Division by Zero in Nature, and Decomposition of Time.

starman wrote:
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.

Being unusually interested in mathematics as a child, I'd heard of at
least the googol before I watched Cosmos (Episode IX: The Lives of the
Stars, in case anyone wants to look it up), but it's true that I hardly
heard anyone else use the term before Cosmos rolled around.

The story about Kasner's nephew is also told in Cosmos.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
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LEFTY wrote:
Take a look at http://math.rice.edu/~lanius/fractals/dim.html

There are valid reasons to think that fractals have a non-integral
dimension in the euclidean sense.

That is not Euclidean dimension described in the page cited above. It
is approximately what is meant by Hausdorff dimension.

As soon as you have length--even a fractal with length--you have one
dimension. As soon as that line has even a little bit of breadth, you
have two dimensions. As soon as it has even a little bit of thickness,
you have three dimensions. It's not a matter of intuition--Euclidean
geometry is defined, not investigated as a matter of science.

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

If fractals have non-integral dimension, then we have something really
very amazing. If they dont, then there is little consequence for the
argument at hand.

If 4-dimensional spacetime decomposes to a lower dimensionality
(relative to an observer), then it would be interesting if the
dimensionality were non-integral, but if that is'nt the case, then it
must decompose to a 3-dimensional manifold.

If this is really happening, then you have a very good explanation for
certain quantum "weirdness". Specifically "action at a distance".

Information travels instantaneously across a 3D "point". The fact that
information appears to be travelling faster than light is just an
illusion - caused by information taking a shortcut across the
3rd-dimension.

I see it but I cant believe it. And I cant believe that nobody ever saw
this before.

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.

It's full of words, but they're all very simple, and the only math
required is division.



-----------------------------------------
Our understanding of time, and our ability to measure it is based on cycles
in nature.

You can build a clock out of the solar system, and maybe even some larger
things. But at some point, things become so vast that their gross motion is
zero or very near zero, relative to man. In other words, the universe is
vast and nearly motionless relative to man.

Earth spins on axis ~365.25 times per every revolution round the Sun.
Basically, a 1 : 365 ratio.

Moon goes round Earth 12 times per year. Essentially a 12 : 1 ratio.

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).

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

-WK-

----------------------------------

Comments, criticism & outrage - please post.
What's this all about? I must have come to it late. Maybe a previous
message is missing. For what it's worth, take a look at Siefe's recent book
Zero, The Biography of a Dangerous Idea. It's an easy and enjoyable read.
I'll bet you thought the Arabs invented the arabic numbers? Surprise ...

(I see this was cross posted. How unfortunate.)

--
Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
(121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
Obz Site: 39° 15' 7" N, 121° 2' 32" W, 2700 feet

Most vehicle/deer accidents occur at sunset.
Vehicle deer whistles are ineffective.

Web Page: home.earthlink.net/~mtnviews

We seem to gotten into the area of modern quantum mechanics
gymnastical-linguistics somehow.



So, one question which I have, and I dont even know if this is
possible, how to make a smooth transition from R1 to R2 to R3 to R4 etc
etc.

Certainly, nonintegral dimension is difficult, maybe impossible to
visualize. But, it seems that spacetime might be exhibiting this very
behaviour "relative to an observer".

So, how the hell do you model such a thing ?

-----------------------------

Next question -

Suppose you set up an experiment with beam splitters to reproduce the
famous experiment with interference patterns. But instead of using just
one beam splitter, you set up a whole cascade of beam splitters, so
that one beam is split into 2, then 4, then 8 separate beams. One beam
goes in, and 8 beams come out.

What happens to the beams when one of them is disrupted ? Anybody know
?

LEFTY wrote:
My SSN is a product of two primes both greater than 161.
What are the odds of that ?

I dunno. Offhand, I'd guess maybe 1 in 40 or so?

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

I think it's probably less than 1:40, but I'm just too lazy to work it
out completely.

I guess you'd first have to look at the set of all possible SSN's.

A SSN has 9 digits. Assuming that every possible combination of digits
could be a real SSN, you have 9*10^8 different possible permutations.
There are 900,000,000 possible SSN's.

You would need to know how many primes exist between 161 and
999,999,999, and then try to figure out how many of these could
multiply to yield a 9 digit number.

If one factor is 161 or more, then the other would be less than
6,211,180 or less.

The 100,008th prime is 1,299,827, so there are quite a few more primes
before you get to 6,211,180.

OK - enough FermiMath. I think that nobody will be able to figure it
out, not that it matters.

For something _really_ interesting -

Suppose that the nonsense that I'm spewing in this thread is true,
about dimensions, and universes, and bla bla bla.

If the 4th dimension "melts" into the 3rd dimension due to relativistic
considerations, it must be either a sharp transition from 4D to 3D, or
it is a smooth transition - sort of a continuous situation.

Imagine for a moment that the transition is smooth. You have the
strange situation where math might be invented through observing the
universe. The exact opposite of the classical approach in modelling !!!
ROFLMAO - Certainly is it difficult to contemplate non-integer
dimensions, and it dosent seem to make sense even to discuss it. But,
if the transition from 4D to 3D is smooth, then non-integer dimensions
must make sense, and there must be a means to treat the situation
algebraically !!!

It's mind boggling. I keep hearing this little voice that there is
something really interesting to uncover here, perhaps some type of
infinite cardinal, or something relating to the structure of space
where 3D and 4D are mixed together so intimately - there must be some
profound number theoretic truth buried here, waiting to be uncovered. I
wonder. Then, maybe it's all just perceptual nothingness based on a
loopy relativistic argument.

Still wondering.

This is going to sound crazy, but, with the caveat that continuity in
spacetime has not been proved, and discussion of cardinality of
continuum is for illustrative purposes only - here goes nothing.


If spacetime is 4D, and a 3D manifold is a "point" in spacetime, then
it is very straightforward that a "3D point" has the cardinality of the
continuum. This is because we are using this "spacetime" definition of
"point".

But what does that mean if the above relativistic arguments arguments
are valid ? Perhaps the point in spacetime really does have the
cardinality of the continuum !!!! - and this is simply insane, and yet
somehow it seems reasonable. It's relativistic.

I am NOT saying that a point in R3 or R4 has the cardinality of the
contniuum. R3 and spacetime are not the same thing !
Damn relativistic madness - it's absolute sorcery. I QUIT !

On 2 Feb 2005 17:05:13 -0800, "LEFTY"
wrote:

I think it's probably less than 1:40, but I'm just too lazy to work it
out completely.

I guess you'd first have to look at the set of all possible SSN's.

A SSN has 9 digits. Assuming that every possible combination of digits
could be a real SSN, you have 9*10^8 different possible permutations.
There are 900,000,000 possible SSN's.

Since mine happens to start with a zero, there doesn't seem to be any
reason to eliminate the ones below 100-00-0000. I have no idea if any
start with two or more zeros.


You would need to know how many primes exist between 161 and
999,999,999, and then try to figure out how many of these could
multiply to yield a 9 digit number.

If one factor is 161 or more, then the other would be less than
6,211,180 or less.

The 100,008th prime is 1,299,827, so there are quite a few more primes
before you get to 6,211,180.

OK - enough FermiMath. I think that nobody will be able to figure it
out, not that it matters.

For something _really_ interesting -

Suppose that the nonsense that I'm spewing in this thread is true,
about dimensions, and universes, and bla bla bla.

If the 4th dimension "melts" into the 3rd dimension due to relativistic
considerations, it must be either a sharp transition from 4D to 3D, or
it is a smooth transition - sort of a continuous situation.

Imagine for a moment that the transition is smooth. You have the
strange situation where math might be invented through observing the
universe. The exact opposite of the classical approach in modelling !!!
ROFLMAO - Certainly is it difficult to contemplate non-integer
dimensions, and it dosent seem to make sense even to discuss it. But,
if the transition from 4D to 3D is smooth, then non-integer dimensions
must make sense, and there must be a means to treat the situation
algebraically !!!

It's mind boggling. I keep hearing this little voice that there is
something really interesting to uncover here, perhaps some type of
infinite cardinal, or something relating to the structure of space
where 3D and 4D are mixed together so intimately - there must be some
profound number theoretic truth buried here, waiting to be uncovered. I
wonder. Then, maybe it's all just perceptual nothingness based on a
loopy relativistic argument.

Still wondering.



Remove the del for email

LEFTY wrote:

My SSN is a product of two primes both greater than 161. What are
the odds of that ?

I dunno. Offhand, I'd guess maybe 1 in 40 or so?

I think it's probably less than 1:40, but I'm just too lazy to work it
out completely. [...]

I think that nobody will be able to figure it out, not that it matters.

It's actually very close to 1:15, and not hard to figure out.

Define an SSN as a string of 9 digits, p1 and p2 as the two primes, and
N as the number of primes between 161 and 10^9 / 161.

You only get an SSN if p1 * p2 10^9, or

p2 10^9 / p1

Given a table of prime numbers from 161 to 10^9 / 161, it's easy to
count the number that are less than 10^9 / p1. A binary search will
find this count in log time. Call it C. The number of SSNs is then

sum(C from 1 to N) * N

which can be interpreted as: For every prime in the table, there are C
other primes that can be used to form a product that's an SSN. Add up
all the Cs.

It turns out it's also easy to generate the prime table. Even by brute
force, it takes only a few seconds.

There are about 67 million SSNs that are the product of two primes
greater than or equal to 161. Or 1 in 15.

The more interesting question is, What are the odds people will be able
to guess your SSN with the information you've supplied?

- Ernie http://home.comcast.net/~erniew