> Dear Alan,

> It is with great joy that I have accepted the invitation to write you a personal letter. Even in your scientific writings your presence as a person is very strong, which is unusual for a mathematician. The traces of your personal life and your dramas extend beyond the limits of your own personal circumstances to concern us all ...

> ...

> Perhaps the greatest catastrophe of anti-scientific computationalism can be seen in the recent theory of "The End of Theories". In a series of widely quoted articles, informaticians or managers of very large databases explain that: "Correlation supersedes causation, and science can advance even without coherent models, unified theories". In short, networked computers, bringing to light very extended correlations in huge databases, make it possible to predict and act, without the need to "understand": scientific intelligibility is an uncertain luxury that is subjective and outdated, and theories are fallible proposals. Data, especially in large quantities – tera-terabytes, Big Data – is objective, is a new form of the absolute, is individually exact, expressed in digits. Thus, they argue, the larger that databases become, the more that statistical regularities, brought to light by computers, can govern us without the need to understand the meaning of the correlations, to interpret them, and without the need for theories about them, for interpretations.

> Fortunately, mathematics allows us to demonstrate the absurdity of these claims: Cristian Calude and I have written an article about this. Precisely the immensity of data involved has allowed us to apply the theorems of Ramsey and Van der Waerden. These make it possible to show that, given any "regularity", or any correlation between sets of numbers, you can find a number p large enough, such that every set with at least p elements contains a regularity (or a correlation between numbers) with the same structure. Now, since this applies to every sufficiently large set (with at least p elements), this also applies when it is generated … by a random process. Indeed, we observe, almost all sets of fairly large numbers are algorithmically random (one can give a mathematical definition of them, in terms of incompressibility), i.e., the percentage of non-random tends to 0 as p goes to infinity. So, if you observe regularities in increasingly large databases, it is increasingly likely that the inserted data are due to chance, in other words are perfectly without meaning and do not allow prediction nor action.

> ...

"Letter to Alan Turing" – Giuseppe Longo (2018) [pdf]