Wittgenstein's language games and counting

In language games Wittgenstein takes counting very lightly. "We can picture that both the provider and the taker count by reciting the numbers 'one' to 'three' -- which are all the numbers in the tribe's language".

Counting most probably started counting sheep. To find out all sheep went out came in, knots on the rope or pebbles were compared to the number of sheep.

Though humans have 10 fingers it cannot be the start of counting because the five fingers are different. Two hands may be, but two is not enough to develop the counting concept.

To develop the counting concept you need to visually see number of similar items.

In developing number theory symmetry played a major role. Especially in division. After dividing by 2 it might have extended to 3 and so on.

Therefore a primitive language cannot have counting.

Original concepts of mathematics were created to mitigate the difficulties encountered by the brain in comprehending certain phenomena.

Maths is used keep track what brain cannot.

Language links the world to the brain. But not fully. (The main argument of Wittgenstein) certain things are not linked to language("cannot be said but can be shown")

Mathematics helps linking certain concepts to the brain.

Parts of maths is embedded in language. Symbols of one, two are examples. But the concepts of one and two beings to maths.

Million is nonsense to brain, but not to maths. When we think of million we can only think of the symbol of one and six zeros. We will also think people whom we know as millionaires. But like one or two, we cannot visually comprehend a million.

Mathematics and Time

A child was learning to count. He was saying, one, two, three, five, seven, four...It is obvious he was not doing it right, but it struck me that the order has a relation to time.
Counting, can happen without equal items like marbles. As the child did the order is time related. He was not counting something like marbles, from by heart, from his memory, he was reciting the numbers in order. He said "one" first, then "two", next "three", balance though he knew the words for the numbers, he couldn't remember the order properly.
This reflects a cardinal point! Counting is related to time. It is related to before and after.
First you have a set of labels, a set of names, say, first of all these labels do not have any meaning. One person gives an order for the labels. He recite the labels in that order. The others follow, and everyone learns to recite I the same order. That is counting. No equal items were involved.

Then counting had to be useful. Or else there's no difference between counting and a song.
When there are marbles, and while counting we will be putting marbles in to a box, we give meaning to the counting song.

Mathematics and sense perceptions

Suppose we do the following experiment. There are two marbles in a box and another two in another box. When we put the contents of two boxes to a different box. We know that there should be four marbles, but suppose we observe six marbles, instead of four.

Can we have a world with different mathematics, that can make this possible? Maybe! We think it is strange, but if it is the world order we can't do anything about it. We cannot prove it is wrong!

But, think without the box, each two marbles separated from each other, their are two groups, of two marbles. When they are brought together, in fact it should be four, can it be six ?

Now I am going to show that there is a world that this can happen. Replace the marbles with living cells, two marbles are male and the other two are female. When they are brought together we may have six. This can actually happen in a world consisting of living cells. The cells don't think it is strange. It is the world order for them. They will have a different mathematics.

So our mathematics is not independent of the world we live in. And on the other hand we can imagine that two plus two is four without the marbles, therefore mathematics is also not dependent of the world. It should be something outside, something dependent and independent of the world we live in.

Two plus two equals four, is not a quality of marbles, or any other physical object, though all physical objects reflects this property. It is a quality of the world. World is created in such a way to reflect this property. At creation it might have been different.

Normal languages interpret the world directly. Say when we see 100 marbles we instantly say "a lot of marbles".
But to be more precise, we use mathematics, and count the marbles. Then we say "one hundred marbles". The use of counting process is outside the perception part of our brain. IT uses a process learned by us - counting. The process counting has many parts. Symmetry, perception, time, memory, etc.

There are fields other than mathematics where extensive learning. Take the example of music. You need to learn to play an instrument. But anyone without any training can enjoy the music coming out of the instrument.

There is a fine distinction between algebra and geometry. We instantly see the symmetries of a geometrical shape. the number 100, cannot be comprehended without counting, further, the person who counts need to know the prices of counting. In algebra we assign x=100 and y=50, without knowledge of algebra, you cannot understand head or tails of what is being done.

Mathematics first used the digits of the hands. It expanded with writing on paper or other mediums. Then it expanded with tools like abacus. Then various mechanical calculating machines were developed. Then came log tables and slide ruler. More recent developments are electronic calculator and the computer. Future development will be most probably the quantum computer.

Take for instance profession of a doctor. A doctor will know how to identify an illness, what medicines to give, how long it will take to heal and how it will heal. The patient will not understand any of these things he can only say what the symptoms are. We cannot say the doctors brain and the patients brain is the same. But hear most of the things the doctor can explain can be understood by the patient. Though the knowledge of the patient and the doctor is not the same, the knowledge can be passed on. No need to have a special training to the patient to understand what the doctor says.
(I am not sure this is the best example but) Take the example of a computer engineer - lot of maths is involved in making a computer, both software and hardware. He tries to explain to a customer, the specifications of the computer. He will of course not try to explain the inner architecture of the computer - the customer may not understand anything. He will explain the specifications like the speed of the processor etc. Customer actually may not know what is the meaning of the speed, but he may know faster the speed of the processor, the computer can do the calculations faster.
Compare the two brains of the engineer and customer. Without special training what is known by the engineer cannot be passed on to the customer.

Another aspect of passing of knowledge, in this case the customer trust the knowledge of the engineer. For instance of he buys the computer to his son, when he come home he will explain to the son what the engineer said. But in this case both the father and the son, don't understand fully what happens, but they will have partial knowledge about the specifications.

The passing of knowledge between father and son here is more near to the doctor and patient than the engineer and customer. The main difference here is the engineer knows a lot of mathematics unlike the doctor.

Does relationships in propositions are mathematical? Consider the relation A is whiter than B. What is the meaning "whiter" ? One method of answering this question is, take a unit of area. Count the number of white spots(tiny spots) and find the percentage of white spots to the total number of spots. A's percentage is higher than B's. This is how a computer will do it, counting the number of pixels from a picture taken by a camera. Human eye and brain does it. It should also employ such a method, though unknown to us. Brain has the capability of doing such things on the fly, the eye may be doing it even before the message goes tho the brain. This is true for a statement like A is shorter than B.

Most of our knowledge is stored in the brain as memory. Knowledge is the product of brain activity. It creates relationships between memories. A structure similar to a tree structure in a database is created by neurons of the brain.
Mathematics is a super structure created in the brain. It's structure is very different from normal knowledge. Example what the doctor knows about an illness. Knowledge that 2 + 2 = 4 should be stored in neurons very differently, to that of the concept "some apples are red".

Interestingly computers, calculators and mobile phones that are used as extension to our brains use mathematics as the main structure, and tries to create data storage and retrieval mechanisms as secondary structures. This is the main reason the fusion of the brain and modern computers is far apart. For instance the problems that computer solves are very difficult to be done manually, on the other hand it is very difficult to emulate what we do by a computer.

The next leap in technology will be production of computers that act in the same lines of human brain. Then there will be a smooth link between human and the computer. All current CPUs of computers depends on mathematics. New architecture need to be distant from this and find other ways. Quantum computers looks more similar to work of the brain, but we need to wait and see.

Symmetry repetition and mathematics

Thinking in brains is shown by animals in finding of food. Strategy, planning is evident in not only in humans but also in animals in finding food. Predators plan how to catch pray.

Symmetry and repetition encouraged humans to start counting.

Ability to count lead to more and more complex mathematical ideas.

Wittgenstein's language games and counting

In language games Wittgenstein takes counting very lightly. "We can picture that both the provider and the taker count by reciting the numbers 'one' to 'three' -- which are all the numbers in the tribe's language".

Counting most probably started counting sheep. To find out all sheep went out came in, knots on the rope or pebbles were compared to the number of sheep.

Though humans have 10 fingers it cannot be the start of counting because the five fingers are different. Two hands may be, but two is not enough to develop the counting concept.

To develop the counting concept you need to visually see number of similar items.

In developing number theory symmetry played a major role. Especially in division. After dividing by 2 it might have extended to 3 and so on.

Therefore a primitive language cannot have counting.

Original concepts of mathematics were created to mitigate the difficulties encountered by the brain in comprehending certain phenomena.

Maths is used keep track what brain cannot.

Language links the world to the brain. But not fully. (The main argument of Wittgenstein) certain things are not linked to language("cannot be said but can be shown")

Mathematics helps linking certain concepts to the brain.

Parts of maths is embedded in language. Symbols of one, two are examples. But the concepts of one and two beings to maths.

Million is nonsense to brain, but not to maths. When we think of million we can only think of the symbol of one and six zeros. We will also think people whom we know as millionaires. But like one or two, we cannot visually comprehend a million.

Living cell paradox

Sell replicating factory, had a paradox. The factory will be giving attributes to the product it is making. This is the meaning of making. The number of attributes of the product needs to be less than that of the factory. Therefore theoretically you cannot make a self replicating factory.
But each living cell does it. Therefore architecture of a cell should have something more than atoms that make the cell. This something is replicated from parent to child.
But catalyst of salt crystal helps in depositing more salt molecules.
Also dividing the DNA looks very similar.

A factory needs tools, instructions for the tools and raw materials. Suppose raw material is available at suitable locations. Instructions is just memory though limited, this also can be provided. In a self replicating factory, the tool need to make a copy of itself. Consider a pliers made out of some epoxy that harden with time. Can it make amount pliers from epoxy. But pliers alone will not be able to do it, someone out something had to do it. It is impossible to imagine how it can be done. We will go round and round in circles, but will not be able to find an answer.

A solution struck me.
1. The living cell was somehow created.
2. It has a unique configuration of atoms.
3. It has the capability of copying itself and creating more of itself.
4. All started from a single living cell therefore every cell have that configuration.
5. Some part or parts allow different attributes to be present. But a certain section is uniform to all living cells.
6. It cannot be thought that universe has many different types of living cells. It may be only one, or a few.
7. Humans will never be able to create such a self replicating factory.
8. Humans are a product of cell architecture.
9. Can they make another completely different type of factory that can replicate itself?
10. If it is so by now there should very different type of self replicating factories. But there exists only the living cell!

Point in Mathematics

There is a marked difference between a physical point and a abstract point. Physically there are no points, only approximation exist. Wittgenstein in Tractatus, said certain things can only be shown and cannot be said by language. In language when you refer a physical point, a whole lot is said about the logical point. Unlike the abstract point it may have a size,a color, it will show what lies outside the point, in the logical space true and false propositions that can be assumed etc. But abstract point is just a point nothing more and nothing less. It is just a concept. It do not being to the physical world.
The same goes to all geometrical shapes consisting of multiple points.
This can be said to all abstract geometrical shapes. These can be comprehended by pour brains only by approximation. Therefore it should apply to the languages that brain uses to think about these shapes.
Maths is the tool brain uses to comprehend approximations of these abstract shapes. Engineering uses applied maths to do all sorts of things with these shapes.