Category Archives: Inquiring minds

The Singularity Part III

Overall, it does not seem that these arguments show that the existence of AI systems with a super-human intelligence is impossible. However, I am not totally sure that human beings will some day realize such systems, for two reasons, both depending on the limitations of human intelligence.


Firstly, have we enough intelligence to succeed? We must create systems that can create systems better than those that we have created. This is very difficult, we have to write rules that write rules, it is far from being obvious. I cannot do it directly: I begin writing something that looks satisfactory. Then, I run it on the computer; usually, it does not work. I improve the initial version, taking into account the observed failures. It is possible that, over the years, we will be better for defining meta-knowledge that creates new meta-knowledge, but it will always be a very difficult activity.

Secondly, the scientific approach is excellent for research in most domains: physics, computer science, and even AI as long as we do not try to bootstrap it. Usually, the reader can observe an improvement of the performances. When one is bootstrapping AI, the progress is not an improvement of the performances, but an increase of the meta-knowledge that the system is capable to generate. Unfortunately, this does not immediately lead to better results. It is difficult for a reader to check this improvement for a system that contains 14,000 rules, such as CAIA.
Moreover, this meta-knowledge has only a transitional interest: it will soon end up tossed into the wastebasket. Indeed, in the next step of the bootstrap, it will be replaced by meta-knowledge generated by a system such as CAIA: its goal is to replace everything I gave to CAIA by meta-knowledge that CAIA has itself created, with a quality at least equal. We must avoid the perfection, we have no time to waste on elements for single use only. The success of a bootstrap can only be assessed at its end, when the system runs itself, without any human intervention: when it has reached the singularity.

To sum up, I think that AI systems much more intelligent than ourselves could exist: there is no reason why human intelligence, which results from evolution, could not be surpassed. However, it is not obvious that our intelligence has reached a level of excellence sufficient to achieve this goal. We need external assistance, and AI systems are the only intelligent beings that can help us; this is why it is necessary to bootstrap AI.
Unfortunately, we are perhaps not enough clever to realize this bootstrap: we have to include a lot of intelligence for designing the initial version, and for the temporary additions during the following stages. We have also to evaluate and monitor the realization of this bootstrap with methods different from those rightfully used in all the other scientific domains. 

It seems that people outside AI have more confidence in the possibility of a singularity than those inside AI, which looks like a church whose priests have lost their faith. A recent report, One Hundred Year Study on Artificial Intelligence, defines many interesting  priorities for weak AI. However, they do not strongly believe in strong AI, since they have included this self-fulfilling prophecy:
“No machines with self-sustaining long-term goals and intent have been developed, nor are they likely to be developed in the near future.”
Naturally, I disagree. Moreover, during the search for singularity, we will develop a succession of systems, which will be more general, and could sometimes be more efficient, than those obtained with weak AI.

Even if we are not sure to succeed, we must try it before our too limited intelligence leads our civilization to a catastrophic failure.

The singularity Part II

Walsh's interesting paper considers six arguments against the singularity.

The fast thinking dog argument
Computers are fast. I agree that it is not fundamental for achieving our goal. Intelligence is more than considering many possibilities as fast as possible. If one handles them badly, one can waste a lot of time. However, it can be very useful.

The anthropocentric argument
Many suppose that human intelligence is something special, and they assume that it is enough to design a system which could reach the singularity. Here again, I completely agree with Walsh: our intelligence is only a particular form of intelligence, which evolution allows us to have. Why could this state allow us to realize systems very much clever than ourselves? And even if we create them, it will perhaps be not enough to reach the singularity.

The meta-intelligence argument
The capacity to accomplish a task must not be confused with the capacity to improve the capacity for accomplishing tasks. With present methods, excellent results have been obtained in several domains; however, the systems have always been realised by teams of many experts; it is not an AI system that solves the problem. Therefore, if a system is learning to play Go, it does not learn to write better game playing programs. An improvement at the basic level, solving a particular problem, does not lead to an improvement at the meta-level, solving large families of problems.
However, there are exceptions: CAIA uses the same methods for solving a problem than for solving some meta-problems. For instance, it finds symmetries in the formulation of a particular problem. Finding the symmetries of a problem (which is a meta-problem) will improve CAIA's performances for solving this problem. In this case, it is bootstrapping.
Unfortunately, this situation happens rarely. The reason is that most of the meta-problems are not defined as the problems solved by AI systems, which have a well-defined goal. Usually, the goal of a meta-problem is vague: can we tell that the monitoring of the search for a solution is perfect? We are glad to have solved it: we feel that we have not wasted too much time, but is it possible to do it better? Their goals cannot be defined as well as checkmate in chess. For achieving a bootstrap successfully, one must solve many meta-problems, where one is interested in the way problems are solved.  They are often very different from the problems for which AI researchers have developed efficient methods. However, learning to monitor the search for a solution would be useful for many problems, including this meta-problem itself: a virtuous circle would be closed. This is a part of the singularity.

The diminishing return argument
It often happens that we have very good results when we begin the study of a family of problems. This explains the hyper-optimistic predictions made in the beginning of AI: we did not see that forto progressing just a little more, a huge amount of work is necessary. Here, I do not completely agree: it may happen that discontinuities suddenly entail an impressive progress. For instance, the appearance of the reflexive consciousness brought an enormous discontinuity of the intelligence for the living beings. It is one of the main reasons of the existing gap between the intelligence of the smartest animals and that of the man. Other kinds of discontinuities may exist, which can also lead to an extraordinary increase of the performances. It is difficult to predict when it is going to arrive, no more than a dog can understand our reflexive consciousness.
Self-consciousness is precisely a domain where we can predict a discontinuity in the performances of AI systems, without any idea of when it is going to occur. Indeed, for us, it is a wonderful tool, but it is very limited: the largest part of what takes place in our brain is unconsciously made. Moreover, we have difficulty observing what is conscious because we do not manage to store it. Yet, we can give to our AI systems many possibilities in this domain: CAIA can study all of its knowledge, it can observe all the steps of its reasoning that it could want to, it can store any event. Naturally, it is impossible to observe constantly everything, but it is possible to choose anything among what happens. The difficulty is that I do not know how CAIA could use these capacities efficiently: I have no model because humans cannot do this. Therefore, I am only using them for debugging. Super-consciousness is an example of what could someday be given in the future AI systems; for the present time, the instructions for use are still missing. This is one of the improvements that could lead to AI systems with behavior as incomprehensible for us as ours is incomprehensible for dogs.

The limits of intelligence argument.
The intelligence of living and artificial beings have limits. This is well known since the limitations theorems such as Gödel incompleteness: some sentences are true, and there does not exist a proof showing that it is a theorem. It is possible that it is the case with a sentence as simple as Goldbach conjecture. However, this does not mean that it is impossible to go considerably further than what we achieve now.

The computational complexity argument
For some problems, even very much faster computers would never be able to solve them with the combinatorial method: there are too many branches. This is true, but it is possible that these problems could be solved by a non combinatorial method. Let us consider the magic squares NxN, with N odd. When N is very large, we cannot use the combinatorial method: there are 2N+2 constraints, each of them has N+1 unknowns, which can take any value among N² possible values. If N=100,001, there are 200,003 constraints, each of them with 100,002 unknowns with 10,000,200,001 possible values. This is a very hard problem, even if we are using heuristics for reducing the size of the tree.
Nevertheless, by 1700, a Belgium canon discovered a non combinatorial method that directly generated the values for all the unknowns. I wrote, a small C program (only 26 lines) that generated a solution in 333 seconds. Therefore, is it impossible that, for many problems apparently insoluble with the combinatorial approach, a super-intelligent system would discover a method for finding solutions without any combinatorial search? Complexity is related to an algorithm, but one may solve this problem without using a combinatorial algorithm.

The Singularity Part I

In the Fall issue of AI Magazine, Toby Walsh has written an excellent paper on the singularity, that is the time where an AI system could improve its intelligence without our help. I am trying for more than 30 years to bootstrap AI, that is to realize such a system, being helped by the limited intelligence of the system itself, even when it has not yet achieved its final goal. Therefore, I am very much interested in this paper. I disagree on a few points; as the progress comes from the discussion, I will give my personal view of the arguments presented within Walsh’s paper. I agree with its conclusion: it might not be close, and personally I am not even sure that we will witness some day this singularity. However, I believe this for reasons which are not always those of the author.

I will start with two points: how can we reach the singularity, and can we measure the intelligence with a number. Then I will consider the six arguments presented in Walsh’s paper.

Toby Walsh does not indicate how this singularity could be reached. I have the feeling that he thinks, as many other AI researchers, that it is enough to bring together many clever and competent AI researchers during many years: perhaps they would be able to achieve their goal. With this method, outstanding programs, such as for Go and Jeopardy!, were realized. I do not think that we could reach the singularity by this method, even if we gather many researchers, very intelligent on our rating scale: I am afraid that their intelligence might not be high enough. In the same way, billions of rats would never be able to play chess. To achieve singularity, we need help, and the only clever systems outside of us are AI systems themselves. The more they progress, the more they will be helpful. Bootstrapping is an essential method in the technological development: we could not build the present computers if the computers did not exist. Bootstrapping is an excellent method for solving very difficult problems; in return, it takes a very long time.

Implicitly, it seems that those who believe in the singularity think that intelligence can be measured by a number; some day, there will be an exponential growth of its value for AI systems. Could such a measure exist? Even for humans, with very similar intelligence, the IQ is not satisfactory. When the intellectual capacities are very different, such a measure has no sense: it is difficult to compare our intelligence with the one of a clever animal, such as a cat. We have possibilities which does not exist in cats, such as the reflexive consciousness. It is extraordinary useful for us, although we can observe only a small part of what occurs in our brain when we are thinking. Therefore, we cannot compare the intelligence of two beings when one has capacities that the other has not. When there is a discontinuity, the intelligences of those before and after this discontinuity are completely different: new mechanisms appear. If the more intelligent being is an AI system, we cannot just consider that it is only super-intelligent. It is something fundamentally new: its intelligence could not be measured on the same scale as ours. We cannot speak of an exponential growth, but of something so different that we cannot use of the same words.

Mathematics have disappointed me


Since Gödel, we know that mathematics have limitations: some statements cannot be proved, and cannot be refuted, that is one cannot prove their negation: for both, no demonstration exists. Many works have been made for this problem, and they show that, in some theories, some statements are true, although no proof exists. Some of these proofs are constructive, and they show statements in this category; usually, these statements use reflexivity. We know the Epimenides paradox, who is Cretan and says that all Cretans are liars. I was not embarrassed that so strange statements could not be proved.

However, for a recent post, I have considered a system that created new conjectures. It found several variants of Goldbach conjecture: every even number greater than two may be decomposed as the sum of two prime numbers. It had been a long time since I knew this conjecture, and I was not really annoyed that it had not been proved, although many mathematicians tried to do it since 1742. Indeed, I believed that it was a very difficult problem, that numbers greater than billions of billions had only one, two or three decompositions: it was ever likely that no decomposition existed. If so, it was possible that this conjecture was false; even true, it would be very hard to prove it.

Writing my preceding blog, I read the Wikipedia entry on Goldbach conjecture, and I saw that the number of decompositions is huge; moreover, it is strongly increasing with the value of the numbers. Therefore, with CAIA, I have made some experiments, I had only to write three rules. I was shocked by the results: large numbers really have a lot of decompositions. The greatest number with at most 1 decomposition is 12, with at most 10 is 632, with at most 100 is 11,456, with at most 1000 is 190,562, etc. I have stated a new conjecture:

The number of decompositions of an even number N, greater than 15,788, into the sum of two prime numbers is greater than the square root of N.

As a matter of fact, the greatest number for which this conjecture is false is 15,788: it has 125 decompositions, less than the square root of 15,788: 125.65….

Naturally, I have not proven this conjecture, but I am pretty sure that it is true. When we consider large numbers, they have even much more decompositions than forecast. Moreover, when a number N has small numbers of decompositions, several of its neighbors have similar values: the curve representing the number of decompositions has no pick towards the bottom. CAIA has studied the first hundred even numbers from 100,000,000: the minimal value of the number of decompositions is 218,281 for 100,000,144 (we can notice that it is much larger than the square root of the smaller of these numbers, which is 10,000); among these 100 numbers, 12 have a number of decompositions between 218,281 and 219,000. On the contrary, the abnormally high values are often isolated from their neighbors, there are picks towards the top: in the preceding interval, the largest number of decompositions is 723,776, and the value of its immediate follow-up is only 595,554. It seems very unlikely that there exists a large number N with less decompositions than the square root of N; it is still harder to believe that there is an even number without any decomposition.

Goldbach conjecture has been checked until 4.1018 ; then, if my conjecture is true, every even number not yet checked has at least two billions decompositions! And mathematics cannot prove that there is at least one!!!! There would be no proof of a result which is ultra-true.

I do not believe that it is due to an inability of mathematicians; I have a tremendous admiration for the way they succeeded in developing mathematics. They are extremely competent, as long as they do not speak of AI. This is a weakness of mathematics: one cannot find a proof because it does not exist. And this happens for very simple statements, such as the Goldbach conjecture, that anybody can understand easily.

Then, one question arises: are there many conjectures of this kind, simple, true, with no existing proof? Some could say that the decomposition of a number as the sum of two prime numbers is an irrelevant problem. I do not agree: a similar problem is the decomposition of an odd number as the product of two prime numbers, and it is very important, especially for cryptography.

It is possible that the true and provable statements are only a small subset of all the true conjectures. In that situation, along with mathematics, we have to create a new field of research where one would find true (and sometimes ultra-true) conjectures for which no proof exists. Then, with all the power of mathematics, we would use them: the absence of formal proof must not deter us to do that. We know the importance of the Riemann conjecture; there are probably several other conjectures that would also be useful.

AI is ideally suited to this kind of research: a system can create and check a huge number of candidates, much more than any human being can do. It is not enough to build artificial mathematicians, whose performances would significantly exceed those of the best human mathematicians. Improving the investigation mentioned in a preceding blog, a new branch of AI will have to create conjectures very cleverly.

They are going to judge us!

Several AI systems currently have performances well above those of the best human experts. This allows the realization of systems that can assess the quality of human performances, much better than we could do.

Particularly, for many games, some AI systems are far better than the world champion: a Go program has recently won against two of the best Go players. Here, we will discuss of an outstanding study made by Jean-Marc Alliot on Chess; it was published in the first 2017 issue of the Journal of the International Computer Games Association.

For about fifty years, a method is used to determine the strength of chess players: an integer, his Elo, is associated with each player. It is computed from the result of every match that he has played (win, draw, loss), and from the Elo of his opponents. Now, Magnus Carlsen, the world champion, has also the highest Elo: 2857; less than 800 players have an Elo greater than 2500, most of them are International Grandmasters. It is difficult to evaluate Elo for the best chess engines: human players are not strong enough. Therefore, matches between human and computer have become very rare. Moreover, when a human agrees to play, he often requires to fight against a crippled engine for instance, without endgame table base or with odds (usually a pawn). As such, Elo for chess engines is mainly based on competitions between themselves. For the present time, the best ones are almost at 3400. With Carlsen, the difference is over 500; this indicates that the engine would win a game with a 0.95 probability.

Lacking anything better, chess players were content to use this rating system, although it can evaluate neither the moves, nor the quality of a game. Now, for the best chess engines, we can consider that they are playing the best move. If a human player chooses another move, one can evaluate its quality: it is sufficient to find the value given by the computer to the position after its move and the one after the human move. The value after the computer move is always greater or equal to the human move: if it was lower, it would not have played its move.

In fact, the author could not use a system with all the Elo difference that is theoretically possible: he cannot access a computer with all the processors which were used for the best performance; moreover, in order to limit computer time, the time allowed to a move was decreased. The system used for these experiments was a chess engine in the top three, STOCKFISH, which has also the benefit of being open source. With the restrictions on the computer speed, the Elo advantage on the world champion is now 300; the engine will still win, but only with a 0.85 probability.

Knowing the difference in value between the computer move and the human move allows to know the quality of each human move exactly. This could be useful to annotate a game, showing the good moves and the weak ones and, for each of these, to indicate what would have been the best move. However, this was not the goal of this paper, which has other purposes. The basic element is the construction of a matrix giving the probability that the move played by a particular player will change the value of the position; this probability depends on the value of the position before this move.

For each year of activity, this matrix has been computed for all the players that have been world champion, but not for those who played against a world champion, and never win: all the Ponomariov games have been considered, but not all those of Kortchnoi. Naturally, one considers only the games played at regular time controls, and in normal conditions: one does not keep blitz, blind, simultaneous, odds games. There is one matrix for playing White, and another one for playing Black. All in all, the system has analyzed 2,000,000 positions.

An element of the matrix is the probability that, when the value of the position is VA, the value of the position after the move has been made is now VB. The values are measured in pawns or in centi-pawns. For instance, we know that, in 1971, if Robert Fischer, playing White, is one pawn late in a position, after playing his move, he would still be one pawn late with a 0.78 probability, 1.4 pawn late with a 0.12 probability, and 1.8 pawn late with a 0.10 probability. The new value can never be better than the old one since we assumed that the machine is infallible.

Thanks to these analyses, the author describes several interesting experiments; for example, it is possible to find the probability of the result of a match between two players, when the matrix is known for both. One assumes that the game is won by a player when he is at least two pawns better. As one has Black and White matrices for Spassky-1971, and the Black matrix for Fischer-1971, it is possible to compute the ten elements vector that gives the probability of the result of a game between these players in 1971. Here are some of these values: Fischer wins (0.40), Fischer’s advantage at the end is 0.6 pawn (0.07), perfect equilibrium (0.14), the final position is -1.4 pawn (0.01), Fischer loses (0.07). I emphasize that, at this step, the computer plays no move: it uses the vectors indicating the performances of each player. It only plays moves for computing the matrices.

These methods play a different role than the Elo, which evaluates a player for all its games against many players from only their result. Here, one is interested in the moves, and not by the result. Moreover, one does not define a vector against any player, but against one particular player in a particular year. With this method, it is possible to find the result of a match between Fischer-1971 and Fischer-1962! The paper gives the results of a virtual competition between the 20 world champions, taking for each one the year where he was the best, which is not always the one where he was the world champion. For instance, we learn that Kramnik-1999 had a 0.60 probability to win against Lasker-1907. In some cases, the result is analogous to Condorcet paradox: Petrosian-1962 wins against Smyslov-1983, who wins against Khalifman-2010, who wins against Petrosian-1962!

I cannot summarize a paper which contains many remarkable results from the analyses made from all the matches played by at least one past, present or future world champion. In his conclusion, the author plans to achieve this also for all the games in Chessbase where both players are above 2500 Elo.

This paper shows that it is extraordinary helpful to have an AI system that is well above the best human beings: one can very precisely appraise human behavior, and one can compare the performances of people who lived at different eras. Studying the capacities of an individual is therefore made with accuracy and completeness, incomparably better than with multiple-choice tests. Who knows, in some distant future, AI students will perhaps compare in their thesis mathematical geniuses such as Euclid and Poincaré!

An impossible task: to foresee the future of AI

Sometimes, we see predictions on an idyllic future of AI or, more often, on the catastrophes that it will cause. We love to scare ourselves, in that way we are sure to make newspaper headlines. However, given the vagueness of these predictions, it is impossible to see whether we could overcome these potential difficulties. Some even want to stop AI research; this is due to a distrust of science, and will leads to the catastrophe that they want to avoid. Indeed, to run efficiently a country or a large company is a daunting challenge; I believe that it exceeds the capacity of human intelligence. Refusing AI’s help will more surely lead to a catastrophe. In particular, some are worried that the robots would take power, and will enslave us. They believe that all intelligence must be similar to the human one; therefore, robots will be aggressive and overbearing, as ourselves. In fact, we have these characteristics because our intelligence is a product of evolution in a resource-constrained environment. However, Darwinian evolution is not the only path for creating intelligent beings; I even think that it is not the right direction in AI research: it requires too much time and too many individuals.

It is unrealistic to predict how AI will turn out for the long term. To be convinced, it is enough to look at what recently happened in Computer Science. Sixty years ago, who saw what it is now? I took my first steps in this domain in 1958, and almost all those who were in this area thought it would be useful for scientific computing and business management; nevertheless, in those days, no one was thinking about the Internet and the Web. Moreover, we did not think that the cost of computer time would decrease so fast. Only one hour of computing on the fastest machines was very expensive, it far exceeded a one-month salary. Their power seemed amazing: almost one Million Instructions Per Second for the IBM 704, the workhorse of many of the first AI realizations! We did not think that their power would incredibly increase, while their cost would incredibly decrease: c.1965, someone suggested (and I am not sure that he believed it) that, in the future, the computer plant visitors would receive the CPU as a key fob. We all laughed at this joke, how could such a precious component could become so cheap? Changing drastically the cost of computing has made it possible to realize applications that were unthinkable. This is the main reason in the mistakes that I had made in 1962, when I had written a paper describing the state of AI. Naturally, there was a section on its future; among my predictions, some were true, and some false. The main reason of my mistakes: I had not seen that the computer cost would go down so much, and that the computer power would go up so much.

However, it is possible to predict some specific achievements: for instance, there will be self-driving cars: this is the normal course of events for a research well under way. It is reasonable to think that with AI improvements, some professions will disappear, such as it already happened with computers. Unfortunately, many changes are impossible to foresee: they will depend not only on new research directions for AI, but also on progress in other domains, particularly with computers.

I strongly believe that all human activities, without any exception, could be undertaken by AI systems, and they would be much better than us. However, I do not predict that this will happen, even in the far future: human intelligence is perhaps not enough to reach his goal. Creating systems that create systems is an extremely difficult area, and evolution did not optimize our capabilities in this field.

Moreover, the research structure does not encourage what needs to be done. Many researchers do an excellent thesis but if they want to pursue a career, they must quit the kind of research that is interesting to the future of AI. New ideas come naturally when one develops a large system with a computer; to do that, for many years one must spend at least half of his time on it. This is impossible if one also has important responsibilities as a teacher and as a manager. Besides, the weight given to publications is not a favorable element in AI research: how can we describe a system that uses much more than 10,000 rules? It is almost impossible to do for a system with many meta-rules that create new rules. It is much easier to write a theoretical paper, which will be understood easily. It is no coincidence that several teams that recently achieved spectacular results were not from the university, but from the industry. However, the industry’s goal is not to develop research for the very long term: profitability is important for any business. I believe about the importance of bootstrapping AI, although this will take a lot of time and the results will be poor for long enough. This encourages neither the university, nor the industry to engage in this way.

I do not want to give precise predictions for the long term, mission impossible. Nevertheless, I am sure that if we succeed to bootstrap AI, the consequences will be immeasurable: intelligence is essential to the development of our civilization. However, we cannot conceive what could be a super-intelligence, in the same way that a dog cannot conceive what is our intelligence. And, finally, it is very possible that this goal will never be achieved because human intelligence is too limited for such a huge task; even so, it is worth a try.

Algorithms to Live By

 This book, published in 2016, was written by a science journalist, BrianChristian, and by a specialist of Cognitive Psychology, TomGriffith; its subtitleis: The Computer Science of Human Decisions. AI researchers have always been very interested by human behavior: when we are developing a system that solves problems also solved by human beings, we try to find what methods we are using, and we include them in our programs. Here, the authors have a goal that is quite the opposite: they show that we, humans, can learn from the way computer systems solve problems, even for problems of our everyday life. They are not at all focused on AI: for them, every computer system may be interesting.

Sofar, I did not particularly think on this issue, but this is indeed an interesting idea. They are using many real-life examples of situations from everyday life, such as getting the best apartment, searching for a parking place, finding a restaurant, and so on. Some come from the authorspersonal experience.

I enjoyed their practical approach, but some academics may not like it, preferring to be abstracted from the real world. In the October 2016 issue of the AI Journal, ErnestDavis published an interesting review of this book; however, he does not like that way of presenting their views: «After reading about how Michael Trick used an algorithm to choose a wife, and how Albert McLay organizes breakfast for her children, and….., I started to have a craving for impersonal technical papers written in the passive voice.» For my part, I like this way of choosing situations easy to understand, without the need of a cryptic formalism.


I cannot consider all the topics examined in this book: when to stop looking, forget about it, when to think less, when to leave it to chance, the minds of others, and so on. The authors show that we could be more efficient if we borrow some of the methods used in computer systems.

For instance, in the chapter “Sorting-Making order”, they consider a problem that concerns all sports persons: how to order the best athletes. For tennis, the loser of a game is eliminated from the tournament. This provides the best player at the end, but produces little information about the strength of the others: the second best one was perhaps eliminated by the winner in the opening round. On grounds of efficiency, a race is much better than a fight: this gives a measure on the performance for all the participants. It is no longer necessary to fight again many players: at the end of a marathon, every runner knows his position compared to all the others.

Unfortunately, it is not always possible to eliminate fights everywhere. However, the solution chosen by the mammals for determine the alpha male is not very satisfactory because it often leads to too many fights. For their part, fish use a simpler method: the dominant is the biggest. With computers, sorting and ordering is made more quickly that fifty years ago, there are no longer unnecessary operations.

Tennis is not a perfect example: we are not so much interested in knowing who are the best players, we want many beautiful contests. If the ordering method is inefficient, we will watch more tennis matches! 150 years ago, Lewis Caroll showed that it was necessary to improve this method. Since that, there was some progress, particularly with the introduction of seeding; however, improvements are still possible. Personally, I think that one could use the difference in playing strength between the players during a match: the result was tight, one player was severely beaten, etc. A computer scientist knows that one can improve a result when an important information is not used.

Apart providing advices on how to organize ourselves better, this book also explains our behavior from understanding how computers work. For instance, it is well known that our memory deteriorates when we grow older. Wagging tongues discreetly hint to Alzheimer but, in the caching chapter, the authors explain that we have the same difficulties as computers to handle a lot of information. The more elements are in the memory, the more it takes time to retrieve what one is looking for: they call it “the tyranny of experience”. A ten years old child knows a few dozen friends; twenty years later, we know hundreds of people: in the towns where we spent some time, in the corporations where we have worked, the friends of our spouse, not to mention Facebook. Finding something can take more time if we stored it in an almost non-accessible area; we may even have decided to forget it in order to make room. When they have accumulated a substantial amount of information, old people and computers have the same problem: how to store it so that what will probably be useful will be quickly and easily accessible. Unfortunately, for everything remaining, one has to wait or to fail.

The authors essentially refer to Computer Science, although they mention several times “machine learning”, an AI subdomain. In my view, chapters inspired by AI could be added. Certainly, some AI methods cannot be used by human beings, mainly because our brain does not work fast enough: we cannot consider billions of Chess positions! However, in some domains, AI may be a source of inspiration, especially problem solvers that use heuristics.

Too often, teachers do not explain their students how they could solve a problem, and many students believe that there exist a special math skill (which they do not have) which is a prerequisite for solving mathematical problems. Let us take an example from Gelertner‘s Geometry Theorem Proving Machine: it must prove that an isosceles triangle (two equal sides) has two equal angles. Here is a machine proof:

It is assumed that triangle ABC has two equal sides: AB=AC. Triangles ABC and ACB are equal because their three sides are equal: AB=AC, AC=AB and they share BC. Therefore, the angle ABC of the first is equal to the corresponding angle ACB of the second.

If I had to write a Geometry program, I would have introduced a rule such as: if one must prove that two angles are equal, consider two triangles, each one containing one of these angles, then prove that these triangles are equal. It does not always succeed, in the present situation five triangles containing the angle ACB can be compared to triangle ABC: ACB, BAC, BCA, CAB, et CBA. The last four are not working, but the first one leads to the solution given before. With this rule, the student can understand how this solution has been found, and he can use it for other problems.

When an AI system makes many trials for finding the solution, it can indicate why it has to consider them. Even when they fail, it is interesting to show them because, in other situations, they may be successful. If the students could see how an AI system has found a solution, including its unsuccessful attempts, this would certainly allow them to perform more effectively afterwards.

This book is a most enjoyable read, but it could be completed by chapters adding Artificial Intelligence to Computer Science as a source of inspiration.

Everything but the essential

One Hundred Years Study in Artificial Intelligence is the title of a very interesting report that has just been published by a group of prominent researchers in AI. One of their goals is that «the report can help AI researchers, as well as their institutions and funders, to set priorities».

The report considers a large variety of domains; it shows that AI could be very helpful in situations where it is difficult to find an adequate staff. This is especially the case for health care. In particular automated assistance for the clinicians, image interpretation, robotics, elder care, etc. are very promising directions of research in this domain. Self-driving cars and home robots will change our day-to-day life. With intelligent tutoring systems, the students will get help adapted to their needs. This report provides an overview of many activities where AI systems will be able to help us in the next fifteen years.

It seems that the authors have begun to explore what the future needs will be; then, for each one, they have carefully examined what AI techniques could be useful. For that purpose, they did a wonderful job: if we make the required effort, many applications will be in widespread use throughout the world in 2030.

Curiously enough, the authors have completely forgotten a domain with really high needs, which they should be familiar with: to help the development of AI research!

It is very difficult to conduct AI research, especially if we just don’t imitate human behavior, where we improve our own results thanks to powerful computers. This vision of intelligence is anthropomorphic: other forms of intelligence exist. Unfortunately, building a super-intelligent system is perhaps too complex for human intelligence with all its limits: we have been shaped up by evolution only for solving the problems of our hunter-gatherer ancestors.

Serendipity allows us to produce acceptable results in new domains, such as computer science, mathematics, management, etc. However, they are necessarily limited: evolution lacked time so that we can adapt to their specific requirements. Our geniuses are probably not as good as they think, in the kingdom of the blind, the one-eyed is king. We are awfully handicapped by our working memory, with only 7 elements, and by our reflective consciousness, which ignores almost all the events that occur in our brain. Therefore, we will not get far without AI help. If we want to increase more and more AI performances, we must call upon AI assistance.


This has been completely ignored by the report, where the word “bootstrap” does not even occur. However, this is a technique well adapted to the resolution of very difficult problems; moreover, developing AI is an intelligent activity, therefore it depends on AI. The authors only say: «No machines with self-sustaining long-term goals and intent have been developed, nor are they likely to be developed in the near future.». This is almost true for the existing state of AI, but it is imprudent to predict what will happen in the next 15 years: progress is very slow in the beginning of a bootstrap then, suddenly, things move quickly. Naturally, if this kind of research has no priority, this is a self-fulfilling prophecy: we will be at the same situation in 15 years. Nevertheless, if this kind of research receives a small part from the funds rightly allocated to the applications described in the report, the results will likely surprise us.


The importance of bootstrapping AI is seen since its beginning: in 1959, Allen Newell and Herbert Simon considered the possibility for their General Problem Solver to find the differences necessary for GPS itself. The bootstrap has two major drawbacks: it is slow, and hard to achieve. However, many achievements of our civilization come from a bootstrap: we could not design our present computers if they did not exist.


Few AI researchers are presently interested in this approach. I suspect that many AI researchers even think it is impossible, while most of the others believe it is much too difficult to embark on this path, taking into account the current state of development of our science. Stephen Hawking is really a genius: although he is not an AI researcher, he has seen the strength of such an approach. It is unfortunate that he wrongly concluded on the dangers of AI.

What is in this report is excellent, I am only critical of what is missing, which is essential for the future of AI. In the end, it lacks coherence: the authors rightly say that AI will significantly help the resolution of many important problems in many domains. However, they do not think to use AI for the most important task: to advance AI, which is central to the success of all the other tasks considered in this report!



Ladies and Gentlemen Mathematicians, now it is your turn

A turn for what? Well, I have seen twice the same succession of events. Firstly, outstanding specialists of a domain assert, without any justification, that an AI system could never outsmart the best human experts of this domain. For many years, they are right, and they laugh at the poor results obtained by the first programs. Then, suddenly, everything changes: artificial systems outperform the best humans.

This happened for Chess, and recently for Go. I believe that the next domain where this sequence of events will occur is mathematics, a propitious domain for several reasons. Firstly, as games, mathematics is far removed from reality; the researcher has not to confront the many constraints coming from the real world, such as it is the case for driving a car. Secondly, games have been created by humans, based on what they can do best: from the start, we, humans, are in a good situation. On the contrary, mathematics has not been developed to solve problems that are not too difficult, but to solve useful problems. It is not obvious that mathematics is as well suited to our capacities as games; therefore, artificial beings are in a much better situation than for games: they could use all their qualities, in situations where they are essential, and where we are not very good. Our intelligence results from the importance for our ancestors of hunting and fighting for surviving and breeding. The fighting aspect is important in games, but not in mathematics. There is no reason why human intelligence would be well adapted to mathematics. It is simply the case that some capacities developed for other goals are somewhat helpful for mathematicians.

For the present time, no limit is known that would prevent AI systems to outperform human mathematicians. The well-known incompleteness theorems restrict what can do any cognitive system, human or artificial. Nobody could ever prove a result if no proof exists for this theorem in this theory.

Fist-class mathematicians have claimed that machines could never be very strong in mathematics, but they never justify this assertion. For them, it is not necessary, it is evident. However, a good mathematician should know that, when there is a mistake in a proof, it is often when one says that something is evident. Probably, they are so confident because they do not see how this could be made. This is normal: they are mathematicians, not AI researchers, this is not their job. In the same way, Chess and Go players’ job was not to write Chess and Go programs: they could not foresee what happened.

Mathematics is also a very interesting domain for AI because their results are extremely helpful. It is natural to invest in artificial mathematicians: their discoveries will be more useful than those of a Chess program. Naturally, their role will not be only to prove conjectures: they will have to build new mathematical theories. Pioneering works, such as those of Douglas Lenat, have shown that an artificial mathematician could discover concepts it did not know. For instance, for a function, it is interesting to consider the situations where the values of two arguments are the same: from addition one discovers the concept of double, and from multiplication, the concept of square. As extreme situations are often remarkable, considering them leads to the concept of number with few divisors, the prime numbers. Surprising its author, Lenat’s program studied also the numbers with many divisors; then Lenat discovered that Ramanujan had already studied them. Naturally, a lot of work is necessary for developing systems with many more possibilities that this old system, but this is certainly not impossible.

CAIA has a powerful method for solving problems where it cannot use a combinatorial method because there are too many possibilities, and even sometimes an infinite number. With the meta-combinatorial search, one does not consider all the possible values of a variable, or all the legal moves; instead, one considers many methods for trying to solve the problem. One can waste a lot of time, with methods that fail; however, at the end, one has an excellent solution, as one keeps only the methods that are necessary for justifying it. When one has a good set of methods, one may find sometime surprisingly elegant solutions. As computers are much faster than human brain, they can perform a meta-combinatorial search wider than those made by human mathematicians.

To date, AI has progressed rather slowly in the Universities, which are certainly not the right place for developing very complex systems quickly. Since recently, industrial firms have heavily invested in AI realizations; it is no coincidence that IBM succeeded for Chess and Jeopardy!, and Google for Go. They moved to the upper category very fast: before AlphaGo, I did not think that an AI system would win again one of the best professional Go player before ten years.

In view of the importance of mathematics, it will be tempting to create a competent team, with substantial resources: they could rapidly have results more valuable than would be expected. Human mathematicians would help us to understand the results of their artificial colleagues, so that they could be used efficiently and effectively. Naturally, they will also continue to do mathematics for the fun, in the same way as Chess and Go players are always playing their favorite game.

A long-awaited success for Go

 In recent years, for most games, programs won against the best human players. However, one game was still dominated by human experts: Go.

Go has a unique place among games: the number of legal moves is around 250, and the game length is near 150. If one wants to consider all the possible moves, the tree is so large that it is infeasible. For such games, a solution is to have an evaluation function, that predicts the value of the corresponding terminal position. Go is so complex that researchers were not able to find a satisfactory function. Winning against the best Go players was the holy grail of AI.

Therefore, for a long time, human Go players made fun of programs, which did not even have the level of a beginner. In the 70s, Chess players had the same contempt for Chess programs.

Google Deep Mind has just developed an extraordinary system, which has won 4-1 against one of the best Go players in the world: Lee Sedol. For this achievement, AlphaGo received an honorary “ninth dan” professional ranking, the highest possible level. This citation was given in recognition of AlphaGo’s “sincere efforts” to master Go’s Taoist foundations and reach a level “close to the territory of divinity”.

AlphaGo is based on general purpose AI methods, which have already been used for Go programs, but with far less success. A paper, published in Nature, gives a lot of information on this system: Mastering the Game of Go with Deep Neural Networks and Tree Search.

It uses neural networks for learning from a huge set of results: the more results, the better. In that way, it builds several functions: one of them estimates the value of a position, and another predicts good moves in this position. For one of these functions, it has used a database with 30 millions moves. It is also able to use the moves generated when AlphaGo plays against itself. It is extraordinary that AlphaGo already plays well using only the neural networks, without developing a tree.

However, it plays better when it develops a tree, while always using its neural networks. For considering the future possible moves, AlphaGo uses random Go, that has been introduced in most-recent Go programs, after Bruno Bouzy shown that it gave a strategic vision to the program. For evaluating a move, one plays it; from this position, one develops thousands of paths. At each step, one move is chosen randomly among the best moves found by the neural network. When this is completed, it chooses the move that has the highest mean of all the terminal positions of its paths. Naturally, parallelism is very useful for this kind of search: At Seoul, AlphaGo had 1202 CPU and 176 GPU. However, if it develops a very large tree, it is significantly smaller than the trees developed by Deep Blue against Kasparov. This method was very efficient in the end game, where it was playing perfectly, because the number of legal moves is not high. Its opponent had no chance of winning the game, if it had not an advantage at the end of the middle game.

The authors of this program have masterfully coordinated all these methods for developing a program with outstanding performances. I believed that some day Go programs would be stronger than the best human players; I did not expect that it would happen so fast.

It is interesting to note that an industrial team achieved this success story. Google provided appropriate means to face this challenge, and the researchers could dedicate all their energies to this goal. On the contrary, a university researcher has many additional time-consuming tasks: teaching, writing papers, administration, seeking funds for his projects, etc. At least 50% of our time must be affected in the development of a complex computer system: without this, it is impossible to control anything. It is exceptional that a university researcher has this possibility. Probably, the future of AI is not in the Universities, but in large industrial companies such as Google, IBM, Facebook, etc.

I am slightly less enthusiastic on a minor point. In a preceding post, I have said that AI researchers have two flaws: they are too clever, and they work too much. Therefore, their systems include too much human intelligence, and not enough artificial intelligence: modules designed by humans must be replaced by meta-modules that create these modules. My criticism may be a bit exaggerated, since many important components such as the functions used by neural networks have been automatically learned. However, the Nature paper was co-authored by 20 researchers, and that makes a lot of human work and intelligence.

A negative consequence: AI has no longer a holy grail! We need a new spectacular task that is not too easy, but not impossible. Google, which just removed the preceding one, could use its search engines to find a new holy grail from its massive amounts of data.

To conclude, one cannot help but admire this result, which happened long before the most optimistic researchers expected it.