Passion for cars

Computer science and programming in particular are already inseparable from our lives. This is "our bread" and "our spectacle." They make our lives ... Easier? More difficult? Let us dwell on the fact that they make our lives. Computer science affects humanity like literature, philosophy, physics, and mathematics. Solving our problems with its help, we once again (as is the case with all the sciences, theories) describe life itself, its laws.

I do not want to make far-reaching conclusions, to breed empty demagogy. I will try to just hold, seemingly interesting, some parallels between the laws of informatics and the laws of the world in which we invented this informatics.

This text will even be a little humorous, but I think you will find some food for thought. Perhaps this is not the last text on this topic. Therefore, here we just remember a little Discrete Mathematics. The result of hard copulation of Mathematics and Logic, from which Information Technology will later grow ...
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They didn’t stint on toys for the newborn, and Uncle Turing presented the baby with a car. The boy grew up, studied the machine, developed.

Having learned to say at least something reasonable, the child told Uncle Turing and Uncle Church (and then us) that any intuitively computable function is partially computable, or, which is the same, can be computed by some Turing machine. Well, they said and said ...

And then McCulloch and Pitts proved mathematically rigorously that it is possible to build a network from neuron-like elements that can carry out any algorithmized computation. In other words, it was shown that, at least potentially, the brain is a universal computer capable of calculating (according to Church’s thesis) everything that is computable in an intuitive sense (in particular, computable using a Turing machine). On the other hand, the function of any nervous network can be (as practice shows) simulated using an appropriate computer program. This means that the brain is identical in its functionality to the Turing machine and can be evaluated only by quantitative parameters: memory size and speed (since all universal computers potentially have the same capabilities — they solve the same class of problems, known as algorithmically solvable problems). Those. the brain, by virtue of its device, is able to calculate any algorithmically computable functions, if it has enough memory and speed for that.

But let us return to the already grown-up child, to Discrete Mathematics. I do not know what offended his parents by him then, but in the letter that the teenager, leaving his father’s house, he passed on to Godel, and which Godel later gave out for his scientific work, it was written about the following: “Mom and Dad, in every rich enough a consistent first-order theory (in particular, in any non-contradictory theory including formal arithmetic), there exists a closed formula F such that neither F nor - | F are deducible in this theory. ” Gödel called it the “First Incompleteness Theorem”.

I have no idea how, but then they realized that in other words, in any sufficiently complex non-contradictory theory, there is an assertion that it is impossible neither to prove nor disprove by means of the theory itself. For example, such a statement can be added to the axiom system, leaving it consistent. Moreover, for a new theory (with an increased number of axioms) there will also be an unprovable and irrefutable assertion.

And all at once it became clear that the offended teenager hid in philosophy. I must say that it was just then that Diskrka met Religion and later often recalled how they painted the bullet by the fireplace for three of them. Then in 1931, Gödel would find in his diary a note on Discrete Mathematics about Religion: “ In any sufficiently rich, consistent first-order theory (in particular, in every non-contradictory theory, including formal arithmetic), the formula asserts the consistency of this theory is not deducible in it ” . Gödel called it the “Second Incompleteness Theorem”.

In other words, the consistency of a sufficiently rich theory cannot be proved by the means of this theory. However, it may well be that the consistency of one particular theory can be established by means of another, more powerful formal theory. But then the question arises about the consistency of this second theory, and so on.

This theorem has broad consequences both for mathematics and for philosophy, in particular, for ontology and the philosophy of science. Moreover, “the power of the set of true statements is greater than the power of the set of provable statements”. And if you translate from mathematical to human - there are infinitely many statements that are fundamentally impossible to prove, but which are nevertheless true! So is it possible to demand from believers evidence of the existence of God and, without receiving any, to assert that there is no God?

Passion for cars in the future at Discrete Mathematics grew into a serious occupation, one might say the young man was a real racer. He had several cars similar to the one that Uncle Turing had once given him. You should have seen these cars! I would not come close. But a brilliant young man, without exception, reached the finish line, no matter how difficult the track was! Do you understand now those very first words? “In a Turing machine, I will drive any track that humanity can ever build!” Sebastian Loeb "nervously smoked on the sidelines," when the Diskretka approached this machine. Yes, the Diskr was a famous racer!

George Cantor himself once boasted that he communicated with Discrete Mathematics about the uncountable set of all real numbers, the significant difference between infinite sets by their power, that is, by the number of elements contained in them. But in my opinion, and then the Discrete drive was chasing)!

This is the Discrete Mathematics was Informatics in his youth. Parents of techies and atheists, and he believed in God, fell in love with Religion, adored cars.


Further: "Without fools"