How can we prove that we are not living in the matrix?

After the release of the movie "The Matrix" and its sequels on the wide screen, many people thought: do we really live in the matrix? How can you prove that this is really not the case?

The main proof that we all do not live in a 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 below), 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 storage, which would be obviously finite in that other imaginary "real world". Otherwise, it would have "taken" the whole world to create such a carrier, and this is identical to the fact that we simply would live in it, since it was all created for us, i.e. again, we do not live in a matrix.

Now let's return to the question of where to get the infinite amount of data about our world. Then, of course, it immediately comes to mind that there is so much still unknown, and the more we learn, the more it turns out to be learned ... It's true, but an infinite amount of information about our world can be found in much more familiar "things". These are Pi and Exponent numbers. 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 according to any algorithm, which means that the recording of their "exact" value contains infinity of information.

Therefore, at least these two numbers show us that in order to write down the properties of our world, we need to have an infinite storage of information, and if we add there all the other properties of all objects and phenomena observed in this world, then we will certainly need no less than infinity of bytes.

By the way, the numbers "Pi" and "Exponent", let's call it this way, are "objectively" irrational, i.e. no matter in which counting 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 whole numbers).

In relation to such a proof that we do not live in a matrix, two logical (at first glance) remarks can be made: first, what prevents us from simulating our world using a supercomputer using only the approximate values ​​of the constants "Pi" and "Exponent", for example, with a million decimal places, would it not take a lot of memory? People manage to somehow simulate entire worlds in computer games using some algorithms. And secondly, after all, people know the way by which you can calculate more and more decimal places in these constants ad infinitum, i.e. a supercomputer could surely do the same. We cannot write the whole number "Pi" at once, but we can write it down 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 it is objective, and independently of the will and the existence of a person in general, and of what a person can and cannot do, real objects exist and real processes, 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 with certain properties, which are based on the "ready-made" numbers "Pi" and "Exponent" in all the fullness of the irrationality of these numbers, i.e. processes that “take into account” all the decimal places in these numbers, all the infinity of these signs, and if at least one of these signs were different in these numbers, 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 process of modeling does not suit nature, or rather, nature "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 model it, he would need accurate and ready-made values ​​of the numbers "Pi" and "Exponent", which require infinity of information to record. But again, this is not the argument, no matter that we or someone seemingly can simulate a world similar to ours using some methods and approximate (or calculated in the process) values, our world already contains infinity information, which characterizes many of the processes occurring in it, since among other numbers that characterize them, there are "objectively" irrational ones.