Posted on 10/25/2004 1:46:25 AM PDT by accipter
CONSIDER a verbal description of the effect of gravity: drop a ball, and it will fall.
That is a true enough fact, but fuzzy in the way that frustrates scientists. How fast does the ball fall? Does it fall at constant rate, or accelerate? Would a heavier ball fall faster? More words, more sentences could provide details, swelling into an unwieldy yet still incomplete paragraph.
The wonder of mathematics is that it captures precisely in a few symbols what can only be described clumsily with many words. Those symbols, strung together in meaningful order, make equations - which in turn constitute the world's most concise and reliable body of knowledge. And so it is that physics offers a very simple equation for calculating the speed of a falling ball.
Readers of Physics World magazine recently were asked an interesting question: Which equations are the greatest?
Dr. Robert P. Crease, a professor of philosophy at the State University of New York at Stony Brook and a historian at Brookhaven National Laboratory, posed the question in his Critical Point column and received 120 responses, nominating 50 different equations. Some were nominated for the sheer beauty of their simplicity, some for the breadth of knowledge they capture, others for historical importance. In general, Dr. Crease said, a great equation "reshapes perception of the universe."
(Excerpt) Read more at nytimes.com ...
The pen exists. It's the same pen, regarless of whether, it's blue, foamy, stinks, dried up, or has any other particular quantification. It exists and is what it is, regardless of whether any sentient being exists to comprehend it.
It's the "same pen" despite the fact that in reality its physical makeup is in a constant state of change?
You seem to be saying that the concept of "the same pen" has its basis in something other than physical reality -- it's an abstract concept of the sort that Plato talked about in his theory of "forms."
No. The basis is in reality. I'm also the same person I was yesterday, even though I had some more coffee, took a few leaks and gobbled up a bag of candy bars.
Aha! So you admit that A is NOT A. If fact, because nothing is even itself, as you yourself admit, then nothing is anything! QED
</bizarro mode>
So you're "the same person" despite the fact that your physical state has changed considerably since yesterday. Clearly, then, physical reality is not the basis for what makes you "the same person."
If we grant that you are, nevertheless, the "same person," then the reality in which your claim is based must be something other than physical reality. Can you describe that reality? Again: you seem to need something akin to Plato's "forms." Or, perhaps, you may need to invoke the concept of a soul that exists independent of your corporeal body....
Wrong, physical reality is what enables objects to exist. W/o physical reality, there is nothing.
"you seem to need something akin to Plato's "forms.""
Nope.
" perhaps, you may need to invoke the concept of a soul that exists independent of your corporeal body....
If it is not real, meaning not having a physical basis, or foundation, it doesn't exist. If the soul exists, it is real and is physical.
Well then, what does this wavelength do? Anything? It would be equivalent to the DeBroglie wavelength if the electron was moving at the speed of light. I think that neither the Compton "wavelength" nor E = hv represent physical objects. In the case of E = hv, it doesn't mean that radiation comes in "bundles" of energy but rather that the interaction of an electromagnetic wave and a charged particle results in the transfer of that amount of energy. The wave or "photon" doesn't contain that amount of energy, its that the electron only absorbs that amount from the wave.
What's interesting is that a full semiclassical analysis of the Compton experiment produces the Compton "wavelength" as part of the double Doppler shift. It also produces the E = hv equation, constant transfer of angular momentum (still haven't figured out the factor of 2 error yet), etc. Required field strengths are extreme but the theory works. It also leads to what I call the "Compton Catastrophe" where the energy in the wave goes up as the frequency cubed. Yikes.
If you're interested in this all at, see the paper I wrote on the topic (pdf format):
The Classical Photon: Absorption
It is mostly a review of what is already known and put in practice in ultrahigh intensity laser acceleration of particles. My only real contribution is the second paragraph of the Discussion section. I think it's significant because it turns quantum theory on its head.
W/o physical reality, there is nothing.
Is mathematics "physical?"
"Especially if he was a union guy endorsing Kerry"
I found the sandwich easier to swallow.
Like a dem voter, the thread is back from the dead.
I see dead voters.
You're gonna see a whole lot more next Tuesday.
I see dead campaigns.
We can do very well without the Equator, thank you very much. After all, do we really need a stripe of toxic paint encircling Spaceship Earth?
I know the banned whackos are still lurking. Eat your hearts out. Hee hee hee.
In four dimensions (as opposed to three) there are two orthogonal axes of rotation (as opposed to one.) If a hyphersphere is rotated about both axes at the same rate, all points on the surface have the same speed. Everywhere is an equator. (Not all points are on the same equator though.)
Isn't geometry fun?
What, never? </Pinafore_mode>
I've been here longer and posted more replies, but you are about 5 to 1 ahead of me on threads.
Most of my replies are brief and pointless bad puns.
BTW, how do you access those stats?
They're at the top of your "personal menu" page, which you'll see as soon as you click on "more" at the top of your "my comments" page.
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