Enhance Your Quote Experience
Enjoy ad-free browsing, unlimited collections, and advanced search features with Premium.
"As a result I early asked the question, "Why should I do all the analysis in terms of Fourier integrals? Why are they the natural tools for the prob… - Richard Hamming
"As a result I early asked the question, "Why should I do all the analysis in terms of Fourier integrals? Why are they the natural tools for the problem?" I soon found out, as many of you already know, that the eigenfunctions of translation are the complex exponentials. If you want time invariance, and certainly physicists and engineers do (so that an experiment done today or tomorrow will give the same results), then you are led to these functions. Similarly, if you believe in linearity then they are again the eigenfunctions. In quantum mechanics the quantum states are absolutely additive; they are not just a convenient linear approximation. Thus the trigonometric functions are the eigenfunctions one needs in both digital filter theory and quantum mechanics, to name but two places.
Now when you use these eigenfunctions you are naturally led to representing various functions, first as a countable number and then as a non-countable number of them-namely, the Fourier series and the Fourier integral. Well, it is a theorem in the theory of Fourier integrals that the variability of the function multiplied by the variability of its transform exceeds a fixed constant, in one notation l/2pi. This says to me that in any linear, time invariant system you must find an uncertainty principle."
English
Collect this quote
About Richard Hamming
Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for computer science and telecommunications. He received the 1968 Turing Award "for his work on numerical methods, automatic coding systems, and error-detecting and error-correcting codes."
Biography information from Wikiquote
Also Known As
Native Name:
Richard Wesley Hamming
Alternative Names:
Richard W. Hamming
Related quotes. More quotes will automatically load as you scroll down, or you can use the load more buttons.
Additional quotes by Richard Hamming
If you cannot drop a wrong problem, then the first time you meet one you will be stuck with it for the rest of your career. Einstein was tremendously creative in his early years, but once he began, in midlife, the search for a unified theory, he spent the rest of his life on it and had about nothing to show for all the effort. I have seen this many times while watching how science is done. It is most likely to happen to the very creative people; their previous successes convince them they can solve any problem, but there are other reasons besides overconfidence why, in many fields, sterility sets in with advancing age. Managing a creative career is not an easy task, or else it would often be done. In mathematics, theoretical physics, and astrophysics, age seems to be a handicap (all characterized by high, raw creativity), while in music composition, literature, and statesmanship, age and experience seem to be an asset. As valued by Bell Telephone Laboratories in the late 1970s, the first 15 years of my career included all they listed, and for my second 15 years they listed nothing I was very closely associated with! Yes, in my areas the really great things are generally done while the person is young, much as in athletics, and in old age you can turn to coaching (teaching), as I have done. Of course, I do not know your field of expertise to say what effect age will have, but I suspect really great things will be realized fairly young, though it may take years to get them into practice. My advice is if you want to do significant things, now is the time to start thinking (if you have not already done so) and not wait until it is the proper moment — which may never arrive!
Without real experience in using the computer to get useful results the computer science major is apt to know all about the marvelous tool except how to use it. Such a person is a mere technician, skilled in manipulating the tool but with little sense of how and when to use it for its basic purposes.
Limited Time Offer
Premium members can get their quote collection automatically imported into their Quotewise collections.
In closing I want to remind you yet again of Pasteur’s remark, “Luck favors the prepared mind.” Yes, it is a matter of luck just what you do; it is much less luck you will do something if you prepare yourself to succeed. “Creativity” is just another name for the great successes which make a difference in history.
Loading...