(For those who have already read the previous parts of the translation of this lecture, rewind to ) [Hamming speaks very unintelligibly in places, so if you have any suggestions for improving the translation of individual fragments, please write in a personal message.]
This lecture was not in the schedule, but it had to be added so that there was no window between classes. The lecture, in essence, is devoted to how we know what we know, if, of course, we really know it. This topic is as old as the world - it has been discussed for the last 4000 years, if not longer. In philosophy, a special term has been created for its designation - epistemology, or the science of knowledge.
I would like to start with the primitive tribes of the distant past. It is worth noting that in each of them there was a myth about the creation of the world. According to one ancient Japanese belief, someone stirred up the mud, from the spray of which the islands appeared. Other peoples had similar myths: for example, the Israelites believed that God created the world for six days, after which he got tired and finished creation. All these myths are similar - although their plots are quite diverse, they all try to explain why this world exists. I will call this approach theological, since it does not offer explanations other than “it happened by the will of the gods; they did what they saw fit, and that's how the world came into being."
Around the XNUMXth century BC. e. the philosophers of ancient Greece began to ask more specific questions - what does this world consist of, what are its parts, and also tried to approach them more rationally than theologically. As you know, they singled out the elements: earth, fire, water and air; they had many other concepts and beliefs, and slowly but surely, all this was transformed into our modern ideas of what we know. However, this topic has puzzled people at all times, and even the ancient Greeks wondered how they knew what they knew.
As you will remember from our discussion of mathematics, the ancient Greeks believed that geometry, which limited their mathematics, was reliable and absolutely indisputable knowledge. Nevertheless, as shown by Maurice Kline, author of Mathematics. Loss of Certainty,” which most mathematicians would agree, there is no truth in mathematics. Mathematics gives only consistency for a given set of reasoning rules. If you change these rules or the assumptions used, the mathematics will be very different. There is no absolute truth, except, perhaps, the ten commandments (if you are a Christian), but, alas, nothing about the subject of our discussion. It is unpleasant.
But you can apply some approaches and get different conclusions. Descartes, having considered the assumptions of many philosophers who preceded him, took a step back and asked the question: "How little can I be sure of?"; he chose the statement "I think, therefore I am" as an answer. From this statement, he tried to derive philosophy and get a lot of knowledge. This philosophy was not adequately substantiated, so we never received knowledge. Kant argued that everyone is born with a solid knowledge of Euclidean geometry, and a host of other things, which means that there is an innate knowledge that is given, if you like, by God. Unfortunately, just at the moment when Kant was describing his thoughts, mathematicians were creating non-Euclidean geometries that were as consistent as their prototype. It turns out that Kant threw words into the wind, just like almost everyone who tried to talk about how he knows what he knows.
This is an important topic, because science is always turned to for justifications: you can often hear that science has shown this, proved that it will be like this; we know this, we know that - do we know? Are you sure? I am going to consider these issues in more detail. Let's remember the rule from biology: ontogeny repeats phylogeny. It means that the development of the individual, from the fertilized egg to the student, schematically repeats the entire previous process of evolution. Thus, scientists argue that during the development of the embryo, gill slits appear and disappear again, and therefore they suggest that our distant ancestors were fish.
Sounds good if you don't think about it too seriously. This gives a pretty good idea of how evolution works, if you believe it. But I will go a little further and ask: how do children learn? How do they get knowledge? Perhaps they are born with predetermined knowledge, but that sounds a bit unconvincing. To be honest, it's extremely unconvincing.
So what are the kids doing? They have certain instincts, obeying which, children begin to make sounds. They make all these sounds that we often call babbling, and this babbling, apparently, does not depend on the place of birth of the child - in China, Russia, England or America, children will babble in basically the same way. However, depending on the country, babble will develop differently. For example, when a Russian child says the word "mama" a couple of times, he will receive a positive response and therefore will repeat these sounds. Through experience, he discovers which sounds help to achieve what he wants and which do not, and so he learns a lot of things.
Let me remind you what I have already said several times - there is no first word in the dictionary; each word is defined in terms of others, which means that the dictionary is circular. In the same way, when a child tries to build a coherent sequence of things, he has trouble running into inconsistencies that he must resolve, since there is no first thing for the child to learn, and "mother" does not always work. There is confusion, for example, such as I will now show. Here is a famous American joke:
popular song lyrics (gladly the cross I'd bear)
and the way children hear it (gladly the cross-eyed bear, gladly the cross-eyed bear)
(In Russian: violin-fox / creak of the wheel, I am a jerking emerald / cores - pure emerald, if you want bull plums / if you want to be happy, a hundred shitty ass / a hundred steps back.)
I also experienced such difficulties, not in this particular case, but there are several times in my life that I could recall when I thought that I was reading and speaking probably correctly, but those around me, especially my parents, understood that that's quite different.
Here you can observe serious errors, as well as see how they occur. The child is faced with the need to make assumptions about what the words of the language mean and gradually learn the correct options. However, fixing such errors can take a long time. You can't be sure that they are completely fixed even now.
You can go very far without understanding what you are doing. I have already talked about my friend, a doctor of mathematical sciences from Harvard University. When he was graduating from Harvard, he said that he could calculate the derivative by definition, but he doesn't really understand it, he just knows how to do it. This is true for a lot of the things we do. To ride a bike, skateboard, swim, and many more things, we don't need to know how to do them. It seems that knowledge is something more than words can express. I dare not say that you do not know how to ride a bicycle, even if you cannot tell me how to do it, but you pass in front of me on one wheel. So knowledge is very different.
Let's sum up a little what I said. There are people who believe that we have innate knowledge; if you consider the situation as a whole, perhaps you will agree with this, considering, for example, that children have an innate tendency to make sounds. If a child was born in China, he will learn to pronounce many sounds in order to achieve what he wants. If he was born in Russia, he will also make many sounds. If he was born in America, he will still make many sounds. The language itself is not so important here.
On the other hand, a child has an innate ability to learn any language just like any other. He memorizes sequences of sounds and understands what they mean. He has to put meaning into these sounds himself, since there is no first part that he could remember. Show the child a horse and ask him: “The word “horse” is the name of a horse? Or does that mean she's quadrupedal? Maybe that's her color? If you're trying to tell a child what a horse is by showing it, the child won't be able to answer that question, but that's what you mean. The child will not know which category the word belongs to. Or, for example, take the verb "to run." It can be consumed when you're doing a fast move, but you can also say that the colors on your shirt have run out after washing, or complain about the rushing clock.
The child experiences great difficulties, but, sooner or later, he corrects his mistakes, admitting that he understood something wrong. As the years go by, children become less and less able to do this, and when they are old enough, they can no longer change. Obviously people can be wrong. Think, for example, of those who believe that he is Napoleon. No matter how much evidence you present to such a person that this is not so, he will continue to believe in it. You know, there are a lot of people with strong beliefs that you don't share. Since you may think that their beliefs are insane, saying that there is an infallible way to discover new knowledge is not entirely true. You will say to this: “But science is very accurate!” Let's look at the scientific method and see if that's the case.
Thanks to Sergey Klimov for the translation.
10-43: Someone says: “A scientist knows science like a fish knows hydrodynamics.” There is no definition of Science here. I discovered (I think I told you this before) somewhere in high school different teachers were telling me about different subjects and I could see that different teachers were talking about the same subjects in different ways. Moreover, at the same time I looked at what we were doing and it was something different again.
Now, you've probably said, "we do the experiments, you look at the data and form theories." This is most likely nonsense. Before you can collect the data you need, you must have a theory. You can't just collect a random set of data: the colors in this room, the type of bird you see next, etc., and expect them to carry some meaning. You must have some theory before collecting data. Moreover, you cannot interpret the results of experiments that you can do if you do not have a theory. Experiments are theories that have gone all the way from beginning to end. You have preconceived notions and must interpret events with this in mind.
You acquire a huge number of preconceived notions from cosmogony. Primitive tribes tell various stories around the fire, and children hear them and learn morals and customs (Ethos). If you are in a large organization, you learn rules of behavior largely by watching other people behave. As you get older, you can't always stop. I tend to think that when I look at ladies my age, I can see a glimpse of what dresses were in fashion in the days when these ladies were in college. I may be fooling myself, but that's what I tend to think. You've all seen the old Hippies who still dress and act the way they did at the time when their personality was formed. It's amazing how much you gain this way and don't even know it, and how hard it is for old ladies to relax and give up their habits, recognizing that they are no longer accepted behavior.
Knowledge is a very dangerous thing. It comes with all the prejudices you have heard before. For example, you have a prejudice that A precedes B and A is the cause of B. Okay. Day invariably follows night. Is the night the cause of the day? Or is day the cause of night? No. And another example that I really like. Poto'mac River levels correlate very well with the number of phone calls. Phone calls cause the river level to rise, so we get upset. Phone calls do not cause river levels to rise. It is raining and for this reason people call the taxi service more often and for other related reasons, for example, informing loved ones that because of the rain they will have to be delayed or something like that, and the rain causes the river level to rise.
The idea that you can tell cause and effect because one comes before the other may be wrong. This requires some caution in your analysis and your thinking and may lead you down the wrong path.
In the prehistoric period, people apparently animated trees, rivers and stones, all because they could not explain the events that took place. But Spirits, you see, have free will, and in this way what was happening was explained. But over time we tried to limit the spirits. If you made the required air passes with your hands, then the spirits did this and that. If you cast the right spells, the tree spirit will do this and that and everything will repeat itself. Or if you planted during the full moon, the harvest will be better or something like that.
Perhaps these ideas still weigh heavily on our religions. We have quite a lot of them. We do right by the gods or the gods grant us the benefits we ask for, provided, of course, that we do right by our loved ones. Thus, many ancient gods became the One God, despite the fact that there is a Christian God, Allah, a single Buddha, although now they have a succession of Buddhas. More or less of it has merged into one God, but we still have quite a lot of black magic around. We have a lot of black magic in the form of words. For example, you have a son named Charles. You know, if you stop and think, Charles is not the child himself. Charles is a baby's name, but it's not the same thing. However, very often black magic is associated with the use of a name. I write down someone's name and burn it or do something else, and it must have an effect on the person in some way.
Or we have sympathetic magic, where one thing looks similar to another, and if I take it and eat it, certain things will happen. Much of the medicine in the early days was homeopathy. If something looks similar to another, it will behave differently. Well, you know that doesn't work very well.
I mentioned Kant, who wrote a whole book, The Critique of Pure Reason, which he undertook in a large, thick volume in difficult to understand language, about how we know what we know and how we ignore the subject. I don't think it's a very popular theory about how you can be sure of anything. I'll give an example of a dialogue I've used several times when someone says they're sure of something:
- I see that you are absolutely sure?
- Without any doubts.
- No doubt, okay. We can write down on paper that if you are wrong, firstly, you will give away all your money and, secondly, you will commit suicide.
Suddenly, they don't want to do it. I say: but you were sure! They start talking nonsense and I think you can see why. If I ask something that you were absolutely sure of, then you say, “Okay, okay, maybe I'm not 100% sure.”
You are familiar with a number of religious sects who think the end is near. They sell all their possessions and go to the mountains, and the world continues to exist, they come back and start all over again. This has happened many times and several times in my lifetime. The various groups that did this were convinced that the world was coming to an end and this did not happen. I try to convince you that absolute knowledge does not exist.
Let's take a closer look at what science does. I told you that, in fact, before you start measuring you need to formulate a theory. Let's see how it works. Some experiments are carried out and some results are obtained. Science attempts to formulate a theory, usually in the form of a formula, that covers these cases. But none of the latest results can guarantee the next one.
In mathematics there is something called mathematical induction, which, if you make a lot of assumptions, allows you to prove that a certain event will always happen. But first you need to accept many different logical and other assumptions. Yes, mathematicians can, in this highly artificial situation, prove the correctness for all natural numbers, but you cannot expect a physicist to also be able to prove that this will always happen. No matter how many times you drop a ball, there is no guarantee that you will know the next physical object you drop better than the last one. If I hold a balloon and release it, it will fly up. But you will immediately have an alibi: “Oh, but everything falls except this. And you should make an exception for this item.
Science is full of similar examples. And this is a problem whose boundaries are not easy to define.
Now that we have tried and tested what you know, we are faced with the need to use words to describe. And these words can have meanings different from those with which you give them. Different people can use the same words with different meanings. One way to get rid of such misunderstandings is when you have two people in the laboratory arguing about some subject. Misunderstanding stops them and forces them to more or less clarify what they mean when they talk about various things. Often you may find that they do not mean the same thing.
They argue about different interpretations. The argument then shifts to what this means. After clarifying the meanings of words, you understand each other much better, and you can argue about the meaning - yes, the experiment says one thing if you understand it this way, or the experiment says another if you understand it another way.
But you only understood two words then. Words serve us very poorly.
Thanks to Artem Nikitin for the translation
20:10… Our languages, as far as I know, all tend to emphasize “yes” and “no,” “black” and “white,” “truth” and “falsehood.” But there is also a golden mean. Some people are tall, some are short, and some are between tall and short, i.e. for some may be high, and vice versa. They are average. Our languages are so awkward that we tend to argue about the meanings of words. This leads to a thinking problem.
There were philosophers who argued that you only think in terms of words. Therefore, there are explanatory dictionaries, familiar to us from childhood, with various meanings of the same words. And I suspect that everyone has had the experience that when learning new knowledge, you couldn’t express something in words (couldn’t find the right words to express it). We don't really think in words, we just try to do, and what actually happens is what happens.
Let's say you were on vacation. You come home and tell someone about it. Little by little, the vacation you took becomes something you talk about to someone. Words, as a rule, replace the event and freeze.
One day, while on vacation, I talked to two people to whom I told my name and address, and my wives and I went shopping, then we went home, and then, without discussing with anyone, I wrote down as best I could about what happened events for today. I wrote everything I thought and looked at the words that became an event. I tried my best to let the event take the words. Because I know well that moment when you want to say something, but don’t find the right words. It seems that everything is happening as I said, that your vacation is becoming exactly as described in words. Much more so than you might be sure. Sometimes you should ramble on about the conversation itself.
Another thing that came out of the book on quantum mechanics is that even if I have a bunch of scientific data, they can have completely different explanations. There are three or four different theories of quantum mechanics that more or less explain the same phenomenon. Just like non-Euclidean geometry and Euclidean geometry study the same thing but are used in different ways. There is no way to derive a unique theory from a set of data. And because the data is finite, you are stuck with it. You won't have this unique theory. Never. If for all 1+1=2, then the same expression in the Hamming code (the most famous of the first self-monitoring and self-correcting codes) will be 1+1=0. There is no certain knowledge that you would like to have.
Let's talk about Galileo (Italian physicist, mechanic, astronomer of the XNUMXth century), with whom quantum mechanics began. He assumed that falling bodies fall the same way, regardless of the acceleration constant, the friction constant, and the influence of air. That ideally, in a vacuum, everything falls at the same speed. What if one body touches another when falling. Will they fall at the same speed because they have become one? If touching doesn't count, what if the bodies were tied with a string? Will two bodies connected by a string fall as one mass or continue to fall as two different masses? What if the bodies are tied not with a string, but with a rope? What if they are glued to each other? When can two bodies be considered one body? And at what speed does this body fall? The more we think about it, the more obviously “stupid” questions we generate. Galileo said: “All bodies will fall at the same speed, otherwise, I will ask the “stupid” question, how do these bodies know how heavy they are? Before him, it was believed that heavy bodies fall faster, but he argued that the speed of fall does not depend on mass and material. Later we will experimentally verify that he was right, but we don’t know why. This law of Galileo, in reality, can not be called a physical law, but rather a verbal-logical one. Which is based on the fact that you don't want to ask the question, "When are two bodies one?" It doesn't matter how much the bodies weigh as long as they can be considered one single body. Therefore, they will fall at the same speed.
If you read the classic works on relativity, you will find that there is a lot of theology and little of what is called actual science. Unfortunately it is so. Science is a very strange thing, needless to say!
As I said in lectures about digital filters, we always see things through a “window”. A window is not only a material concept, but also an intellectual one, through which we “see” certain meanings. We are limited to perceive only certain ideas, and therefore we are stuck. However, we understand well how this can be. Well, I guess the process of believing what science can do is a lot like a child learning a language. The child makes guesses about what he hears, but later makes corrections and gets other conclusions (inscription on the board: “Gladly the cross I'd bear/Gladly, cross eyed bear.” Pun: like “Gladly bear my cross/With pleasure, little bear”) . We try some experiments, and when they don't work, we make a different interpretation of what we see. Just like a child understands intelligent life and the language he is learning. Also, experimentalists, eminent in theories and physics, have held some point of view that explains something, but is not guaranteed to be true. I am putting forward to you a very obvious fact, all the previous theories that we had in science turned out to be wrong. We have replaced them with current theories. It is reasonable to think that we are now coming to reconsider all of science. It's hard to imagine that almost all of the theories we currently have will be false in some sense. In the sense that classical mechanics turned out to be false compared to quantum mechanics, but at the average level that we tested, it was still probably the best tool we have. But our philosophical view of things is completely different. So we're making strange progress. But there is another thing that is not thought about and that is logic, because you are not given much logic.
I think I told you that the average mathematician who gets his PhD early soon finds that he needs to refine the proofs of his thesis. For example, this was the case with Gauss and his proof for the root of a polynomial. And Gauss was a great mathematician. We are raising the standard of rigor in evidence. Our attitude towards rigor is changing. We are beginning to realize that logic is not the safe thing we thought it was. There are as many pitfalls in it as in everything else. The laws of logic are how you tend to think the way you like: “yes” or “no”, “either-and-that” and “either that”. We are not on the tablets of stone that Moses brought down from Mount Sinai. We're making assumptions that work pretty well a lot of times, but not always. And in quantum mechanics, you can't say with certainty that particles are particles, or particles are waves. At the same time, is it both, or neither?
We would have to take a sharp step back from what we are trying to achieve, but still continue what we must. At this time, science should believe this rather than proven theories. But these kinds of workarounds are quite lengthy and tedious. And people who understand the matter understand quite well that we do not and never will, but we can, like a child, become better and better. Over time, eliminating more and more contradictions. But will this child understand perfectly everything he hears and not be confused by it? No. Given how many assumptions can be interpreted in very different ways, this is not surprising.
We now live in an era where science is nominally dominant, but in reality it is not. Most newspapers and magazines, namely Vogue (a women's fashion magazine), publish astrological forecasts for zodiac signs every month. I think that almost all scientists reject astrology, although at the same time, we all know how the Moon influences the Earth, causing the ebb and flow of the tides.
30:20
However, we doubt whether the newborn will be right-handed or left-handed, depending on the location in the sky of a star that is 25 light years away. Although we have observed many times that people born under the same star grow up different and have different destinies. So, we don’t know whether the stars influence people.
We have a society that relies heavily on science and engineering. Or perhaps too much depended when Kennedy (the 35th President of the United States) announced that within ten years we would be on the Moon. There were many great strategies to adopt at least one. You could donate money to the church and pray. Or, spend money on psychics. People could have invented their way to the Moon through various other methods, such as pyramidology (pseudoscience). Like, let's build pyramids to harness their energy and achieve a goal. But no. We depend on good old fashioned engineering. We didn't know that the knowledge we thought we knew, we only thought we knew. But damn it, we made it to the moon and back. We depend on success to a much greater extent than on science itself. But none of this matters. We have more important things to do than engineering. This is the welfare of humanity.
And today we have many topics to discuss, such as UFOs and the like. I'm not suggesting that the CIA staged Kennedy's assassination or that the government bombed Oklahoma to cause panic. But people always hold on to their beliefs even in the face of evidence. We see this all the time. Now, choosing who is considered a fraudster and who is not is not so easy.
I have several books on the topic of separating genuine science from pseudoscience. We have lived through several modern pseudoscientific theories. We experienced the phenomenon of “polywater” (a hypothetical polymerized form of water that can be formed due to surface phenomena and have unique physical properties). We have experienced cold nuclear fusion (the supposed possibility of carrying out a nuclear fusion reaction in chemical systems without significant heating of the working substance). Big claims are made in science, but only a small part of it is true. An example can be given with artificial intelligence. You constantly hear about what machines with artificial intelligence will do, but you don't see the results. But no one can guarantee that this will not happen tomorrow. Since I argued that no one can prove anything in science, I must confess that I cannot prove anything myself. I can't even prove that I can't prove anything. A vicious circle, isn't it?
There are very big restrictions that we find inconvenient to believe anything, but we have to come to terms with it. In particular, with what I have already repeated to you several times, and which I have illustrated using the example of the fast Fourier transform (an algorithm for computer calculation of the discrete Fourier transform, which is widely used for signal processing and data analysis). Forgive me for my indiscretion, but it was I who was the first to put forward ideas on the merits. I came to the conclusion that the “Butterfly” (an elementary step in the fast Fourier transform algorithm) would be impractical to implement with the equipment that I had (programmable calculators). Later, I remembered that technology has changed, and there are special computers with which I can complete the implementation of the algorithm. Our capabilities and knowledge are constantly changing. What we cannot do today, we can do tomorrow, but at the same time, if you look carefully, “tomorrow” does not exist. The situation is twofold.
Let's get back to science. For about three hundred years, from 1700 to the present day, science began to dominate and develop in many fields. Today, the basis of science is what is called reductionism (the methodological principle according to which complex phenomena can be fully explained using the laws inherent in simpler phenomena). I can divide the body into parts, analyze the parts and draw conclusions about the whole. I mentioned earlier that most religious people said, “You cannot divide God into parts, study his parts and understand God.” And the proponents of Gestalt psychology said: “You must look at the whole as a whole. You cannot divide a whole into parts without destroying it. The whole is more than the sum of its parts."
If one law is applicable in one branch of science, then the same law may not work in a subdivision of the same branch. Three-wheeled vehicles are not applicable in many areas.
Therefore, we must consider the question: “Can the whole of science be considered to be substantially exhaustive by relying on the results obtained from the main fields?”
The ancient Greeks thought about such ideas as Truth, Beauty and Justice. Has science added anything to these ideas in all this time? No. We now have no more knowledge of these concepts than the ancient Greeks had.
The King of Babylon Hammurabi (reigned approximately 1793-1750 BC) left behind a Code of Laws that contained such a law, for example, “An eye for an eye, a tooth for a tooth.” This was an attempt to put Justice into words. If we compare it with what is currently happening in Los Angeles (meaning the racial riots of 1992), then this is not justice, but legality. We are unable to put Justice into words, and the attempt to do so only gives legality. We are unable to put the Truth into words either. I try my best to do this in these lectures, but in reality I cannot do it. It's the same with Beauty. John Keats (a poet of the younger generation of English Romantics) said: “Beauty is truth, and truth is beauty, and that is all you can know and all you ought to know.” The poet identified Truth and Beauty as one and the same. From a scientific point of view, such a definition is unsatisfactory. But science doesn’t give a clear answer either.
I want to summarize the lecture before we go our separate ways. Science does not simply produce certain knowledge that we would like. Our basic problem is that we would like to have certain truths, so we assume that we have them. Wishful thinking is the great curse of man. I saw this happen when I worked at Bell Labs. The theory seems plausible, research provides some support, but further research does not provide any new evidence for it. Scientists are beginning to think that they can do without new evidence of the theory. And they begin to believe them. And essentially, they just talk more and more, and desirability makes them believe with all their might that it is true what they say. This is a character trait of all people. You give in to the desire to believe. Because you want to believe that you will get the truth, you end up constantly getting it.
Science doesn't really have much to say about the things you care about. This applies not only to Truth, Beauty and Justice, but also to all other things. Science can only do so much. Just yesterday I read that some geneticists received some results from their research, while at the same time, other geneticists received results that refute the results of the first.
Now, a few words about this course. The last lecture is called , but it would be better to simply call it “You and Your Life.” I want to give the lecture “You and Your Research” because I have spent many years studying this topic. And in a sense, this lecture will be the summation of the entire course. This is an attempt to outline in the best possible way what you should do next. I came to these conclusions on my own; no one told me about them. And in the end, after I tell you everything you need to do and how to do it, you will be able to do more and better than I did. Goodbye!
Thanks to Tilek Samiev for the translation.
Who wants to help with - write in a personal or email [email protected]
By the way, we have also launched the translation of another cool book - )
Book content and translated chapters
- Intro to The Art of Doing Science and Engineering: Learning to Learn (March 28, 1995)
- "Foundations of the Digital (Discrete) Revolution" (March 30, 1995)
- "History of Computers - Hardware" (March 31, 1995)
- "History of Computers - Software" (April 4, 1995)
- "History of Computers - Applications" (April 6, 1995)
- "Artificial Intelligence - Part I" (April 7, 1995)
- "Artificial Intelligence - Part II" (April 11, 1995)
- "Artificial Intelligence III" (April 13, 1995)
- "n-Dimensional Space" (April 14, 1995)
- "Coding Theory - The Representation of Information, Part I" (April 18, 1995)
- "Coding Theory - The Representation of Information, Part II" (April 20, 1995)
- "Error-Correcting Codes" (April 21, 1995)
- "Information Theory" (April 25, 1995) Done, it remains to publish
- "Digital Filters, Part I" (April 27, 1995)
- "Digital Filters, Part II" (April 28, 1995)
- "Digital Filters, Part III" (May 2, 1995)
- "Digital Filters, Part IV" (May 4, 1995)
- "Simulation, Part I" (May 5, 1995)
- "Simulation, Part II" (May 9, 1995)
- "Simulation, Part III" (May 11, 1995)
- Fiber Optics (May 12, 1995)
- "Computer Aided Instruction" (May 16, 1995)
- "Mathematics" (May 18, 1995)
- "Quantum Mechanics" (May 19, 1995)
- "Creativity" (May 23, 1995). Translation:
- "Experts" (May 25, 1995)
- "Unreliable Data" (May 26, 1995)
- Systems Engineering (May 30, 1995)
- "You Get What You Measure" (June 1, 1995)
- (June 2, 1995) translate in 10 minute pieces
- Hamming, "You and Your Research" (June 6, 1995).
Who wants to help with - write in a personal or email [email protected]
Source: habr.com