Alan Kay: How are things for all mankind, the view "from space"

Why, then, is science and its cartographic language — mathematics — considered difficult to learn? I believe that this is not because they are so complex, but rather because they are surprisingly simple, but very different from ordinary, sound human thinking.

My favorite examples of early science and a remarkable general metaphor about what science is doing are attempts to accurately map, which was started by the Greeks and subsequently lost for thousands of years, and then resumed in the 15th century. By the end of the 1700s, people were delighted with the fact that they could buy a pocket globe "of the world as it looks from space." After 200 years, we went into space, remembered the past, took photographs and saw what the compilers of the map identified in the 18th century long ago.


All scientific processes and knowledge are of this character: they are attempts to “see” and present things very precisely from different points of view, which are not part of our reasonable conjectures about the world. We want to make the invisible visible. Most of the history of mankind, our theories about ourselves and the world in which we live were, in the main, built on unfounded beliefs that served as consoling stories. A few years ago, we discovered a new way of seeing, which allowed us to perceive the physical world as if “from space” with much less prejudice. In the 21st century, we need not only to do this for the physical world, but also to understand our human condition as if we are looking at it “from space”, without any comforting stories, but with a deeper understanding of how we deal with our human nature and upbringing.



"Globe" of the Middle Ages .
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Map of Tolkien Middle-earth.


Mojave Desert.

(*) Maps, like all our ideas for ideas, are rather arbitrary and do not have any internal accuracy requirements by default. For example, here are three cards. The first is the map of the Middle Ages, the second is the map from the “Lord of the Rings” of Tolkien, the third is the map of the Mojave Desert. The medieval map shows the world the way people thought the world was supposed to be, this map includes the Garden of Eden (above in the far east), the Mediterranean (middle of the world), which is a vertical “T”, Jerusalem as the center of the world, attached to “T ”And the boot of Italy is nothing more than a bulge here. The Tolkien map was drawn up in as much detail as possible to help readers (and probably the author) visualize the fictional world of the Hobbit and the Lord of the Rings. A map of the Mojave Desert was made last year using both preliminary geodesy methods and satellite imagery to accommodate objects.

It is important to understand that from the point of view of traditional logic, none of these cards is “real”, since none of them is in exactly one-to-one correspondence with all the details with which these cards are trying to compare. In other words, each of these cards is a kind of story, which is written mostly with images, not words. Within the map we can observe the ideal logic - for example, if Rome is the north of Alexandria, and Paris is the north of Rome, then Paris is the north of Alexandria. This internal logic works perfectly with all three cards. Mathematics is also a kind of display system, which is set to be completely consistent by itself - in fact, this involves creating maps like these (Earth Dimension in Greek is Geometry). When we try to relate cards to what they have to represent, this makes it difficult for us, and we find that none of these cards are “real” in terms of the truth that should be inside the map. But if you were in the Mojave Desert, which “unreal” card would you decide to take with you? Many features of “false” cards really make a difference in modern thinking.

From our point of view, the reason to teach “new thinking”, which has been gaining popularity over the last 400 years, is not to provide more technical professions or to keep the country strong or even to create better citizens. All of these are good results, which are byproducts of new thinking, but the real reasons are related to sanity and civilization. If the cards in our heads are not similar to what is outside of them, then we are at best “insane” (unsane), as Alfred Korzybsky said. Our definition of true insanity is that when cards in our heads for whatever reason become so different from what is “beyond” (including what is in other people's cards) this is noticeable and sometimes dangerous. Since we cannot make the maps exactly correct, we are always a little insane with respect to the physical world. Since our actual internal maps cannot be directly divided, we are even more insane with respect to comparing maps of this world with each other, including ourselves. Because we think within our internal maps — a kind of theatrical presentation of our beliefs before us — it is no exaggeration to say that we live not in reality, but in a delusional, hallucinatory dream that we like to call “reality”. We definitely want to build the “least false” version of this reality as far as possible!

Civilization is not a condition that can be achieved and not the journey itself, it is a way to travel. For me, the most interesting and wonderful, even amazing, thing about science is that it is created by us, although we are creatures with only different stories in our heads that should rather make us want to lead saber-toothed tigers than to understand the centuries-old climate change. But the process of scientific thinking can cope with many of our inability to think and other shortcomings in a sufficiently strong manner to come up with more accurate representations of more complex parts of our universe. That is why we need to help the children of this world learn to do this.

But why then is science and its cartographic language - mathematics - considered difficult to learn? I believe that this is not because they are so complex, but rather because they are surprisingly simple, but very different from ordinary, sound human thinking. Science and mathematics develop a completely unusual view of what is there? And what it means to declare that knowledge of this is the basic process of teaching science. One way to look at this is that part of what needs to be learned is a new kind of common sense — Alan Cromer calls it “counterintuitive” (uncommonsense).

And just as it does not require anything more than a normal mind to study ideas, it also does not require any major expenses, although many people like to justify themselves by saying that “they do not teach science, because they do not have computers, scientific equipment, books, etc. ”Science is now about 400 years old, and we have about 20 years of personal computers, so science and mathematics have been studied for about 380 years without using high technologies. Some of the most important discoveries were made before the industrial revolution using a very small amount of equipment.

I think that, mainly, regardless of funding, we lack adults who understand science and want to work with people and we also lack teachers. Shame on my profession! Most of us stay in laboratories away from children, parents, teachers, and schools. How can we teach science "without money"? First of all, we must learn to observe and be interested in phenomena in a non-categorical manner, that is, we don’t want to give up things whose names we only learned - most things become almost invisible after we learn them and remember their names. Therefore, we must find ways to “make the invisible visible” in order to avoid “premature recognition”. Science is all around us and much can be revealed through a more careful study of what we think we see.

One way to do this is to learn how to draw. As Betty Edwards notes (“Right-hand Drawing”), learning to draw means learning to see (as opposed to learning to recognize). For many things, we need to find ways to delay quick recognition in favor of slower observations of these things.


This is somewhat different from the “artistic part” of visual art in that we try to basically express the visual details of “that is”, and not how we feel about it, but not so simple. As my grandfather once remarked in an article he wrote for Saturday evening about whether photography can be art: “Art appears when we work with a specific goal; that is, when we are freed from actions that are merely mechanical. ” Feelings manifest in any of our carefully crafted creations.

Another good example of a “high estimate of low cost” is the measurement of the circumference of a bicycle tire for a class 5 project. Most of the philosophical gold in science is in this wonderful activity. The students used different materials and received different answers, but were quite sure that there was an exact answer in centimeters (partly because the training encourages them to give accurate, not real answers). One of the teachers also thought so, because on the side of the tire was indicated 20 in diameter. The teacher “knew” that the circumference equals the number pi multiplied by the diameter, that pi equals 3.14, and inches are converted to centimeters with respect to 2.54 and all this is multiplied to get an accurate measurement of the tire circumference = 159.512 cm. I suggested that they measure the diameter and they found that it is actually 19 whole and ¾ (the tire was not inflated). It was a shock, since they were all accustomed to believing what was written and the idea of ​​conducting an independent test to check the correctness of what was written simply did not occur to them.

This led to questions about deflating the tire under certain pressures, but still the majority believed that there was an exact circumference length. Then one of us contacted the tire manufacturer (who turned out to be Korean) and there were many interesting and fascinating correspondences between us until an engineer was found who wrote back that they actually did not know the circumference or the diameter of the tire. They press them and cut them to a length of 159.6 cm ± 1 mm!

It really shocked and impressed the children - the tire manufacturer did not even know its diameter or the circumference! - and it made them think on a more global scale. It may not be possible to measure things accurately. Don't things consist of atoms? Do not the atoms fluctuate? Do not atoms consist of things that fluctuate? And so on. A good analogy with the eternal question "how long is the coastline?" The answer is partly related to the scale and tolerance of measurement. As Mandelbrot and other scientists interested in fractals have proven, the length of a mathematical coastline can be infinite, and physics shows us that the physical dimension can be “almost” just as long (which is very long).


There are many ways to use the powerful “tolerance” idea. For example, when children make their gravity project and come up with a model for which gravity approaches objects on the surface of the Earth, it is very important for them to realize that they can measure only one pixel on their computer screens and that they can also make small blunders. If they are fixated on measurement accuracy, they will lose sight of what is happening - uniform acceleration. So they must be tolerant of small mistakes. On the other hand, they must be reasonably vigilant about inconsistencies that differ from typical measurement errors. Historically, it happened that Galileo could not accurately measure how the balls roll on an inclined plane, and Newton did not know what the orbit of the planet Mercury actually does when he looked at it.

In 2004, it was 400 years since the first case in history, when a good model of what happens when a body falls near the surface of the Earth under the influence of gravity appeared. Galileo did not have home video cameras, computers and Squeak to come up with this model. He made his discovery "without money", being very diligent in studying and simply observing until he found a way to copy what he saw, in order to compare it with mathematics.

How did he do it? There is absolutely no definite answer to this question, but there are many stories about this that were collected from the notes and writings of Galileo. Galileo’s father was a professional musician, and Galileo had an excellent reputation as
a music lover who plays a variety of instruments, including flute and lute.


He conducted many experiments with inclined planes, using balls of the same size from different materials and having different weights. He found that the balls of the same size, but of different weight, apparently walked along an inclined plane with the same amplitude of increasing speed, regardless of the angle.

One day, he may have had a little fun, rolling a ball or two at the top of his lute. You may notice that the frets of the lutes and guitars are unevenly distributed. At some point, he noticed that the ball clicks at the frets were almost the same and realized that a wider fret interval compensated for the increase in ball speed. The wonderful thing about the lute is that, unlike guitars, their frets are made from the same material that strings are made of and therefore they are simply tied. Therefore, Galileo could move them. He began to move them until he heard an absolutely identical sequence of clicks (at some point, he probably began to connect the fret material through his inclined plane). When he received exactly the same clicks, he measured the distances and found that the increase in speed (acceleration) was constant!

One of the most important conclusions is the fact that there are many scientific studies that can be carried out with the help of available materials, if the teacher understands the real science. This is one way to do this research "at no cost", another way is to roll a toy truck with an open can of ink on an inclined plane.

Do not let the absence of a computer or hardware slow down. Science and mathematics around us. The world in which we live is an extensive laboratory, full of equipment, if it can be noticed. There are free public libraries even in the most disadvantaged areas of the United States, in which there are books where it is written how to do all this: knowledge is not worth the money, but it really takes time, interest and attention.

You are reading this book because you are interested in all these problems - you may have found it in the free public library, regardless of whether you can afford to use your computer today. If you cannot, then there are still a lot of things that you can do just as there is a lot of real music that you can play with children without formally using any instruments. If you can afford a musical instrument or a computer, then you have obtained wonderful amplifiers for your musical, mathematical, and scientific impulses.

The computer, in the literal sense, transforms mathematics into phenomena, thereby providing a complete cycle of “assembled parts into a whole”, added to “disassembled into parts” the nature of science. This is one of the most important applications of computers in adult science and engineering, and therefore, children and adults are firmly tied to the same art and sport, and children's baseball and tennis are the real versions of sports.

A further understanding is that the range and depth of the structures that children can perform can be greatly expanded using a suitable computer environment. Many researchers have found that children are capable of deeper thoughts that they can easily build: for example, they can think more widely than how robots and animals can find their place in the world and children can create truly subtle and thoughtful computer programs that they bring these ideas to life in a way that is far beyond their capabilities; at that age they still cannot create the physical embodiments of these ideas.

In a few years, the computers themselves will become almost free and become part of a truly global communications network. And so, all the materials described in this book are within the reach of virtually every child on the planet. But we still need to find ways not to forget what is really important here.

The most important difference that we should not lose sight of is between “doing real science” and “learning what scientists have already done”. This is similar to the difference between “music” and “music score”. The latter has to be done in both cases, but both cases require a study of the real process in order to understand what “evaluation knowledge” really means. For example, there are no important differences between giving a “holy book” full of statements and asking them to remember them all and faithfully believing them, and giving the “scientific book” complete statements and asking them to remember them and believing them. As with the difference between two values ​​of logic (true and false) and the many-valued logic of science (many invaluable lies), the difference between what science means when it says "we know it" and what previous systems of knowledge mean when they say it, it cannot be even more awesome. When science claims that it "knows" something, it is so different from previous applications that you should not even try to use the word "know", because in fact it is meant that: "we have a great map model that it works in this way, but if you don’t figure everything out, it’s as good as you would like here and there, and by the way, here’s how you can help us check it out and conduct our own criticism, etc. ”

I hope that the projects presented in this book, and what you have read before it, will convince you that these actions are not just “mathematics and science”, but deep, real and important aspects of mathematics and science. What if more problems of the physical world were considered in this slow, measured perception, skeptical, careful, powerful, in the manner of constructing maps and models? , , , , .

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