Rule forming and custom

Wittgenstein grammatical and material propositions. Rule forming and customs.

Is it that we cannot imagine anything new in our minds that are byproducts of our earlier thoughts plus material inputs from our senses.

Take for instance the discovery of benzene structure and the dream of Kekule, a snake eating its tail and atoms dancing in a ring. There is nothing new here, all are everyday happenings. Only thing is a new concept was formed using some old concepts.

What about Archimedes theorem? It was not a random finding. Ancient Greeks saw the relationship of 3, 4 and 5 satisfying the theorem. Like 2 apples plus 2 apples gives 4, they formed the rule 2+2=4.

But is it not possible to have a completely random form become a rule that everyone follows? The problem is this rule should be directed to some physical thing, only then it will be cemented as a rule accepted by everyone. Therefore all mathematics started somewhere physical, two or more rules created new rules and so on.

Is thinking only limited to this? What will be like if align comes to our world and say something completely align. Can we understand it. In a way it is better the don't come - so much of conflicts in the world where it is possible to communicate meaningfully, think of the chaos that can be created. Maybe that is why we don't find them - SETI program has failed.

So what is knowledge? Is it all inputs from environment thorough our senses, from birth, and creating links - concepts, to these inputs?

So we cannot have crazy ideas at all, we can have only known ideas or a mix of them.

This is very evident if you think of a computer. All what we get, is, what we put in, no more, no less. A sudden demon won't spring up from it, this we are certain. Our brain is not much different from a computer. Computer is a calculator it odd the same with our brain.

I should say something about art and music. What about these, aren't they create new things. We will not term as art or music anything newly created. We call it noise, visual or acoustical. If we cannot find patterns, it is noise. If we find patterns, then it is related to our earlier thoughts. Then we have art and music.

Our brain is an instrument smart in finding patterns. Much smarter than all current computers. It might change with the invention of quantum computers.

If this theory is accepted as correct, it will have far reaching consequences. A cyclone cannot create an aircraft. Random movements cannot create something very organised and structured. In the same way life cannot be created by random movement of atoms. Then this begs the question was there a beginning in the universe?

Sometimes what is wrong with everything like the conflict that can arise with this theory and big bang is because of our upstanding of time. We take for grant what we think of time without much thought. Suppose time is very different, and there was no beginning then it confirms this theory. Humanity in earth or life on earth can end with an astronomical action. Therefore life should exist in other places.

Symmetry Music and Maths

Music is not a universal factor it is specifically human. Even among humans it varies. For instance there are some who don't like music, some who can't play any music instrument how much effort put into it. Then some don't need even to learn, it comes naturally to them. Animals can't make head or tails of our music, but they have their own music, like dolphins or whales. Therefore without our ears and brain there will be no music.

There are lot of similarities with music and symmetry.

Symmetry it's an essential part of mathematics.  Most geometry is based on this. Even the number line is based on symmetry. E.g. positive and negative numbers. Then all series, need some form of symmetry. These are foundations of mathematics.

But is symmetry a universal factor, independent from man? It is true that symmetrical objects are present in nature. But are they truly symmetrical? Or approximately symmetrical? Salt crystals are symmetrical but atoms vibrate we need absolute zero temperature to stop the vibrations. But the universe is not absolute zero. And further it is impossible to have fixed coordinates.

Therefore, humans take naturally occurring forms which are approximations and create abstract forms that are symmetric.

Suppose there was no electromagnetic forces in the universe, then there can't be rigid bodies. Without rigid bodies hire can we have salt crystals, or rulers to measure distance? Therefore without electromagnetism we cannot imagine symmetry. Then we can say mathematics depends on electromagnetism. Chicken and egg situation, regarding mathematics and physics.

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.

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.

Problem off 100 marbles in a box

How can you say their are 100 marbles in the box? It involves someone counting and then saying that their are 100 marbles. How reliable that person is? Is he capable of counting? Did he make a mistake? Is he truthful? Did we hear clearly when he pronounce the result? Well the questions can be endless. Suppose we are going to employ a machine to do it. Is the machine reliable? Due to wear and tear it may not give the correct result. The same countless questions can be asked.
So how can we know the number of marbles in the box?
The truth is we can never know definitely. We can only get a probable result.

When the concept of color is formed in the human brain, say dark red and light red, these concepts are formed in the brain, and will be different from individual to individual.
Contrast this with the number 106, the human brain do not form a concept.(here again it should be said this is the normal case, but a brain excellent in maths will have more concepts than a normal person. Sometimes looking at 100 marbles arranged in 10 x10 rows will instantly recognize it. Sometimes there may be smart people who can identify 106  unarranged marbles instantly.)

The conclusion we can come to is maths is there to do a fine tuning our understanding.

Because of mathematics capacity of brain had increased immensely. We can go into details of our environment that is impossible for the brain to comprehend.

When you see 7 marbles human brain can distinguish it is different from 8 marbles. Even when randomly arranged it will be able to visually separate to 5 and 2 or 5 and 3. But it won't be able to distinguish 96 and 97 randomly arranged marbles. Though there is no sharp boundary, when the numbers get large it gets increasingly difficult to comprehend. Mathematics is the tool we use to understand large numbers.

Wittgenstein criticise the proposition 'there are two apples on the table' but it is possible to picture it by the brain. But it can't picture 'there is one million in my bank account'.

Human brain cannot keep time - this is obvious. It needs a tool and mathematics.

Then regarding mass it is the same, but have some ability in evaluating weight. Lifting heavy and light objects human brain can compare.

Distance, brain can get some idea, but to measure accurately you need a tool and mathematics.

The situation becomes more complicated when very small measurements are made, quantum theory need to fine tune mathematics.

Measurements disturbs the environment. Therefore what we get is not a measurement of the environment, but an approximation. When measuring a length the mark of the ruler has some width, without that width we are unable to see the mark therefore it is impossible to get the exact measurement. Heisenberg uncertainty principal gives the limit of accuracy in certain measurements.The reason for this limit is not because of shortcomings of the measuring apparatus but due to the structure of the world itself.It is impossible to separate world and the observer. Recent findings show that traveling photos and electrons behaves like a wave when no observer is present and behaves like particles when observed.