Mathematics is an interesting intellectual sport but it should not be allowed to stand in the way of obtaining sensible information about physical processes.
Richard HammingScience is concerned with what is possible while engineering is concerned with choosing, from among the many possible ways, one that meets a number of often poorly stated economic and practical objectives.
Richard HammingScience is composed of laws which were originally based on a small, carefully selected set of observations, often not very accurately measured originally; but the laws have later been found to apply over much wider ranges of observations and much more accurately than the original data justified.
Richard HammingMost of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture. For example, in education, a teacher might say in the next class he was going to "explain Young's modulus and how to measure it," rather than, "I am going to educate the students and prepare them for their future careers".
Richard HammingGood teachers deserve apples; great teachers deserve chocolate. A favorite quotation, written in calligraphy on his office door.
Richard HammingIf you don't work on important problems, it's not likely that you'll do important work.
Richard HammingThe most dangerous thought you can have as a creative person is to think you know what you’re doing.
Richard HammingMathematicians stand on each others' shoulders and computer scientists stand on each others' toes.
Richard HammingMost people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance.
Richard HammingWhen you are famous it is hard to work on small problems. This is what did [Claude Elwood] Shannon in. After information theory, what do you do for an encore? The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go. So that is another reason why you find that when you get early recognition it seems to sterilize you.
Richard HammingIt may be said "In research, if you know what you are doing, then you shouldn't be doing it." In a sense, if the answer turns out to be exactly what you expected, then you have learned nothing new, although you may have had your confidence increased somewhat.
Richard HammingIf you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But ten years later somehow, you dont quite know what problems are worth working on.
Richard HammingA parable: A man was examining the construction of a cathedral. He asked a stone mason what he was doing chipping the stones, and the mason replied, "I am making stones." He asked a stone carver what he was doing. "I am carving a gargoyle." And so it went, each person said in detail what they were doing. Finally he came to an old woman who was sweeping the ground. She said. "I am helping build a cathedral." ...Most of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture.
Richard HammingI have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable.
Richard HammingOften the great scientists, by turning the problem around a bit, changed a defect to an asset. For example, many scientists when they found they couldn't do a problem finally began to study why not. They then turned it around the other way and said, "But of course, this is what it is" and got an important result.
Richard HammingNewton said, "If I have seen further than others, it is because I've stood on the shoulders of giants." These days we stand on each other's feet!
Richard HammingOnce in a while a person does only one thing in his whole life, and we'll talk about that later, but a lot of times there is repetition. I claim that luck will not cover everything. And I will cite Pasteur who said, "Luck favors the prepared mind." And I think that says it the way I believe it.
Richard HammingOne of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can't, almost surely you are not going to.
Richard HammingIf the prior distribution, at which I am frankly guessing, has little or no effect on the result, then why bother; and if it has a large effect, then since I do not know what I am doing how would I dare act on the conclusions drawn?
Richard HammingPerhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way.
Richard HammingGiven two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime.
Richard HammingThere are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think.
Richard HammingYou can tell other people all the alibis you want. I don't mind. But to yourself try to be honest.
Richard HammingKnowledge and productivity are like compound interest. The more you know, the more you learn; the more you learn, the more you can do; the more you can do, the more the opportunity. I don`t want to give you a rate, but it is a very high rate. Given two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime.
Richard HammingIt is better to do the right problem the wrong way than the wrong problem the right way.
Richard HammingTrue greatness is when your name is like ampere, watt, and fourier-when it's spelled with a lower case letter.
Richard HammingHe who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important.
Richard Hamming