From: Chuck Simmons
Organization: You jest.
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Subject: Re: How does a mixer work?
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Date: Fri, 25 Oct 2002 23:58:11 GMT
NNTP-Posting-Date: Fri, 25 Oct 2002 16:58:11 PDT
Kevin Aylward wrote:
> "Chuck Simmons" wrote in message
> > Kevin Aylward wrote:
> > >
> > > "Chuck Simmons" wrote in message
> > > news:3DB94D04.9D42B3C@webaccess.net...
> > > > Kevin Aylward wrote:
> > > > >
> > > > > Yes, the Fourier transform is well defined, i.e. F(f(t)).
> > > > > The standard deviation is well defined Sd(x)
> > > >
> > > > By standard deviation, do you mean L2 metric distance rather than
> > > > usual meaning from probability? If so, is there any particular
> > > > why you could not say that you mean L2 metric distance?
> > >
> > > Its standard practise in signal information theory to call it the
> > > standard deviation.
> > >
> > > No idea what L2 means. I know what a metric is though:
> > >
> > > ds^2 = dx^2 + dy^2 dz^2 -c^2.dt^2
> > That is not a metric! It is the pseudometric in relativity. A metric
> > cannot take on negative values by definition! Look that one up.
> Now why did I just *know* that you would nit pick at this. Yeah yeah,
> technically a metric in Riemann geometry is positive definite, such that
> a metric in GR, actually isn't. However, it is *always* referred to as
> the metric despite this. Indeed, it is so much the norm that in essence,
> the word has been redefined by its common usage, much like "hey, that's
> bad dude", which actually means "that's good".
I can't see any evidence in mathematics that common usage has changed
the definition. Books published quite recently define metric as it has
been defined for more than a century and refer to creatures that are not
positive definite as pseudometrics. This is true because various
features of the underlying topology change drastically if the metric
form is not positive definite. The notion of open sets gets difficult.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons firstname.lastname@example.org