jbuck@epimass.UUCP (02/17/87)
Matt "Phlame" Weiner recently tore into Morris Kline for saying,
among other things, that number theory had no applications. Of
course sci.crypt readers are under no such delusions.
In this book Schroeder demonstrates the use of number-theoretic
concepts in acoustics, error-correcting codes, fast algorithms for
digital signal processing, fractals, radar, strange attractors, and
of course, cryptography. His explanation of public-key cryptography
is particularly good.
The book is filled with interesting anecdotes. For example, when
Heisenburg discovered "matrix" mechanics in 1925, he didn't know
what a matrix was, and didn't know what to make of it. David Hilbert
suggested that he try to find a differential equation with the same
eigenvalues, if that would make him happier. He didn't. If he had,
he would have discovered the Schroedinger wave equation.
I do have one strong beef with him: he blurs the distinction between
his own work and that of others, and doesn't give much credit to
contemporary researchers. How can you spend a chapter explaining RSA
without mentioning the names R, S, and A (even in a reference?) It
would have been very tricky to discuss fractals as much as he does
and say Mandelbrot's name fewer times. I've seen him do this quite a
bit in other papers as well. It helps to be dead; Gauss, Fermat, and
Euler get far more reverent treatment. But in spite of this problem,
it's a very useful book.
--
- Joe Buck {hplabs,ihnp4,sun,ames}!oliveb!epimass!jbuck
Entropic Processing, Inc., Cupertino, Californiagreg@endor.UUCP (02/17/87)
>It >would have been very tricky to discuss fractals as much as [Schroeder] does >and say Mandelbrot's name fewer times. Except for the set named after him, Mandlebrot's name needs no mention when discussing fractals or any other area of mathematics. His only achievement is that he *popularized* fractals among computer scientists and applied mathematicians. I know this because I took a course from him, read some of his papers, and read his book. None of the three had any mathematical depth. ---- Greg
jbuck@epimass.UUCP (02/19/87)
Followups to sci.math only, as we aren't talking about cryptography any more. In article <1247@husc6.UUCP> greg@endor.UUCP (Greg) writes: >>It >>would have been very tricky to discuss fractals as much as [Schroeder] does >>and say Mandelbrot's name fewer times. > >Except for the set named after him, Mandlebrot's name needs no mention when >discussing fractals or any other area of mathematics. His only achievement is >that he *popularized* fractals among computer scientists and applied >mathematicians. Perhaps. But he coined the term, and he combined a bunch of ideas others had into a synthetic whole. He pointed out a large variety of fields that might benefit from a certain approach, and people listened, some went in the indicated directions, and found fruit. Popularization is an important function, often trivialized by the experts (maybe partly because of envy because the popularizers sell more books -- but then they write better). In any case, the relevant chapter in Schroeder's book is basically a summary of Mandelbrot's books, presenting ideas in the same order. Schroeder's talent also seems to be in synthesis -- combining ideas from several fields in ways that those who are too specialized cannot. -- - Joe Buck {hplabs,ihnp4,sun,ames}!oliveb!epimass!jbuck Entropic Processing, Inc., Cupertino, California