Richard Hamming. "Non-existent chapter": How do we know what we know (1-10 minutes out of 40)

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 about how we know what we know, if, of course, we really know it. This topic is as old as the world - it has been under discussion for the last 4,000 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 splashes of which the islands appeared. Other nations had similar myths: for example, the Israelites believed that God created the world for six days, after which he was tired and finished the 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 imply an explanation, except for “this happened at the behest of the gods; they did what they thought was necessary, and so the world appeared. ”

In the area of ​​the VI 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 about what we know. Nevertheless, this topic perplexed people at all times, and even the ancient Greeks wondered how they knew what they knew.

As you remember from our discussion of mathematics, the ancient Greeks believed that geometry, to which their mathematics was limited, was reliable and absolutely unquestionable knowledge. Nevertheless, as shown by Maurice Klein, the author of the book “Mathematics. The loss of certainty, ”which most mathematicians agree, does not contain any truth in mathematics. Mathematics gives only consistency for a given set of rules of reasoning. If you change these rules or used assumptions, the math will be completely 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.
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But you can apply some approaches and get different conclusions. Descartes, having considered the assumptions of many of the philosophers who preceded him, took a step back and asked the question: “How small can I be sure of?”; as a response, he chose the statement “I think, therefore I exist.” From this statement, he tried to derive the philosophy and get a lot of knowledge. This philosophy was not adequately justified, so we did not receive knowledge. Kant argued that everyone is born with a solid knowledge of Euclidean geometry, and many other things, which means that there is innate knowledge that is given, if you will, by God. Unfortunately, just at the moment when Kant described his thoughts, mathematicians created non-Euclidean geometries that were as consistent as their prototype. It turns out that Kant was throwing words to the wind, just like almost everyone who tried to talk about how he knows what he knows.

This is an important topic, since science is always asked for justification: one can often hear that science has shown something, proved that it will be like this; we know that, we know that - and we know that? Are you sure? I am going to consider these issues in more detail. Let's remember the rule from biology: ontogeny repeats phylogenesis. It means that the development of the individual, from the fertilized egg to the student, schematically repeats the entire preceding process of evolution. Thus, scientists claim that in the process of embryo development, gill slits appear and disappear again, and therefore they assume that our ancestors were fish.

It sounds good if you do not think about it too seriously. It gives a good understanding of how evolution takes place, if you believe in it. But I will go a little further and ask: how do children learn? How do they get knowledge? They may be born with predestined knowledge, but this sounds a bit unconvincing. Honestly, extremely unconvincing.

So what do children do? They have certain instincts, obeying which, children begin to make sounds. They make all these sounds, which 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 the children will be babbling, basically the same. However, depending on the country, babble will develop differently. For example, when a Russian child utters the word “mother” a couple of times, he will receive a positive response and therefore will repeat these sounds. Empirically, he discovers which sounds help to achieve the desired, and which not, and so he studies many things.

Let me remind you what I have said several times already - there is no first word in the dictionary; each word is defined through the others, which means that the dictionary is circular. Similarly, when a child tries to build a consistent sequence of things, he is having difficulty encountering inconsistencies that he must resolve, since there is no first thing that the child could 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, gladly carry your cross)
and the way children hear it (gladly the cross-eyed bear, with the joy of a cross-eyed bear)

(In Russian: violin-fox / wheel creaking, I am a drooping emerald / kernel - pure emerald, if you want bullish plums / if you want to be happy, gossip / a hundred steps back.)

I also had such difficulties, not in this particular case, but there are several cases in my life that I could remember when I thought I was reading and speaking, probably correctly, but the people around me, especially my parents, understood that something completely 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 learns the right options. However, the correction of such errors may take a long time. One cannot be sure that they are completely corrected 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 finished 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 many things that we do. For cycling, skateboarding, swimming, and many more things we don’t have to know how to do them. Knowledge seems to be more than words can express. I do not dare to say that you can’t ride a bike, even if you can’t tell me how to do it, but you pass in front of me on one wheel. Thus, knowledge is very different.

Let's summarize a little of what I said. There are people who believe that we have innate knowledge; If you look at the situation as a whole, you may agree, considering, for example, that children have an inborn tendency to make sounds. If the child was born in China, he will learn to pronounce a variety of sounds to achieve the desired. If he was born in Russia, he will also make a lot of sounds. If he was born in America, he will still make a lot of sounds. The language itself is not so important.

On the other hand, the child has the innate ability to learn any language, just like any other. He remembers the sound sequences 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: “Is the word“ horse ”the name of a horse? Or does it mean that she is four-legged? Maybe this is her color? ”If you try to tell a child what a horse is by showing it, the child will not be able to answer this question, but this is what you mean. The child will not know which category this word belongs to. Or, for example, take the verb "to run." It can be used when you are making an accelerated movement, but you can also say that after washing the colors on the shirt ran, or to complain about the hurrying hours.

The child experiences great difficulties, but, sooner or later, he corrects his mistakes, recognizing that he understood something wrong. Over the years, children are becoming less and less capable of it, and when they become old enough, they can no longer change. Obviously, people can be mistaken. Recall, for example, those who believe that he is Napoleon. No matter how much you present to such a person the evidence that this is not so - he will continue to believe in it. You know, there are many people with strong beliefs that you do not share. Since you may believe that their beliefs are insane, to say that there is an unmistakable way to discover new knowledge is not entirely true. You will say to this: “But science is very careful!” Let's look at the scientific method and check if this is so.

For the translation, thanks to Sergey Klimov.

To be continued...

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