From: lambdac-AT-globalserve.net
Date: Thu, 06 Aug 1998 00:21:30 -0500
Subject: On green rabbits shooting point-bullets, lines&etc



Yair - what came before indicates that you are not the superior masterly
spectator sitting from high above and enjoying the gladiators tearing
each other apart as you had earlier asserted; what comes now
demonstrates that we are, if it makes you happy, light-centuries away in
'our respective systems', since - like it or not- there is also a
politics to the usage and abuse of mathematics.  So this goes here to
mark an event - for in the entirety of everything you wrote, you only
made one useful or interesting utterance:

>there is not reason why time
>(...) won't be quantified.

In fact, there are plenty of excellent reasons why it hasn't been
quantified and why it cannot be quantified with the present set of tools
at the disposal of physicists and mathematicians.  So we realize at once
that you know presque rien of these.  And magnanimously excuse you -
since it must have been the good intuition that has preserved some flame
_at such a point_.  To reward you, here go some answers - and by the
same token, a declination to further pursue this matter.

>The mathematical point is a definition. 

Thanks Yair - we were distracted - we could swear it was an
indefinition, a mathematical indefinition for paranoiac mathematicians,
in fact even an undefined element of geometry - an indivisible undefined
which could only satisfy the insensible postulates of a certain
You-Clod, and which a well-co-ordinatized Of-the-Cards rescued by giving
it an origin when the basest degree of the recomposed, ray-diative trace
of a polynomial scribble vanished ever so infinitesimally hesitant (in
one or all of its skewers) to...zero.

It's true, it is not easy to be this stupid.  One must work at it.  

>It is defined by different means in
>different mathematical systems. 

Fascinating.

>For example, in Cartesian geometry a point can
>be an ordered set of numbers that determine its location in a predefined
>coordinate space. It can conversely be defined by the intersection of N
>subspaces (N being the dimension of the space), each with dimension N-1, such as
>the intersection of two straight lines on a surface or the intersection of three
>flat planes in a three dimensional space. 

For a space with N dimensions (which, by the way, is already ludicrous
as a notion, but that shall stay as a private joke) or subspaces
(another fantastic joke), any lines, straight, curved, kinky,
intersecting or not (like ours and yours) would only have each, and
still, N-(N-1)=1 dimension; which is called length, for those of us who
are still in this Race.  And not in the other.

>Since it is merely a definition in a
>closed logical/mathematical system it cannot be a metaphysical anything

That's right - it is a metaphysical _nothing_, just as every closed
system, whether logical, mathematical, thermodynamic, etc, is a
metaphysical nothing.  All of them, metaphysical systems ruled by a
transcendent plane.  One could almost blurt that the point is the God of
mathematicians, just like the void is the God of relativists (Ha! Ha!
Ha!).

>it doesn't even mean that such a point exists.

Material points, isolated points, point-particles, point-charges, all
figments of a burdened imagination that arose when and where
understanding became impotent.  That's the point - points do not exist;
they are useless fictions, elements of the game of the transcendent
mathematician -- filled with points, but lineless.

"Non-parallel evolutions - which do not proceed by differentiation, but
which jump from one line to the next - between beings entirely
heterogeneous; cracks, imperceptible ruptures, that break the lines
liable to have the lines pick up and continue somewhere else, jumping
underneath the signifying breaks...The rhizome is all of that.  To
think, within things, between things, is precisely to make a rhizome,
and not a root, _making the line and not the point_" (C. Parnet)

>As for the line, we do not have to think about it at all, with or without gaps.

Yes, it is true, most like you somehow manage to avoid thinking the line
- such is the portentous impact of the points to be chalked.  The line
is the continuous - if you do not think the continuous, how do you
propose to operationally define a point by the intersection of
unidimensional lines?  Oh yes by the indefinite definition of the
undefinable...The problem is: two lines determine a point, a knot, but
two (of your lousy) points do not make up for a single line!

>The word has many uses (my line of thought contains many gaps, I'm sure, in any
>resolution :)), even in mathematics. If we'd like to return to Cartesian
>geometry, 

No, not again - is this a mania!?  Please some Minkowsky, some Riemann,
some Peirce, some Witty or some Heidi - at least our failure at math
double-O-one would be more glorious!

>a (straight) line is usually related a linear function, and this set
>of functions has been proved to comply with yet another mathematical definition
>termed "continuous". And the proof involves non discrete set of discrete series
>of numbers, or points.

A problem of ax+by+c=0; if a=0, b*0, etc.  Fascinating.  We think we
have had enough.  Ours is not -- yes you can relax all those angry dogs
-- the problem of Cantor's continuum either ("How many points are there
on a straight line in euclidean space? (...) How many different sets of
integers do there exist? (...) The problem is to find out which one of
the [cardinal numbers] is the number of points of a straight line or
(which is the same) of any other continuum (of any number of dimensions)
in a euclidean space", Gödel) or whether the Zermelo-Fraenkel conception
of the iterative set can or could ever address it.  How many are the
angels dancing on the head of a pin?  Ours is the problem of thinking
the absoluteness of a line of motion, the line of escape as active and
continuous - it is, first and foremost a problem of physics - and
philosophy - and not one of isolated and enclosed mathematical logic:

"The relative is the speed of a movement taken from one point to
another.  But the absolute is the speed of a movement inbetween the two,
at the middle of the two, and which inscribes a line of escape. 
Movement does not go from one point to the next, it rather occurs
between two levels as in a difference of potential" (C. Parnet).  Trace
the line, not: make the point.

It is a problem of thinking a difference of potential as an absolute
speed, as a pure wave function (if modern physics could do so, the
equation relating Beta=v/c to electric potential would not be the so
called 'gamma-formula'; where we disagree from D&G is that we know a
_different_ physics _can_ secure pure wave functions).  "And now let us
hear Bergson: "attach yourselves to the movement whilst disengaging
yourselves from the divisible space which subtends it so that only the
mobility is considered" (de Broglie, "Physics and microphysics").  Why
de Broglie's theory of the double-solution? -- because any physicist
must admit "the existence, behind the statistical wave of wave
mechanics, of a wave of singularity which would be the physical
reality".  If one could provide a mathematical solution for waves of
singularity, the entirety of the coordinatization problem of physics and
its metaphysical mathematics (with all those superfluous logical
principles) would be wiped out.  Ours is an interest in geosophy,
psychogeography, not in transcendental geometries.

>All this does not contradict the statement that lines do not have to exist
>/because/ of the points. 

Hum??  So that you may inscribe it on your forehead - lines, no,
differently, wavelines, are the a priori of Space and Time.  The
indivisible.  The eternal.  The limitless.  The continuous.  No one
knows why energy moves, but it moves, a priori as it were (Reich).  And
everywhere it moves in waves, in wavelines.  Points only have existence
in and by the minds of dysfunctional mathematicians who, with their
pirouettes seek applause for the vague notion they peddle of a Space
that has as many dimensions as we care to chose from and a Time, well, a
little Time which is a fourth dimension, either on its own, or subject
to Space.  

>You are more than welcome to devise a mathematical
>system which defines lines and continuity without any use of points (or knots!),

Thank you very much, we shall, of course, follow your advice at once.  

>> Further even, points do not exist as unidimensional (or worse still,
>> dimensionless) elements.
>
>Agreed. It escapes my imagination how a mathematical point can exist, not to say
>measured or sensed. By the way, a unidimensional object is usually termed a
>line.

That's enough!  If you are a mathematician you must definitely be of the
explosive-paraplegic type, a la Hawking & Co (you know, classic,
intuitionist and paraplegic?) - but just for the alms: a Dirac-point
particle is (in principle...) a point with one dimension, that of mass. 
Note, it is not called a Dirac-line particle, even though linacs and
other monsters cough out these things (so we must metaphysically accept
it, ie _believe_).  By the way, frequency is also unidimensional.  By
the way, stupid mathematicians are also unidimensional.  By the way,
only the mind can be made into a flat land.  By the way, a single line
can define a plane and even a volume.  By the way.  

>Mathematical abstractions are just that, do you also want to
>discard infinities because they cannot be verified on the basis of empirical
>data?

Yes, let's do that, it sounds like fun.  More partons or put-ons a la
Gell-Mann.  More renormalizations.  More Alephs and deferred omegas:

"Immediately after all stages zero, one, two, three,..., there is a
stage; call it stage omega. (...)
Immediately after all of stages zero, one, two,..., omega, omega plus
one, omega plus two,...., there is a stage, call it stage omega plus
omega (or omega times two).  At stage omega plus omega form all possible
collections of individuals and sets formed at earlier stages. At stage
omega plus omega plus one..... ...
...omega plus omega plus omega (or omega times three)...
...(omega times four)...
...omega times omega... ...
Keep on going in this way...." (G. Boolos)

-which makes us sigh with Deleuze-

"Even in mathematics: Poincaré used to say that only too many
mathematical theories lack any usefulness, have no interest.  He did not
say they were false - it was even worse" (Deleuze, oh pactuations!)

>Is the simple difference between Aleph 0 and
>Aleph 1 so difficult to grasp?!

For those beholders who do not worship an ox, frankly yes.  We will
leave you the segment line - our lines run somewhere else.

>Question: Does the continuous one exist as such?
> Answer: what is a wave space?

Lambda Cycloid 

PS - Filled with piety at this point we see ourselves compelled to
_continue_ a little further:

> When we now shift from the realm of mathematics to that of
>physics, we have to admit that any discrete set, packed densely enough, is
>indistinguishable from a continuum.

An admission of ignorance.  And an effect of perspective in a synoptic
Space.  That incidentally to this day proves the critical element of
Zeno's paradoxes, since this pedantic ignorance has never permitted
modern physics to resolve the functions of any continuum, nor even
enabled physical chemistry from formulating functional equations of
state.  A little like the fact that the best atomic quantization is
still to this day that of Bohr's model and yet it cannot predict the
exact position of the discrete spectrum.  Ha! Ha!

>If, for example, we consider the wave equation of the entire universe

If there is no adequate wave function for the electron other than a
probabilistic one, what is the wave equation of the entire universe BUT
sheer metaphysics?  

PS - It is in horror that we saw a third message from Yair arrive!-

>You
>can never assume the existence of a point where your measurement devices are too
>coarse to determine the volume of an object 

Why would one want to assume the existence of Dirac-point particles, and
why would Hans Dehmelt have spent all those years and money
demonstrating that the geonium atom is not a Dirac-point particle?  

>as much as you can never assume the
>existence of a mathematical continuum where they are too coarse to find any
>discreteness.

Lambda C has never argued otherwise, so this is a moot point you have
been belabouring.  What we have argued is that there is plenty of proof,
physical, chemical, biophysical, biochemical for the existence of a
physical continuum of energy.  It is this empirical reality that SED
tries to address.  Two examples only - the cosmic heat bath discovered
by Penzias&Wilson; the properties of the hydrogen atom explained alone
by the ZPE.  We could be here for another twenty posts.

>These are usually referred to by the global name "elementary
>particles", and it is quite reasonable since if any structure was found in them
>it would suggest that they were built out of more elementary particles, which in
>turn were considered point like. 

That is the trap of useless mathematics into which the eager physicist
tumbles: we can assure you, dear Sir, that actual (and not imaginary)
elementary particles have fine structure, volumetric at that, and that
this structure (boggled as your mind already is) is not some bad
conception of the infinite as a regression, where still more undefined
and undefinable points peel off from other points, but a
structure-machine that synthesizes very elegant singularities on a
smooth wave space.  

>There is, however, a strong reason to suspect
>that at least some, if not all, of these particles are truly elementary 
[read, truly cough no more points]
>since
>any kind of internal structure or volume leads to a ruthless theoretical
>contradiction, 
[read - since the mathematical point is at odds with the physical point,
and the result is nonsense, followed by more nonsense, namely the
invention that elementary particles have no volume BECAUSE we are unable
to discover theoretically or practically how to determine this volume]
>while the idea of point like particles collides merely with our
>inability to perceive it.

...and that is perfectly fine ('merely collides'), since we survive in a
metaphysical world (the other Race), and we need metaphysics to
legitimize our specialty as journaputas and mathoputas and etc.  Yes, we
can all live with points, the more molar and massive the better.

>By a curious coincidence, the mathematical notion which gives particle physics a
>much bigger headache is that of the line.

It must a curious coincidence - from the undefinable point to the
headache line, could this be the simulation of a continuum framed
between points?  OK Yair, what you and we mean by lines could never ever
be the same.  Ever.  Take that as an absolute.

Lambda Crux-ified


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