Re: Democratic candidates address the issue of global warming while Republicans snooze...

On Sat, 5 Jan 2008 12:02:33 -1000, "Alvin E. Toda" <aet@xxxxxxxx>
wrote:

On Sat, 5 Jan 2008, Rumpelstiltskin wrote:

On Sat, 05 Jan 2008 07:55:00 -0800, Islander
<nospam@xxxxxxxxxxx> wrote:

Rumpelstiltskin wrote:
On Fri, 04 Jan 2008 18:24:22 -0800, Islander
<nospam@xxxxxxxxxxx> wrote:

<snip>


OK, I think that the two of you are talking about
different things. My response to Jean had to do
only with the change in the tilt of the earth's
axis, not the difference in the distance of the
earth from the sun.

The change in the tilt is a maximum of only 3
degrees and that occurs over a period of about 41K
years. The specific cycles that Jean referred to
happen over shorter cycles, but are still pretty
long.

The change of distance between the earth and the
sun is only about 4 million miles (95M at aphelion
and 91M at perihelion. But, don't forget that the
intensity of the sun's rays varies as a cube law
(space is 3D). So, the difference in intensity
between perihelion and aphelion as a percentage is
(95M**3 - 91M**3)/95M**3 = 13%


Hmm. That's actually only as the square, isn't
it? not the cube. It's true that the volume of a
sphere increases by the cube of the diameter, but
when we receive light rays, we're not receiving
them from the volume, but only from what portion of
the spherical shell containing the light emitted
from the sun at a given instant in the past falls
on us or our measuring device. The surface area of
such a shell increases by the square of the
diameter, not the cube. (Disregarding any
absorption by interstellar gas, of course.)

http://tinyurl.com/25dc9q

That correlates (and has to correlate) with the
fact that the apparent size of the sun in the sky
diminishes by the square of the distance we are
from it. The brightness per apparent unit area
doesn't change (disregarding absorption), but the
net luminosity received diminishes in proportion to
the diminishing apparent size, which is the square
of the distance.

The brightness of a distant star identical to
the sun is the same (disregarding absorption) as
the brightness we receive from an "average" piece
of the sun exactly the same area as the apparent
size of the distant star (if we could make out the
diameter of the star, which we usually can't).

<snip>



You are right! But, you are also younger. That was
a dumb mistake, but at least I'm still young enough
to admit it!

That reduces the difference to 8.2%



Actually, your post sounded pretty good at first.
I read it just before going out, and wasn't really
thinking about it in the front of my mind, but then
the thought popped up that if luminosity diminished
by the cube rather than by the square from the
source, then we wouldn't be able to see stars at all!
I'm not sure if that was what made me realize
something had to be wrong, or if it was the fact that
the proportion of the sky occupied by the sun
diminishes only by the square of the distance, so if
the luminosity diminished by the cube, that would
violate conservation of energy.

There are greater worries about planetary orbits. It's
an oldie but once astronomers were not sure that Saturn
and Jupiter were in stable orbits. Since the many body
problem is non-linear (varies as the square), it is an
unsolvable problem.


I'm not yet completely willing to give up and say
that the three-body (mult-body) is unsolvable, but
some people, such as Steven Wolfram, I think
have speculated that the only way to solve the
problem is algorithmically, and that's why time
exists - the steps of time (presumably quantized)
are the working-out of the algorithm. (I hope that's
not just something I made up, but it might be.)
That idea fits in nicely with the idea that time
doesn't actually move at all, but that each slice
of time is just the next step in the algorithm, and
that's also why each slice has a "memory" of
the previous step in the algorithm, but no
forward-looking equivalent of "memory" because
the next step has not "yet"been, and cannot
"yet" be, computed, until the algorithm proceeds
to the next step based on the status at the
previous step.

Or we may just need a new mathematics to
solve the three-body problem. That's why I've
used the three-body problem of an example of
how someone could prove he had contact
with interstellar aliens and wasn't just delusional.
If he could get the aliens to hand him a book
describing the mathematics that would solve
the three-body problem non-algorithmically, it
would be easy to convince other people that
he really had seen aliens. If people still didn't
believe him, at least other people would have
to think of him as a mathematical genius to end
all mathematical geniuses, and give him lots of
money. Unfortunately, though, all interstellar
contact so far has been indistinguishable
from delusion, because no such persuasive
proof has ever resulted from those contacts.

The same argument could also be applied to
visions of God, except of course that God
wants to test man's Goodness by seeing if
man will believe stuff without any evidence
and in contradiction to all appearances, or
something equally convenient.



But purturbations about the current
stationary orbits under all circumstances might be done
to see if there are any instabilities. IIRC it took
quite a while (until the 20th century) before the
mathematics were deemed to converge (I guess series
expansions of an integral expression?). But I think
that it's obvious that if they have not left the solar
system for billions of years due to some instability,
that their orbits are stable. The earth is much further
in and closer to the sun, that it's orbit is probably
much more stable that either Jupiter or Saturn.


Perturbations are another way of talking about
steps in the algorithm, except that as far as I
know it hasn't been compacted into a process
such as calculus but remains in the state of the
pre-calculus "delta process". If it can be
systematized, that would pave the way to a
solution such as calculus offers, of course. If
not, and if time is quantized as I presume it
"must" be, we still have to get down to the
individual quanta of time (which will be quanta
of a particular situation, not quanta that apply
to the whole universe at once, just like other
kinds of quanta). If we do that though, and if
time is the working out of the algorithm,
finding that theoretical delta-process that
completely maps out the three-body problem
will be intellectually satisfying, but can never
solve actual three-body problems faster than
time actually works out the process. The
reason for that is the original conjecture, that
that's what "time" is: the fastest way of
working out the algorithm.



It's a metaphor really, but as in electron systems, it
the spins that usually cause magnetic properties rather
than orbitals. Pairing of the spins of the outer
electrons cause strong covalent bonds with other atoms.
The internal pairing in the lower orbitals are so
strong that usually the electrons from the completed
inner shells do not enter into any properties of the
substance-- chemical or physical.

.

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