Not QGS

0:00 I'm now going to test the Sony microphone. That's the large double-ended stereo Sony microphone with this recorder. It's the evening of the 5th of August 2005 and I'm in the Balassi hostel overlooking Budapest, looking across at the castle hill. And we'll be recording Eamon's talk tomorrow. I'm very concerned that some of the recordings of the Fouché-Lancôme trial with Ludwig, Cartier, Collin and the others may have been compromised through the use of the smores in the microphone, which appears to be completely defective. I'm not sure when it became defective. Fortunately, I have audio backups of most of those, of all of those, but again, the audio backups were made using this not-sandy microphone. I must now check all of the tapes, audio and digital, for 2005 and 2004 and 2003. Check all of them. I've got to go through everything. I've got to go through everything anyways. In order to get the entire recordings archive catalogued. Okay, I'm going to switch off now, and the next recording will be using the small Sony microphone, the one which we think is a result of, sorry, Sony microphone I should say, the small Sony microphone. The next recording will be using the small Sony microphone with the Sony recorder, which is the one which appears to be in damage, which wasn't recording at all on track 4 of the digital recording, so the consequences of using that are... Well, the registration of the recording level seems to be registering OK, so I don't know what's going on here. I am now using the small microphone. Let's see how both of those passages recorded.

2:30 You can see the following description there, which I will just show you. An alphabets, I took a bio-alphabet. Then we have to choose a natural number. And then we have to define correspondence for each number of our alphabets. And all these things we don't know, so I'm going to immediately explain them all, so it's a 0 corresponds to 0, and 1, 1, 1, 0, 5. At last we have to choose an initial assertion to start with. I'll just choose an arbitrary one. What do we do? We use the natural number p. To eliminate the first three letters of our string, and then we add the string corresponding to the first letter of our string, so we add, I will, this should be the same, and we add 1, 1, 0, 1, then we do the same again. So, as you can see these systems are very very different from each other. This is the same example. So what is the problem of that? There were two variants post-formulated. The first was to obtain a finite procedure to determine for any initial secrecy whether the resulting iterative process does or does not terminate.

5:00 The second form, which is very closely related to the Philips problem, was that the second formulation, or initial assertion, is part of the basis of the system. The second problem, then, is to determine for any given sequence on the alphabet of the basis whether that sequence will or will not be generated in the course of the determined process. So, Post wanted to solve these two problems for attack systems, but he did not try to find the proof first. He began to work out These are specific cases, so he tested what the results would be when choosing an alphabet with three letters, with four letters, with different keys, and so on, so that's how he started to perform real calculations for mathematics in a way, and that is what is interesting here, is that it was these calculations that... That surprised him very much because he thought that the systems would be very, very simple to understand because of their own simplicity, but they gave rise to what he calls the Wildring complexity. Here you can see on this slide the number of letters of the alphabet in these natural numbers. So we showed how mu smaller than or equal to 2 and p smaller than or equal to 2 are solvable. Then you can see... Well, when we're bigger than two and we're equal to two, we call them tractable, and when we're greater than two and we're equal to two, we identify as being of devising complexity. To further illustrate that, that systems are indeed very, can indeed be derived through some kind of complexity, and we're too small. For example, there you see the evolution of the system for thousands of steps or so. You see the regularities induced by all three elements moving from the left, the lines going to the left.

7:30 I think black is zero, and zeros and blacks are the ones. I used to iterate a DAX system, and then every hundred string I measured the length and got it from the graphic, and then I compared two strings which were partly identical, that it was only one digit, and as you can see the behavior. The behavior of their legs, the evolution of their legs is quite erratic and they also seem to diverge, although they were almost identical when they were installed. So, Post was really frustrated by this problem of that, because of his idea that it would be very straightforward to solve the problem of that. And finally, Levin, to the conclusion, he had not expected that at all, because when you read his evaluation, it is very clear that he was very much convinced of the solvability of the... For a while, the case PS2 seemed to be more promising, since it seemed to offer a greater chance of a finally great series of problems, but when this possibility was explored in the early summer of 1921, It rather led to an overwhelming confusion of classes of cases, with the solution of corresponding problems depending more and more on problems in ordinary non-material. Since it had been our goal that a non-difficult piece of non-material would, as it were, be dissolved in the particularities of this more primitive form of mathematics, The solution of the general problem of tech appears hopeless, and with it our entire program of the solution of the finiteness problem.

10:00 This frustration, however, was largely based on the assumption that tech was but a minor, So, after nine months of work on tax systems and his experiences with these tax systems, he got to his major results of the government anticipation. He first constructed these systems in canonical form C. I do not know if you know post-production systems, but these are systems in canonical form C. And through that system in canonical form B can be reduced to a canonical form C. Then, deconstructing the importance of systems in normal form. These normal form systems we later used in his illustration on recursivity in the order of sex and decision problems, which was one of the founding principles of our recursion theory. I will not go into the details of it. Normal form is very simple, you just have an initial assertion and a finite alphabet to start with, and all your production rules have to be of the form G, P, T, U, Z, P, G, S, G, M. Which means that when you have an initial string, you choose... Maybe I should give an example... So I will only give an enormous system with one production room. For example, let's say that our production room is and that system is in fact a subclass of a system in which we now have four. So when you have a stream starting with this stream and then the rest of the stream, that produces Then you get this tree with this area here, so... That's why you need several productions, because when you take only one, only a very small clause of initial streets, you would get... So we're just... You get two better normal systems. This is my comment on normal systems.

12:30 He further showed, and that was very important, that systems in canonical form C can be reduced to systems in normal form, systems in canonical form C or more. All of these are involved and more difficult than systems in normal form and by showing that these could be reduced to systems in normal form, he was led to what Martin Davis calls post-thesis because that convinced him of the computational powers of systems in normal form because of the fact that this difficult form could be reduced to a system in normal form. He said that everything that can possibly be generated by any system of unitary symbolic logic can also be generated by a system in normal form, and that is due to its normal form theory. But of course, his analysis, and he notices it himself, was not satisfactory. As he says, for full generality, a complete analysis would have to be given of all the possible ways in which the human mind set up finite processes for generating sequences. This he would do in his He also described the Knit Combinatory Processes Formulation 1 in 1936, in which he describes ghost machines which are widely identical to Turing machines. It's less famous, but it's quite the same. He did not have the formalism of the universal machine, and not the decision problem in 1936. Maybe that's why it's not so famous. It is true, of course, that there are absolutely unsolvable problems, because through diagonal methods we showed that the finitivist problem for systems in normal form is unsolvable.

15:00 We further showed that there are relatively undecidable propositions. We showed that every system of finitary logic is incomplete. This is incomplete. And that every time you export such a system, it will be incomplete again. After this, we close the circle by showing that systems in all forms are reducible to systems that cannot be formed in each hand, and that all these systems became equivalent to each other, except for the stack system, which was shown by Martin Minsky, that the stack systems are equivalent to the universe of tuning machines, so we saw the impersonal sortability of stack systems in 1961. So, for me, what's for me? Okay, okay, then I'll end this. So, I just want to state clearly again that this problem of tech, and especially the fact that we had to do these calculations to reorient this complete program, that this problem of tech is really fundamental to this research. They showed him that we feel that this problem might not be solvable, and they also led to this... There are several quotes he gives which clearly show that his staff systems led to his normal systems, but I cannot give them here, so I just conclude. So from theory to practice and back again, what I like very much in a post account of an anticipation is As probably is already very clear, is that he started with a very theoretical program and it was only through the ugly calculations that he completely reconsidered this program and changed the direction of this entire program. And I think this is a fact that is often obscured in the published results on logic and mathematics for the sake of elegance.

17:30 While they are often necessary to get at these elegant results, so, and I think most people need to put them into their space. It's time for one question. At the beginning you made it clear that most wanted to prove the decidability to believe in themselves. I was surprised to hear that because I thought that it was Hilbert in the late 1920s who first... Go to the question of whether this is... So I wonder, how did Post think about the readings, particularly of Seneca? What did he mean by the readings of Seneca? He meant the same as Seneca. The same as Seneca? Yeah. Okay. I would also like to state that I should really like to... I also wanted to discuss about the publicity for the text of his books, because I think it is particularly that his work is often that he really anticipated these results of real Jewelry and Church, and his approach is very different from that of real Jewelry and Church, for example, has a different kind of numbering system, he used a slightly different diagram on it, and things like that. I also wanted to discuss it, but it is particularly important. I think it's very important that this text invests more mathematicians and mathematicians. Any questions? Maybe you could give us the reference, the exact reference where this is published. It's in the only sign of it. I'm often late from 65. It's been published in 2002, I think. It's also traditionally collected to our experience books, but that's more difficult to get.

20:00 What journal was it originally? It was not published before Multimath. He submitted it in 1941. He did not dare to submit it in 1921. He had problems with his health and he already had some difficulties in getting certain results published. And in 1941 he submitted it to the journal. It was rejected because of the fact that the results were already there.

30:00 Inferences generally extended to the point of the information between now past and to a certain point. Also, the staff at each path node will consist of establishing the certain possible information into the definition going forward and the definition going backward.

32:30 In the first case, we depart from a rather crude affirmation in data physics. All those things include the affirmation which we find in their consequences. Whereas in the second case, with the power of rules, we verify the certain consequences. All the consequences must also be verified in this sense. And we turn back to the test. This transforms its affirmation into a new sub-objective or the proof. Searching rules where it can appear. All are the process when we find the required affirmation in the last consequent problem or the last antecedent according to the selected method. The rules hold a free advantage for the classical logic. In the classical logic, as you know, the reasoning were monotonous without contradiction with the present tense. In the RBS, we can relate back dimensions of BF according to the new inferences. This way, the resulting numbers, because we can modify the conclusion. Then, a new question appears. What should we do with the conclusion that we mentioned now in math?

35:00 For this project, we need to introduce The concept of type of dependence of a rule, which probably is reversible if we relate affirmation then we relate automatically the above infrared fact and irreversibility if the fact, according to Paris, cannot be related neither change. And in the case of some rules of vital time, which must be executed first, such rules Constituted in each step the complete set of dynamic set of decisions or control of results. There exists a strategy for electing each time a rule in the complex set such as order of rules, control of agenda, criteria for actuality, This includes and determines the most recent information. The AI must take care of the control of the repetitive model. The term of specificity allows to execute first the most specific rules, that is, those with more facts in each and every one. So, between 1, A, B, and C, we must say R2, because it is more specific than R1. So, with mechanism of preparatory, we prevent executing only a rule one uses. Thus, exist more information which allow or recommends that, in general, anomalous case. Activating all neutrals.

37:30 Meta-rules, reasoning about others. Such meta-rules can collaborate in the control of reasonings. Change or assignation of priorities to another group, according to the simple set of some different elements. For instance, the intervention of rules in the brain system, the usual way of abilities. Such system as it is. We must distinguish between phases, the properties of the field, and develops the procedures associated to the brain system. Types of assets. Defectarium, model, value, restriction, certainty, the passing of assets. Types of results. There is TCD, modification, relating, assignation, and liberal law of assets. They are a structure of knowledge. Which organizes the information relative to the economical-spiritual situation, that is, always or almost always identical to those of our students, or at least very similar, for instance, to a cinema or a bookstore. The words in the suggesting ideas are similar to me. The object still can be seen, rolled, object, place, name, position, instrument, and result. Its implication is almost evident. According to their name, for instance, design, the energy, secondly, the result, the mass of time, when we have to find out about the net, the studies, nets, before they appear, the purpose of any useful system for the medical diagnosis by classical statistical techniques.

40:00 Such as the space theorem. Hilbert's analysis is a pair of G-D where G is a diagram of a cyclic connected graph. D is a distribution with the variables. D must verify the property of directional separation. According to which the probability of a variable doesn't depend on depth of the sentence. The PN consists in studies on the net. For the no variable, there is value. The commonality of the respective PN is finding the probability of success that can be given to determine the diagnosis. No certain symptoms. We need to work with the subsequent hypotheses. Exclusivity, sensitivity, and conditional independence according to the... With the hypothesis of exclusivity, two different diagnoses cannot be right at time. With the hypothesis of desensitivity, we should hold at all dispositions all the possible diagnoses. In addition to evidence, evidence must be mutually independent to a certain diagnosis. To the rigor walk of this revision, we need to introduce the V.A. In certain cases, as the vascular problems of predisposition to a heartbreak from the symptoms, there is a really reasonable system of revision and diagnosis of the main variables. Search methods begin. The essential process is the whole dimension of the blend search, in which we search.

42:30 In the first case, in blend search, we can, according to the type of problem between searching extent, search in depth. Search without the progression of the domain appears to be an initial attempt to the original model. For the real world, very important for the study of mathematics or mathematical theory. The searching process could be in a series of steps. Such searching procedures, yes, have applicability on problems with certain characteristics, as we can associate in the statement. There is a different situation of the mind. There is a series of initial states. There are operators which allow the step to be successful in the state. There is a finalistic process. It is obvious that the correspondents will read a state, a note of the gap, or read to the gap an operator. With each graph, we can exchange through the motion of the power the corresponding mathematics, physics and mathematics. In the study in Spain, for instance, we have done in the dream of the graph two levels. Logically, we can say for all the graphs, we can show this procedure from left to right. So, we obtain the least-cost solution if it exists. One line each time from the root node is every length added into the graph. We come back from this with one re-implication in the tree. An exponential living or dead living by saying the maximum length of the path from the root. For the same graph, we have nodes in this picture.

45:00 Also, we do searching with nodes on the domain in any cell type. It was generally so that all the paths can be explored by the computer. This tool is optimistic. And such exploration can frequently be very difficult because of the phenomena of combinatorial expansion, of the representation where we stand. Very special and temporal complexity can advise us against the realisation. For this reason, we need to select first. The most promising trajectories. In this way, we cannot obtain the best solution of an alpha and efficient approach to error. Now, we introduce a new mathematical tool, the heuristic evaluation function. For this function, we assign a value to each node. We use the estimate of the real distance node of the actual node N until the final node F. There is another procedure as a gravity method or liquid charge. In the structure of each node, we must select the link which connects with the node of the subsequent level where the value is linear, F, and so on. There are two distinct areas because of productivity. They find both solutions but not necessarily them. This may contain the introduction of the algorithm ASTAR with its useful property of completeness and admissibility according to this property C. There is solution 5. ASTAR is a particular case of the searching procedure of 5DL. There are many strategies for alternative exploration. We belong to the procedure of general searching. Against that, we will receive the opal leaf.

47:30 Initially, such is empty. The opal leaf is not empty or doesn't reach us. Taking this step, we go on with the process. Standing the subsequent node... The course of this iteration will be based in the previous assignment to each node of the value of fd. The selection of each node is obtained according to the smallest value of the heuristic function of the node of their level as an error. The cooperation is carried on into the operatives with the independence of the original level of each node. Generally, we prefer the solution of lesser problems. On the other side, the node will pass through a story in the closed space. Such a node remains inactive in the rest of the process. The resulting function can be decomposed into parts of a whole. A gate, for instance, a gate. G gives the real cost, node, of the best path, for instance, node to the current node, gate. It is known that graphically it is decided for the track signal of certain problems of the K-theory, as he said previously. The products created by classical logic show the inefficiencies for AI products. We need a more flexible tool with possibility of relation in the circuit. Indicating different degrees of non-versions to a set or in the fulfillment of a relation is simple.

50:00 Still more, capacity of subtleties in one word. For each time, we know the capital period set, where the limit element belongs totally to the set, although it doesn't belong absolutely, without possibility of intermediate separation. Also, the relation can be verified or not verified, but does not have one-third verification for each time. This must be possible because it is so in the real world, very different than in the formal world. The inclusion of concepts, concepts and methods of passive logic for the idealized set, the idealized set as one, must be modulated in the sense occurring adequately in the intervention or intercision of the real world. Now with the basic set, of course, with the time, when the classical logic reveals its linear equations for AI, a really more sophisticated logic, instead of the classical, not only the basic logic, is possible. Also, the present logic, with the IMDB, implements the model of energy. This extension of the predicate logic made possible to evaluate arguments including the concepts of necessity and possibility. The symbol would be a square and a triangle, but would be curved most of the way through. For this reason, the name of A is an A.

52:30 There are three types of physics. Necessary, if it is true in all the possible world. True, if it is verified in the real world. And possible, if it is true in some possible world, which is not necessarily considered with the real world. In combination with the logical equation, we can obtain the suitable new rule of Newton. This is passed in the mode to negation with a combination of square and diagonal interchange the order. Finally, about multiprogrammaries or theories, we can say that to formulate the knowledge of the domain in a more effective and efficient way, a theory becomes the key. According to the first of them, retinence formula must be demonstrable in two regions. According to the second, consistency, the new contribution to the system, must not generate inner competition with the previous asset or asset. The ductility must give a moderate complexity, at least in the daily calculates according to all experiments. The different processes must not result in excessive temporal, existential complexity. This includes the problem of the law of the class B and B.