The Art of Doing Science and Engineering, by Hamming

Saturday July 25, 2020

You should definitely read Hamming's "You and Your Research" talk, and probably also his 1996 book (both freely available). I read the beautiful new printing from Stripe Press, with a forward by Victor. Hamming may not be perfect, but he has a lot of ideas.

"We live in an age of exponential growth in knowledge, and it is increasingly futile to teach only polished theorems and proofs. We must abandon the guided tour through the art gallery of mathematics, and instead teach how to create the mathematics we need. In my opinion, there is no long-term practical alternative." (page v, epigraph quoting Hamming)

The book is roughly Hamming's lectures from a graduate course he taught after he could teach whatever he felt like. It is "Hamming on Hamming" in that it's largely him expounding on whatever he liked. It's a bit like a (very technical) grandparent telling stories and giving advice to their grandkids.

book cover

The cover image is a visual form of the book's inspirational message: A random walk won't take you anywhere, but if you have a vision, a direction that you keep trying to pursue, then even if not every step is correct, you will make progress in that direction.

"What is wanted in the long run, of course, is that the man with the problem does the actual writing of the code with no human interface, as we all too often have these days, between the person who knows the problem and the person who knows the programming language. This date is unfortunately too far off to do much good immediately, but I would think by the year 2020 it would be fairly universal practice for the expert in the field of application to do the actual program preparation rather than have experts in computers (and ignorant of the field of application) do the program preparation." (page 55; writing around 1995)

"You read constantly about "engineering the production of software," both for the efficiency of production and for the reliability of the product. But you do not expect novelists to "engineer the production of novels." The question arises: "Is programming closer to novel writing than it is to classical engineering?" I suggest yes! Given the problem of getting a man into outer space, both the Russians and the Americans did it pretty much the same way, all things considered, and allowing for some espionage. They were both limited by the same firm laws of physics. But give two novelists the problem of writing on "the greatness and misery of man," and you will probably get two very different novels (without saying just how to measure this). Give the same complex problem to two modern programmers and you will, I claim, get two rather different programs. Hence my belief that current programming practice is closer to novel writing than it is to engineering. The novelists are bound only by their imaginations, which is somewhat as the programmers are when they are writing software. Both activities have a large creative component, and while you would like to make programming resemble engineering, it will take a lot of time to get there—and maybe you really, in the long run, do not want to do it! Maybe it just sounds good. You will have to think about it many times in the coming years; you might as well start now and discount propaganda you hear, as well as all the wishful thinking which goes on in the area! The software of the utility programs of computers has been done often enough, and is so limited in scope, so it might reasonably be expected to become "engineered," but the general software preparation is not likely to be under "engineering control" for many, many years.

"There are many proposals on how to improve the productivity of the individual programmer, as well as groups of programmers. I have already mentioned top-down and bottom-up; there are others, such as head programmer, lead programmer, proving the program is correct in a mathematical sense, and the waterfall model of programming, to name but a few. While each has some merit I have faith in only one, which is almost never mentioned—think before you write the program, it might be called. Before you start, think carefully about the whole thing, including what will be your acceptance test that it is right, as well as how later field maintenance will be done. Getting it right the first time is much better than fixing it up later!

"One trouble with much of programming is simply that often there is not a well-defined job to be done; rather, the programming process itself will gradually discover what the problem is! The desire that you will be given a well-defined problem before you start programming often does not match reality, and hence a lot of the current proposals to "solve the programming problem" will fall to the ground if adopted rigorously." (pages 57-58)

"Many studies have shown programmers differ in productivity, from worst to best, by much more than a factor of ten. From this I long ago concluded the best policy is to pay your good programmers very well but regularly fire the poorer ones—if you can get away with it! One way is, of course, to hire them on contract rather than as regularly employed people, but that is increasingly against the law, which seems to want to guarantee even the worst have some employment. In practice you may actually be better off to pay the worst to stay home and not get in the way of the more capable (and I am serious)!" (page 59)

"I made the comparison of writing software with the act of literary writing; both seem to depend fundamentally on clear thinking. Can good programming be taught? If we look at the corresponding teaching of "creative writing" courses we find most students of such courses do not become great writers, and most great writers in the past did not take creative writing courses! Hence it is dubious that great programmers can be trained easily.

"Does experience help? Do bureaucrats after years of writing reports and instructions get better? I have no real data, but I suspect with time they get worse! The habitual use of "governmentese" over the years probably seeps into their writing style and makes them worse. I suspect the same for programmers! Neither years of experience nor the number of languages used is any reason for thinking the programmer is getting better from these experiences. An examination of books on programming suggests most of the authors are not good programmers!

"The results I picture are not nice, but all you have to oppose it is wishful thinking—I have evidence of years and years of programming on my side!" (pages 60-61)

"People often make the mistake of saying, "Thinking is what Newton and Einstein did." But by that definition most of us cannot think—and usually we do not like that conclusion!" (page 79)

"... Of course robots will displace many humans doing routine jobs. In a very real sense, machines can best do routine jobs, thus freeing humans for more humane jobs. Unfortunately, many humans at present are not equipped to compete with machines—they are unable to do much more than routine jobs. There is a widespread belief (hope?) that humans can compete, once they are given proper training. However, I have long publicly doubted you could take many coal miners and make them into useful programmers. I have my reservations on the fraction of the human population that can be made into programmers in the classical sense; if you call getting money from the bank dispensing "machine programming," or the dialing of a telephone number (both of which apply the human input to an elaborate program which is then executed, much like an interpreter acts on your program input), then of course most people can be made into programmers. But if you mean the more classical activity of careful analysis of a situation and then the detailed specification as to what is to be done, then I say there are doubts as to what fraction of the population can compete with computers, even with nice interactive prompting menus.

"Computers have both displaced so many people from jobs, and also made so many new jobs, it is hopeless to try to answer which is the larger number. But it is clear that on average it is the lower-level jobs which are disappearing and the higher-level jobs which are appearing. Again, one would like to believe most people can be trained in the future to do the higher-level jobs—but that is a hope without any real evidence." (pag 94)

"We started to play games on computers to study the human thought processes and not to win the game; the goal has been perverted to win, and never mind the insight into the human mind and how it works." (page 100)

"Thus AI requires your careful thought and should not be dismissed lightly just because many experts make obviously false claims." (page 103)

"Information theory was created by C.E. Shannon in the late 1940s. The management of Bell Telephone Labs wanted him to call it "communication theory," as that is a far more accurate name, but for obvious publicity reasons "information theory" has a much greater impact—this Shannon chose and so it is known to this day." (page 163)

"It is always wise to adopt a standard notation and framework of thinking of diverse things—one field of application may suggest things to do in the other. I have found it of great value to do so whenever possible—remove the extraneous scale factors and get to the basic expressions. (But then I was originally trained as a mathematician.)" (page 184)

"It is another example of why you need to know the fundamentals very well; the fancy parts then follow easily and you can do things that they never told you about." (page 186)

"Many people had the opportunity to discover (really rediscover) the Gibbs phenomenon, and it was Gibbs who made the effort. It is another example of what I maintain, that there are opportunities all around and few people reach for them. As Pasteur said, "Luck favors the prepared mind."" (page 201)

"It must be your friends, in some sense, who make you famous by quoting and citing you, and it pays, so I claim, to be helpful to others as they try to do their work. They may in time give you credit for the work, which is better than trying to claim it yourself. Cooperation is essential in these days of complex projects; the day of the individual worker is dying fast. Teamwork is more and more essential, and hence learning to work on a team, indeed possibly seeking out places where you can help others, is a good idea. In any case the fun of working with good people on important problems is more pleasure than the resulting fame." (page 210)

"Moral: when you know something cannot be done, also remember the essential reason why, so later, when the circumstances have changed, you will not say, "It can't be done."" (page 218, on how he missed the opportunity to help develop FFT)

"Let us analyze carefully what we do and its implications, because what we do to a great extent controls what we can see." (page 219)

"If you will only ask yourself, "Is what I am being told really true?," it is amazing how much you can find is, or borders on, being false, even in a well-developed field!" (page 227)

"When I went to Bell Telephone Laboratories in 1946 I soon found myself in the early stages of the design of the earliest Nike system of guided missiles." (page 238)

"I have emphasized the necessity of having the underlying laws of whatever field you are simulating well under control. But there are no such laws of economics! The only law of economics that I believe in is Hamming's law: "You cannot consume what is not produced." There is not another single reliable law in all of economics I know of which is not either a tautology in mathematics or else sometimes false. Hence when you do simulations in economics you have not the reliability you have in the hard sciences." (page 250)

"Now this fact, once understood, impacts design! Good design protects you from the need for too many highly accurate components in the system. But such design principles are still, to this date, ill understood and need to be researched extensively. Not that good designers do not understand this intuitively, merely it is not easily incorporated into the design methods you were taught in school. Good minds are still needed in spite of all the computing tools we have developed. But the best mind will be the one who gets the principle into the design methods taught so it will be automatically available for lesser minds!" (page 269)

"You also realize any dictionary must be circular; the first word you look up must be defined in terms of other words—there can be no first definition which does not use words." (page 307)

"When stuck I often ask myself, "If I had a solution, what would it look like?" This tends to sharpen up the approach, and may reveal new ways of looking at the problem you had subconsciously ignored but now see should not be excluded. What must the solution involve? Are there conservation laws which must apply? Is there some symmetry? How does each assumption enter into the solution, and is each one really necessary? Have you recognized all the relevant factors?" (page 327)

"...saturate the subconscious with the problem, try to not think seriously about anything else for hours days, or even weeks, and thus the subconscious ... is left with only the problem to mull over. We simply deprive it of all else as best we can! ... In a way, I am repeating Pasteur, "Luck favors the prepared mind." You prepare your mind for success "by thinking on it constantly" (Newton), and occasionally you are lucky." (page 328)

"Probably the most important tool in creativity is the use of an analogy. Something seems like something else which we knew in the past. Wide acquaintance with various fields of knowledge is thus a help—provided you have the knowledge filed away so it is available when needed, rather than to be found only when led directly to it. This flexible access to pieces of knowledge seems to come from looking at knowledge while you are acquiring it from many different angles, turning over any new idea to see its many sides before filing it away. This implies effort on your part not to take the easy, immediately useful "memorizing the material" path, but to prepare your mind for the future. It is for this reason I have urged you in many of the chapters to get down to the fundamentals of a field, since it implies you must examine things in many ways before you can decide what is fundamental and what is frills. In fact, for one person they may be in one order, and for another in the opposite order. What is fundamental partly depends on the individual and their mental makeup. It is obvious you need many "hooks" on the knowledge if you are to use it in new situations.

"... I can only advise you to do what I do—when you learn something new, think of other applications of it, ones which have not arisen in your past but which might in your future. How easy to say, but how hard to do! Yet what else can I say about how to organize your mind so useful things will be recalled readily at the right time?" (pages 328-329)

"The person who thinks they understand the problem and does not is usually more of a curse (blockage) than the person who knows they do not understand the problem." (page 333)

"It has been my experience, as well as the experience of many others who have looked, that data is generally much less accurate than it is advertised to be." (page 345)

"From that experience I learned never to process any data until I had first examined it carefully for errors. There have been complaints that I would take too long, but almost always I found errors, and when I showed the errors to them they had to admit I was wise in taking the precautions I did. No matter how sacred the data and urgent the answer, I have learned to pretest it for consistency and outliers at a minimum." (page 348)

"Second, you cannot gather a really large amount of data accurately. It is a known fact which is constantly ignored. It is always a matter of limited resources and limited time. The management will usually want a 100% survey when a small one consisting of a good deal less, say 1% or even 0.1%, will yield more accurate results! It is known, I say, but ignored. The telephone companies, in order to distribute the income to the various companies involved in a single long-distance phone call, used to take a very small, carefully selected sample, and on the basis of this sample they distributed the money among the partners. The same is now done by the airlines. It took them a long while before they listened, but they finally came to realize the truth that small samples carefully taken are better than large samples poorly done—better both in lower cost and in greater accuracy." (page 355)

"Of the things you can choose to measure some are hard, firm measurements, such as height and weight, while some are soft, such as social attitudes. There is always a tendency to grab the hard, firm measurement, though it may be quite irrelevant as compared to the soft one, which in the long run may be much more relevant to your goals. Accuracy of measurement tends to get confused with relevance of measurement, much more than most people believe. That a measurement is accurate, reproducible, and easy to make does not mean it should be done; instead, a much poorer one which is more closely related to your goals may be much preferable. For example, in school it is easy to measure training and hard to measure education, and hence you tend to see on final exams an emphasis on the training part and a great neglect of the education part.

"Let me turn to another effect of a measurement system, and illustrate it by the definition and use of IQs. What is done is a plausible list of questions—plausible from past experience—is made and then tried out on a small number of people. Those questions which show an internal correlation with others are kept and those which do not correlate well are dropped. Next, the revised test is calibrated by using it on a much larger sample. How? Simply by taking the accumulated scores (the number of people's score which are below the given amount) and plotting these revised numbers on probability paper—meaning the cumulative probabilities of a normal distribution are the horizontal lines. Next, the points where the cumulative actual scores fall at a given percentage points are related, via a calibration table, to the corresponding points on the cumulative normal probability curve. As a result it is observed intelligence has a normal distribution in the population! Of course it has, it was made to be that way! Furthermore, they have defined intelligence to be what is measured by the calibrated exam, and if that is the definition of intelligence, then of course intelligence is normally distributed. But if you think maybe intelligence is not exactly what the calibrated exam measures, then you are entitled to doubt intelligence is normally distributed in the population. Again, you get what was measured, and the normal distribution announced is an artifact of the method of measurement and hardly relates to reality." (pages 374-375)