"The purpose of computing is insight, not numbers […] sometimes […] the purpose of computing numbers is not yet in sight." (Richard Hamming, “Numerical Methods for Scientists and Engineers”, 1962)
"Computer based simulation is now in wide spread use to analyse system models and evaluate theoretical solutions to observed problems. Since important decisions must rely on simulation, it is essential that its validity be tested, and that its advocates be able to describe the level of authentic representation which they achieved." (Richard Hamming, 1975)
"Probability is the mathematics of uncertainty. Not only do we constantly face situations in which there is neither adequate data nor an adequate theory, but many modem theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential. Statistics is the reverse of probability (glibly speaking). In probability you go from the model of the situation to what you expect to see; in statistics you have the observations and you wish to estimate features of the underlying model." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)
"Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of 'noise' is officially admitted. The newer aspects of many fields start with the admission of uncertainty." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)
"There is a universality about mathematics; what was created to explain one phenomenon is very often later found to be useful in explaining other, apparently unrelated, phenomena. Theories that were developed to explain some poorly measured effects are often found to fit later, much more accurate measurements. Furthermore, from measurements over a limited range the theory is often found to fit a far wider range. Finally, and perhaps most unreasonably, quite regularly from the mathematics alone new phenomena, previously unknown and unsuspected, are successfully predicted. This universality of mathematics could, of course, be a reflection of the way the human mind works and not of the external world, but most people believe it reflects reality." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)
"There is always a gap between the mathematics and reality. Most of us believe that the world is made out of molecules, and when you try to make very, very accurate measurements, the random movement of the molecules will defeat your attempts at ultimate precision. In the modem theory of quantum mechanics, it is widely believed that you cannot, even in principle, precisely measure both the position and momentum (velocity times mass) of a particle at the same time; thus in this interpretation of quantum mechanics it is impossible, even theoretically, to get arbitrarily accurate measurements at the same time on certain properties of a particle. In practice, from the physical world we abstract a mathematical idealization of what is going on, and then we operate on the mathematical model. Finally, we try to interpret the mathematical results back into physical reality. Surprisingly often we get useful results, but now and then we get nonsense. You need to develop your intuition about the reality of the mathematical models you see." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)
"A model can not be proved to be correct; at best it can only be found to be reasonably consistant and not to contradict some of our beliefs of what reality is." (Richard W Hamming, "The Art of Probability for Scientists and Engineers", 1991)
"A model is often judged by how well it "explains" some observations. There need not be a unique model for a particular situation, nor need a model cover every possible special case. A model is not reality, it merely helps to explain some of our impressions of reality. [...] Different models may thus seem to contradict each other, yet we may use both in their appropriate places." (Richard W Hamming, "The Art of Probability for Scientists and Engineers", 1991)
"All of engineering involves some creativity to cover the parts not known, and almost all of science includes some practical engineering to translate the abstractions into practice." (Richard W Hamming, "The Art of Probability for Scientists and Engineers", 1991)
"It is generally recognized that it is dangerous to apply any part of science without understanding what is behind the theory. This is especially true in the field of probability since in practice there is not a single agreed upon model of probability, but rather there are many widely different models of varying degrees of relevance and reliability. Thus the philosophy behind probability should not be neglected by presenting a nice set of postulates and then going forward; even the simplest applications of probability can involve the underlying philosophy." (Richard W Hamming, "The Art of Probability for Scientists and Engineers", 1991)
"Mathematics is not just a collection of results, often called theorems; it is a style of thinking. Computing is also basically a style of thinking. Similarly, probability is a style of thinking." (Richard W Hamming, "The Art of Probability for Scientists and Engineers", 1991)
"A neural net, in case you are unfamiliar with them, can learn to get results when you give it a series of inputs and acceptable outputs, without ever saying how to produce the results. They can classify objects into classes which are reasonable, again without being told what classes are to be used or found. They learn with simple feedback which uses the information that the result computed from an input is not acceptable. In a way they represent a solution to 'the programming problem' - once they are built they are really not programmed at all, but still they can solve a wide variety of problems satisfactorily. They are a coming field [...], but they will probably play a large part in the future of computers. In a sense they are a 'hard wired' computer (it may be merely a program) to solve a wide class of problems when a few parameters are chosen and a lot of data is supplied." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"[...] a systems engineering job is never done. One reason is the presence of the solution changes the environment and produces new problems to be met. [...] A second reason the systems engineers design is never completed is the solution offered to the original problem usually produces both deeper insight and dissatisfactions in the engineers themselves. Furthermore, while the design phase continually goes from proposed solution to evaluation and back again and again, there comes a time when this process of redefinement must stop and the real problem coped with - thus giving what they realize is, in the long run, a suboptimal solution." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"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." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"All things which are proved to be impossible must obviously rest on some assumptions, and when one or more of these assumptions are not true then the impossibility proof fails - but the expert seldom remembers to carefully inspect the assumptions before making their 'impossible' statements." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"Another curious phenomenon you may meet is in fitting data to a model there are errors in both the data and the model. For example, a normal distribution may be assumed, but the tails may in fact be larger or smaller than the model predicts, and possibly no negative values can occur although the normal distribution allows them. Thus there are two sources of error. As your ability to make more accurate measurements increases the error due to the model becomes an increasing part of the error." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"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." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"If the data is usually bad, and you find that you have to gather some data, what can you do to do a better job? First, recognize what I have repeatedly said to you, the human animal was not designed to be reliable; it cannot count accurately, it can do little or nothing repetitive with great accuracy. [...] 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. [...] Third, much social data is obtained via questionnaires. But it a well documented fact the way the questions are phrased, the way they are ordered in sequence, the people who ask them or come along and wait for them to be filled out, all have serious effects on the answers." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"If you want to be certain then you are apt to be obsolete." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"In an argument between a specialist and a generalist the expert usually wins by simply: (1) using unintelligible jargon, and (2) citing their specialist results which are often completely irrelevant to the discussion. The expert is, therefore, a potent factor to be reckoned with in our society. Since experts are both necessary, and also at times do great harm in blocking significant progress, they need to be examined closely. All too often the expert misunderstands the problem at hand, but the generalist cannot carry though their side to completion. 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." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"It has been my experience, as well as many others who have looked, data is generally much less accurate than it is advertised to be. This is not a trivial point - we depend on initial data for many decisions, as well as for the input data for simulations which result in decisions." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"Machines do not produce logical novelty when working properly, but they certainly produce psychological novelty - programmers are constantly being surprised by what the program they wrote actually does! But can you as a human produce logical novelty? A careful examination of people's reports on their great discoveries often shows they were led by past experiences to finding the result they did. Circumstances led them to success; psychological but not logical novelty. Are you not prepared by past experiences to do what you do, to make the discoveries you do? Is logical novelty actually possible?" (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"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 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." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"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." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"Sometimes the mathematician can accurately estimate the frequency content of the signal (possibly from the answer being computed), but usually you have to go to the designers and get their best estimates. A competent designer should be able to deliver such estimates, and if they cannot then you need to do a lot of exploring of the solutions to estimate this critical number, the sampling rate of the digital solution. The step by step solution of a problem is actually sampling the function, and you can use adaptive methods of step by step solution if you wish." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"Systems engineering is the attempt to keep at all times the larger goals in mind and to translate local actions into global results. But there is no single larger picture. [...] Systems engineering is a hard trade to follow; it is so easy to get lost in the details! Easy to say; hard to do." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"The computers make it possible for robots to do many things, including much of the present manufacturing. Evidently computers will play a dominant role in robot operation, though one must be careful not to claim the standard von Neumann type of computer will be the sole control mechanism, rather probably the current neural net computers, fuzzy set logic, and variations will do much of the control." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"The desire for excellence is an essential feature for doing great work. Without such a goal you will tend to wander like a drunken sailor. The sailor takes one step in one direction and the next in some independent direction. As a result the steps tend to cancel each other, and the expected distance from the starting point is proportional to the square root of the number of steps taken. With a vision of excellence, and with the goal of doing significant work, there is tendency for the steps to go in the same direction and thus go a distance proportional to the number of steps taken, which in a lifetime is a large number indeed." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"[...] the human brain has many, many components in the form of nerves interconnected with each other. We want to have the definition of 'thinking' to be something the human brain can do. With past failures to program a machine to think, the excuse is often given that the machine was not big enough, fast enough, etc. Some people conclude from this if we build a big enough machine then automatically it will be able to think! Remember, it seems to be more the problem of writing the program than it is building a machine, unless you believe, as with friction, enough small parts - will produce a new effect - thinking from non-thinking parts. Perhaps that is all thinking really is! Perhaps it is not a separate thing, it is just an artifact of largeness. One cannot flatly deny this as we have to admit we do not know what thinking really is." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"The Turing test is a popular approach, but it flies in the face of the standard scientific method which starts with the easier problems before facing the harder ones. Thus I soon raised the question with myself, 'What is the smallest or close to the smallest program I would believe could think?' Clearly if the program were divided into two parts then neither piece could think. I tried thinking about it each night as I put my head on the pillow to sleep, and after a year of considering the problem and getting nowhere I decided it was the wrong question! Perhaps 'thinking' is not a yes-no thing, but maybe it is a matter of degree." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"Things change so fast part of the system design problem is the system will be constantly upgraded in ways you do not now know in any detail! Flexibility must be part of modern design of things and processes. Flexibility built into the design means not only you will be better able to handle the changes which will come after installation, but it also contributes to your own work as the small changes which inevitably arise both in the later stages of design and in the field installation of the system." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"Until we understand languages of communication involving humans as they are then it is unlikely many of our software problems will vanish." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"We are beginning to find not only is intelligence not adequately defined so arguments can be settled scientifically, but a lot of other associated words like, computer, learning, information, ideas, decisions (hardly a mere branching of a program, though branch points are often called decision points to make the programmers feel more important), expert behavior - all are a bit fuzzy in our minds when we get down to the level of testing them via a program in a computer. Science has traditionally appealed to experimental evidence and not idle words, and so far science seem to have been more effective than philosophy in improving our way of life. The future can, of course, be different." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
"You must struggle with your own beliefs if you are to make any progress in understanding the possibilities and limitations of computers in the intellectual area." (Richard Hamming, "The Art of Doing Science and Engineering: Learning to Learn", 1997)
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