Division by Zero in Nature, and Decomposition of Time.

I think you need to read up on limit theory. Your argument is very
similar to Zeno's Paradox.

By a similar argument, nothing can ever go into motion after being
at rest, because the initial acceleration from zero to something, as
you examine intervals closer and closer to the start of motion,
is infinite, and one would have to apply an infinite amount of
energy to provide the necessary infinite acceleration.

I think you're guilty of what my Physics professor used to call
model-itis. You are confusing a mathematical model of reality for
reality itself. It's not time itself "decomposing relative to an
observer", it's your mathematical model of cosmology showing that
it cannot handle that particular case.

Consider the Ideal Gas Law. It models the behavior of gaseous matter
extremely well at high temperatures, high volumes, and low pressures.
It does not predict the behavior of gasses at all well at low
temperature, low volume, and high pressure (conditions under which
matter leaves the gaseous state and behaves in a manner entirely
inconsistent with the Ideal Gas Law). The behavior of space and time
is similar. At the quantum scale, time is merely another spatial
dimension, and particles routinely travel backwards in time. For
some important classes of particles (such as photons), the direction
in time becomes completely irrelevant.

Our perception of the fourth spatial dimension (time) occurs in the
direction of increasing entropy (see Stephen Hawking's "A Brief
History of Time"). That is merely a perception, not the reality
itself. Similarly, all of our observations of the universe depend
on the exchange of photons--particles that have the property that
their amplitude to travel at a speed other than C decreases as
distance of travel increases. At our huge scale, the amplitude
for a photon to travel at speeds other than C (or in ways other than
a straight line) is so vanishingly small that we say the speed of
light is constant, and light always travels in straight lines.
And that approximation leads directly to Einsteinian relativity.

Bottom line: the universe is the universe, and phenomena happen as
they happen. If a mathematical model of the universe yields absurd
results such as 1/0, it merely means that the model is flawed or is
incomplete.

-Paul W.

On Sat, 01 Jan 2005 14:07:21 GMT, "Lefty" wrote:
[regarding the similarity of his argument to the one Douglas
Adams used to prove that the universe is uninhabited]

Unfortunately, I dont see the connection between this and the original post.
I gave a very simple piece of arithmetic, it involves only one simple
operation, namely division, and showed how as things become larger and
larger, the ratio of natural cycles which we observe becomes closer and
closer to 1:0.

The universe cannot divide by zero, and so time itself must decompose
"relative to an observer".

Now, I'm really hoping that I'm wrong here, but you guys are'nt doing much
to disprove my claim. Please try again.

-WK-

On Sat, 01 Jan 2005 07:08:44 GMT, "Lefty" wrote:

An example of division by zero in nature. Also, a justification of a
multidimensional space, possible of non-integral dimension. The
decomposition of time, and an approach to the fabric of spacetime.

[snip]

Now, lets see you build a clock out of the whole universe! There is a
problem. It is so huge, that even if it has some gross, collective motion
such as rotation, it is just so vast that we simply cannot observe such
motions. They cant be measured with any instrument, and even if you could,
they would be either zero or very near zero relative to everything else in
the universe.

So, you have a ratio which is basically 1 : 0 or something like that, and
the universe simply cannot divide by zero. So, the only reasonable
conclusion, and it's really very simple, is that 4 dimensional spacetime
decomposes into 3 dimensional space as time becomes unobservable (relative
to an observer).

What exactly do you mean by "4 dimensional spacetime decomposes"?
Define "decompose".

I think if you were to work out the math of at exactly what point the
size of the "universe clock" becomes too big, it will be the point at
which photons emitted at the outer edge of the clock will never reach
the observer. In other words, you won't be able to observe the other
three dimensions, either. It becomes similar to trying to see beyond
the event horizon of a black hole.

You cannot build a clock out of the the whole universe because the large
scale motions are so close to zero, relative to us. Time is therefore
unmeasurable, and unobservable, relative to us. And, if it is unmeasurable,
and unobservable, then time ceases to exist on that scale, relative to us.

The same must also be true of the quantum world. Things can become so small
that they simply do not exist relative to an observer such as us.

It IS true at the quantum scale. The act of observing always perturbs
the thing being observed. At a large enough scale, the perturbation
is way below the precision of the measuring instrument and can be
ignored as irrelevant. But when the absorption or emission of a
photon (necessary for observation to take place) becomes significant
in proportion to the event being measured, you can't accurately
measure the event anymore. This is the Uncertainty Principle.

It seems that we are trapped between two worlds, the extremely large, and
the extremely small. We are somewhere in the middle.

Absolutely true. Phenomena at both the very large and very small
scaled don't behave according to the physical laws we're accustomed
to.

Additionally, it seems
that the fabric of 4D spacetime decomposes into a 3 dimensional state,
possibly decomposing into a state which is nonexistent relative to an
observer.

It's hard to argue with this, since I don't know what you mean by
"decompose".

A summary of your reasoning seems to be, motion of objects very, very
far away from the observer becomes so hard for the observer to measure
that it becomes useless for measuring the passage of time. Therefore
one can disregard the time dimension when considering these objects.

There is another aspect of the "universe clock" to consider. Since
all observation depends on the exchange of photons between observer
and subject, and since over large distances the speed of light is a
constant, simultanaity (two things happening in different places at
the same time) can never be observed. I can observe where object X
was and what it was doing at the time in the past when it emitted the
photon that I receive to make the observation, but I can never observe
where X is and what it is doing RIGHT NOW. Applying this to the
universe clock, the events are happening so far away that by the time
I see them, they're irrelevantly far in the past, and they are useless
for measuring time. It's kind of an "inverse uncertainty principle".

It's an interesting paradox, but IMO not significant otherwise.

-Paul W.

On Tue, 04 Jan 2005 00:44:56 GMT, "Lefty" wrote:

I always thought that real scientists had rather open minds to things unless
there was a good reason to believe that something is wrong.

Open minds, yes, but not so open that our brains fall out. :-)

I did _not_ actually suggest that anyone should divide by zero, or that it
can happen, but rather that it cannot. So, you have completely
misinterpreted some very plain English, and you have not pointed otu why
this idea would be so incorrect.

If it's wrong, then there should be a reason, but you have'nt given one.
What I am proposing is not a question of pure mathematics, but physics. So -
where is your physical justification that this is wrong ?

The division by zero that you arrived at very clearly indicates
something IS wrong--with the mathematical model you are using.

This sort of thing (absurd infinities) occurs all the time in
mathematical models in Physics. Quantum mechanics is riddled with
it, which is why they keep casting about for better mathematical
models. The problem exists (as I pointed out elsewhere) with more
mundane things such as the Ideal Gas Law, as well. The Ideal Gas
Law predicts zero volume for a gas at absolute zero. This is absurd
and experimentally patently not true. The discrepancy of model vs.
reality happens for two main reasons: (1) the particles in a real
gas are not mathematical points, as they are in the Ideal Gas Law,
and (2) real substances change state (and are not gasses anymore)
at those sorts of temperatures.

I think the problem is that your mathematical model doesn't hold at
the distance scales you are applying. I haven't tried to run the
numbers, but I suspect that at the point where time would break down
in your model, light from the objects at that point would never be
able to reach the observer, and so the observer and that edge of the
clock would for all intents and purposes not be in the same universe,
anyway.

-Paul W.

Basically, 1/0 dosent make any sense. So, if you have a naturally occuring
phenomena which appears to divide by zero, then this process is going to
have problems.

The problem is that your definitions are wrong because nature and numbers
are never wrong.

The substance of the idea is worthless philosophical drivel because it is
saying precisely nothing

I agree. For some reason my respoce has not made it. Basically, if you make a
premise, and it leads to a conclusion that doesent make sence, then the premise
is wrong.

Lefty wrote:
Depends on who you read. There is speculation that fractals may qualify as
objects of truly non-integral dimensionality in the Euclidean sense of the
word dimension.

Anyone who speculates to that effect doesn't understand Euclidean
geometry. There are senses in which fractals have non-integral
dimension, but they ain't Euclidean.

I haven't slogged all the way through Elements yet, but I don't
think I've seen any mention of dimension at all.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

doesn't say too much about
how big the universe can be. Search google for ``dirac''
and ``large number''. You sho

In The book "Mathematics and the Imagination" by Kasner and Newman (late
forties) they discuss large numbers. The Google is 1 followed by 100 zeros.
The googleplex is a google to the google power. The discussion also included
its relation to infinity.
In more recent times I have been dissapointed to find that Google is a name
for a search engine.

"HAVRILIAK" wrote in message
...
doesn't say too much about
how big the universe can be. Search google for ``dirac''
and ``large number''. You sho

In The book "Mathematics and the Imagination" by Kasner and Newman (late
forties) they discuss large numbers. The Google is 1 followed by 100
zeros.
The googleplex is a google to the google power. The discussion also
included
its relation to infinity.
In more recent times I have been dissapointed to find that Google is a
name
for a search engine.
I think it might have been googol.

Havriliak wrote:
In The book "Mathematics and the Imagination" by Kasner and Newman (late
forties) they discuss large numbers. The Google is 1 followed by 100 zeros.
The googleplex is a google to the google power. The discussion also included
its relation to infinity.

The numbers are actually written "googol" and "googolplex." The search
engine's name is inspired by the number's name, but they aren't spelled
the same.

As Google's web pages mention, the word "googol" was invented by Kasner's
nephew, whose name escapes me at the moment.

Maybe it's time to develop a web search engine called "Skewes"?

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Brian Tung wrote:

Havriliak wrote:
In The book "Mathematics and the Imagination" by Kasner and Newman (late
forties) they discuss large numbers. The Google is 1 followed by 100 zeros.
The googleplex is a google to the google power. The discussion also included
its relation to infinity.

The numbers are actually written "googol" and "googolplex." The search
engine's name is inspired by the number's name, but they aren't spelled
the same.

As Google's web pages mention, the word "googol" was invented by Kasner's
nephew, whose name escapes me at the moment.

Maybe it's time to develop a web search engine called "Skewes"?

The first time I heard the expression 'googol' and 'googolplex' was in
one of the episodes of Carl Sagan's 'Cosmos'. That's probably when it
began to be used colloquially.


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