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Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <email@example.com> <firstname.lastname@example.org> <3DB88D9C.50F75FA0@webaccess.net> <0f5u9.161$OM6.email@example.com> <3DB93622.BB09A3DB@webaccess.net> <3DB94D04.9D42B3C@webaccess.net> <3DB96654.F7847216@webaccess.net> <3DB9DA7E.5B5B09B9@webaccess.net>
Subject: Re: How does a mixer work?
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X-Inktomi-Trace: public1-pete2-5-cust19.pete.broadband.ntl.com 1035623788 11003 184.108.40.206 (26 Oct 2002 09:16:28 GMT)
Date: Sat, 26 Oct 2002 10:16:27 +0100
NNTP-Posting-Date: Sat, 26 Oct 2002 10:16:29 BST
"Chuck Simmons" wrote in
> Kevin Aylward wrote:
> > "Chuck Simmons" wrote in message
> > news:3DB96654.F7847216@webaccess.net...
> > > 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
> > the
> > > > > usual meaning from probability? If so, is there any particular
> > reason
> > > > > why you could not say that you mean L2 metric distance?
> > > >
> > > > Its standard practise in signal information theory to call it
> > > > 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
> > > 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
> > technically a metric in Riemann geometry is positive definite, such
> > a metric in GR, actually isn't. However, it is *always* referred to
> > the metric despite this. Indeed, it is so much the norm that in
> > the word has been redefined by its common usage, much like "hey,
> > bad dude", which actually means "that's good".
> I can't see any evidence in mathematics that common usage has changed
> the definition.
The "effective" definition. You must be blind. Seriously.
>Books published quite recently define metric as it has
> been defined for more than a century and refer to creatures that are
> 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.
Ahmmm. You *obviously* don't read *any* General Relativity books. This
is not debatable.
Try Google.com search on +"general relativity" +metric.
Out of 25,000 hits, I doubt very much if any will point out the
distinction between a true metric and a pseudo-metric.
Look, mate, they don't call it the pseudo-metric tensor, its just the
"metric tensor". Duh....
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
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