Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.
Interpretation
The quote emphasizes the importance of rigorous mathematical principles in practical applications.
Richard Hamming's quote highlights the significance of foundational mathematical concepts, such as the difference between Lebesgue and Riemann integrals, and poses a rhetorical question about their relevance to real-world phenomena, like the ability of an airplane to fly. Hamming suggests that if the underlying mathematics were flawed or misunderstood, it would be unreasonable to trust the outcomes they produce in practical applications like aviation.
In practice
During a lecture on the importance of mathematical foundations in engineering.
When 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.
Science 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.
If you don't work on important problems, it's not likely that you'll do important work.
Beware of finding what you're looking for._x000D_ _x000D_ A favorite aphorism he often used.
One 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.
Put glibly:_x000D_ _x000D_ In science if you know what you are doing you should not be doing it._x000D_ _x000D_ In engineering if you do not know what you are doing you should not be doing it._x000D_ _x000D_ Of course, you seldom, if ever, see either pure state.
In the original introduction to the word meme in the last chapter of 'The Selfish Gene,' I did actually use the metaphor of a 'virus.' So when anybody talks about something going viral on the Internet, that is exactly what a meme is, and it looks as though the word has been appropriated for a subset of that.
Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect.
A great power imposes the obligation of exercising restraint, and we did not live up to this obligation. I think this affected many of the scientists in a subtle sense, and it diminished their desire to continue to work on the bomb.
Human societies vary in lots of independent factors affecting their openness to innovation.
To stop short in any research that bids fair to widen the gates of knowledge, to recoil from fear of difficulty or adverse criticism, is to bring reproach on science. There is nothing for the investigator to do but go straight on, 'to explore up and down, inch by inch, with the taper his reason;' to follow the light wherever it may lead, even should it at times resemble a will-o'-the-wisp.
A big misconception is that a black hole is made of matter that has just been compacted to a very small size. That's not true. A black hole is made from warped space and time.
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