Richard Hamming: Chapter 1. Orientation

“The goal of this course is to prepare you for your technical future.”

Hi, Habr. Remember the awesome article "You and your work" (+219, 2265 bookmarks, 353k readings)?

So Hamming (yes, yes, self-checking and self-correcting Hamming codes ) has a whole book based on his lectures. Let's translate it, because the man is talking.

This book is not just about IT, it is a book about the thinking style of incredibly cool people. “This is not just a charge of positive thinking; it describes the conditions that increase the chances of doing a great job. ”
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We have already translated 10 (out of 30) chapters.

Chapter 1. Orientation

(For the translation, thanks to Savva Sumin, who responded to my call in the "previous chapter.") Who wants to help with the translation - write in a personal or mail magisterludi2016@yandex.ru

The goal of this course is to prepare you for your technical future. There is practically no technical content in it, although I will often refer to it, in the hope that such a course structure will become useful for you to repeat the fundamental foundations of your disciplines. Just do not think that the technical content is the course itself - this is just an illustrative material. The subject of the course is the style of thinking. My goal is to train, not train you.

I will examine, criticize and demonstrate different styles of thinking. To illustrate the stylistic features, I will use technical knowledge that is familiar to most of you, which, again, I hope, will be useful for you to repeat the basics. You should consider this course as a supplement to the technical courses you have already studied. Many things that I will talk about have no place in standard courses, but I am deeply convinced that you need to know about them. This course exists because the Department of Electrical and Computer Engineering of the Graduate School of the University of Marines recognizes the need for a general, broad education, along with specialized, technological training that your future will require.

The subject of this course is style, and by definition it is impossible to teach it in its usual form using words. I can only get closer to the subject by describing particular cases, examples that you will probably be able to understand, although they are mostly taken from my personal 30 years of experience in the mathematical department of the Bell Lab Research Unit (before the department was disbanded), and some - from the works of other people.

The early Greek philosophers (Socrates, Plato, Aristotle) ​​unconditionally adhered to the opinion that about anything one can "speak" with words. This view unconditionally ignored the opinion of the “mystery cults” of that time, who believed that a person needed to “feel” something that cannot be expressed in words. Examples include gods, concepts of truth and justice, art, beauty and love. Your scientific education has, as a basis, faith in the descriptive capacity of words, along with steadfast faith in reductionism; so to demonstrate the possible limitations of the language, I will periodically return to this topic throughout the book. As I said, style is a similar theme.

My approach in this course (using personal experience, personal knowledge and observations) implies that I will have to break the standard taboo and talk about myself in the first person, instead of the traditional impersonal approach of science. Here you will have to excuse me, since there seems to be no equally effective impersonal approach. If I do not use personal experience, the material may seem to you just a set of "righteous" words and not produce the desired effect on your mind, and changing your mind is just the main criterion of the effectiveness of my work.

Because of the discussion of personal experience, the mother will show off boasting, although I bring some of my own serious mistakes to balance this effect. Learning through observing the mistakes of other people can save you from committing your own mistakes, but I still consider learning success more important than learning failures. I often say (and come back to this topic afterwards) that there are a huge number of erroneous ways, but very little - the right ones, thus learning success more effectively and, when your time comes, you will know how to make the right decisions, and not how to make mistakes. !

I'm just a "coach." I can't run your mile for you; At best, I can discuss different styles and criticize yours. You know that it is you who will have to run a mile, if you want athletics to be useful - which means you have to think carefully about the things read in this book so that they can change you effectively - which obviously should be the goal any course. I will say it again - you will get just as much benefit from this course, how much effort you dedicate to it, and if your efforts are limited to attending classes and reading a book, it will be just a waste of time for you. You will need to fully digest and assimilate the content, compare it with your personal experience, discuss with each other and integrate some points into your own methods of interaction with the real world.

Since the subject of the course is “style”, I will give a comparison with the teaching of the visual arts. Having mastered the basics of fine art, you study under the guidance of a master, whom you yourself recognize as an excellent artist; but you realize that you have to create your own style from the elements of the artists of the past and your natural abilities. Also, you will have to adapt your style to the future, since simple copying of the past will not be sufficient if you strive for great achievements - we will return to this topic many more times. I will try to explain the features of my style as clearly as I can, but, again, you have to borrow from it those elements that suit you and, in the end, create your own style. You will become either leaders or followers, but my goal is to make you leaders. In one way or another, you will not be able to adopt all the qualities that I have noticed in myself and others and described for you; you have to choose, adapt, and make the appropriate qualities a part of yourself.

But there is a problem and more difficult choice: the successful style of one time may well not be suitable for another! My predecessors at Bell Lab used their style; and I and three of my colleagues got there at about the same time, were almost the same age, found our own styles and, as a result, completely changed the cumulative style of the Mathematics Department, as well as some other parts of the Laboratory. Between ourselves, we called ourselves “Four Baby Tricks,” and after many years I learned that top management called us too!

Let's return to the topic of education. You all understand that there is a big difference between education and training.

Education teaches what, when and why to do it, and training how to do it.

One without the other does not make much sense. You need to know and what to do, and how to do it. I have already compared mental and physical training, saying that in both areas the amount of benefit received is directly proportional to the amount of effort invested - all that a coach can do is to suggest styles and criticize from time to time. Because of the large size of these classes (or because you are reading a book), I cannot directly criticize your thinking, therefore you will have to do it on your own or for each other, in conversation and apply things that I tell about my own experience. It may seem to you that education should precede training, but the type of education that I do should be based on your experience and technical knowledge. Hence, this kind of “inversion” of what may seem reasonable. In fact, I am engaged in “meta-education”, the subject of the course is education as such, and therefore our discussion should be above it - “meta-education”, just as metaphysics should have been above physics in the days of Aristotle (strictly speaking, “follow for "and" exceed "- the values ​​of the prefix" meta ").

This book is aimed at your future, why we should understand what the technological sphere will be like (Science and Engineering) at the time when you will have to develop it. It is well known that after Isaac Newton (1642-1727) the amount of knowledge of the type of interest to us increased about 2 times every 17 years. First of all, it is possible to measure it by the number of published books (a classic observation is that libraries have to double the volume of books registered every 17 years in order to maintain their relative position). Secondly, when I came to Bell Lab in 1946, they tried to reduce the staff from the volume available to World War II to approximately 5,500 employees. However, during the 30 years I spent there, I observed a fairly stable doubling of staff every 17 years, despite the fact that the administration from time to time imposed a moratorium on the reception of employees. Thirdly, the growth in the number of scientists also went exponentially and there is a perception that almost 90% of scientists who have ever lived are alive now! It is hard to believe that in the future these expected growth rates will have to slow down, and therefore you, even more than before me, will have to learn all new things.

Here I will allow myself a small digression to demonstrate what is often called “[back of the envelope calculations - count on a napkin]”. I noticed that engineers and scientists do this more often than “ordinary people”, hence the need for illustration. I will take the two statements quoted above (“the amount of knowledge doubles every 17 years” and “90% of scientists who have ever lived are alive now”) and check how compatible they are. The current growth model is exponential, both for the number of scientists and for the amount of knowledge proportional to the number of living scientists. To begin with, we assume that the number of living scientists at time t is equal to:

$$

$$y (t) = a \ exp {(bt)}$$

while the amount of knowledge produced annually has a constant coefficient of proportionality k in relation to the number of living scientists. If we start with a minus of infinity in time (the error is small and, if desired, you can make a correction for Newton's time), we get the following formula:

$$

$$\ frac {1} {2} = \ frac {\ int _ {- \ infty} ^ {t-17} kae ^ {bt} \, \ mathrm {dt}} {\ int _ {- \ infty} ^ {t } kae ^ {bt} \, \ mathrm {dt}} = \ frac {(ka / b) e ^ {b (t-17)}} {(ka / b) e ^ {bt}} = e ^ { -17b} = \ frac {1} {2}$$

from here we know b. We turn to the second statement. Having accepted the standard life of a scientist for 55 years (it seems, the statement includes a period of life when a scientist does not practice, but excludes childhood), we get:

$$

$$\ frac {\ int_ {t-55} ^ {t} ae ^ {bt} \, \ mathrm {dt}} {\ int _ {- \ infty} ^ {t} ae ^ {bt} \, \ mathrm { dt}} = \ frac {e ^ {bt} - e ^ {(bt-55b)}} {e ^ {bt}} = 1 -e ^ {- 55b} = 1 - \ left (\ frac {1} {2} \ right) ^ {55/17} = 1-0.106 \ dots = 0.894 \ dots$$

which is very close to 90%.

Usually, “counting on a napkin” for the first time, we use certain numbers (it is easier to work with them), and then we repeat the calculations with the parameters in order to fit them closer to the data and understand the general situation. Take the period of doubling in D, and the life of the scientist in L.

Now, the first equation will look like this:

$$

$$\ frac {1} {2} = e ^ {bD}$$

And the second is:

$$

$$\ frac {9} {10} = 1 - e ^ {bL} = 1 - \ left (\ frac {1} {2} \ right) ^ {L / D}$$

$$

$$\ left (\ frac {1} {2} \ right) ^ {L / D} = \ frac {1} {10}$$

$$

$$\ frac {L} {D} = \ frac {\ log {10}} {\ log {2}} = \ frac {1} {0.30103} = 3.3219 \ dots$$

Taking D for 17 years, we get 17 * 3.3219 = 56.47 ... years of a scientist's lifetime, which is close to 55 (our initial assumption). We can adjust the L / D ratio until we find a better match with the data (which were approximate, although I believe in doubling more than 17 years than in 90%). "Calculations on a napkin" showed that the hypotheses are adequately compatible. Note that this relationship applies throughout the time, provided that the integrity of the simple relationship is preserved.

Now it becomes clear why great scientists actively use “calculations on a napkin” - they give a good idea of ​​the soundness of the assumption and an understanding of what factors you were not prepared to reason about - for example, what exactly is meant by the term of a scientist's life. By doing the calculations, you increase the likelihood that the result will be deposited in your head. Also, such calculations retain your ability to simulate situations in full readiness until the moment it is needed to solve serious problems. Therefore, I recommend when you hear such quantitative observations — conduct a quick simulation to understand how much you believe them, especially when their source is the press or television. Very often these statements turn out to be nonsense: either the argument is undefined and the possibility of modeling is absent; or modeling is possible, but its result does not match the original statement. This method proved to be very valuable at the table of physicists with whom I had dinner; sometimes I managed to dispel misconceptions right in the process of their formation, which helped us all move forward.

To the problem of the growth of new knowledge is also added the problem of their obsolescence. Many people believe that the “half-life” of the technical knowledge you received at school will be approximately 15 years - in 15 years, half of them will not be relevant (we will either choose other areas of development, or replace them with new material). For example, after learning more about vacuum tubes / radio tubes (because at that time they were clearly an important subject at Bell Lab), I began to help develop transistors - which made the newly acquired knowledge unnecessary!

To understand the relationship of this doubling to your own life, imagine that you have a child when you are x years old. Enrolling in college, your child will face a volume of knowledge that is y times larger than the one that you faced in due time.



This doubling is found not only in mathematical theorems and technical results, but also in musical works (such as Beethoven's Ninth Symphony), in choosing a resort or television programs, worthy or not worthy of attention. If you have ever been confused by the mass of knowledge that you encountered when you were in college, or even now - imagine what your children will encounter! The total amount of technical knowledge that you are facing now will quadruple in 34 years, and by this time many of you have reached the highest point of your career. Estimate the number of years remaining until your retirement, and then take a look at the left column, at the likely factor of increasing the amount of knowledge over this period!

What is my answer to this dilemma? The first way out is to concentrate on basic knowledge, on "fundamentals", or at least on what seems to be basics at a certain time, and also develop the ability to master new areas of knowledge so that after they appear they will not be left behind (which happens in the long run with many talented engineers). My position in the Laboratory (where I, it seemed, was the only one who understood the necessary degree in computations) obliged me to study quantitative analysis, computing machines, and also practically all areas of physics to the extent sufficient, at least, in order to successfully deal with new computational problems, the solution of which could benefit both the Laboratory and certain social and biological scientific fields. Thus, I became a successful example of how a person can not only receive enough new knowledge not to "drown" in the stream of progress, but not devote excessive time and energy to this, while continuing to contribute to the work of the organization. We had to start learning actively during the development and management of the computer center. In your career you will encounter similar problems, and there will be problems that seem insurmountable.

How to recognize these "foundations"? Successfully passed the test of time is a good sign. It is also good if it is possible to get all the other knowledge of the discipline from these "fundamentals" using its standard methods.

I need to show the difference between science and engineering.

This is how it will look in a somewhat brisk form:

In science, if you know what you are doing, then you are doing something wrong.
In engineering, if you don’t know what you’re doing, you shouldn’t.

Of course, you hardly have to observe these phenomena in pure form. In engineering, ingenuity is required, if you will, to compensate for unknown moments; in science, practical application of engineering is necessary to translate abstract models into reality. Most modern science relies on the use of engineering “tools”, and engineers need more and more scientific knowledge. Many large scientific projects require solving serious engineering problems - these areas are developing in parallel! Among other reasons for this situation, we can mention the growth rate of technical progress; now we simply cannot afford the peace of mind resulting from the separation of these disciplines. In addition, more and more scientific and engineering knowledge that you will need in the future will appear after you finish your studies. Sorry, but you just have to independently explore new areas as they appear, without the opportunity to passively wait for someone to teach you.

Note that you should not identify engineering and applied science - it is a separate, third area (which, however, not everyone recognizes as such), which lies between science and engineering.

I read somewhere that there are 76 methods for predicting the future - even this number itself implies the absence of a method that is reliable enough to gain universal acceptance. The most trivial method is to assume that tomorrow will be the same as today, which is often true. The next level of “enlightenment” is to use the current pace of change, assuming that they themselves will not change; linear prediction for the selected variable. Of course, the choice of a variable can greatly affect the prediction result! However, none of these methods are suitable for long-term forecasting.

History is often used as a basis for long-term predictions, but some believe that history repeats itself, others have diametrically opposed beliefs!
And that's what becomes obvious:

The past was once the future, and the future is destined to become the past.

Anyway, I will often use historical data to extrapolate. I believe that the best predictions are based on the understanding of the fundamental forces involved in the process, and I will rely on them. It often happens that the evolution of science and the movement of humanity forward are governed not by natural limitations, but by human laws, habits, organizational processes and rules, personal egos, and inertia. It seems to me that you were taught the specifics of this specificity less than it should, therefore I will delve into them of necessity.

There is a saying: "Short-term forecasts are always optimistic, long-term forecasts are always pessimistic." The reason that the latter is true for most people lies in the difficulty of understanding the results of an exponential increase in knowledge. For example, in the case of money, annual growth of 6% doubles their number in just 12 years! And for 46 years, growth will be 16-fold. A good example of the correctness of the statement about the pessimism of long-term predictions is the growth of the computer sphere in terms of speed, density of components, price cuts, etc., as well as the spread of computers to all corners of modern life. However, the field of Artificial Intelligence gives us a wonderful counter argument. Practically all the leaders in this field made long-term forecasts, which almost never came true, would not come true during your life, but probably come true in the future.

I will often use history as an example, despite what Henry Ford said, “History is nonsense.” [Note translator: the original: “History - by and large nonsense. These are traditions. And we do not need tradition. We want to live today, and the only story that is worth something is the one we are doing today. ”]. Perhaps his arguments were similar to these:

1. History is seldom written in any precise way; I could not even find 2 reports between which there would be a consensus on what happened in Los Alamos during World War II.
2. Due to the pace of progress, the future is always somewhat “cut off” from the past; modern computers are a wonderful example of this difference.

Reading some historians, there is a feeling that the past was largely predetermined by big trends, but at the same time you feel that the future contains a huge amount of possibilities. This contradiction can be resolved in at least four ways:

1. It can simply be ignored.
2. It can be recognized.
3. It can be decided that the past was much less predetermined than some historians suggest that the actions of individuals may at times have a huge effect. Alexander the Great, Napoleon and Hitler had a great influence on the material side of life, and Pythagoras, Plato, Aristotle, Newton, Maxwell and Einstein - on the non-material.
4. You can decide that the options are not as many as we would like, and the choice is less than it seems.

It is likely that the future will be more limited by the slow evolution of man and the corresponding laws, social institutions and organizations, than the rapid evolution of the technological sphere.

Despite the difficulty of forecasting and the fact that:

Unforeseen technological innovations can destroy even the most accurate predictions.

You should try to anticipate the future that you will encounter. To illustrate the importance of trying to predict the future, I often use this story.

It is well known that a drunk sailor swaying left and right and taking n steps in a random direction will sooner or later be at a distance from the starting point, approximately equal to the square root of n. However, if in one of these directions he sees an attractive lady, his steps will strive in that direction and, in the end, he will cover a distance proportional to n. In life, which constantly makes you make a choice, big or small, a career with a vision of the future will help you to go a distance proportional to n, but without a vision you will pass, perhaps, a distance approximately equal to the square root of n. In a sense, the difference between those who go far and those who do not leave it, is that the first have a vision, and the second - no. In the end, all that the second can do is react to events as they occur.

One of the main objectives of this course is to help you begin forming a more or less accurate vision of your future. If it does not work for me, I consider that I failed the whole course. Perhaps you will challenge this position by the fact that the vision that has been formed now has a big chance of being wrong. My answer would be as follows: from practical experience, I learned that the accuracy of vision actually means less than it might seem; to come somewhere better than to drift forever; for you there are many potential paths to greatness and it’s not so important which one you choose if it takes you there. As with your own style, you need to find a vision for your future career and follow it as well as you can.

No vision, no future.

To what extent history repeats itself or does not repeat itself is a hotly debated question. But it can become the basis of guiding principles, why history will play a large role in our discussions - I try to give you some perspective that can help you develop your vision of your future. Another significant tool that I used to try to understand what will happen in the future is active imagination. For years, I devoted about 10% of my time (Friday nights) to attempts to understand what the future of computing is waiting for, both as a tool of science and a factor shaping the social world. When creating a plan for your future, you should distinguish between three questions:

1. What can happen?
2. What is likely to happen?
3. What would we like to see happen?

In a sense, the first is science, which in principle can occur. The second is engineering - what were the human decisions that resulted in a concrete, happened future (and not another of the set of all possible future). The third is ethics, morality, or any other word that means value judgments. It is important to consider all three questions and, if the second is different from the third, it will be clearer what should be done to put the desired future into practice, instead of letting the inevitable happen and deal with the consequences. Here it becomes clear that most often the leaders from the slave [/ followers] are distinguished precisely by the presence of a vision.

The standard process of distributing knowledge across faculties and departments, as well as further fragmentation into different courses, is addressed by hiding the homogeneity of knowledge and omitting what does not correspond to the content of specific courses. And the optimization of these courses, in turn, means that many important elements of engineering practice are skipped due to inconsistencies. One of the goals of this book is to recall and demonstrate many of these missed topics important to Science and Engineering. Another goal is to show the integrity of all knowledge in the aggregate, and not fragments that “pop up” as individual subjects are studied. In your future, all your knowledge may be useful; however, if you are convinced that the problem is in a certain area,you will tend not to use relevant [useful / relevant / relevant] information learned from another course.

The center of course content will be computers. The reason for this direction is not that I spent the majority of my career in the areas of Computing and Computer Engineering. It just seems to me that in the near future computers will occupy a dominant position in your technical lives. Throughout the book, I repeat the following facts several times about the superiority of computers over people in some areas:

• Savings are much cheaper and continue to fall.
• Speed ​​is much, much faster.
• Accuracy is much more accurate.
• Reliability - a significant advantage (many computers have built-in search and error correction algorithms).
• The speed of control - many modern aircraft are unstable and require accelerated control by the onboard computer for greater practicality.
• Freedom from boredom - extreme superiority.
• ( ) — , .
• — , .
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I believe that it makes no sense to list the advantages of people over computers - almost every one of you has already internally disagreed with the above list and began to select them independently.

And finally, in some way, this course is religious - I preach that you in your life (and you have one) should make a serious contribution to the development of humanity instead of “going with the flow” comfortably; that the pursuit of mastery in any field is in itself a worthy goal in life. We often hear that the meaning is not victory, but struggle — life without a struggle for perfection is hardly worth living. It is worth noting that this is, of course, an opinion, not a fact, but it is based on observing the lives of many people and reasoning about their “aggregate” happiness, and not on impulsive pleasures. Again, this view of their happiness is certainly only my interpretation, since no one is able to fully realize the life of another person. Many people,Those who wrote about "decent life" agree with this opinion. Notice that I leave the choice of specific goals on the path to perfection for you, but I declare that life without these goals is meaningless - it is, the essence, only existence (in my opinion). In ancient Greece, Socrates (469 - 399) said:

Misunderstood life is not worth living.

To be continued...

Who wants to help with the translation - write in a personal or mail magisterludi2016@yandex.ru