Recently passed away Fields Medalist Vladimir Voevodksy gave an interview center about his "spiritual" experiences, namely encounters with "supradimensional" beings very similar to those one can meet on DMT.

Here is the first part:

https://www.math.cinvestav.mx/~mostovoy/Papers/voevodsky.htm...

In the second part, he delves into the topic of synchronicities, and his attempt to base them on a mathematical foundation:

https://www.math.cinvestav.mx/~mostovoy/Papers/voevodsky/voe...

First I'll say something about a very general idea that I had a hard time accepting; however, based on the experience of the last five years, I cannot invent anything else. Around us there are non-human consciences. By the word "consciousness" I mean a computer system with memory, motivations, and the ability to shape the outside world and to plan. They are not "extraterrestrial" but genuinely terrestrial and, most likely, older than humans. These consciousnesses affect the lives of humans actively (and sometimes negatively).

The world of these consciousnesses is very complex, perhaps, comparable in complexity with the part of the world that we call "physical reality." I don't want to speculate on the structure of this world because, for this, I lack facts, observations. Even the simplest questions for me today do not have unequivocal answers. I am sure that these consciousnesses interact with humans; they almost certainly interact with higher animals. And how do they interact with lower animals? With inanimate matter? The logical considerations that must be satisfied by a global scheme of the world suggest that there must also be interaction. In this sense, they are also a part of "physical reality", only they are a part of which we know very little. This part of the world must be studied,

Of course, there were attempts at this type of study. Above all, at the end of the 19th century; but back then there weren't enough possibilities for that. Now, it seems to me, such a study can begin with the group of phenomena called synchronicity (or "synchronicity") by Jung. In simple words, they are the patterns (not natural from the point of view of existing models) in individual or collective behavior of humans.

Now, for the first time, there is a possibility of documenting these patterns (that is, recording them with apparatus) and beginning to study their structure. We have this possibility thanks to the existence of a gigantic number of recordings, both of human voices (for example, in interviews on the radio) and of human movements (for example, those recorded on security cameras). These data must be analyzed taking into account the time of the recording. I am almost certain that, in this way, patterns can be found in people's behavior that, on the one hand, are not explained by their conscious activity and, on the other, are too complex and too well defined in physical time as in order to be explained as individual subconscious.

Personally, I don't want to spend my time on this, although sometimes I feel an inner urge in this direction. I am very hopeful that there are people who will have both the access to the necessary data, as well as the courage and desire to dedicate themselves to this problem. This will be a true science. From here will begin the path towards a true understanding of the structure and the driving forces of the historical process and, later, of the global process of the evolution of life.

Here is a concrete idea: make a web page (for example, a LiveJournal page ) where anyone could leave a comment if a synchronicity happens, that is, while they listen to the radio or television thinking about their own thing and, suddenly, they hear a word that continues their thinking or answers a question they had on their mind. The main thing in a comment of this type should be the word or phrase heard. As additional information, the context of the thoughts, the time and the radio station or television channel may or may not be left. The most valuable cases in this regard occur at the time of turning on the radio and these cases should be noted.

My conjecture consists of the following: in the flow of words that we hear on the radio there are regularities in the appearance of certain words or certain groups of words linked by their meaning that depend on physical time (with precision of seconds) and that are not registered in the minds of those who speak these words. Afterwards, a good speech recognition software can be taken that matches the moments of time with the individual words and a database of the sequences of the exact times of pronunciation can be generated for each of the words that appear more frequently in synchro reports. Finally, we must look for the deviations from randomness in these sequences.

Now there is an entire field of mathematics called "pseudo-random sequence theory." They are sequences that, at first glance, appear random but are, in reality, highly predictable. We have a whole group here that is dedicated to them. So it is mathematically possible to find the existence of the hidden patterns.