Probabilistic Dragons

I am a new American and I am still interested in Russia. It s also interesting to my 12-year-old grandson Ivan, an old New Yorker. We both enjoy math, especially probability theory. This theory fairly well explain s the behavior of different things from tiny elementary particles to huge dragons generally the physics of our entire world.

The mathematics of quantum mechanics is unusual because it describes unusual physics. The Heisenberg Uncertainty Principle in quantum mechanics sets the limit of accuracy of the simultaneous determination of pairs of quantum observables characterizing the system, which is described by non-commutating operators (such as position and momentum, current and voltage, or electric and magnetic fields). This gives rise to some problems which can be eliminated in an unexpected way. Why not take the bull by the horns and do not apply the principles of quantum mechanics to integers?!

In fact, why are the integers the wors t of the other mathematical operators? Why and how are they integers? Is this not a beautiful and seemingly natural meaning only the maximum probability of the numbers? With what accuracy is one equal to one? And most importantly with what accuracy does zero equals zero?! Incidentally, this hypothesis allows extremely delicately removing the bad infinity in the pursuit of modern physics, which typically eliminates renormalization and other tricks.

I often think about the probability of zero. And about probabilistic dragons now everyone has heard, especially the Russians. They even do not need to read brilliant Stanislaw Lem, who developed the theory of probabilistic dragons, and so they know in practice that these monsters are virtually real!

By the way, it is necessary to clarify: virtuality now somehow become synonymous with improbabilities, whereas the situation is exactly the opposite and virtualis in medieval Latin means possible. This object or state that does not really exist, but may occur under certain conditions. The word virtual takes the origins by vir (Lat. man). And the Romans formed from this word another virtus , which was used to denote the set of all the excellent qualities of men (physical strength, heroic behavior, moral virtue).

But in Russia, all these concepts are not very popular, so we d best talk about probability, the more so because my grandson is just studying it in school. And to the question, what is chance of meeting a dragon at the exit to the street; this young dogmatist looked at me with youthful excellence and replied that, of course, it is very close to zero. And was very surprised when I told him that he was a pessimist, not entrusting his judgments to common sense, and that this probability is 50%:

Either you meet a dragon or you do not.

Here intervened my six-year-old granddaughter, a first-grader. The girl is extremely intelligent, but she has encountered zero only in conjunction with the unit a ten, a hundred, a thousand. It was of interest: if the probability of a dragon almost zero, then how many zero dragons need to get half of a dragon?

I had to deal with her arithmetic. The fact that zero plus zero is zero, she knew. And that zero minus zero is zero, she also realized. The multiplication of zero by zero is also not difficult. But division caused a problem.

Zero! Stated the emphatically dogmatic grandson.

The girl was thoughtfully silent and I played up to her:

It depends on what size zero and showed two ringlet with my fingers, one larger and one smaller.

If the zero above is even for just a little larger, what happens?

Grandson thought, and then said in surprise:

Infinity?!

Well, yes. And what if it s the opposite case?

The result will approach zero?

Good for you! Only in extremely rare cases, when the zeros are equal, what will happen?

Zero! Joyfully exclaimed my grandson. Granddaughter again wisely said nothing.

Are you sure? Lidia, what is one hundred divided by one hundred?

One!

Hmm. But the number one hundred and contains two zeros. Then how much will be ten divided by ten?

One!

‑ And one-by-one?

Grandson was shocked, silent, and thoughtful. Then he said:

‑ But zero is nothing! How to get a one out of nothing?

Really how did one appear from zero, and even as in Russia ‑ with 143 million zeros? How would Russia answer this question?