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How can we prove that we don't live in the matrix?

matrix

...Probably everyone has seen this movie

And some people think that we really live in the matrix...

After the release of the film "The Matrix" and its sequels on the widescreen, many people wondered:and, really, do we all live in the matrix? How can we prove that this is not the case?

The main proof that we all do not live in the matrix is the fact that an infinite amount of data can be collected about the world in which we live (we will discuss how to do this later), i.e. this world is real.

Indeed, if we lived in a matrix, then the properties of this matrix, i.e., the virtual world in which we would be immersed, would have to be recorded on some medium that would obviously be finite in that other imaginary "real world". Otherwise, the creation of such a carrier would "take" the whole world, and this is identical to the fact that we would simply live in it, since it was all created for us, i.e., again, we do not live in the matrix.

Now back to the question of where to get the infinite amount of data about our world. Here, of course, it immediately comes to mind that they say so much is still unknown, and the more we learn, the more it turns out that we still have to learn… This is true, but an infinite amount of information about our world can be found in much more familiar "things". These are the numbers Pi and "Exponent". As you know, these numbers reflect the properties of our world and at the same time are irrational, i.e. they have infinitely many decimal places, which are not ordered in any way and are not repeated by any algorithm, which means that the record of their "exact" value contains an infinity of information.
Therefore, only these two numbers show us that in order to record the properties of our world, you need to have an infinite storage medium, and if you add all the other properties of all objects and phenomena observed in this world, then you can certainly not do less than infinity of bytes.
code
By the way, the numbers "Pi" and "Exponent", let's call it so, are "objectively" irrational, i.e. it does not matter in which number system we work and what units of measurement of physical quantities we use. In any of them these numbers will remain irrational (unlike, for example, the speed of light, Planck's constant, elementary charge, gravitational and other similar constants, for which you can always come up with such a system of measurement of units, in which they will be integers).
In relation to such a proof that we do not live in a matrix, we can make two logical (at first glance) observations: first, what prevents us from modeling our world using a supercomputer using only approximate values of the constants "Pi" and "Exponent", for example, with an accuracy of up to a million decimal places, this would not require a lot of memory? People somehow manage to model entire worlds in computer games using certain algorithms. Secondly, after all, people know a way by which you can calculate more and more decimal places in these constants to infinity, i.e., a supercomputer could probably do the same. We can't write the whole number "Pi" at once, but we can write it up to any specific number of decimal places.
The answer to both of these objections will be the same statement: "The fact is that in nature objectively, and independently of the will and the existence of man in general, and of what man can do and what he cannot do. There are real objects and processes that take place, which, among other things, are characterized by these 'objectively' irrational numbers". This means that in fact, there were, there are, and there will be processes and objects that have certain properties that are based on the "ready-made" numbers "Pi" and "Exponent" in all the fullness of the irrationality of these numbers, that is, on the basis of the "ready-made "numbers" Pi" and "Exponent". Such processes that "take into account" all the decimal places in these numbers, the entire infinity of these signs, and if at least one of these signs were different in these numbers, then it would be a different world, with different laws of nature.

The fact that the numbers "Pi" and "Exponent" can be calculated with any accuracy already in the modeling process does not suit nature, or rather it "does not care" about this fact, because it does not calculate anything, it exists, and is only characterized by these numbers. This is someone who would like to model our world would need these numbers, and if he wanted to fully simulate it, then he would need accurate and ready-made values of the numbers Pi and " Exponent", which require an infinity of information to write. Once again, the argument is not this, regardless of the fact that someone or we would seem to be able to model a world similar to ours using some methods and approximations (or calculated in the process). Of course, our world already contains an infinity of information that characterizes many processes occurring in it, since among other numbers that characterize them, there are "objective" irrational ones.

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