Re: Kinda Miss TG...

On Nov 11, 1:45 am, "Richard Yates" <rich...@xxxxxxxxxxxxxxx> wrote:
<big snip>L
I agree with the general point of your post, although I think it was
overstated and hence Richard's response(s). The case is clearer with
dividing by fractions than with multiplying by them. I know that I always
think of that as multiplying by the inversion of the fraction. I would be
interested to read of any concrete examples that Richard can think of where
dividing by a fraction is the natural way to think about a concrete
operation. (I also am waiting to hear how many photons turned out to be
hitting that sensor!) RY

Computing the number of photons hitting the camera sensor is just such
an example of dividing by a fraction to get a real world result. One
of the photometric units involved amounts to 1/683 watts per square
meter of light energy falling on a surface. To convert this into
photons per second, you divide by the energy content of a single
photon.

The energy of a single photon is Planck's constant x the frequency of
the light in cycles per second.

The frequency of green light is about 5.4545x10^14 Hz (cycles per
second). Or, if you prefer,
545,450,000,000,000 Hz.

Planck's constant is
66,261/100,000,000,000,000,000,000,000,000,000,000,000,000.

Multiplying Planck's constant by the frequency of green light results
in a number that is still a very small fraction,
36,142/100,000,000,000,000,000,000,000.

The numerators have been rounded off to five digits, but the
denominators are perfectly precise. Dividing 1/683 by the last
fraction gives

405,100,000,000,000 photons/sec/square meter=1/683 watt/square meter.

The only way to get this answer from the physical concepts is to
divide one fraction by another. Of course, I used a spread*** to do
the calculations. I would say this is the real world, because you can
make accurate predictions of the camera's performance by calculations
incorporating this one.

A more interesting point would be that to a mathematician, multiplying
and dividing by any non-complex number (such as 1/pi) is regarded as
precisely the same operation as multiplying or dividing by a whole
number. You might go about the arithmetic a little differently,
depending upon how the number is expressed. In most computers, the
only digits are 0 and 1. The algorithm (recipe for calculation) for
division in the binary system looks different from the one in the
decimal system, but you get the correct answer either way.

RNJ
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