Vladimir Voevodsky interview

Vladimir Voevodsky interview

=== Part I (translation of http://baaltii1.livejournal.com/198675.html)
This is an interview with mathematician Vladimir Voevodsky. Normally interviews with scientists are about the formalities of their research that are almost obvious without Q&A sessions, with matters that are actually interesting and important being left out. Vladimir Voevodsky is a Fields Medal laureatte, a full professor at the Institute for Advanced Study in Princeton, creator of motivic homotopy theory and univalent foundation of mathematics. We'll talk not only about mathematics, but about life as a whole and many things that are normally not disccuseed, at least in scientific circles.

We started this discusion in Princeton, walking around and enjoying the beautful sunset. It looked like this conversation might be of interest to many people, mathematitcians or anyone on their life journey.

- Next academic year at the Institute for Advanced study is mostly devoted to the univalent foundations of mathematics. You appear to be the founder of this branch of mathematics. But at the same time, your primary achievements that brought you acknowledgement and fame, are related to a completely different area: algebraic geomerty, motivic cohomology. As you put it on your website, you devoted about 20 years to it and no longer interested in it. Did you radically change research area?

It's a rhetorical question...

- Proof of Milnor's conjecture (https://en.wikipedia.org/wiki/Milnor_conjecture) is the most well known of your results. You did it in 1996. What happened after that? How did your scientific interests change in the following years?

First of all, it was important to prove the generalization of this conjecture, which is today known as Bloch-Kato conjecture (https://en.wikipedia.org/wiki/Norm_residue_isomorphism_theorem). I formulated basic ideas of this proof in late 1996, about the same time when I completed the full proof of Milner conjecture. But the approach that I used to prove Bloch-Kato conjecture had some problems. First, it depended on a special conjecture, a generalization of Markus Rost's results (https://en.wikipedia.org/wiki/Markus_Rost). Second, it depended on development of more advanced concepts in motive theory than the ones required to prove Milner's conjecture. It was obvious that Markus most likely could do the first part, and I would have to do the second. In the end, the first part was completed in 2007 or 2008 by Suslin (https://en.wikipedia.org/wiki/Andrei_Suslin), Joukhovitski (https://www.linkedin.com/in/sevajoukhovitski) and Weibel (https://en.wikipedia.org/wiki/Charles_Weibel), and was based on earlier Markus work. I finished preliminary work and the proof only in February, 2010.

It was very difficult. In the essence, it was 10 years of routine work on a problem that I was not interested in during 5 of those 10 years. It was pulled almost only with the willpower.

In the fall 1997 I realized that I have already made my main contribution to motive theory and motivic cohomology. Since then I started looking actively and consciously. I looked for a problem I would devote myself to, when I fulfill my obligations with Bloch-Kato conjecture. I soon realized that if I want to achieve something truly important, I need to utilize knowledge and experience in math that I had. On the other side, seeing trends in mathematics as a science I realized that the times come when proving yet another conjecture wouldn't change a lot. I sensed that mathematics is on the verge of crisis, even two crises. The first is related to the gap between pure and applied mathematics. Obviously, sooner or later the society will rise a question why it should spend money on people busy in areas that don't have any kind of immediate practical application. The second, less obvious crisis, is related to pure math becoming more complex, which sooner or later will make publications too complex for a thorough review, leading to accumulation of unnoticed errors in math. And since math is a very rigorous science, where results of a single publication usually depend on results of many earlier works, error accumulation is extremely dangerous for math.

So I decided I should try to do something that will help prevent these crises. In the first case it meant that I needed to find a practical problem that would require pure math methods developed during last years or decades to be solved.

I was interested in natural sciences since I was a child (physics, chemistry, biology), and I was also interested in programming languages theory, and since 1997 I have read a lot about these areas, and even took a few courses for students and postgraduates. In fact, I refreshed and deepend the knowledge I had considerably. All this time I was looking for new problems in these areas that would be interesting to me and where I could apply modern mathematics.

В результате я выбрал, как сейчас понимаю неправильно, проблему восстановления истории популяций по их современной генетической композиции. Я провозился с этой задачей в общей сложности около двух лет и в конце концов, уже в 2009 году, понял, что то, что я придумывал, бесполезно. В моей жизни, пока, это была, пожалуй, самая большая научная неудача. Очень много работы было вложено в проект, который полностью провалился. Какая-то польза, конечно, все-таки, была -  я выучил много из теории вероятности, которую знал плохо, а также узнал много нового про демографию и демографическую историю.

In the end I have made a choice, a wrong one from today's perspective, the problem of populations history reconstruction by their modern genetic composition. I've spent about two years on this problem and finally in 2009, I realized, that what I was working on was useless. So far, it was the biggest scientific failure in my life. I've put a lot of effort in this project, which completely failed. There was some profit from it - I've learnt a lot in probability theory, which I knew knew poorly, and learnt a lot about demographics and demographic history.

At the same time I was looking for an approach to solve the problem of accumulating errors in pure math. It was obvious that the only solution was creating a language that would allow writing mathematical proofs in a form that could be verified by a computer. Until 2005 I believed that this poblem is much more difficult than the one about historical genetics that I was working on. Mostly, this feeling was due to an established and very popular option among mathematicians that abstract math is impossible to formalize in some sane form carefully enough for a computer to understand.

In 2005 I managed to formulate several ideas that surprisingly opened a new approach to one of primary problems in modern mathematics foundations. One can formulate this problem informally as a question: how to correctly formalize intuitive understanding that "similar" mathematical objects have same properties. Arguments based on this principle are very often used in modern math proofs, but existing foundaions of mathematics (Zermelo-Fraenkel set theory (https://en.wikipedia.org/wiki/Set_theory)) are completely useless for such arguments formalization.

I was familiar with this problem and thought about it back in 1989, when Misha Kapranov (http://www.math.toronto.edu/kapranov/) and I worked on polycategory theory. Back then, we thought it was impossible to sovle it. Things that I realized in 2005, integrating ideas from homotopy theory (https://en.wikipedia.org/wiki/Homotopy, branch of modern topology) and type theory (part of modern programming languages theory) was astonishing, and opened real opportunities for building the language for people to write proofs in to be then checked by a computer. After that there was a long break in my mathematical activity. I wasn't doing math since June 2006 up to November 2007. We will discuss what was happening to me during that time later in the interview. Today these events often remind me of "Definitely Maybe" novel by Arkady and Boris Strugatsky (https://en.wikipedia.org/wiki/Definitely_Maybe_(novel)). I returned to math in late 2007. I worked periodically switching between my ideas about genetic history and completing set of work to prove Bloch-Kato conjecture. I returned to ideas about computer proof verification only on summer 2009, when it became clear, that I won't make progress in historical genetics. And just in a few motnhs there were two events that advanced these ideas from being drafts (I thought I would have to work on them a few years) to the point where I could say that I came up with new foundations of mathematics, that would allow to solve problem of computer proof verification. Today it's called "univalent foundations of mathematics", with both mathematicians and programming languages theorists being involved in its development. I'm almost sure these foundations will soon replace set theory and that the problem of abstract math language comprehensible for computers will be mostly solved.

- How are these ideas received by modern mathematical community, especially by category, logic, homotopy specialists? Are there people among professional mathematicians ready for serious commitment to univalent foundations development?

Very differently. I've found many allies, and their number is growing. Of course it's quite difficult for logic and math foundations specialists because what I offer will upstage classic logic and set theory.

- Is it true that what you are now trying to do is to make computers understand what is categorial and homotopical intuition, on which many modern math constructions are based?

No, that's not the case. It was the first step and it was completed in the fall 2009. It's mostly technical work on improving the language itself that is currently in progress. First examples of languages family that I work with were created in the late 70s, they are known as "Martin-Lof type theories". Surprisingly, these languages existed, programming systems using them languages were developed and even became popular (especially Coq assistant developed in France), but there was no understanding what all these languages allow to express. It just so happened that only a tiny fraction of language was used, the one that allows reasoning about sets. But the language as a whole allows reasoning about homotopic types of any complexity. That makes a huge difference. As a consequence, these languages were not developing much, just because it wasn't obvious what should be changed. Now that we realize what's the most important in these languages, there are opportunities to make them much more powerful and practical.

- In your opinion when will computers be able to verify your proof of Milner's conjecture?

If you just task yourself with writing a formal variant of the proof using the Coq, already existing system for formal proofs verifications, then I guess it's possible to accomplish it in 3-4 years. I'm not planing to do it because I find it more important and interesting to develop a new formal proof system that would take into account univalent semantics and this new vision of "meaning" of type theory languages offered by univalent semantiscs. But I'm completely unaware about how much time this would take.

- About two years ago there was a conference in St. Petersburg about general scientific problems. You spoke there and you told that "What we call Russian science crisis is not a crisis only in Russia, it is a crisis in science all over the world. The actual progress will come from a seriuous fight with religion, which will end in the two combining together." I'll admit that when I read this I was laughing because someone expressed something deep and not related to politics-finance-economics, but something really important. But this statement still remains confusing to many people. You are the person that grew up in materialistic paradigm with a proper ideology, aesthetics, moral. You actually belong to soviet intelligentsia class (https://en.wikipedia.org/wiki/Intelligentsia) who did an excellent scientific career. According to the stereotype, there is no place for religion and mysticism in life of a person like you. And still you openly talk about integration of religion and science, you have a lot of Hindu books on your desk at home, Sanskrit textbooks, books in Ancient Greek, your shelves are stuffed with books about supernatural phenomena, shamanism, history of religion. Why?

Let me explain. I already told that I know natural sciences quite well, for an amateur. Few areas of physics, biology, chemestry, a bit of geology and paleontology. Also, I was very interested in artificial intelligence and language semantics. During 1997-1999 years I have read a lot of modern books, where authors tried to create a "scientifict philosophy", i.e. to combine modern scientific theories into a common worldview. I especially rememeber Edward Wilson's book "Consilience" (https://en.wikipedia.org/wiki/Consilience_(book)). As a mathematician I'm very sensitive to argument flaws, where the conclusion doesn't formally follow from premises, but is instead far-fetched. After reading all these books I became quite confident that those who are saying that the science explains our world are wrong. Yes, some sciences are quite good at explaining some phenomena. But these explanations do not create a common picture of the world. More than that some of so called scientific explanations are just profanity. The most important example of this is darwinism. No doubt that Earth biosphere was and is still developing, and the process of natural selection and random mutations play some role in this development. But there's no way they explain this development. Please note that today professional biologists start discussing it, but if a biologist would express this idea ten years ago in the US, he would be risking his career.

Realization of how little is explained by the science came to me when I was about 35 years old, in 2001. Back then I didn't associate that with the fact that in XX centiry science ignored everything that today is called "supernatural". I still treated everything mystical and religious as a lie and delusion. I was pretty sure in that until 2007. Years 2001-2006 were very difficult. I saved myself only by doing wildfly photography. Some of the photos I've made back then can be found here: http://pics.livejournal.com/vividha/.

- It happens so that a person starts looking for answers after encountering something that doesn't fit into their old understanding of the world. For example, there's a story that Gurdjieff (https://en.wikipedia.org/wiki/George_Gurdjieff) witnessed a religious act in his childhood, when children drew a circle around a boy, and he colud not escape that circle. Stiken but what he had seen and by human cruelty, Gurdjieff started looking for new knowledge about the world and humanity. Did you have any events, unexplainable phenomena that forced you to revisit your world view?

In 2006-2007 I experienced many events, external and internal, that radically changed my opinion about supernatural. What was happening to me in these years, probably, should be compared to what happend with Carl Jung in 1913-1914. Jung called it "confrantation with unconscious". I don't know how to call it, but I can explain it in a few words. While staying more or less sane, excluding the fact that I tried to discuss what was happening to me with people I probably shouldn't have discussed it with, I had experienced visions, voices, sometimes I couldn't control my body parts, plus there were many incredible coincidences. The most interesting was time in between mid April in 2007 when I spent 9 days (7 of them in "Mormonic capital" Salt Lake City) without sleep.

Almost from the very beginning I notcied that I can control many of these phenomena (voices, visions, different sencory hallucinations). So I wasn't afraid and didn't feel myself sick, but perceived everything that was happening as something very interesting and I was very actively trying to interact with those "creatures" in audial, visual and sensory spaces that appeared (by themselves or by a call) around me. I guess I should note that I didn't take any drugs to avoid possible speculations, I tried to eat and sleep a lot, and drank diluted white wine.

One more detail, when I say "creatures", I'm referring to complex hallucinations in modern terminology. The word "creatures" just means that these hallucinations behave themseles independently, had their own memory independent of my memory, and reacted to my attempts to communicate. More than that, I often experienced them together in different sensory modalities. For example, I played an imaginary ball with an imaginary girl several times, and I saw that ball and felt it with my palm when I was throwing it.

Despite that being very interesting, it was also very difficult. It happend during several periods, the longest one lasting from September, 2007 until February, 2008 without a break, and there were times when I could not read, and days when my coordination was disturbed so much that it was difficult to walk.

I managed to get myself out of this state by forcing myself to start doing math again. By mid spring 2008 I was more or less normally functioning and could even go to Salt Lake City to see places where I wandered without knowing where I was during spring 2007.

I must say that despite many conversations with non physical creatures during that time, I have know idea what exactly happened. I was offered many explanations, including hypnotists, aliens, demons and secret societies of people with supernatural abilities. None of it explained everyting that I have experienced. In the end, I needed some terminology to use in conversations, I started calling these creatures spirits, although I know think it's a wrong name. Also there were terms "world system" (for controlling humans, I guess) and, especially in the beginning, "game hosted by fear"

After I was back in a more or less normal state, and in particular was able to read serious books again, I started actively learning areas that I previously ignored. First of all, I tried to find descriptions of similar events experienced by other people. I'd say, I couldn't find any, with the exception of Jung. Someting very similar but whithout visions happened to Karen Armstrong (https://en.wikipedia.org/wiki/Karen_Armstrong) who started reading books about different religions after that. There were many descriptions of people experiencing visions, voices, unusual emotional states, etc, during hours or days ("mystical experience"). Most of the time, it either strengthened their belief in religion they grew up in or made them religious.

Classic and very interesting example of this events happening with a person for long time is Swedenborg(https://en.wikipedia.org/wiki/Emanuel_Swedenborg). Although it doesn't look like my case - Swedenborg accepted what he experienced as something coming from God, and then the process went differently. I guess the most interesting to me was the story of "confronation with unconscious" by Carl Jung, but that was different too, because Jung, unlike me, has encountered supernatural events in his childhood and believed in God.






=== Part II, http://baaltii1.livejournal.com/200269.html
This is second half of the interview with Vladimir Voevodsky. Readers showed a lot of interest in the first half. We are very thankful for good questions. Let's move on.

- For me, it's very difficult to imagine what's going on with an atheistic person, when he encounters unusual aspects of reality. For a religious person, it's part of the way, states of mind revealing new aspect of existence are kind of normal, or somehow expected. Personally, I always gravitated to mysticism, I believed, I was looking for and was finding, joined sects and secret societies. You, on the countrary, were pulled into the "unknown" at some point, the reality just forced you to face the strangeness. Like, what are going to do when angels look at you, and after you close your eyes and then open them again, angels are still there looking at you? What's normal and natural for a religous person, or a person who's into mysticism, could drive another person insane.

I guess my views at the moment were not so much atheistic as agnostic. I had mixed reaction. First, it was resentment, because what was revealed to me was mostly dirt, mockery of the people. Second, excitement and hope, when glimses of love, beauty and intellect started to show among all that dirt.

I wasn't crazy, although sometimes it was too much and I started to seriously believe in some "theories". Usually, I got through it fast, in a few hours. Periods of hopelessness were more serious. When they happened, I was warmed by the thought that I had to fight, because the inner (spiritual) life of modern children was more or less depending on it.

- You mention a "game owned/hosted by fear". What is fear?
First of all, there are a lot of different fears. There's kind of fear that makes you act, and there's paralyzing fear that makes your legs give out. The first kind is the one you can understand, it's your body's response to situations that appear to be dangerous, and it helps to avoid or cope with such situations. Second type of fear is not so clear. I had a hypothesis that it's one of mechanisms that regulates ecosystems. For example, if there are too much deers in a forest, hidden mechanism can be enabled that switches deer's fear from the first type to the second, and that makes it simple for wolves to haunt deers.

Fear can be hallucinative, it's not the same as paranoia, because the person experiencing it can be quite rational and can realize that there's no reason for fear, but still experience it and have shaking hands.

You can cope with the fear, but symptoms (shaking hands, legs giving out) can stay, which is quite uncomfortable.

From the perspecitve of spirits, as I understand it, fear can be seen as one of convenient and efficient tools for influencing people.


- We're taling about a bunch of aspects of a very unique experience, but it looks like and uncontrollable flow of complex phenomena. Did you learn and remember something important from this experience?

The most profound thing that I learnt during these year is an ability to observe your inner world on verbal and other levels, and analyze these oservations rationally. It is, for example, ability to notice when new voices interweave with my stream of consciousness and distinguish kinds of visual or other sensory hallucinations. These abilities more or less require clear thinking, even when you are deep in sensory-emotional state, and to notice details, development techniques of experiences you have, and not only their contents.

Another group of observations, that I find important, is reduced to the fact that what we perceive as inner world experiences that we actively create in real time, are most often something else. Most of them are templates that are played in such a way that there appears to be a very realistic illusion that what currently happens is created with us being involved right now.

- What is madness?

If you ask for a constructive definition, then madness is inability to be a productive part of society, not related to physical inabilities.

But seriously, I don't know.

- You mentioned that you were offered different world views. And as far as I understand, all of it appeared to be a metaphysical scam. You were breaking through layers of explanations, realizing that some mind manipulations were taking place, that someone builds philosophical systems, and it happens to be an external intrusion. Is that correct?

Building a real philosophical system only on external effects is hard. Externally (for reasons unclear to me) I receive small "seeds" - short idea, associations, etc. Most of the time, if you just let them freely grow, if you let it, is useless or harmful. I once heard an interesting name for such systems, "harness". Meaning something that can be used in future to control human behaviour. Whether a person let these seed grow or rejects them, dependes on how skillful you are in working with your inner world.

The problem is worsened by the fact that sometimes these seeds are accompanied by not only mental pehomena, but emotional or even real ones, it seems like they start to confirm a philosophical system that starts developing. Another property of these seeds and systems that grow from them is that they usually contain (especially in the beginnging) really important and interesting ideas. It's often not eeasy to spot the transition from truth to lies. A person acquires an instictive trust in thoughts flow and starts to believe its extension, which becomes untrue. After that, it's quite difficult to admit to yourself that he believed in that nonsense and he starts to deceive himself to avoid feeling seeing himself as a fool. Often systems develop in such a way that starting from some point they start supporting themselves with fear.

- I'll tell about my perception of similar phenomena. You know, two years ago I started learning card tricks, to better understand structure of a lie. At first I thought it was impossible, that people ccan't deceived by such tricks, but my practice showed that tricks almost always succeed. The more I studied this activity, the more I was amazed by how much card tricks there are, as well as their impudance. There methods of forcing, when you palm off the right card, and the spectator gets a feeling that he chose it randomly. It's something similar, because these manupulations are performed on metaphysical level. On the other side, you realize that archives of mental hospitals keep many stories of those who tried to fight scams, those who built their metaphysics, trying to fight through hierarchies of lies, trying to see the truth, who dreq cosmological schemes. Textbooks with all these are probably kept there. And the world of sicentific society, with superior aesthetics, with reflections and accepted values, maybe it's a scam too? It's just a rhetorical question. You know, if I wasn't extremely sensitive to awareness of these scam hierarchies, I wouldn't see any deep meaning in this interview. Sometimes I look inside myself and shout "build your own metaphysics, or else you'll be fed with prepared ideas, and you'll puke all your life". Sorry, I'm becoming very emotional about it. Let's continue the interview.

- How is your life in the US?

- I have a feeling that when all this was happening to me in April, 2007, there was a social component, besides a mystical one. Only after all these I started feeling myself comfortable in the US. I kind of passed an "initiation", using the criminal code term.

- You've been to India twise, you were int he South and visited Allahahabad, Kanpur, Delhi. After a walink in Magh Mele you asked local professors question about local social struture, sometimes funny and unexpected, like whether Magh Mele gurus pay taxes on their dakshns. What do you think of the country? Do you plan to return their? Can you imagine staying and working there?

It's a very big and very sophisticared country. For examples, places I visited in the South are very different from the places we visited in central India. In general, I thing I'll visit it again. I don't really think I'll be staying there living and working.


- After we published the first part of the interview, there was a lot of questions. In particular, readers were very interested in your statements about the gap between pure and applied math. Almost all mathematicians feel it, but they make very different conclusions. Personally, I like it; it gives an opportunity to work in "deep worlds" without a risk to harm existence. But from what you said, you have a radically different attitude, more than that, you spend a lot of time seeking the ways to apply modern advanced math, and you didn't find it. One of our readers asks following questions: "Is there any hope left that it's still possible to do? Or does it seem that the problem is fatal?"

Speaking about pure and applied math convergence, I see it this way. Pure math works with models of advanced level of abstractness and low complexity (mathemtaticians love to call this low level of complexity "elegance"). Applied math requires working with specific but much more complex models (a lot of variables, equations, etc). Interesting applications of modern pure math are most likely in the area of advanced abstratness and high complexity. This area is almost not accessible today, mostly because of human brain inability to work with such models. As soon as we learn to use computers to work with abstract mathematical objects, this problem will gradually disappear and we'll see interesting appications of moderd abstract math ideas.

So I believe that the work I do in the area of programming languages, allowing us to work with such objects, will in future help to use modern math ideas to applied problems.


- There were several more interesting questions, for example, about the time when you tried to apply some interesting math to historical genetics. What did you want to achieve and why you couldn't succeed?

At first, I wanted to figure out dynamics of recombinant genome, and to understand if it's possible to extract from it the inforation about the dynamics of populations in history, i.e. from today to 10.000 years ago.

But I soon realized that it was extremely difficult. There's not enough information about demographic structure of populations even for the last few hundred years. For example, distribution of amount of children of an average man and a woman is known for a given city. It's possible to find this data. But what about distribution of grand children? You can, of course, assume, that the number of children does not depend on the number of siblings. But that's obviously not true. What about grand children? This is the first problem. Historians and demographers should work on this problem, and some work is in progress in Europe based on parochial books. The data is comprehensive, so this data will someday be available.

On the other hand, I realized that noone really knows neither how recombination works statistically, nor how mutation works statistically. It's difficult to measure. There is more and more information from police databases and from companies working on genetic geneaology, and the problem is slowly being solved. But when I started working, there was nothing at all.

From mathematical point of view, the situation was no better, because no one ever seriously studied such complex and heterogeneous procecesses. In the end I built a new Markov process formalisation base on the notions of path systems. The publication turned out to be very long and technocal, and it is still unfinished. I thing about returning to it and completing it with a convenient computer proof assistant.


- There was another question. "Alan Kay, creator of Smalltalk, said that the science looks for compact theories/explanations. So you're doing science and looking for compactness?"

I don't agree with it. I mean I do science sometimes, but that's not the matter. Science must collect and analyze new knowledge. Collection is very important. There's this opinion that, you know, all observations are already made, common picture of the world is clear, and what's left is putting all the knowledge in order, packing it in a compact and beautiful theory. It's fundamentally wrong. Not only wrong, but also leads to a very harmful trend to ignore everything that doesn't fit predefined theories or hypotheses. It's one of the most serious issues in modern science.




- Another quote. "I hope that there will be a crytical analysis of the reasons of those visions you experienced, and how they were related to the physical reality".
First of all, the general idea that was very difficult for me to accept (but based on all the experiences that I had for the last five years, I couldn't conclude  anything better). There are inhuman minds around us. By "minds" I mean information systems, having a memory, motives, ability to model external world and to plan. They are not aliens, but primordially Earth inhabitants, and, most probably, evolutionary older than humans. These minds actively (and sometimes negatively) influence human lives.

The world of these minds is very complex, maybe as complex as that part of the world that we call physical reality. I don't want to speculate about the structure of that world, because I don't have enough facts and observations for it. Even my simplest question don't have simple answers. I'm sure these minds interact with people. Almost sure, that they interact with higher animals. How do they interact with lower animals? With insentient substance? Full world picture must be logically consistent, this suggest they they must communicate somehow. In this sence, they are part of physical reality, too. But that' the part we know very little about. This part of the world must be studies, using scientifict methodology.

Surely there were attempts to make this research. Especially, in the end of XIX centiry, but there were not enough capabilities for that. Today I think such research could begin with the group of pehomena that Jung called synchronicity. In simple words, it means unnatural (from the perspective of existing models) patterns in individual and collective human behaviour.

Today we have an opportunity to document such patterns and figure out their structure. This opportunity exists because of huge amound of records of human speech (radiostation interview, for example) and people movements (for example, security cameras in airports). All this data must be analyzed considering linked physical time. I'm pretty sure it's possible to discover patterns in human behavior that can't be explained by their conscious behavior and are complex enough and linked to physocal time to be explained by individual unconscious.

Personally I don't want to work on it, but I sometimes I feel some desire to work in this area. I really hope that there will be some researches, having access to proper data and courage and desire to work on this prlblem. It will be real science. It can become a starting point in understanding of structure and driving forces of historical process. And then the process of evolution.

One specific idea is to make a web service where people can leave comments if they experienced synchronicity when they were listening to the radio or tv thinking about something and accidentaly heard the word that continues their thought or answering a questions they asked inwardly. The important part of the comment must be a word or a phrase they heard on the radio. Optionally you could put a context, time when it happened and tv/radio station. Especially important are those cases when synchronicity happens in the moment of enabling radio, these cases must be specially marked.

My hypothesis is that the flow of words that we hear on the radio contains patterns of specific words or word groups linked to physical time, with second accuracy, not known to minds of people saying these words. Then you take decent voice recognition software capable of generating transcripts with timestampts per separate words and build a huge database of sequences of timestamps when each word (most often associated with synchronicity) was said. Then you find deviations from randomness in this database.

There's a whole are of math called theory of pseudorandom sequences. These sequences look random, but they are extremely predictable. We have a whole group working on them. So finding hidden regularities is mathematically possible.

- There were a few questions about doctors and schizophrenia. Oviously, for many peopls revelations look like schizophrenia. You publicly talk about visions and complex hallucinations.

I'll try to answer. Fist thing I did returning from Salt Lake City was visiting a hospital and get standart tests and x-ray of several body parts, because besides mental effects there were a lot of unusual somatic sensations. I was told that I was completely healthy. Generally, my physical health became better during last five years, although I became older.

I didn't go to psychiatrists with that. I wa pretty sure that it was not schisophrenia.

There's also a more general subject - link between mental disorders and those minds I talked about previously. It's a very complex subject and I think that it must be researched by honest, intelligrnt and brave specialists. I don't want to go deeply into this subject.

- Some final thoughts?

I feel that a lot of things we discussed are left unexplained. Let's return to that, say, in a year, and see what changes.