**Deterministic true random numbers?**

It may seem rather heretical to some if we claim that deterministic true random numbers exist. To answer this question, we need to analyze the constituent properties of true random numbers. Why the good PRGNs like MT19937 or XOshiro256** don't generate true random numbers? These PRNGs are algorithmic mathematical procedures that generate quite reasonable random numbers. However, they involve running through large periods, in the case of MT19937 even a very large period. Nonetheless, both inventors claim that these are equally distributed random numbers and that all possible values occur equally often after passing through the period. This fact alone indicates that they are not genuine random generators. True random numbers would have to follow the laws of probability even with the huge quantities of random numbers and the number per pattern would have to follow the normal distribution. In addition, statistically relevant deviations from probability can be found when analyzed closely.

The question of why deterministic random numbers can be true random numbers becomes interesting. Let's go back to the beginnings of "high-speed computation", to the contribution of John von Neumann at the symposium "Monte Carlo Method" from June 29, 30 and July 1, 1949. The section before the famous quote: "Any one who considers arithmetical methods ..." reads:

"We see then that we could build a physical instrument to feed random digits directly into a high-speed computing machine and could have control call for these numbers as needed. The objection to this procedure is the practical need for checking computations. If we suspect that a calculation is wrong, almost any reasonable check involves repeating something done before. At that point the introduction of new random numbers would be intolerable. I think that the direct use of a physical supply of random digits is absolutely inacceptable for this reason and for this reason alone. The next best thing would be to produce random digits by some physical mechanism and record them, letting the machine read them as needed. At this point we have maneuvered ourselves into using the weakest portion of presently designed machines - the reading organ. Whether or not this difficulty is an absolute one will depend on how clumsy the competing processes turn out to be."

We are firmly convinced that this statement is still valid today. The possibilities of storing and re-accessing physically generated random numbers have grown to an unimaginable extent. Nevertheless, there are still limits in this respect today.
The following example proves the untenability of the statement "Deterministic random numbers are automatically to be regarded as pseudo-random numbers": Using ID-Quantique's generator, during many weeks in 2008, we recorded two data files of 2000 gigabytes each. Since then, these files have been read out for various tests, as this is the only way to make repeatable calculations (in line with John von Neumann's statements) and, on the other hand, direct processing would be ineffective due to the low production rate.

It is indisputable that the random bits read from the physical random number generator deserve to be called "true random numbers". We now use these random numbers to perform a calculation that we call a "simulation generated with true random numbers". We save the random numbers in a file for later checking. According to the generally accepted theory, the random numbers saved in this way have now degenerated into pseudo-random numbers, since the saved "true random numbers" have now mutated into "deterministic random numbers" if we were to insist on applying the false rule that all deterministic random numbers are automatically pseudo-random numbers! There is no doubt that random numbers read from a file are deterministic random numbers. We would now have to call the first simulation "with true random numbers", while the second simulation is called "with pseudo-random numbers", even though the same sets of numbers were used twice.

This distinction contradicts the principles of science, because one must not automatically and incoherently make a statement of properties that are different in essence just to promote one's own marketing ideas. We would therefore make it clear that, in our opinion, there are "true random numbers" that have been generated using appropriate procedures in accordance with John von Neumann's maxim. These can exist both as non-deterministic or deterministic random numbers, the latter as stored values or as latently existing true random numbers.