From: Chuck Simmons
Organization: You jest.
X-Mailer: Mozilla 4.61 [en] (X11; U; Linux 2.0.33 i586)
Subject: Re: output impedance
References: <firstname.lastname@example.org> <_FTy9.email@example.com>
Date: Tue, 12 Nov 2002 15:31:31 GMT
NNTP-Posting-Date: Tue, 12 Nov 2002 07:31:31 PST
Reg Edwards wrote:
> > The sampling theorem
> > is concerend with bandwidth not frequency, or that the Nyquist theorem
> > allows gain greater then one at 0 degs, yet still be quite stable etc.
> > etc. However, understanding these theorems correctly can give one a
> > significant advantage.
> Yes, without the user ever having heard of Nyquist !
> Pick up another text book and the same subject, of which the theorem is an
> inessential small part, can be covered without dropping his name. (As you
> have just done to impress me you are correct. ;o) )
> There's only one theorem I'm familiar with - Pythagoras'. Have I spelt it
I am at a loss to understand why being "familiar with' only one theorem
is a virtue.
Of course, the idea of a theorem is to make some general statement with
wide application. A theorem is worthless without a proof. For example,
the Fundamental Theorem of Calculus which connects integration and
differentiation is worthless without proof that it is a true theorem.
Some theorems are very hard to prove. Fermat's Last Theorem was proposed
in the 1660s but was not proved until just a few years ago. Actually the
proof of the squaring of the circle problem did not come for nearly 2000
years. A theorem, along with its proof, is distinguished as a true
statement that can always be used. An important theorem might be
Parseval's Theorem that says, in a way, that a power spectrum will give
the same result as measuring power with so called time domain
measurement. It is useful to know this is true in audio and RF work.
Theorems sometimes have names to distinguish them or to help us remember
what they are about. The Parallel Axis Theorem in mechanics is an
example of suggestive naming as is the Theorem of the Mean or the
Fundumental Theorem of the Calculus of Variations (also called Noether's
Theorem although she did not propose it - she proved it). A calculus
book I have, written by Edmund Laundau, mentions no names for theorems
at all yet the book is nothing but theorem and proof all the way through
with almost no text. My copy has notes I wrote in the margins connecting
the theorems with their common names. With more than 200 theorems in the
book, it was a little hard to keep track of the most important ones.
Kevin, to whom you replied, does a great deal of numerical analysis and
signal processing. Naturally, he must know the theorems which apply to
his work to be successful at it. He probably "knows" several hundred
theorems whether he could name them off when asked or not. These
theorems are psrt of his tools to attack the problems of his work.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons firstname.lastname@example.org