Geometry- does it restrict matter?

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Geometry- does it restrict matter?

Postby Simeon » Tue Jan 06, 2004 8:44 pm

Assumptions that such things as chemical molecules and black holes are
radically different in the 4th dimension, are equivalent to the idea that only in
a mirror is my face exactly reversed.
If dimensions, geometrically speaking, are inherent in space rather than
superimposed on it, then - for a domain of n dimensions - any domain of n-1
dimensions is a shadow world, with no more substantiality than reflections in
a mirror. We can see them, but they don’t exist. And if there are an infinity of
dimensions, reality is an unreachable illusion always beyond the visible. A
reality defined by boundaries, so that the infinite cannot exist, as a manifest
at least.
A guided tour of the universe - “here we have a 1-space, and over here a 4-
space” - would be absurd. In 4-space, our realm wouldhave to be an
infinitely thin cross-section of something; otherwise its chemistry would fail.
Personally, I think space can exist without dimensions, just as a line can be
without points. Insofar as either are real. And that it becomes, say, 4-space
only after 4-space geometry is ‘put into it’, and disappears when empty.
An infinity of points can be assigned to a finite line only because there is no
space between them. In spite of which they all occupy different positions. In
the same way, isn’t our realm merely an infinity of planes (‘flat’, or curved
like onion-skins), each having no thickness whatever, packed on top of each
other?
Or maybe I should stay off the liquor.

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Re: Geometry- does it restrict matter?

Postby Geosphere » Tue Jan 06, 2004 8:59 pm

Simeon wrote:equivalent to the idea that only in a mirror is my face exactly reversed.

What does that mean?

Simeon wrote:We can see them, but they don’t exist.

And why not? If existance is all you perceive, then to your perception it exists. Reflections are most certainly real. Read Descartes for further elaboration.

Simeon wrote:reality is an unreachable illusion always beyond the visible.

What does this mean and how do you arrive at this?

Simeon wrote:In 4-space, our realm would have to be an infinitely thin cross-section of something.

You assume dimensions 'nest'. IF they do, why would it have to be a cross section?

Simeon wrote:its chemistry would fail.

Define chemistry and why it would fail.

Simeon wrote:a line can be without points.

No, it can't. A line is defined as the path between 2 points. Remove the points and you have no line.

Simeon wrote:An infinity of points can be assigned to a finite line

No, only two points may define a line. When another point is added, a new line segment is defined.

Simeon wrote:isn’t our realm merely an infinity of planes

While it can be divided up as such, that would imply those planes have no interaction and segments can be removed. Obviously untrue. For mathematics sake, you can infinitely fractalize our realm, but that does not make each its own organic dimension.

Simeon wrote:maybe I should stay off the liquor.

Not if you enjoy it and it poses no health risks.
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Re: Geometry- does it restrict matter?

Postby alkaline » Tue Jan 06, 2004 9:32 pm

Geosphere wrote:
Simeon wrote:a line can be without points.

No, it can't. A line is defined as the path between 2 points. Remove the points and you have no line.
Simeon wrote:An infinity of points can be assigned to a finite line

No, only two points may define a line. When another point is added, a new line segment is defined.

I think you are misunderstanding Simeon here. He is talking not just about the 2 endpoints that you are talking about, but also all of the other points in between those two points that define the substance of the line itself. You can have two points and add a third point, and the third point can be on the same line, thus not *necessarily* creating a new line segment or a plane. So, when you take all of the points that are colinear, they form a single line.
Geosphere wrote:
Simeon wrote:maybe I should stay off the liquor.

Not if you enjoy it and it poses no health risks.

liquor has proven health risks - it slowly destroys your motor coordination over the course of your life.
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Re: Geometry- does it restrict matter?

Postby Geosphere » Tue Jan 06, 2004 9:43 pm

alkaline wrote:liquor has proven health risks - it slowly destroys your motor coordination over the course of your life.


Yeah, but if you have enough, you won't care that you have no motor coordination.
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Points and lines

Postby Simeon » Wed Jan 07, 2004 9:59 pm

A line has always seemed to me very mysterious indeed. Along it is an
infinity of positions, with apparently none left out, and hence no spaces
between. Yet these points are not concentric. According to Zeno’s ‘Arrow’
paradox, motion is impossible, since the arrow could never at any speed it
travelled cover the infinite number of journeys from one successive position
to another in its trajectory. Or, if these points have no distance between them,
then there is no trajectory and again motion is impossible, since however
slowly it travelled, the time factor would be nil. Plato, in ‘Timaeus’ (Time)
adopts the idea that infinity/eternity are really quite small, like a gold coin
held in the hand, for which tiny copper change is being paid out forever. The
difficulty seems to stem from thinking of time or distance as an infinitude of
‘atoms’, points or moments, rather than a whole independent of such ‘parts’.
3-space can be considered as an infinite pile of 2-space. Squares piled high
enough, though having no thickness whatever, yet an infinitude will make a
cube. Actually, an infinitude of planes which DO have finite thickness will
also make a cube. As in the ant story:-
Ants and Transcendental Numbers
Imagine a race of talking ants. The ants can compress the infinite digits of pi
in an interesting way. For example, let us imagine that the ants can speak by
manipulating their crude jaws. The first ant in the long parade of ants
screams out the first digit, "3". The next yells the number on its back, a "1".
The next yells a "4", and so on. Further imagine that each ant speaks its digit
in only half the time of the preceding ant. Each ant has a turn to speak. Only
the most recent digit is spoken at any instant. If the first digit of pi requires
30 seconds to speak (due to the ant's cumbersome jaws and little brain), the
entire ant colony will speak all the digits of pi in a minute! (Again, this is
because the infinite sum 1/2 minute + 1/4 minute + 1/8 minute + ... is equal
to 1 minute.) Astoundingly, at the end of the minute, there will be a quick-
talking ant that will actually say the "last" digit of pi! The geometer God,
upon hearing this last digit, may cry, "That's impossible, because pi has no
last digit!"

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Postby Aale de Winkel » Thu Jan 08, 2004 9:54 am

These are all familiar problems one encounters when dealing with infinity.
pe. the familiar function 1/x, no matter how large x gets it never will be 0
with a line no matter how deep one zooms in, one allways sees a line.

this is the nature of IR (the real number system). the basic number system for IR[sup]n[/sup].

It is quite possible to define other types of spaces:
pe. IN[sup]n[/sup], hyperspaces based on the natural numbers.

one then works with lattices with a descrete amount of disjunct points on a line.

Our trionian realmspace is IR[sup]3[/sup], however pe molecules are discrete objects so some matter could be approximated with IQ[sup]n[/sup] (space base on rational numbers). Which gives latice spaces.

However the movement of molecules also move through values between members of IQ, so the IQ[sup]n[/sup] description of matter would also be approximate.

Is is surely possible to investigate IQ[sup]n[/sup] and ignore the IR-numbers between the IQ-numbers. Points on a line in IQ[sup]n[/sup] are countable!
.
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Postby Simeon » Fri Jan 09, 2004 2:50 am

Now that I find very interesting, Aale. Number theory appears to be covered with the fingerprints of man - the denary system for a start. Just as we can hardly think of a chair except in terms of the use we put it to; whereas the equally valid conclusions of the nature of a hungry caterpiller in regard to it are ignored. We made it, ergo we must know all about it!
Euclid wrote his geometry thousands of years before Klein took to the bottle or Moebius joined the band. Flat, on wax tablets. If he had used wax spheres, then his unproven 5th postulate about parallels would have resulted in a geometry totally different to that we now call the geometry of the plane.
It again occurs to me that space disappears when not being used by matter, energy or geometry. Like lazy furniture in the rooms of computer games which are not being played. Or the argument that Mt. Everest contains within it every statue that will ever be carved (you only have to uncover it by removing rock extraneous to its shape). So all dimensions and geometries, Euclidean and non-Euclidean, lie within formless unmanifested space, as potentialities waiting to be intellectualised.

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Postby Aale de Winkel » Fri Jan 09, 2004 6:15 am

Simeon wrote:Number theory appears to be covered with the fingerprints of man


It is just as the saying goes: God created the integer, anything else is created by man.

uptill the big bang space was presumably empty, whatever "banged" (I don't know) but since then space is filled, with stars, planets, background radiation etc etc.

Some trench in the ocean can contain the Mt Everest top side down, which is merely a relation between the respective sizes. Even with integer algebra one can conclude this. I don't know where you want to go with this remark.

According to some phylosopher you are a figment of my imagination, in empty space I wouldn't exist and therefore nothing else would. This would mean that in your "unmanifested space" nothing exists! not even (non-) Euclidean geometry.

As said all things a function of ones point of view (ie phylosophy), according to my phylosophy I live in some curved IR[sup]3[/sup] space (curved due to the existence of masses, according to Einsteintonian physics).

So unless someone invents warp-technology (thereby falsifying the current limitation of travel (see Popper)) I believe we won't travel beyond the speed of light (and stay within future time, "tachions" travel faster then the speed of light backwards in time :lol: :lol: (according to Einsteintonian physics))
.
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Postby RQ » Fri Jan 09, 2004 6:46 am

First of all, how could a line exist without any points in it? Xeno's paradox was solved by the Cantor sets...
Also you there is a dimension 0.6915 (phi) where the points have spaces between them (also proven by Georg Cantor).
Infinity isn't really something anyone should be messing with with the common sense they use with plain numbers like 2 and 3. For example if you keep dividing a number by 1 forever you get 0. Or 0.99999.....=1.
Basically there are infinite sets where x/0 and you have the big infinity 0/0 and all addition and subtraction is useless/ Not to mention the multiplication and division difficulties with the special zeros .....
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Postby RQ » Sun Jan 18, 2004 8:57 am

The only way that last ant would be able to say the last digit of pi is if there were an infinite number of ants. I think that if we assume that a point has a 0D of 1 unit, and that pretty much defines our length of a line, area of a plane, volume of space, hypervolume of tetraspace and so on, then we should be able to say that a line is at least 2 points or that it has an infinite number of points, just like realm objects have an infinite number of planes.
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