Cecil Moore wrote:
Tom Donaly wrote:
Cecil Moore wrote:
Richard Clark wrote:
On Wed, 21 Nov 2007 14:00:39 GMT, Cecil Moore
wrote:

What is the momentum of 50.95 W?

momentum? Please be specific.
ditto. :-)

If 50.95 watts is the Poynting vector, actually
watts/unit-area, then the momentum is 50.95/c^2.
Please reference pages 56,57 of "Optics", by Hecht,
4th edition.

50.95 divided by the speed of light squared? So, for all
practical purposes - if that's right - it's zero. Why not
just say so?

The percentage difference between zero and that momentum
is infinite. And whatever value it is must be conserved.
Sweeping it under the rug in violation of the laws of
physics is just not acceptable.

Actually, you're writing about momentum density. Momentum is
conserved, but momentum density isn't, any more than energy
density, or any other kind of density, with the possible
exception of the bone density in the heads of some people.
As for any finite number being an infinite percentage above
zero, I think you should take that up with the next mathematician
you meet. Mathematicians need to laugh once in a while, too.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
Actually, you're writing about momentum density. Momentum is
conserved, but momentum density isn't, ...

The momentum density may certainly change with area just
as the energy density may change with area. But in either
case, the total energy and total momentum are conserved.

As for any finite number being an infinite percentage above
zero, I think you should take that up with the next mathematician
you meet.

The equation for any percentage change from zero is
100(X-0)/0 Plug any value of X into that equation and
see what you get.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Tom Donaly wrote:
Actually, you're writing about momentum density. Momentum is
conserved, but momentum density isn't, ...

The momentum density may certainly change with area just
as the energy density may change with area. But in either
case, the total energy and total momentum are conserved.

As for any finite number being an infinite percentage above
zero, I think you should take that up with the next mathematician
you meet.

The equation for any percentage change from zero is
100(X-0)/0 Plug any value of X into that equation and
see what you get.

Division by zero is not infinity, Cecil, it's undefined.
It's good to see you agree that there's no conservation of
______ (fill in the blank)density, any more than there's a
law of the conservation of power. Have a good thanksgiving.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
Division by zero is not infinity, Cecil, it's undefined.
It's good to see you agree that there's no conservation of
______ (fill in the blank)density, any more than there's a
law of the conservation of power. Have a good thanksgiving.

Division by a quantity as it approaches zero is not
always undefined, Tom. The limit, as the denominator
approaches zero, is often the first infinity, aleph-null.

The momentum in any volume of space must be conserved.
The joules in the joules/sec must be conserved. Please
don't try to hoodwink the uninitiated into believing
otherwise.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Tom Donaly wrote:
Division by zero is not infinity, Cecil, it's undefined.
It's good to see you agree that there's no conservation of
______ (fill in the blank)density, any more than there's a
law of the conservation of power. Have a good thanksgiving.

Division by a quantity as it approaches zero is not
always undefined, Tom. The limit, as the denominator
approaches zero, is often the first infinity, aleph-null.

The momentum in any volume of space must be conserved.
The joules in the joules/sec must be conserved. Please
don't try to hoodwink the uninitiated into believing
otherwise.

But you didn't write anything about "The limit, as the
denominator approaches zero," Cecil. I just wrote that
energy and momentum are conserved, but their rate of
delivery certainly isn't. You're just arguing for the sake of
hearing yourself argue, Cecil. As for Aleph-null, that's a
mathematico-logical fantasy that was brought into existence
by giving a name to a made-up abstraction, and then using
a set of artificial, logical manipulations on the name as proof of
its existence. It's a stunt Western philosophers have been using
for centuries to confuse the gullible. I'm surprised
an intelligent man of science, like you, fell for it, Cecil.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
But you didn't write anything about "The limit, as the
denominator approaches zero," Cecil.

I assumed that any reasonably rational person would
understand what I was talking about. I apologize for
misjudging you.

As for Aleph-null, that's a
mathematico-logical fantasy that was brought into existence
by giving a name to a made-up abstraction, and then using
a set of artificial, logical manipulations on the name as proof of
its existence. It's a stunt Western philosophers have been using
for centuries to confuse the gullible. I'm surprised
an intelligent man of science, like you, fell for it, Cecil.

Good grief, Tom. Aleph-null is the number of natural numbers,
a very useful concept. I'm surprised you are ignorant of such.

Incidentally, truth, love, and justice are all names
given to made-up abstractions. Too bad you reject them.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Tom Donaly wrote:
But you didn't write anything about "The limit, as the
denominator approaches zero," Cecil.

I assumed that any reasonably rational person would
understand what I was talking about. I apologize for
misjudging you.

As for Aleph-null, that's a
mathematico-logical fantasy that was brought into existence
by giving a name to a made-up abstraction, and then using
a set of artificial, logical manipulations on the name as proof of
its existence. It's a stunt Western philosophers have been using
for centuries to confuse the gullible. I'm surprised
an intelligent man of science, like you, fell for it, Cecil.

Good grief, Tom. Aleph-null is the number of natural numbers,
a very useful concept. I'm surprised you are ignorant of such.

Incidentally, truth, love, and justice are all names
given to made-up abstractions. Too bad you reject them.

The turkey meat must have been real dry at your place this
Thanksgiving, Cecil. So dry, it dried up your
reason. Better luck at Christmas.
73,
Tom Donaly, KA6RUH

On Nov 23, 9:56 am, "Tom Donaly" wrote:
snip
As forAleph-null, that's a
mathematico-logical fantasy that was brought into existence
by giving a name to a made-up abstraction, and then using
a set of artificial, logical manipulations on the name as proof of
its existence. It's a stunt Western philosophers have been using
for centuries to confuse the gullible. I'm surprised
an intelligent man of science, like you, fell for it, Cecil.

Guess what? EVERY SINGLE LAST BIT of mathematics
is "made up abstraction". All mathematics, *all of it, is an
abstraction! You have a problem with abstraction?
Then what do you suggest be used in it's place?
You claim that "Western philosophers" have made it
up just to "confuse the gullible". So then what
alternative philosophy do you suggest should be
use that does _not_ confuse the gullible? If you cannot
provide it and prove that it indeed has more merit than
the already-existent philosophies then why bother
with it?

mike3 wrote:
On Nov 23, 9:56 am, "Tom Donaly" wrote:
snip
As forAleph-null, that's a
mathematico-logical fantasy that was brought into existence
by giving a name to a made-up abstraction, and then using
a set of artificial, logical manipulations on the name as proof of
its existence. It's a stunt Western philosophers have been using
for centuries to confuse the gullible. I'm surprised
an intelligent man of science, like you, fell for it, Cecil.

Guess what? EVERY SINGLE LAST BIT of mathematics
is "made up abstraction". All mathematics, *all of it, is an
abstraction! You have a problem with abstraction?
Then what do you suggest be used in it's place?
You claim that "Western philosophers" have made it
up just to "confuse the gullible". So then what
alternative philosophy do you suggest should be
use that does _not_ confuse the gullible? If you cannot
provide it and prove that it indeed has more merit than
the already-existent philosophies then why bother
with it?

So, an attack on one part of mathematical theory is an attack
on all mathematics? I like your vigorous defense of mathematics,
but I think you missed the point.
73,
Tom Donaly, KA6RUH