The Achilles Heel of String Theory.

S D Rodrian wrote:
The confusion, if there is any, arises from the purely
mathematical convenience of speaking about our reality
being a "3" dimensional reality. Whereas no purely
three-dimensional object could possibly exist "in
reality."

The three dimensional aspect of space is very simple.
Take an object like the tip of a pencil.
Place it in a square room.
You will find that three measures sufficiently represent its position
relative to the room.
Any more will be wasteful and any less will be broken.
In this sense the Euclidean three dimensional space is an empirical
discovery that takes very little to demonstrate.

Do you deny this?
These are the three dimensions that you are disputing.
Even if more dimenions do exist this behavior must be resolved.
Three dimensions are an observation.

-Tim

On 5 Jul 2006 17:28:48 -0700, "Timothy Golden
BandTechnology.com" wrote:

S D Rodrian wrote:
The confusion, if there is any, arises from the purely
mathematical convenience of speaking about our reality
being a "3" dimensional reality. Whereas no purely
three-dimensional object could possibly exist "in
reality."

The three dimensional aspect of space is very simple.

No doubt, no doubt! Who can't count to three?
Well, there ARE a number of drinks beyond which...

Take an object like the tip of a pencil.

What is a tip of a pencil! Certainly to an ant
it must be a mountain top. And to our dear ole
Planck Length Creature it is its universe in all!
But, what is the tip of a pencil to the elephant,
or to the whale! O, what is a tip of a pencil
to the world!

(Good Heavens, I've still got it! --The Poet In Me.]

Place it in a square room.

Why does it always HAVE to be a square room?
Every time I am placed in a square room I feel
compelled to only walk in "2" dimensions! Unless
I manage to wiggle out of my strait jacket, of course.
And then I can walk "3" dimensionally (via the rope
my kind keepers like to leave for me tied to a hook
on the ceiling).

You will find that three measures sufficiently
represent its position
relative to the room.

Why bother? Why not simply ask, "You
can't see it?!?! It's right in front of you nose!"

HINT: However way you point it out.... said "way"
is all in your head:

Unless your "lines" are the thickness of a Planck's
Length's Planck's Length's Planck's Length's Planck's
Length's (ad infinitum) your triangulation will only
always ONLY succeed in giving a general direction
as to where the thing is. (Cross you fingers and see
just how large the area is over which they cross.)
And, yes, it works both ways... or try to triangulate
the position of the earth with such itty bitty "lines."

We live in an approximate world only. And this is
the achilles heel of all attempts by Mathematics
to "rule" the universe, I'm afraid. (Who knows not
this, is doomed to waste a lot of his life de-noodling
his mind with infinite minutia.) --SDR

And how comes it that we just happen to live in
an approximate world only, you might ask. Because
in reality we live IN OUR MINDS, and there's very
precious little in there that's not but an estimation.
Or something close to it...

Certainly none of it will have to do with "dimensions"
but only with different approaches to it (or, directions).

START QUOTE

Imagine a one-dimensional wall... From where would one
even "see" such a wall? Certainly if we are NOT
looking at it dead-on we are using other dimensions
than its merely one to "see it" (since we would have
to look at it from a little to the side).

Throw a left-hook and freeze your punch in mid-air:
Your floating arm is describing an impossible
journey through an infinite number of (certainly
more than just three) dimensions! And thus too any
circumference such as the earth's...

And because all it would take would be a very tiny
"little" ... no huge human eye could ever see it. (And
we are talking strictly theoretically here.)

The wall itself would have to be infinitesimally
tiny. Impossibly tiny. Let's say that a Planck's
Length is the smallest thing (and that there are no
lengths as small as a Planck's Length to our Planck's
Length, although I do not know of any objection to
that). Then the wall would have to be a Planck's
Length AND the observing eye would also have to be a
Planck's Length and be looking at it perfectly head-on
because if it were but even the smallest fraction to
any side it would have to look at it from a second,
third, or additional dimension. [You can see why it's
much more easy to just look at a comic strip and
believe the fiction that it's a two-dimensional
drawing... even though we know that no true purely
two-dimensional object can exist in our reality.]

HINT: It's your mind agreeing to "go along with"
the fiction that the comic strip/painting/photo
graphic is two-dimensional.

And if no purely one-, or purely two-, or even purely
three-dimensional object can exist in our reality,
then any talk of the existence of ANY-numbered-
dimension is also nonsense... whether in or outside
our reality. And if you can't see this, you're not
really very smart, no matter how clever you may be
(and not even though you be even as clever as a
checkers-playing computer).

END QUOTE

Repeat after me: IF A ONE-DIMENSIONAL
ANYTHING IS IMPOSSIBLE, THEN A TWO-
DIMENSIONAL ANYTHING IS TWICE AS
IMPOSSIBLE. AND A 3-DIMENSIONAL ANY-
THING IS 3 TIMES AS IMPOSSIBLE & SO ON.

A balloon only has two-dimensions. But only
because that's a convenient short-hand in
mathematics: That two-dimensional balloon
helps mathematics neither to add to nor to
substract from REALITY anything whatsoever,
though we speak about it until the Word of God
at last falls silent in the universe. Amen.

Any more will be wasteful
and any less will be broken.
In this sense the Euclidean three
dimensional space is an empirical
discovery that takes very little to demonstrate.
Do you deny this?
These are the three dimensions that you are
disputing.
Even if more dimenions do exist this
behavior must be resolved.
Three dimensions are an observation.-Tim

You are right at last, Tim: "3" dimensions ARE only
a requirement of the mind (in the mind) and have
nothing whatsoever to do with reality:

Imagine that man has finally become extinct. Then,
to the world that continues without him, what use
are the methods he used to use to point out things
to himself?

I don't mind your use of whatever method you wish
to point things out to yourself, Tim. But don't then
ORDAIN that your brain commands reality, Tim!

That's positively bonkers, ole boy.

An interesting way to conceptualize this
is to imagine a large
screened TV in front of you. Then,
in your imagination, expand
the width and height to infinity.
Next, in your imagination, toss
the hardware aside, leaving
only the image in place.
Persons in this image perceive
their space as 3-dimensional.

That would be a nice trick for such "persons"
to perform, since they would have to do it
with "brains" which have no "depth" at all.

That
is, they can move in any direction they want to.

With "muscles & limbs" which have no "depth"
at all.

To them, a meter
stick will appear to be one meter long,
any way they orient it.

Well, certainly, if they try to orient it from "width" to
"height" they are going to have to make it travel
through a zillion dimensions other than their only "2."

As I've said: I don't mind Mathematics describing
every point in a circumference. But do not let then
Mathematics try to describe the "dimensions" of
reality! (Because, as I said, it's absurd to limit them
in any way... in effect, by any number. It offends
the laws of physics.)

However, from your perspective,
these people are limited to
something very close to two dimensional
space. Granted, the image
has some thickness, albeit very small.

Ah! A little bit of sanity creeps into this petty pace!
Not much, but a little bit does. That's a start.

Now, in your imagination, shrink the
image's thickness on down to
less than a Planck Length.

Does it really matter how thick the image is?
And, who sez when we get to a Planck's Length's
thickness we won't get bitten by an even tinier tick?

From your perspective it is no longer
discernable, but it is still there.

"In your imagination" everything is possible, yes.

From your perspective, their
third dimension is rolled up to less
than a Planck Length. But,
from their perspective their third
dimension is no different than
their other two dimensions.

A truly "really" three-dimensional "thing" could
only be observed from "six" very specific, very
specifically placed very infinitely infinitesimal
"impossible" positions (hint: no such positions
are possible in reality, ole boy):

BEGIN QUOTE

Imagine a one-dimensional wall... From where would one
even "see" such a wall? Certainly if we are NOT
looking at it dead-on we are using other dimensions
than its merely one to "see it" (since we would have
to look at it from a little to the side).

Throw a left-hook and freeze your punch in mid-air:
Your floating arm is describing an impossible
journey through an infinite number of (certainly
more than just three) dimensions! And thus too any
circumference such as the earth's...

And because all it would take would be a very tiny
"little" ... no huge human eye could ever see it. (And
we are talking strictly theoretically here.)

The wall itself would have to be infinitesimally
tiny. Impossibly tiny. Let's say that a Planck's
Length is the smallest thing (and that there are no
lengths as small as a Planck's Length to our Planck's
Length, although I do not know of any objection to
that). Then the wall would have to be a Planck's
Length AND the observing eye would also have to be a
Planck's Length and be looking at it perfectly head-on
because if it were but even the smallest fraction to
any side it would have to look at it from a second,
third, or additional dimension. [You can see why it's
much more easy to just look at a comic strip and
believe the fiction that it's a two-dimensional
drawing... even though we know that no true purely
two-dimensional object can exist in our reality.]

HINT: It's your mind agreeing to "go along with"
the fiction that the comic strip/painting/photo
graphic is two-dimensional.

And if no purely one-, or purely two-, or even purely
three-dimensional object can exist in our reality,
then any talk of the existence of ANY-numbered-
dimension is also nonsense... whether in or outside
our reality. And if you can't see this, you're not
really very smart, no matter how clever you may be
(and not even though you be even as clever as a
checkers-playing computer).

END QUOTE

Repeat after me: IF A ONE-DIMENSIONAL
ANYTHING IS IMPOSSIBLE, THEN A TWO-
DIMENSIONAL ANYTHING IS TWICE AS
IMPOSSIBLE.

This is not a real-world kind of thing,

There ya go! THAT's my whole point in a
banana peel.

but it does provide a
rather nice way of getting the concept.

I'm sure that as long as you understand, Gordon,
the world/the universe will sleep soundly tonight.

Those other dimensions
could very well be right her in our midst,

There ya go! THAT's the whole problem right there
out of the safety of its banana peel:

The instant you even so much as HINT at the
mere possibility that it's possible to assign a
(necessarily limiting) number to the dimensions
of "anything" you are literally knocking all sorts
of bits from "it" OUT of existence (in our reality).

And THAT would be a jolly nice trick indeed. Gordon!

but if they are less
than a Planck Length, they are completely
indiscernible to us.
Gordon

Gordon, if something exists, it does (or, if it doesn't
it doesn't). But you can't cheat on the rule by ANY
means. (And I should think CERTAINLY NOT by merely
shrinking the thing out of sight... or tossing a hanky
over it and hollering, "Abracadabra!")

Voila!

S D Rodrian
http://poems.sdrodrian.com
http://physics.sdrodrian.com
http://music.sdrodrian.com
http://mp3.sdrodrian.com

I hardly banish the notion of higher dimensions.
In fact I believe that I have a construction that supports them while
also supporitng spacetime:
http://bandtechnology.com/PolySigned/PolySigned.html
It is not necessary to deny the 3D observations that we make.
By working out the puzzle of how they come to be we may find the best
theory.
They are generally imposed on theories as empirically evident.
But theory is supposed to predict the empirical, not rely upon it.
The polysign claim is that higher dimensions are poorly behaved
according to the usual concept of dimensionality. Oddly enough these
heigher dimensions are very well behaved arithmetically under the
polysign construction. They just don't conserve distance in their
product above P3.
So the usage of a ruler in the product space will only lead to
cohenernt measures in three of the dimensions. Time is accounted for as
well under this natural construction. There are no special laws in it.
Just special behaviors as a result of those laws.

-Tim

In graph theory, you can consider graphs as dimensionless objects. Fine.
It is known that some graphs can not be drawn on paper without crossing edges. Fact.
Graphs are connected with several kinds of matrices: incidence, Laplace Kirchhoff, adjacency, distance, etc.. Fact.
These matrices have eigenvalues. Fact
The number of nonzero eigenvalues determines the dimensionality of the
graph (at least the mathematical one). Hypothesis.
Elements of distance matrices are the number of edges between two vertices.
The largest distance in the linear chain x-x-x-x is 3, similarly as the
largest distance in cube. Fact
Try to use squared distances, 9 for the linear chain, 3 for the cube. in this case, the number of nonzero eigenvalues is determined by the shape of the arranged objects, not by their number. Fact
Physical, chemical and biological properties of molecules depend on eigenvalues of their matrices (or their sums). Fact
It is simpler to consider molecules as multidimensional objects embedded into 3 dimensions than to explain observed facts by other theories.
kunzmilan