is no more number with such a property as 41, since, starting from 27, the number of characters does not match.
An interesting fact, up to 1 * 2 * 3 * 5 * 7 * 11 = 2310 primes 343 = 7 3 without the number 1.
Why is the number 1 not prime?
Simple, but it has the property duality... Because of what counting 1, it makes no sense! Try to count part of a series of Fibonacci numbers 1,1 , 2,3,5,8,13,21,34,55. If you point your finger at each number once - there are two units, and do not count one unit - this is no longer counting.
The palm, like the crown of a tree, is a clear manifestation of the law of symmetry and asymmetry.
I heard "ours" are going on an interplanetary journey. The Martians will laugh. They will say: "Here are earthlings, they do not know why there are five fingers on the hand, but they are pinned to Mars."
2010 - 2014 Saransk G.P. Vetchinnikov
Thus, it is possible to mathematically prove a number of mathematical laws in the structure of the body. So if there was an Architect, then he used formulas.
And at the same time I took into account the unit 2 times.
That is why there are 5 fingers on the hand!
By the way, the question of why lower vertebrates have fewer fingers remains open.
But usually we have five fingers, because that is how many fingers were in the monkeys from which we descended, and the monkeys inherited five-toed limbs from their ancestors, and so on, up to the ancient amphibians that lived more than 300 million years ago. This is for those who believe in the theory of Evolution,.
Apparently, the common ancestor of all modern terrestrial vertebrates had five-toed limbs. In other words, the five-toed limb is a primitive, original limb structure for all terrestrial vertebrates. In most species, including humans, this structure has been preserved to this day.
Why did it happen?
SOME VERTEBRATES HAVE A DECREASE IN THE NUMBER OF FINGERS or even a complete loss of them, sometimes together with the limbs themselves. Usually this happened in those animals, which, for some reason, some fingers began to interfere, became "superfluous". For example, the ancestors of horses developed a large hoof on the middle toe, the toe itself increased greatly, and the rest of the fingers became unnecessary, they only interfered with the growth of the middle toe, and gradually disappeared. The ancestors of man, apparently, did not have such situations that some fingers became "superfluous". Therefore, they all survived.
The question, therefore, boils down to why the common ancestor of all modern terrestrial vertebrates had a five-toed limb. Scientists today believe that there was no special reason for this. The five-toed limb does not have any fundamental design advantages over the four- or six-fingered. Apparently, five-fingeredness was fixed in the evolution of vertebrates purely by chance.
Among the most ancient fossils of tetrapods, as paleontologists have found out, there were forms with a different number of toes: for example, ichthyosteg had seven toes on its hind legs (the front ones were not preserved), acanthosteg had eight toes on its front legs and at least the same number on its hind legs. ... The legs evolved from the fins of fish, the fingers from the rays of these fins, and the number of fin rays in those fish from which terrestrial vertebrates evolved was variable.
Apparently, in the most ancient terrestrial tetrapods, the number of toes also varied. It happened by chance that it was the five-toed forms that gave rise to the whole variety of modern tetrapods, and animals with a different number of fingers became extinct. But they died out, most likely, not because they had an unsuccessful number of fingers, but for some completely different reasons, in connection with some other, more significant "shortcomings" of their structure. In principle, it could well have been "lucky" not with five-fingered, but, say, seven-fingered ancient amphibians. And then, perhaps, people would now have seven fingers on their hands.
We need to be properly balanced in order for our body to function easily and correctly. For those born with extra fingers, things are not so easy. Nature has also tried to work on animals and insects: insects usually have 6 legs, and a spider has 8, and this is the right amount for them to exist normally. This is why the dog has exactly 4 legs, not 5, and so on. Many people believe that our number system is decimal precisely because we have 10 fingers. If we had 6 or 8 fingers, the system would probably change.
There is another interesting question. Do we really need all the fingers? The answer is no, or rather, not quite. Surprisingly, the most essential toes on the feet are large, they help to maintain balance. Some are convinced that all fingers are needed. On the hands, the thumb and forefinger are the most important. The rest are just helping, but the main manipulations are carried out by these two.
Would life become worse if six fingers developed on a person's hands?
An extra finger near the little finger would make some tasks easier. We could play more complex musical instruments, type faster, and grip objects more tightly. "A wider arm would make it easier to play basketball," says Cliff Tabin, a geneticist at Harvard Medical School who studies limb evolution in vertebrates. “But the fine motor skills of our hand are mainly the thumb and forefinger. An extra little finger wouldn’t have played a big role. ”
However, the greatest impact would be in the field of mathematics, and a different counting system would have surprisingly profound implications.
Counting man
All over the world, people count in dozens. Anthropologists believe that we owe this ten-digit counting system to the number of fingers on our hands. It seems natural to us, but this is only because we are used to it. If we had six fingers on each hand, we would definitely get used to the 12-digit system, Tebin is sure, while the numbers would be like this: 1, 2, 3, 4, 5, 6, 7, 8, 9, x, y, 10. "We would think that the 12-digit system is the simplest and most natural, and the 10-digit system would be as incomprehensible as the 14-digit system," says the scientist.
Perhaps there is not much difference how to count - tens or dozens, but Mark Shangizi thinks differently. The head of the laboratory for the study of properties of human perception at the research institute in Idaho, USA, believes that many human achievements, be it mathematics, speech or music, progress rapidly when human culture takes the most natural form of expression of this achievement.
“In my book The Revolution of Visual Perception, I argued that our ability to read so well is related to the shape of the letters, which in the process of cultural development began to look natural. Their shapes and curves can be seen in nature, and therefore they activate our visual object recognition mechanism, which allows us to read, explains Shangizi. - In my next work, I explained that we have the ability to understand speech due to the fact that, culturally, speech developed as something natural. That is, in its sound, the noise from solid objects can be traced, which could be heard in the habitats where we evolved. "
When culture uses evolutionary conditions and creates natural ways of doing things, we are doing great. When culture fails to engage human evolution, we undertake a new task uncertainly, unnaturally and pitifully, the scientist notes. For example, performing logical tasks is a classic case when we seem to be insufficiently adapted, since even the simplest concepts in logic are frankly complex and for really smart people.
Coming back to counting fingers, it should be noted that 12 fingers would significantly affect the mathematical ability of people. After all, the number 12 has many more factors than the number 10.
“The choice of counting system can affect reading as well. As a result, instead of reading letters that we are used to, we would have to read bar codes (and we would never be able to do it well, despite long training), ”explains Shangizi.
According to the scientist, it is difficult to say for sure whether the transition from a 10-digit system of counting to a 12-digit system would turn us into a person who counts. But it would surely be a major blow to our "digital technology", which makes the most of cultural evolution for our achievement.
The rule of thumb?
Extra toes sometimes appear as a birth defect. This is called "polydactyly" and is a common genetic error. But natural selection hasn't made these extra fingers permanent. Why not? According to Cliff Tabin, one more finger does not provide anything new, and therefore does not provide any evolutionary advantages on a global level. If we had developed a truly necessary sixth finger, it would probably grow out of the wrist as an extra thumb.
This is the standard model for the few tetrapods (tetrapods) inhabiting Earth, such as the panda, which have an extra thumb. It is actually an extension of the wrist bone used by pandas to support when grasping bamboo.
But Shangizi argues that humans could not have had an extra thumb. He developed a theory to explain the five-digit number of fingers on a limb in the animal kingdom, which he called the "law of finiteness." It is a simple mathematical formula derived from the rules for the number of nodes in computer networks, which provides the optimal number of limbs needed by the body to communicate with the outside world based on its size. The law states that when the limbs are very long relative to the body, there should ideally be six (for example, insects). With the shortening of the limbs, their number increases to large values (for example, millipedes). The law also suggests the number of toes required for a limb based on their size. Considering that they must be of the correct length to cover the palm, the optimal number of fingers for a person's hand is the number five.
"If we needed one more finger to perform newfangled tasks (typing, surgery, fanning, etc.), this would be a significant deviation from the optimal morphology for which our hands have evolved, namely, grabbing various objects." - explains Shangizi.
Some neurologists agree that six fingers are too many. V
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