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.

Why world is not imaginary

Suppose there is a mountain and then there are people who sees the mountain. Each one who sees the mountain has a mental picture of the mountain in their brain. This can be represented by a set of data. Each one who sees the mountain will have a set of data. Mostly each of these data sets will be different. Further if one observer moves the set of data will change.

Then suppose that there is no mountain but only different data sets in the brains of each observer. When the observer moves the movement data is used in calculating a new data set continuously. All the data in these sets will be enormous.

Then consider the mountain is real and it's location, size and other details are given by a data set. Then also the location and movement of each observer is given by data sets. All this data will be a finite number.

When you consider the two options, imaginary mountain needs a large amount of data compared with the existence of a real mountain.

Therefore on the theory of minimizing data mountain should exist outside the imagination of the observer. Further it can be assumed that the world is real and not imaginary inside the observers brain.

Why Quantum theory instead of Classical Theory?
Using randomness uses less data than the Classical theory?
If so it will be proof why the world is Quantum.
If wave particle duality consumes less data than either waves or particles, that will be a good enough proof why duality exists.
If we can prove that if wave remains after observation need more data than becoming a particle that will be a good enough proof about the wave particle duality.

Human Brain and Quantum Theory

Lot of philosophers have said that God is the super mind. Each human being have a mind. All these minds are different. And at the same time all these minds have lot of similarities. If we create the super mind with all the good qualities of all of humans we get a super mind - this is one of the interpretation of God.

This human super mind has to be different that of a lion or any other animal. Lions vision is catered to find a pray. This shows that the makeup of a lions brain is very different of humans. The male lion kills the cubs not sired by him, then the mother of the cubs willingly cohabit with it's cub killer. This behavior is nonexistent in humans. So configuration of brains of lions and humans are very different. God of lions will be different from God of humans.

The world is perceived by our brains. When we define the qualities and attributes of the world around us, we assume that we can do a good job doing it independent of our brains. This is a mistake. It is evident from the discoveries of quantum theory and connected subjects of physics.

For instance 1+1 = 2 or A and B is true if and only if A is true and B is true, these are eternal truths according to our brain. What if we are wrong! What if these are just constructs of our brains. suppose someone has a gut feeling that 1+1 is not 2. Then we say that he is a lunatic. We have a group of people who has a gut feeling that 1+1 = 2. These are the normal people, these are the scientists and so on.

These normal people cannot comprehend how two distant particles can be entangled in such a way when qualities of one is derived the distant other half derives the opposite. When it is observed entities behave like particles and when unobserved behaves like waves.

The classical theories that can be comprehended by our brains cannot explain these pronominal.

If at some stage we can come up with a theory that could explain these effects then we can put in our basket of understanding our environment, what is happening. Sometimes it may not be possible. At the time when people considered the earth is flat not a globe they could not comprehend certain phenomena. They could not in the beginning understand that world is a globe even after someone explained it. In this way gradually people started believing earth is a globe. Now if someone say it is flat he will be considered as a lunatic

Similarly try to explain the properties of a torus to a two dimensional creature. If the torus is vertical and cut by a horizontal plane we get only two circles. Suppose the torus is horizontal the the circles will be one inside the other. If the torus is slanted the circles will not have the same center. This is what a two dimensional creature will see. In no way you will be able to explain to this two dimensional creature, what a torus is. But there is a certain tool where it can be done. It is mathematics! Using a algebraic equation of a torus, a two dimensional creature will be able to know it's properties. In this way using mathematics we have come to know most of the intricate details of our surroundings. But we can never be able to know all the details. When a new theory in physics is formed we come to know certain details. But we miss a lot.

Binary theory of space time

Heisenberg Uncertainty Principle is a derivation of a larger principal which says when information is available in a certain event the behavior of the participants are modified.

Traveling of a wave or particle can be seen as a transmission of information from one location to another. Even location can be considered as information, then traveling is change of information.

A particle is at a certain location at a certain time is information. This applies even to a wave. The difference is, a wave gives lesser amount of information.

We may be able to visualize the universe not as a system where waves and particles are located at a certain instant, but as a system of information only.

Waves and particles are a convenience given to us by our senses.

All information of the universe can be represented by a binary map meaning that all information of the universe in an instant can be given by a binary number. After any change in the next instant it can be shown by a different binary number.

Another thing change from one instant to another instant only one binary can change, multiple binaries cannot change. This may be treated as a definition at the moment, until it is proved why it has to be so.

Flow of time is a series of changes in the binary number. We do not need a different definition for time, outside this binary number, since we treat change of universe is a basic attribute and change of one binary as the basic change. The larger the binary number the smaller the change becomes. The size of the binary number is limited by the size of the universe. It should be noted that this binary number incorporates all particles of the universe as well as all waves, visible matter, dark matter and even dark energy.

This binary number is finite, at the moment it is accepted that the universe is finite, therefore it is compatible to treat this number as finite.

 Unfortunately this binary number will explain only the classical physics, quantum theory and uncertancy principal need modifications to zeros and ones. It may be necessary to be replaced by a probability function.

Further, to incorporate principal of causality, we need to connect in some way, or link two or more locations of zeros and ones.

Observer of universe

Intelligence, knowledge will not occur without an observer. Try to visualise a system of events without an outside observer. There will be no meaning in such a system if each element of the system were to analyse it's own experience and come to conclusions about the environment as a whole.Even if each element advertise it's own experience, you will need other elements to do the advertising - like photons, the problem is these advertising elements are also part of the system and there should exist a method to analyze the actions of these advertisers. On the other side, each element needs to know the whole universe which don't look very practical.

A better method is to have outside observers independent of the system to observe the happening of the elements.

This system will have elements which will be basic building blocks where action will be performed. Then there will be massage carriers that are independent of elements. Then there will be observers.
You can draw a parallel with a drama or a play. There will be actors who perform, then there is a medium that carry the message to the ordinance, and there is an ordinance that enjoys the play. The actors being human, cannot be barred from also being ordinance, but, ideally they should not.

The actors, ordinance and medium need to be independent. But like in a play they may be fused together. For instance message carriers - usually photons, are also elements, but the don't have a dual responsibility. When they carry massages the will cease to be elements. Most of the problems arise in a system when responsibilities are fused together. A good example is light signals in special relativity. They are the messenger but they are also elements.

Observer will have a memory that will record the events the elements played out. Then it will have the ability to identify symmetries in these records and compress the data. This will help it to use this compressed data to find out further symmetries and make more compressions. This compression and its symmetries are the knowledge. These compressions and symmetries are embedded in our brains are called knowledge. The more the person is able to find symmetries, the more knowledge he will have.

Memory alone in the brain will not constitute knowledge, when it is able to find symmetries of the memory and compress the data, finding more links in the data, it's knowledge will increase.

There is another twist in the observer. The scientific knowledge or universal knowledge happens when all the observers merge into one universal observer. This will give universal facts that everyone accepts.

Observer gives meaning to the system. Without him the system is just a random  set of events. Observer will find the patterns and the meaning of the system.
Observer can poke the system to obtain desired effects. This is seen in a play when the audience claps.

Observer may poke a system to get a response. There will be no difference between elements themselves doing something or observer poking the system. The difference will be observer can use the knowledge that he poked the system. This is casualty.

There are two kinds of observers, passive and active. Astronomy observers are passive they are unable to participate in astronomical events like birth of a supernova. An observer working in a lab say an particle accelerator will be actively poking on the elements being experimented.

The passive observer cannot guarantee casualty of events.
Active observer can state an event was caused by him. He will have empirical evidence that if he did not act the event will not take place.

We cannot ignore the observer and interpret the happening of events. Special relativity is a case where the influence of the observer is embedded in the theory itself that try to interpret events of moving frames.

The passive observer experiences while active observer experiments.

Racism and nationalism

Original sin, born with a baggage.
Why we need our culture? Can't you live without it? Why do we need our origin?