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.

Limits of Mathamatics

By limits of mathematics I do not mean the limits of achievements to mathematics by indulging on current achievements. This may be limitless. I refer to physical phenomena that is interpreted by mathematics.

Even here there may be limitless achievements based on current achievements. I refer here some new phenomena  independent of all phenomena currently known. Currently known mathematics will never lead you to a new phenomena currently unknown.

Reason for this is maths is a tool and not an end. When basic parameters are given using mathematics we will be able to make more achievements. But there will be a limit. It can't predict other independent phenomena but it will be able to predict phenomena where there is a connection.

Improvement from integers to decimal numbers.
From basic arithmetic to calculus.
World is flat to a globe.
All planets rotate around earth to sun.
Quantum Theory.
Schrödinger Cat
delayed choice quantum eraser

1+1=2 (one plus one equals two)

How do you know that 1+1=2 (one plus one equals two)?

This is a proposition about essence. It is abstract. It exists in thought or as an idea but does not have a physical or concrete existence - meaning or abstract. It is an eternal truth.

Those truths are always called "eternal truths." The gist of the argument is that truths are part of the contents of minds, and that an eternal truth must be part of the content of an eternal mind. There is already an argument not unlike this in Plato where deduces immortality from the eternity of the ideas. But in Leibniz the argument is more developed. He holds that the ultimate reason for contingent truths must be found in necessary truths - The History of Western Philosophy by Bertrand Russell.

When we see two apples we think they have similar qualities, even though each will have a slightly different shape. It cannot be said apple A is exact replica of apple B. In the physical world no two things are the same. Take for instance two hydrogen atoms, they may have different distortions when they strike the container they are in, though these distortions may reduce with time they may not fully disappear for ever. At least at the time the notion 1+1 = 2 appeared in the domains of mathematicians, they were unable to go the the depth of hydrogen atoms but apples are a good example for defining two. Notion of two came about humans seeing similar things. Seeing sheep in a heard, or seeing everyone have two eyes, hands and legs etc build up the concept of two.

Therefore two was not entirely a mental concept. After observing lot of physical things this concept was built in our brains. After the concept was built we do not need the physical things to substantiate it. Like what Wittgenstein said in Tractatus -  My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them - as steps - to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright. Then the concept becomes purely mental. The propositions are the ones explaining about similar things, existence of it, it's properties, why we treat certain things as similar things etc.  It is an eternal truth.

Construction of the human brain has a special ability to group things. Because of this ability we can separate groups of things which has similar attributes. Here it should be noted that all of the attributes need not match. A percentage is sufficient. This percentage is not a well defined thing. It depends on the brain. Two individuals may differ. Usually, we accept that two things are similar when most of the human brains agree that properties of both are sufficiently same.

Strangely enough 1+1 = 2 concept will not be complete without 3, 4 and 5 so on. This can be explained why an orange and a lemon are not grouped as the same type of fruit. Orange and lemon will have some attributes that are similar, but we won't say they are the same fruit. The reason is when we look at a heap of oranges we know that the attributes shown by the orange is different than a lemon. To make this distinction we will need more than two oranges.

Problems of Quantum theory:

• Two different properties of a particle cannot be measured independently.
• Errors of measuring properties depend on probabilities. Unlike in classical physics where these probabilities only depend on measuring instruments, in Quantum theory they depend on measuring of other properties.
•  Measuring of one particle automatically decide the value of other particle.
• Behaves in different ways depending on ability to observer the particle.
• Local Realism -  having a preexisting value before a measurement is done.
• Realism - the world is independent of mind. 
• Radioactive decay.

No one is worried about 1+1 = 2 not having 100% link to the physical world - people have thrown out the ladder long ago. But worried about quantum theory - people have yet to start throwing out the ladder.

Errors in Physics

Take a postulate in geomatry, say similar trangles postulate. Practically it may be proved that 99.99% acculately tested. The thing is measuring errors will be limited to a value below a certain figure.
In quantum theory there are also errors but then the errors are probabilistic. Errores may go above any predified limit.