**Alexander Panov, Astrophysicist, author of "Snooks-Panov curve" which describes the singularity**

I think that I will look a little skeptical at this congress, because I am not going to talk so much about our coming victories, as about possible problems. Specifically, I would like to talk now about three main topics. Firstly, I would like to describe a little what this singularity of evolution is, this infamous vertical which is currently under discussion. Secondly, I would like to discuss the fate of science in the singular and post-singular phase of evolution. And thirdly, I would like to take a brief look at the possible role of artificial intellect as it relates to problems of science.

Evolution is an accelerating process, and this is something that almost everyone agrees with nowadays. And this is not just an accelerating process, but a process that accelerates at a frantic rate. This means that in the course of a finite amount of time, the speed of the process should formally reach an infinite speed, and any linear predictions after this point become impossible.

The concept of the singularity of evolution can be reached by many diverse paths. Historically, one of the first paths was in the form of demographic singularity. This means that the population of the Earth does not grow exponentially, as Thomas Robert Malthus proposed, but at a faster rate. The population of the Earth increases hyperbolically, and there is a certain point, t*, which is the point of singularity, where this hyperbola formally goes into infinity. This point of singularity is not difficult to calculate, and the calculation was made in 1960 by Heinz von Ferster and co-authors, who obtained the value of 2026. Later, the calculation was made by Iosef Samuilovich Shkolvsky in 1965, who obtained the value of 2030, which as you can see is very close. If instead of a hyperbola, you draw the value for the unit at n, then you simply obtain a linear function of time, which should at some point become zero. And Shkolvsky drew a curve where we can see that a linear function is obtained for the unit at n, which at the point t* really become zero.

The second path of singularity, the so-called technological singularity, has been discussed here at such length that I won’t repeat the topic. It is linked with the names of Irving Good, Vernor Vinge, Moravec and Ray Kurzweil, who has already spoken here, and I will perhaps come back to this a little later.

The third path to singularity is the concept of singularity as a general evolutionary singularity. There have been several predecessors here. In 1996, Graham Snooks, an evolutionary scientist from Australia, presented the evolution of the biosphere and then humanity as a common process, expressing it in the terms of the so-called “waves of life”. The “waves of life” are certain fundamental transitions. And it turned out that this process takes place at an accelerated rate with a co-efficient of three. This means that each subsequent phase is approximately three times shorter than the previous one. Most importantly, he examined the process of the evolution of the biosphere and human society as a whole, although he did not bring in concepts of singularity. Then Ray Kurzweil in 2001, at any rate no later than this, also examined the process of the evolution of the biosphere and human society as a single process. He expressed this process in terms of so-called “paradigm shifts”.

Then a very important step was made by Igor Mikhailovich Dyakonov – in 1994 he discussed “Dyakonov’s eight phase transitions in human history”. He also noted that these phase transitions take place at an accelerated rate, i.e. the time interval between each two subsequent transitions is reduced. In 1994, he introduced the concept of historical singularity. This was a completely independent method of introducing the concept of singularity, in comparison with technological and demographic singularity, for example. On this graph, the points of Dyakonov’s eight phase transitions are displayed, and along the vertical axis the frequency of phase transitions per unit of time is displayed. It is clear that here the characteristic vertical asymptote appears, which is in fact what we are discussing.

Then in 1996 Sergei Petrovich Kapitsa added several points to Dyakonov’s phase transitions, which covered the entire history of humanity. And later, I discovered that the so-called boundaries between geological eras, which are in fact boundaries between biological eras, fit comfortably on to this curve.

We get 19 points, and the intervals between the points form a very precise geometric progression. The fact that this is a geometric progression can be easily seen after a short mathematical conversion, in mathematical notion we should get a straight line, and this straight line can be seen very well on this diagram. The co-efficient of acceleration is 2.67, which is close to the number *e*, if you know what the number *e *is, then you will know what this means. And it was not difficult to calculate where the limit of this sequence, the singularity of evolution, is located – for all the points starting from the moment that life arises and ending with the last point, which is the so-called information revolution, this singularity is equal to the year 2004. And if we make an extrapolation solely on the points of the new era, then we get the year 2015. So the value is not very precise, but it is, as Akop Nazaretian correctly said, the first half of the 21st century.

What do I mean by this, what is the meaning of these points? It is important that every point is of course a fundamental change in the evolutionary system. But this is not just a fundamental change, which arises in response to overcoming a certain evolutionary crisis. There are two main types of these evolutionary crises – endo-exogenic and crises of the technical-humanitarian balance. I won’t talk about this simply because there is no time to do so at the moment. It is also important that during these phase transitions, the so-called factor of excessive diversity is used. This means the new things that arise in the new phase do not arise at the moment of the phase transition. The things that previously arose are used, but which existed somewhere on the periphery of the evolving system. For example, mammals appeared long before the dinosaurs died out, but they became the leaders of evolution after the dinosaurs became extinct, and another phase transition took place. Additionally, Sedov’s law of “Hierarchical compensations” is important. This is when a new leader of evolution appears, and the old evolving systems do not vanish, but only change their place in the evolving system, move to its periphery to a certain extent, and perhaps become somewhat reduced.

What is the idea of this general evolving singularity? It is the singularity of the entire evolutionary development, starting from the moment that life appears. Firstly, this is not a point, it is a certain period which indeed does occupy, roughly speaking, the first half of the 21st century, perhaps the first two thirds of the 21st century, something like that. What happens during this time? During this time, the previous rate of evolution breaks down, because this is simple mathematics, evolution cannot accelerate in the same way. And a prediction, purely mechanically and mathematically, for this zone of singularity, is impossible. But nevertheless, can we say anything about what will happen later, avoiding this direct linear extrapolation, which becomes impossible? We can say something. Here we need to remember what these phase transitions were, and remember that the point of singularity or the zone of singularity is practically a concentration of crises, a concentration of these phase transitions. As the zone of singularity is practically a concentration of crises, and we will feel this time of singularity as crises, which come one after another, i.e. humanity will live in a post-singular stage, compensatory mechanisms must be developed for each crisis.

So in the post-singular stage, if humanity is alive, it lives while maintaining numerous crisis compensation mechanisms. This will not be an easy life. We may list many different examples of these compensations mechanisms, for example exhausting mineral resources will mean that closed technological cycles will have to be introduced, which is complex, etc. There may be various bans, for example a ban on certain types of scientific research. There may be a ban on any experiments with living beings. Just imagine how this will slow down the development of sciences relating to living things. Another important problem that we face is the drastic slowing down in space exploration, which Krichevsky discussed. The rates of space exploration have fallen very drastically compared to what we saw last century, and therefore in the coming decades, and perhaps for even longer, the main part of evolution will be limited to the planetary scale, which puts us in a situation of limited resources.

Now I would like to discuss what concerns me most of all. As a scientist, an astrophysicist, I am worried primarily about the future of science. This is what we can say about the future of science in the post-singular stage. Firstly, we can make a few general philosophical propositions. Any progressive phenomenon in evolution cannot be progressive forever, as leaders in evolution replace each other. In this sense, science is a typical progressive phenomenon, it arose in response to certain crises, and served to overcome them. So science in this quality, as the basis of the formation of the vector of the development of human civilization, cannot be a leader forever. From this, it follows that a change in leadership will take place, and another leader must come to replace science, a leader about which we do not yet know anything about. Sedov’s law states that science will not disappear completely, it will move to a more subordinate state, it will occupy another place in human civilization. These are general philosophical statements, but in fact we can say something more specific.

In 1963, Stanislaw Lem introduced the concept of the information crisis connected with science. What is this? Each new discovery leads to the appearance of new scientific problems to which there is no answer. So the amount of unsolved scientific problems grows exponentially. But the number of scientists cannot grow at the same rate, and so after a certain time, there will not be enough scientists for the scientific problems that arise. Something appears that he called the “breach in the frontline of science”: not all scientific problems which should be studied are actually studied, science loses its integrity and starts to degenerate. I would like to point out that this is one of the types of a lack of resources. Another type of a lack of resources can be linked directly with the most fundamental sciences – the science of the microscopic world and the science of space, such as astrophysics and cosmology. The problem is that the cost of scientific studies in this most fundamental sphere is constantly growing. And furthermore, improving methods, developing new technologies etc. does not make it possible to overcome this trend. In particular, we may mention, for example, the increasing size of the collider. The enormous LHC collider has now been built, and perhaps it will simply be impossible to build a bigger collider. Telescopes are also constantly increasing in size, and so on.

However, the world’s resources are limited, and so a limitation should be placed on this growth. Furthermore, the result of this may be expressed in several more precise terms: limitation of resources and the growth of scientific studies will lead to a situation when the number of scientific studies within one unit of time will start to drop. A drop in the number of new discovering within one unit of time will reduce interest in science, and a reduction of interest in science will reduce financing for science. A reduction in financing will additionally reduce the flow of scientific discoveries, and there will be a loop of positive feedback, which may lead to the sudden collapse of financing for fundamental sciences. This is a very simple process, it is possible to build mathematical models of this process, and I have done so. Here is a description of the model, I will not examine it in detail, and will just show the results. In this specific version it is proposed that financing for science will be restricted from the top, as can be seen in this curve, it will initially grow and grow, and then hit a point, a logical curve. This is not a definite proposition, the model also works with other propositions. This is what we get for the quantity of scientific results in a unit of time. Initially they grow, together with a growth in financing, but then this section arises, when financing grows, but the amount of results begins to fall because the unit of scientific study becomes increasingly more expensive.

And then a collapse in financing suddenly takes place, which is connected with the loop of positive feedback which I discussed. I built this model in 1996, I did not have experimental data with which I could compare this. But recently, in 2010, I was able to find data on the quantity of publications per year, starting in 1817 and ending in 2010. As you can see, this is the growing curve, and it has several very interesting places on it. Firstly, I must show this place connected with 2050, here one of the points of my curve is located which is called the information revolution.

As you can see, at the moment of this information revolution, the quantity of scientific articles published suddenly increased. And here is another important place, where you can see that over the last few years, the number of scientific publications suddenly began to drop. This process began in 2008, and naturally people try to connect it with the economic crisis. But this is far from the first economic crisis in human history. There was the Great Depression of the 1930s etc., and there was not previously any drop in the number of scientific publications, this is the first time it fell. And financing of science, as we can see on this curve, although this is for the United States, continues to grow. So here we can see that this looks very similar to the phase that I showed in my model – financing is growing, and the amount of results has already started to fall. So, the natural question, perhaps, is whether only the quantity of ordinary journal publications has started to fall. Nothing of the kind. Here is a well-known electronic journal, the archive of pre-prints, and here the quantity of publications started to fall. So it started to fall everywhere, this is a total process.

How can this crisis be overcome? I don’t yet know how to do this, I only want to discuss whether artificial intellect can be used, which has been discussed extensively here, to overcome this crisis. For example, the insufficient number of scientists could be made up for with robots, or a method of developing knowledge could be introduced instead of ordinary experiments. My opinion is that the hopes for artificial intellect are seriously overrated. Mainly, the hopes for the creation of an artificial intellect greater than the human intellect are linked with the concept of technological singularity and with Moore’s law, the growth of the power of the hardware base. Firstly, I have two questions about this curve. The first question is how the power of the brain was assessed, the speed at which the brain works. It was assessed on the quantity of neurons, the quantity of synapses and the frequently of the functioning of the synapses.

This is a very primitive assessment – let’s take the amoeba. It does not have a nervous system at all, but nevertheless it is capable of very complex behavior. And all these information aspects that the amoeba has should also be present in the brain. And so this value is probably seriously underestimated, perhaps by ten orders of magnitude. And also, what is most important, is that Moore’s law, the increase in the power of the hardware base, only gives the necessary, but not the sufficient conditions for the appearance of a powerful artificial intellect. I will just read one quote: “Over the last 15 years, the reason of our electronic computing machines has improved by millions of times. Over several decades, we should expect an increase in the characteristics of reasoning of machines by at least several dozen thousand times. The reasoning of these machines will certainly surpass human reasoning according to the main parameters.” This was written in 1975, and such statements have been made constantly throughout the development of computer technologies, and they are being made now, in the same form and using the same words.

What is the reason for this error? The error lies in the fact that necessary software is much more conservative, by many orders of magnitudes, than the development of the hardware base. I have several examples of this conservatism, I won’t dwell on them, because my time is running out. I would only like to note that the technologies that are currently being used for programming artificial intellect – neuron networks, heuristic programming, expert systems and evolutionary programming – were invented between 1955 and 1961, more than 50 years ago, and since then nothing fundamentally new has been invented. A profound stagnation can be seen in the field of artificial intellect programming. And the fact is that we simply do not understand how a person really thinks. The problem here is, I would say: a computer processes information, but a person processes meanings. By default, it is assumed that meanings can be expressed by means of information, but no one has ever proved that this is the case.

I will give a simple, primitive counter-example – if meaning is represented as quantum states, then it is not information. Because the most important quality of information is that it can be copied and duplicated. And quantum states cannot be copied according to the theorem of non-cloning of states. I have one minute left, I am running a little over time. This is a very simple counter-example, but in fact the situation could be much worse. We do not understand at all how these meanings are represented. Furthermore, there is the theorem devised by Roger Penrose. Penrose claims the following: there are many activities in the human brain which cannot be represented by the activity of a computer, but it is very difficult to prove that this really is impossible. But there is one type of activity, it is a special type of mathematical activity of the brain, when an absolutely strict theorem can be proved, that any finite automaton based on any known physical principles at the present time cannot represent certain forms of mathematical activity of the mind. This is a mathematical theorem, and it cannot be disputed. In fact, it is akin to Hegel’s first theorem about incompleteness, but I won’t dwell on that – what follows from this then? That in order to create an artificial intellect that surpasses human intellect in power, we must discover these unknown physical principles, and it is impossible to predict when we will discover them.

Here I will conclude, then. I would simply like to say that we shouldn’t put too much hope in artificial intellect as a way of helping us to overcome the crisis that is increasing in science. I don’t actually know of any reliable way to overcome this crisis. Although there are several ways which should be discussed. Perhaps I will be able to talk about them at our round tables, if there is time to do so. Thank you for your attention.