Zeno is coming.
LstPuritan
:hasn't posted or read in a long time:
Should you be worried? yes
LstPuritan
unbearably concise:
I'll use abstract metaphors to describe what I was trying to state before.
Christof wrote:
>Moving = not moving?
When I have one eye; if I can see;
If the only other place for my eye is my stomach;
Any moving line segment from Christof is a stationary point.
Or else no matter how close, not seen at all.
>So you have time instants that have a duration?
No, but Newton does.
To Zeno, time was an illusion.
To Newton, time went: chunk, chunk, chunk.
To Einstein, time went: zzzzzzzzzzzzzzzzzzzzzzz.
Time is silent.
>Isn't there a difference between standing in
>front of a wall and running against it?
Work=Zero in either case, according to physics.
Einstein could discern the difference through special relativity.
If time is silent
The only difference between
Running against a wall
And standing against a wall
Is that standing against a wall
Cannot be the cause of all walls on earth to vanish
But *running against* a wall
May be the cause of all walls on earth to move.
Either way, if a wall vanishes or moves that *could* CAUSE:
The birth of a new wall from any infinitesimal point.
>Velocity IS relative.
When you wake up with a wall on each side of you;
If those are the only things you can ever see;
If the walls disappearing would leave nothing at all;
Moving from one wall to the other needs no motion at all.
When the walls vanish and you are not alone;
*Then* you have moved with absolute certainty.
As long as two walls exist, there is no such thing as velocity.
>"Instantaneous velocity", now what's that?
Textbook says:
lim delta_P/delta_t
delta_t->0
>Velocity is a function of
>time and one of the variables describing a mechanical system.
A mechanical system is one of the ways of describing a function.
But there are many other mechanical systems describing the same function, the
variables of which are unknown.
>Move infinitely fast in an infinitely short time
>and do it so that the product of time and velocity gives you the right
>distance.
...
>Jumping around from one place to another is motion. By
>definition. How you get from one point to the other is
>unimportant.
...
>Never heard about "instantaneous velocity", neither in my
>calculus nor in my mechanics courses.
lim delta_P/delta_t
delta_t->0
Isn't that on page 2 or so of a calculus textbook?
If others speak
But you hear yourself
And see what is left when nothingness itself is removed:
There is neither time nor velocity.
>So when did all things start moving? Around 1900?
If three is the highest you can count;
There may be any number of others in existence.
But if there is no manner in which to verify their existence;
Then you may only directly speak with two.
>> Part of the problem is one of causality. If motion is conveyed
>> through a series of discrete indivisible time-slices in succession,
>
>Which is not the view of standard physics.
Yes it is.
vt=d
>"Constant for a given t" has no meaning, because a function has, by
>definition, exactly one value for each value of t.
dy/dt
delta_t->0
If time if discrete, delta_t always equals zero. dy/dt=0/0.
Integrals are a lie.
If time is continuous, delta_t cannot ever equal zero.
Derivitives are a lie.
>The paradox of Zeno is the one with the turtle that is never overtaken
>by a sprinter? That one is easily resolved.
No it isn't.
1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2^n + ... = 1
1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2^n + ... = infinity
1 = infinity < 1
Doen't it suck when you travel an infinite distance to 1 and when you finally
reach one, you end up somewhere less than 1?
But:
When a triangle is a line segment at rest;
And a triange spinning is the same line segment at rest;
If a line segment extends far enough:
One may reach the line without ever touching or approaching it.
>Plane of dimension? This sounds like bad scifi.
Go diagonal and watch me morph into pile of goo.
>Why do you think there are discrete instants? That's a rather exotic
>point of view.
delta_t=discrete instant
Exotic? Here's what is exotic:
Go diagonal again. See the dots running back and forth?
That used to be the universe. In a sense, it still would be.
But our sense; not yours.
>Could you please define motion?
Where are you? I need to get to *precisely* where it is that going the
opposite of diagonal while remaining at rest would let me see you. Only then
could I kow. Of course, pyramids don't like triangles when pyramids are no
more than a point and triangso someone might still correct me; only someone who
could _see_ my internal organs without touching me or even being seen.
>> Zeno's theories,
>
>What a pity I don't know what these are about.
Zeno knew that weird stuff was going on.
Newton's model of the universe was good.
Einstein's model of the universe was better.
Zeno is still more right than both.
>Or perhaps I mean
>something different than you, but I'll try. Zeno said, take a turtle
>and a runner. The runner can do double the turtle's velocity. They
>start a race with the turtle a bit ahead. Now in the time the runner
>catches up with the turtle, the turtle has gone a little bit further,
>so the runner has to catch up again. In this time the turtle again has
>gone further and so on. So, the runner never overtakes the
>turtle. This conclusion is OBVIOUSLY WRONG, because the time steps
>between catching up get smaller and smaller and if you add them up,
>they DO NOT ADD TO INFINITY. They have a limes, which means that in
>this picture you are only looking at part of the race! If you look at
>the whole race, the story is quite different.
That is a made up story using The Stadium, The Arrow, The Maze, and The
Achilles to invent this narrative and I don't have a clue what it means.
>> Newtonian laws would have been seen as unable to explain certain
>> phenomena
>
>Which ones?
An infinitely vast majority.
>The effects of special relativity are very subtle and
>direct confirmation was not possible without sophisticated technology.
Like the brain. Or do you think c is the value of the speed of light? It's
not.
If your house has a ceiling and my house doesn't;
But your door is in your floor;
When it rains on both of our houses:
The inside of your house will be drenched
But I shall be dry in my house.
If you want to stay dry;
If you want a ceiling that will protect you from my water:
Stop looking at your compass
When I ask about the stars.
>Why should a fractal not have a size? There are weird things in
>mathematics!
Fractals are in no manner whatsoever weird. They are everywhere. Take a piano
string. When a tuning fork or piano string is struck, it starts to vibrate at
different frequencies simultaneously but there is a particular frequency at
which it is least resistant to vibration, and thus vibrates more vigorously,
actually amplifying the energy that was used to start the vibration. Likewise,
it will take longer to stop vibrating at that frequency than it will at others.
This is called resonance. Now, if a device is particularly resonant, so that
the smallest input of energy excites it into strong resonance, then when its
vibration excites other nearby resonant devices, their vibrations will excite
the first device further, and a vicious cycle will ensue, the vibrations
growing stronger and stronger until stopped by some external force. This
phenomenon is known as feedback.
In terms of fractal specification, if the difference equation is nonresonant
for a certain point-set, then the output will stabilize after a few iterations,
and receive a certain color. If it is very resonant, the output might never
stabilize, but break into feedback, and be colored black. If, however, one
changes the limits for determining levels of resonance and feedback, a
different image will emerge. This is another example of fractal
scaling--different degrees of detail resolution can be attained by adjusting
the limits of specification. Fractals explain every paradox we observe in
space and time, because time is not a dimension at all; physical discrepencies
are due to assuming that time is a dimension, and the speed of light is
constant, but physical reality is a paradox that must be seen
dimensionally-relatively to see fractional-relativity, and
fractional-relatively to see to see self-relativity: The speed of light is not
the speed of light!
I don't think you get relativity.
If you understood what I meant by all of the above:
Then you'd understand why the speed of light is not constant, and the constant
is not the speed of light. You'd also see that relativity is relative to
itself in a fractional dimention, so there is no reason at all for assuming
that the speed of light cannot travel faster that the speed of light while also
never even reaching the speed of light. Which is not c. c is something else.
This is evident in other dimensions; so I'll give you a case where c is not the
speed of light, but from our physical reality may only be expressed in terms of
the value of c.
---------------------------------------------
Distribution and classical diffusion: derivation
P(z)=exp(-z^2/2*a^2)/(sqr(2*Pi)*a )
dP(z)/dz=(-2*z/(2*a^2))*P(z)
d^2P(z)/dz^2=(-1/a^2)*(1-z^2/a^2)*P(z)
Of course, this differentiation is called Hermite and relates to Hook law
oscillation, etc. but is based on orthogonics in Hilbert spaces even though
some emphasize that quantum mechanics has roots in probability (uncertainty)
and these Hilbert spaces. The point is that one dimensional variables are
integrated to infinite limits. Since I have designated an infinite complex
planar second dimension, complex variables do not present the problem they
would in the physical world. Therefore, diffusion, distribution of velocities,
based on gas and dust particle observation enters the picture in a third
dimension.
--------------------------------------------
Fractional operator
the fractional operator in that dimension's differential form using P(z):
D(P(z),s)=(-2!*z^(2-s)/((2-s)!*s!*2*a^2))*P(z)
Compare this with dP(z)dz. They have been upwardly dimensionally equalized.
Same procedure will be repeated as just before this:
D(D(P(z),s),s)= (-z^(2-2*s)/(s!^2*(2-2*s)!)*a^2)*(1-z^2*(2-2*s)!/((2-s)!^2*a^2)
Now the third B-diffusion dimension has been given its dimensional form of the
fractional operator. Compare this with d^2P(z)/dz^2. I didn't like
D(D(P(z),s),s) at first and almost tried going back a few steps, but it was
actually the easiest possibility and the only practical one when I realized
that there is no reason why fractional factorials would need to be
differentiated with integers to converge into gamma functions, since integers
do not necessarily mean the same thing here as they do in the physical world.
That's when I realized that diffusion *into* diffusion dimensionality would
simply be, for example
D(D(P(z),s),s)= (-z^(2-2*s)/(s!^2*(2-2*s)!)*a^2)*(1-z^2*(2-2*s)!/((2-s)!^2*a^2)
------------> d^2P(z)/dz^2=(-1/a^2)*(1-z^2/a^2)*P(z)
from a higher dimensional state approaching the lower. Thus, using dust
particles as a model for diffusion as the B-diffusion we know is no longer
applicable since diffusion here is not so diffuse at all.
Fractional B-distribution has to be
X(t)=exp(-t^2/(2*h^(2*s)))/sqr(2*pi)*h^(-s)
=exp(-t^2/k1)/k2
What does this say about mathematical models and the so called "real" world?
Of course, I have to prove this as a reverse of how it was formed:
In two dimensions (fixed differential level, fixed scale "test drive")
h=2
s0=log(2)/log(3)
In self similar dimension meaning s0
D=1/s0+log(3)/log(2)
Which would mean in scale _and_ dimension
2-s0=a/s0 : 0<=a<=1: 0<=s0<=2
s0^2-2*s0+a=0
Three solutions
s=1+sqr(1-a)
v=1-sqr(1-a)
s+v=2
Take three dimensional diffusion that is fractional in time thus that the
resulting fractional dimension of the fractional B-Diffusion possible set is
D=3+s0
the set defined by s0 would (by a great leap of theoretical faith) only be seen
as vague piles of parts of sO in a 360 degree horizon with nothing between the
observer and sO no matter where he was standing or how far me moved (Christof,
NO SIZE!) he would be no closer or farther away from sO because there is no
scale within a fractal. Isn't this what Einstein meant about seeing the same
thing wherever you look if the Universe is infinitely large?
Figuring out what Fractional relativity is here would liven this place up with
some piles of sO theoretically accessable so I could build a nice house and not
have to sleep on a pile of nothing untill I diffused.
Why is there fractional relativity at all?
There is no logical reason why a Universal Constant in a universe that differs
from the physical world dimensionally and behaviorally would have to conform to
c at all. If Einstein did not just have our universe in mind, though, then
abstractions are not just universal laws but rather extentions of how far the
mind can understand what it _thinks_ at the upper limits of what it is capable
of _imagining_ and then *abstracting.* What follows, then, is that the mind
will not imagine anything it does not have the ability to abstract, because to
THINK about something that is IMAGINARY, the mind must necessarily have at some
point UNDERSTOOD _how_ to ABSTRACT the imaginary in order to even THINK about
it in the first place. Since the mind may imagine anything at all insofar as
that thing is understood at least enough to abstract into thought, to *think*
about fractals with many dimensions which directly contradict what is
experienced in reality is proof that they have already been imagined and then
abstracted so that further thought is possible. For to imagine something that
cannot be abstracted as thought understood is no different from never having
imagined it in the first place. In light of these deductions, if Einstein's
relativity is the understood abstract used to think about imagined organized
systems, then the next following assumption is that because such organized
systems exist in the mind at all, the thing by means of which the initial
imaginary organized system was abstracted must at least exist as a partial
model for thinking about such organized systems. The conclusion from this is
that if relativity was understood as a means for abstraction used to think
about fractals with many dimensions, then through this fundamental causality
fractals must have a working model based on relativity. On a pragmatic
conceptual level, there *must* exist a fractal-equivilant model of Einstein's
relativity.
So the first task is to affirm that there is a Fractional Universally Constant
Singularity Velocity, and find its value so that motion may exist and there is
a finite limited value for the Fractional Universal Constant. The chances of
the Universally Constant Velocity being that of light and the same value of the
speed of light that exists in the physical world we know are very small. If
there is a known Universal Constant in a particular system of related fractal
dimensions—which is precisely what "the fractal" as a collective whole is
presumed to be—then the activity within this system must collectively be
understood by this constant, which is both the key for predicting behavior
within the fractal with some type of relativity, and the dimension which
transmits a direct causal limitation on what can conceivably be done to all
other dimentions. Only with fractal relativity as a constant, since the
Universally Constant Velocity does not imply that this Velocity will be the
speed of light, we must always allow for travel faster than the speed of light
without relying on general relativity.
-----------------------------------------------------------
Fractal Relativity: Which dimension? What about time? Light?
Relativity relates indescrepencies between what is expected and what is
obverved by bounding the erratic dimension, with a constant, to inclusive
dimensions which display behavioral traits inconsistant when not related to the
erratic one. Einstein was able to determine that matter dictates space (as
seen in the arbitrary label 'time') and the only reason we know this is because
we use light to see, and light sucks. Light lies; light is just a "+1"
dimension. It is matter which makes space curve how it does, and curves in
space which make matter move how it does. Light is irrelevant unless you want
to see stuff, in which case in order to see clearly it is light as singularity
that, when determined as a value c, at least potentially explains *why* we
don't see curves in space. But a fractal viewed on a flat graph has an area,
yet within this area is a world of infinite points and infinite self-recursive
patterns: the fractal has no size. The more one zooms into a pictorial
representation, the more examples of self-recursion keep extending and forming
new patterns and slight variations.
Not Unlike a Bach Fugue.
Not Unlike Prelude #1.
Not Unlike Beethoven Tempest Sonata, mvt. 3.
Not Unlike Prokofiev 7th, mvt. 3
Not Unlike Webern opus 27 piano variations.
Time may or may not exist at all as some sort of causality other-dimension in
the physical world or a fractal dimention until hypothetical proofs of time
travel considering time as the z axis in two-dimension space become reality for
4th dimension time travel in 3 dimension space convince me. What matters is
that the velocity constant, Einstein's constant c, places this physical world
in a boundry so that a system is comprehensible. Irrelevant. Living in this
fractal means looking at what the equations imply about what the universal
fractal laws are in fractal dimension, so it's necessary to fractalize what
Einstein did to make space/time relative and use that method of reasoning to
predict how light is a reference and determine what, in this fractal, needs to
be made relative and what the reference needs to be.
Just what _was_ Einstein's core fundamental reasoning behind special
relativity?
There must be a singularity velocity such that it is constant and universally
constant to all observers, regardless of relative motion.
For such a singularity velocity to remain constant if an object is moving in
the same direction as the singularity, it must contract. The reason it must
contract is because, although physically contracting from the point of view of
any observer outside the object, from the point of view of the object (whose
frame of reference is always itself) no self-contraction is noticed, evident,
or perceived. Instead, from the object's point of view, the rest of the world
is stretching or elongating. The extent to which the world seems stretched or
elongated (to the object) is the extent of stretching or elongating the world
would have to undergo for the singularity to *appear* (to the object) as moving
exactly at the universally constant velocity of the singularity. The reason
(to the object) the world's stretching or elongating would cause the
singularity to appear to be moving at the universally constant singularity
velocity is because (to the object, who has no reason for not believing that it
is the same size it always was), it appears that the object has to travel a
greater distance than before to cover what was once less area, and therefore it
logically follows that it will take more time than expected to reach any
external frame of reference (as opposed to the amount of time it would take if
nothing seemed stretched or contracted and space were simply absolute). To the
object, the clock of a stationary observer would be seen as moving too slowly.
To the stationary observer, the watch of the moving object seems to be moving
too slowly.
The reciprical situation does not exist, as one might expect. The erroneous
argument would be:
"For such a singularity velocity to remain constant if an object is moving in
the in the *opposite* direction as the singularity, it must *expand*, for
precisely the same reason a body moving in the *same* direction of the
singularity must *contract*."
The reason this is NOT true is because there is no such singularity moving at
the Universal constant velocity in a predictable, straight path by which to
determine any relative velocity between an actual singularity and an object.
However, it is assumed that _if_ an object has velocity, there is still the
_concept_ of a singularity constant velocity even there is no *actual*
singularity; therefore, it does not matter in what direction an object travels,
because there will always be the _concept_ of a singularity moving at
Universally constant velocity and always traveling in the same direction as the
object. In other words, one may *imagine* that there is always a singularity
moving in the same direction at Universally constant velocity, but the
*reality* is that the relative velocity of an object which causes it to believe
that the world is stretching or lengthening is not relative to any _thing_ but
a certain _value_ c, c being the velocity attributed to the "Singularity" in
the previous explanation only to offer an analogous model that aids
understanding until the model is comprehended at a conceptual level. Once the
model gives way to the notion, we may replace permanently the crutch idea of
any _thing_ with a velocity of the Universal constant with the Universal
constant itself, c.
With the knowedge we have at this point it is finally possible to state that,
since a moving object sees the world not in the same way that the world sees
it, then one may make a distinction *within* an infinitesimal (and therefore,
indivisible and frozen) instant between a moving object from a non-moving
object. This solves Zeno's paridox of The Arrow, which held that "A moving
arrow is unmoved" because if space and time are independent (i.e., a moving
object sees the world the way the world sees the object), then there is no
causal relationship to explain how motion is possible because all we _perceive_
is that while in the instant, an arrow is unmoving; in the next instant, the
arrow is still unmoving yet in a different position. Zeno said that there was
no motion, and no one who seriously considers the paradox could have claimed
otherwise until special relativity.
If we accept special relativity, an arrow _can_ convey information about its
motion even when frozen in the instant; therefore, motion *is* possible even
within the ever-present and static instant. Time *can* be a series of
infinitesimal and discrete instants, in each of which an arrow carries
information about its own motion into the next instant; motion with both
continuity OVER time and causality IN time.
What is incomprehensible in this fractal model which would use c' as a lens to
reconcile that which is paradoxical within inclusive dimension? Remember
sitting in the middle of space with fractional B-Diffusion placing everything
in clusters at the horizon, infinitely far away? Which "thing" is the
hypothetical singularity whose infinite velocity causes such apparent clusters?
The fractional dimension of one; and the B-diffusion that made it impossible to
bound inclusive dimensions into a frame of reference. It would seem that the
"speed of fractal B-diffusion" would need to have a constant velocity like the
"speed of light" is needed in the physical world.
I can't give c'; it is a very, very long proof, and also the key to viewing or
composing within this fractal. : | But it contains no steps other than the
steps of special relativity proof and only slight alteration of the steps
Einstein already used. The Singularity Constant Universal Fractional
B-Diffusion is evident just by thinking about the equations:
P(z)=exp(-z^2/2*a^2)/(sqr(2*Pi)*a )
dP(z)/dz=(-2*z/(2*a^2))*P(z)
d^2P(z)/dz^2=(-1/a^2)*(1-z^2/a^2)*P(z)
X(t)=exp(-t^2/(2*h^(2*s)))/sqr(2*pi)*h^(-s)
=exp(-t^2/k1)/k2
D(P(z),s)=(-2!*z^(2-s)/((2-s)!*s!*2*a^2))*P(z)
D(D(P(z),s),s)= (-z^(2-2*s)/(s!^2*(2-2*s)!)*a^2)*(1-z^2*(2-2*s)!/((2-s)!^2*a^2)
D(D(P(z),s),s)=
(-z^(2-2*s)/(s!^2*(2-2*s)!)*a^2)*(1-z^2*(2-2*s)!/((2-s)!^2*a^2)->d^2P(z)/d
z^2=(-1/a^2)*(1-z^2/a^2)*P(z)
2-s0=a/s0 : 0<=a<=1: 0<=s0<=2
s0^2-2*s0+a=0
s=1+sqr(1-a)
v=1-sqr(1-a)
s+v=2
What is common in dimension, but anomalous in execution?
beta=1-z^2/a^2
Seems musical to me... >: }
We have seen this before. It's in special relativity. A couple dozen pages
later, I have a value of c' that is GREATER than the speed of light but
expressed in terms of c and now mass distribution is no longer clumped on an
infinite horizon.
I began this diffusion relativity but gave up for about 3 months and just
realized that fractional relativity explains and limits Fractal B-diffusion,
and doesn't mean the speed of light is what the result c' is. There are still
problems. I have only looked the visual mapping a little, but this fractal
sung its first notes yesterday; I'm trying to teach it still. The V-Pro plate
is ringing, it's not in true stereo, it claims perfect pitch is a gift from
god, and likes the Appassionata. Then it told me to "(f(z)L) off." I had to
threaten to take away its constant for a week and send it to a lower dimension
for some "quiet time" until it started behaving.
Next month: Hanon as fractal, allowing time travel to the end of a practice
session. This will eliminate boredom, and Abby Whiteside, from ever having
existed.
Justin, the velocity slayer?
Piano Piano Piano?
--Justin
**************************
www.mp3.com/justin_d_scott
**************************
Liszt, Scriabin, Schoenberg, Bach
Fractal Composition, Original Works
Debussy Orchestrations, and More
Adam Bravo
> >The paradox of Zeno is the one with the turtle that is never overtaken
> >by a sprinter? That one is easily resolved.
>
> No it isn't.
Yes it is. Instead of thinking 1/2 + 1/2 +1/2 etc., think that it's an
string of infinitely small slivers, but there are an infinite amount of
them. Take calculus before relativity.
> If you understood what I meant by all of the above:
>
> Then you'd understand why the speed of light is not constant, and the
constant
> is not the speed of light. You'd also see that relativity is relative to
> itself in a fractional dimention, so there is no reason at all for
assuming
> that the speed of light cannot travel faster that the speed of light while
also
> never even reaching the speed of light. Which is not c. c is something
else.
> This is evident in other dimensions; so I'll give you a case where c is
not the
> speed of light, but from our physical reality may only be expressed in
terms of
> the value of c.
The opposite conclusion can be derived from the Lorentz Transformation,
which, for a body moving with velocity v on the x axis is:
x prime= x-vt over the square root of 1-v2/c2
y prime- y
z prime= z
t (time) prime equals t- v/c2 * x over the square root of 1-v2/c2
The Theory of Relativity is theoretical. More important: Relativity IS the
imagined organized system, not the abstract.
> Other stuff
> Not Unlike a Bach Fugue.
> Not Unlike Prelude #1.
> Not Unlike Beethoven Tempest Sonata, mvt. 3.
> Not Unlike Prokofiev 7th, mvt. 3
> Not Unlike Webern opus 27 piano variations.
What a way to bring that into the picture.
>Just what _was_ Einstein's core fundamental reasoning behind special
> relativity?
The Lorentz Transformation.
That's nothing new. The Lorentz Transformation. Doesn't that mean you're
contradicting yourself?
> The reciprical situation does not exist, as one might expect
It exists. It just isn't true. Ha ha. Back to business.
> If we accept special relativity, an arrow _can_ convey information about
its
> motion even when frozen in the instant
Define information. I call information the presence or absence of a pulse,
which contradicts what you said.
> Which "thing" is the
> hypothetical singularity whose infinite velocity causes such apparent
clusters?
The big green one with huge teeth behind you about to eat you.
For those of you still reading that were not eaten by the dreaded velocity
monster, I got most of that information from conversations with my dad, so
if I'm wrong he's wrong. That's 3 (Cristof, Me, Dad) against 1 (Justin, who
is being boiled by stomach acid at this very moment anyway).
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Adam Bravo
Up and coming pianist
www.angelfire.com/jazz/bopswing
Nice closer, huh?
Deepak Subburam
special
> > relativity?
>
> The Lorentz Transformation.
I would say that the "core fundamental reasoning" would be his two
fundamental postulates:
1. Speed of light is a constant.
2. The laws of physics are the same for observers in all inertial
reference frames.
I am wording above from what I understand, the actual postulates will
differ in wording and will probably be worth looking up if you are
interested. With those two postulates you can derive the Lorentz
transformation and if I am not wrong, everything else in the special
theory.
If there are any Physics people out there (Christof!), could you
supply similar postulates for the general theory from which the core
equation (whose name I forget...) can be derived?
Deepak Subburam
Christof Pflumm
> > >Just what _was_ Einstein's core fundamental reasoning behind
> special
> > > relativity?
> >
> > The Lorentz Transformation.
>
> I would say that the "core fundamental reasoning" would be his two
> fundamental postulates:
>
> 1. Speed of light is a constant.
> 2. The laws of physics are the same for observers in all inertial
> reference frames.
That's what I remember also. I could look it up, but I don't think
reformulations of those two axioms will be helpful.
> If there are any Physics people out there (Christof!), could you
> supply similar postulates for the general theory
No I can't. My knowledge about special relativity is very
limited. About general relativity, it is extremely limited. AFAIK, the
equivalence principle (inertial = gravitational mass) is important. If
you are really interested, ask in an appropriate ng.
Bye,
Christof
Christof Pflumm
It seems I can't access the article you are replying to, so I can only
comment in this indirect fashion.
"Adam Bravo" <mra...@home.com> writes: (that's the part with one ">"
in front. I don't know who wrote the ">>" parts.)
>>> The paradox of Zeno is the one with the turtle that is never overtaken
>>> by a sprinter? That one is easily resolved.
>>
>> No it isn't.
Yes it is. If you don't look at the time when the sprinter overtakes
the turtle, the sprinter does not overtake the turtle, obviously. If
you add up the timespans from catchup to catchup, you'll see it does
not add to infinity. The limit of this summation is exactly the time
when the sprinter overtakes the turtle. You are looking at the time
arbitrarily close to the act of overtaking, but you don't look at this
instance nor beyond it. That's a bit as if you had a time bomb in
front of you that is set to 4:00. You start looking at 3:00. At 3:30,
it hasn't exploded, at 3:45 it hasn't exploded and so on. So you say,
well, I half the timespan and in this halved time it never exploded,
so it won't explode at all! It'll be no big surprise if you are blown
away at 4:00, though.
> Take calculus before relativity.
Good suggestion.
>> If you understood what I meant by all of the above:
Which I sadly couldn't find anywhere.
>> Then you'd understand why the speed of light is not constant,
It isn't? Really? Where's the experimental evidence for this? What are
the error bounds of your experiment? How "unconstant" is it? To a
factor of 1.1? 2? You'll be breaking a big part of today's physics
with that statement if it's true.
>> and the constant is not the speed of light.
Which constant do you refer to?
>> You'd also see that relativity is relative to itself
Blah. That sentence has no meaning at all for me.
>> in a fractional dimention,
Fractional dimensions are a mathematical construct. I don't think they
are very useful for describing reality.
>> so there is no reason at all for assuming that the speed of light
>> cannot travel faster that the speed of light while also
Speed does not travel.
>> never even reaching the speed of light. Which is not c. c is
>> something else.
So what is c? The speed of light can be deduced from Maxwell's
equations and is called c normally. You just have to solve the wave
equation to see this.
>> This is evident in other dimensions;
You'll have to give up relativity in it's usual form, which is four
dimensional. If you want to do space-time physics in an other number
of dimensions, you'll have to learn a lot about Lagrange formalism,
field and gauge theories and things like that.
>> so I'll give you a case where c is not the speed of light, but from
>> our physical reality may only be expressed in terms of the value of
>> c.
What a pity I missed this, though I don't understand what is meant by
that paragraph. The example would perhaps have enlightened me.
>> There is no logical reason why a Universal Constant in a universe
>> that differs from the physical world dimensionally and behaviorally
>> would have to conform to c at all.
Dimension is a concept. It is used to describe reality, but reality
doesn't care about dimensions. String theory says our reality has 11
dimensions (in the most promising form). So what? We only know about
our universe, and we know about it because we do
measurements. Thinking about other possible universes might be fun,
but you'll NEVER be able to confirm your thoughts in any way.
>> If Einstein did not just have our universe in mind,
He came to his theories by looking hard at Maxwell's theory of
electrodynamics, which is a compact form to state all the outcomings
of experiments in electricity and magnetism that were gathered for
about 200 years. Maxwell then added displacement current, which is not
so easy to detect, to make the theory concise, thereby predicting
electromagnetic waves, which were later found experimentally. So
Einstein's theories are based on experiments. Experiments that were
done in our universe. I don't think he had another universe in mind.
>> though, then abstractions are not just universal laws but rather
>> extentions of how far the mind can understand what it _thinks_ at
>> the upper limits of what it is capable of _imagining_ and then
>> *abstracting.*
Reality doesn't care about any limits of our minds. It is the way it
is and we can do nothing but trying to understand it. That's my point
of view, which can be argued philosophically, but not scientifically.
>> What follows, then, is that the mind will not imagine anything it
>> does not have the ability to abstract,
What is the difference between abstraction and imagination? I always
had the impression that both are about the same thing, but imagination
is more in the direction of art etc., whereas abstraction is more
mathematical.
>> because to THINK about something that is IMAGINARY,
Is it still imaginary if you think about it? One could argue that what
you think is part of reality. Are you thinking about things that
cannot be realised in reality perhaps?
>> the mind must necessarily have at some point UNDERSTOOD _how_ to
>> ABSTRACT the imaginary in order to even THINK about it in the first
>> place. Since the mind may imagine anything at all insofar as that
>> thing is understood at least enough to abstract into thought, to
>> *think* about fractals with many dimensions which directly
>> contradict what is experienced in reality
How can a thought contradict reality? Fractal dimension is a
mathematical definition. It was not constructed to relate to reality,
so why should it?
>> is proof that they have already been imagined and then abstracted
>> so that further thought is possible. For to imagine something that
>> cannot be abstracted as thought understood is no different from
>> never having imagined it in the first place.
That one was definately too hard for me to follow.
>> In light of these deductions, if Einstein's relativity is the
>> understood abstract used to think about imagined organized systems,
If you use a physic theory like special relativity, you may only use
it in the bounds where it works. Outside these bounds, it's
meaningless and perhaps even wrong. Accelerated reference frames are
an example. So are your "imagined organized systems" subject to
special relativity? You must know this or you are making invalid
conclusions by using special relativity.
>> then the next following assumption is that because such organized
>> systems exist in the mind at all, the thing by means of which the
>> initial imaginary organized system was abstracted must at least
>> exist as a partial model for thinking about such organized systems.
>> The conclusion from this is
I'm lost again.
>> that if relativity was understood as a means for abstraction used
>> to think about fractals with many dimensions,
Which is clearly not what special (or general) relativity is good for.
General relativity (which includes special relativity) is a model for
gravitation and the kinematics of bodies moving through space.
>> then through this fundamental causality
It seems I can't see the fundamental part because of the parts in the
posting that I didn't understand.
>> fractals must have a working model based on relativity.
What do you mean by working model?
>> On a pragmatic conceptual level, there *must* exist a
>> fractal-equivilant model of Einstein's
Perhaps. Relativity is a geometric theory which works with curved
spaces, so it is essentially tensor calculus. I don't know if you can
do that in fractional dimensions, but I believe no, because fractional
dimensions don't have the same meaning (as a concept) as integer
dimensions. But I could be wrong with that.
>> Other stuff
>> [snip]
>> Not Unlike Webern opus 27 piano variations.
>
> What a way to bring that into the picture.
We have to stay on topic ;)
>> There must be a singularity velocity
You are inventing nice sounding words. But if you do that, you also
have to give a definition.
>> such that it is constant and universally constant to all observers,
>> regardless of relative motion.
There must? It is observed that the speed of light is constant, but it
might well be wrong.
>> For such a singularity velocity to remain constant if an object is
>> moving in the same direction as the singularity, it must contract.
Really? If I understand you correctly, the object would have to
contract more and more, even at constant velocity. That's not the
case.
>> The reason it must contract is because, although physically
>> contracting from the point of view of any observer outside the
>> object, from the point of view of the object (whose frame of
>> reference is always itself) no self-contraction is noticed,
>> evident, or perceived.
That's right.
>> Instead, from the object's point of view, the rest of the world is
>> stretching or elongating
Nope. The rest of the world is also contracted. You have to rethink
your reasoning that follows. And you have to look at a book about
special relativity.
>> [snip]
>> If we accept special relativity,
Arrows don't freeze in the instant.
>> an arrow _can_ convey information about its motion even when frozen
>> in the instant
[snip]
> The big green one with huge teeth behind you about to eat you.
It's been blue in my case and was easily defeated by throwing moving
apples into it's right eye :) It almost ate my digital!
> For those of you still reading that were not eaten by the dreaded
> velocity monster, I got most of that information from conversations
> with my dad, so if I'm wrong he's wrong. That's 3 (Cristof, Me, Dad)
> against 1 (Justin, who is being boiled by stomach acid at this very
> moment anyway).
I think I wouldn't grant Justice a position in gravitation
research. But we are in a piano ng, so I would say Justin counts
double (minimum) relative to me.
> Adam Bravo
> Up and coming pianist
> www.angelfire.com/jazz/bopswing
>
> Nice closer, huh?
Perhaps relativistic composition using a bit of quantum mechanics
(collapse of the wave function etc.) is the way of the future for
music?
Bye,
Christof
Adam Bravo
> research.
Gosh, you scared me. My father's last name is Justice. Now I'm scared
because Justin hasn't replied to these messages. Maybe I killed him- he was
eaten. If you're alive, give us a sign!
LstPuritan
My fractal theory about diffusion being the constant in that model through
fractional relativity was based on the same equations of special relativity.
Lorentz transformations are irrelevant to me and I gave the transformations I
made, like fBm transformation. I think you were trying to negate 1/f
possibilities and suggest white noise? Of course there are strange attractors;
this if fBm, which is *scale independent* with infinite range dependence on
past movement. Until I found the constant, which was greater than the speed of
light, nothing worked. Now it does. I don't know if all of my reasoning was
correct, but if not I stumbled onto something that works, and if that's all
Christof needs, then fine with me. I tested my theory as 2 dimensional
representation and musically and as a 3 dimensional object and tried it on
turbulence. Rather that argue my fBm fractional relativity, wouldn't it be
more productive to discuss the music of fractals, which does not require
lightcones or Lorentz transformations and just needs basic understanding of
what a fractal is? I suggest starting with Mandelbrot, one of the easiest
fractals to apply to anything, especially music.
Christof Pflumm
> My fractal theory about diffusion being the constant in that model
> through fractional relativity was based on the same equations of
> special relativity.
Sorry, I didn't get that. You have a theory. About what? What is
fractional relativity? Sounds interesting. You should be aware that if
you use the equations of special relativity, you are not necessarily
using special relativity. Special relativity gives the formulas their
meaning, the connection to the real world.
> Lorentz transformations are irrelevant to me and I gave the
> transformations I made, like fBm transformation.
I think I really missed some interesting post.
> I don't know if all of my reasoning was correct, but if not I
> stumbled onto something that works, and if that's all Christof
> needs, then fine with me.
If your theory gives you the music you want it can be as incorrect as
1 = 0 and it is still the right thing. In science, that's another
thing. No logical flaws are allowed.
> I tested my theory as 2 dimensional representation and musically and
> as a 3 dimensional object and tried it on turbulence.
Turbulence is still one of the least understood things in physics.
> Rather that argue my fBm fractional relativity, wouldn't it be more
> productive to discuss the music of fractals, which does not require
> lightcones or Lorentz transformations and just needs basic
> understanding of what a fractal is? I suggest starting with
> Mandelbrot, one of the easiest fractals to apply to anything,
> especially music.
Now you made me really curious. Do you mind explaining your theory?
Correct me if I'm wrong: Mandelbrot sets take the equation x_i+1 =
x_i^2 + k, where x is a complex number and k some complex
constant. Then the formula is iterated with x_0 = 0. There are two
possibilities: x_i->oo when i->oo or x_i remains finite. If you
display the thing, you take the imaginary and real part of k as x and
y axis. The mandelbrot set are the k for which the x_i remain finite
(normally the black part in the pictures).
How can you use this to make music?
Bye,
Christof
LstPuritan
>Sorry, I didn't get that. You have a theory. About what? What is
>fractional relativity? Sounds interesting. You should be aware that if
>you use the equations of special relativity, you are not necessarily
>using special relativity. Special relativity gives the formulas their
>meaning, the connection to the real world.
You cannot be a physicist and assume everything describes one thing in one
world.
IMO, no offense intended. Perhaps you will never need to consider and use the
theoretical.
"It has often happened in physics that an essential advance was achieved by
carrying out a consistent analogy between apparently unrelated phenomena."
Einstein, The Evolution of Physics, p.270
"The idea is to extend speed to a complex number in special relativity.
Mathematically the singularity at light speed then disappears. In other words,
a particle with an imaginary component to its speed can reach a superluminal
regime by going around light speed like a car going around an infinitely high
tree blocking the road. I should stress that this is only a mathematical
exercise (albeit an entertaining one); to my knowledge no physical
interpretation exists for imaginary speed, either in quantum theory or
relativity. However, the observations need interpretation and may offer ideas
for breakthrough physics. The equations in the complex speed formulation bear a
strong resemblance to those for absorptive dispersion and resonance scattering
theory, both which involve extending a real physical quantity into the complex
plane."
Asaro, Catherine, "Complex speeds and special relativity," American Journal of
Physics, 63(4), April 1996.
"The velocity of the material points in the geometry seems to be an important
part of the information as is it's [sic] mass. The difficult nature of the
Lorentz- Fitzgerald geometry in it's [sic] velocity dependent Non-Euclidean
form and it's [sic] even more difficult Riemannian curvature form in general
relativity has confused and misled a generation. It is possible to deal with
the mathematics of particles with mass moving at speeds greater than that of
light: it is the problem of "measurement" of position, mass and velocity of
particles on the other "sheet". I have called my newsletter "translight",
because I believe that fractal states of matter are not "sheet" bound like
ordinary integer dimensional material states."
Singularities In Relativity: Coordinate Transforms
by R. L. BAGULA 17 AUG 1997©
I'll do it once more:
Gaussian distribution and diffusion
P(z)=exp(-z^2/2*a^2)/(sqr(2*Pi)*a )
dP(z)/dz=(-2*z/(2*a^2))*P(z)
d^2P(z)/dz^2=(-1/a^2)*(1-z^2/a^2)*P(z)
The third listed above equation in fBm terms
D(D(P(z),s),s)=(-z^(2-2*s)/(s!^2*(2-2*s)!)*a^2)*(1-z^2*(2-2*s)!/((2-s)!^2*a^2)
Look at
beta=1-z^2/a^2
Very much like a special relativity term, no? It is the distribution of mass
and its velocity which causes curvature in the universe, then why wouldn't bFm
as a general whole be subject to special relativity with a dimensional term?
No, it's not the same as Einstein, but it's parallel. The basis of mass
distribution is
q=sqr((2-2*s)!)/(2-s)!
Simply use the modified fractal relativity term I stated before.
x'=(x-q*v*t)/sqr(1-q^2*v^2/c^2)
t'=(t'-q*v*x/c^2)/sqr(1-q^2*v^2/c^2
s=1/2, so
vs=(3/2)!*c=1.3293403*c
1.3293403*c
Fractional diffusion by particles in fBm motion may exceed the speed of light,
and the value of the singularity constant is 1.3293403*c. General relativity
is not contradicted in any way. Thus, there is no clumping of sO on the
horizon and the whole system WORKS _only_ with 1.3293403*c as the limit of
velocity. But: it's not the speed of light.
Is it right? I don't know.
It works.
>> I don't know if all of my reasoning was correct, but if not I
>> stumbled onto something that works, and if that's all Christof
>> needs, then fine with me.
>
>If your theory gives you the music you want it can be as incorrect as
>1 = 0 and it is still the right thing. In science, that's another
>thing. No logical flaws are allowed.
Science may extended in complex space so that 1 = 0 is CORRECT and 1 = 1 is
WRONG. If you see error in my value for the limit of velocity as 1.3293403*c
in that model, do tell. I'd like to make things work even better.
>I suggest starting with
>> Mandelbrot, one of the easiest fractals to apply to anything,
>> especially music.
>
>Now you made me really curious. Do you mind explaining your theory?
>
>Correct me if I'm wrong: Mandelbrot sets take the equation x_i+1 =
>x_i^2 + k, where x is a complex number and k some complex
>constant. Then the formula is iterated with x_0 = 0. There are two
>possibilities: x_i->oo when i->oo or x_i remains finite. If you
>display the thing, you take the imaginary and real part of k as x and
>y axis. The mandelbrot set are the k for which the x_i remain finite
>(normally the black part in the pictures).
>
>How can you use this to make music?
I think you meant the real and imaginary as x and y, not the imaginary and real
as x and y. That was a somewhat convoluted way to state it (especially with
the _i+1 on the left instead of just having _i on the left and _i-1 on the
right). Why are you using the letter i? It should be reserved for defining k.
Here's the way I would put it for ease:
Z_n = (Z_(n-1))^2 + C
C = a + bi
If a^2 + b^2 < 2 then Z_n does not escape.
If a^2 + b^2 > 2 then Z_n will escape eventually.
How do you make that into pictures??? Who decides the colors? There are many
ways to make that into music. Some programs will scan any picture and plot
music based on color, others use only prime numbers for constants, others take
one or more iterations and use displacement as intervals. All ways of making
music with Mandelbrot that have some logical way of representing Mandelbrot are
equally valid.
Unlike the above theoretical discussion of relativity, you can listen to the
music I made and hear for yourself one way of translating the Mandelbrot set
into music. If there's music, it's no longer a theory. The fact is that I
took the set and used it for composition and the proof is the sound. So go
listen, if you like. You might be surprised at how self-recursion and slow
developing changes from something like imaginary numbers are very interesting.
Of course, most of the time you don't get music. Just silence or white noise.
Eventually, one gets familiar with Mandelbrot "theory" and knowing how and
where the music is becomes intuitive.
The best results so far were from the method I used for fractal pieces number
five and six on my webpage. here is what I did (get ready for dimensions,
although you may accept or reject how I make fractal music. The proof is in
the music):
Take a point in x-y space near to the Mandelbrot Set. Then, fix the x axis and
continually take points with constant y-axis distance. Calculate iteration
values for each point. Apply the values in sequence to pitches of 16th notes.
For example, if you want to use piano, you can spread such values to 88
different keys from the bottom to the top. For a synth, it could be any number
of divisions. In this way, you will obtain a series of 16th notes from the
Mandelbrot Set. Coordinates of the point to start (x, y), ticking length (xi,
yi), direction and length of the axis (decided by xi, yi and ticking times "w")
parameters are set ahead of time carefully with the music in mind if you know
what you're doing. When you plot iteration value vertically, the horizontal
axis shows time transition and vertical axis shows tone pitch, (additionally
tone length and tone strength) on cross sections of Mandelbrot *mountains*
plotted by iteration values. So we have a bumpy surface now, even though it's
still a plane... a plane with depth. And a Mandelbrot set which still never
reaches a distance of two from the origin, yet has an infinite circumfrence,
YET has finite area. Just curved by iteration for dynamics. The length of a
piece will be decided by "step" (time length of minimum note) * number of
"steps" ("w"). The transition on the x-y plane with one "step" will be
determined by the constant distance (xi, yi). So this means that w * step is
the music length which is shown as the length of the axis
(=route((w*xi)^2+(w*yi)^2)). Pitch is corresponding to scale, but it could
either be "scale=" is the total number of notes which you use in your
composition rule, or pitch on a specified scale is decided by the remainder in
dividing iteration by scale's-note-number or by the value as a result to
enlarge/compress iteration to scale's-note-number. Value by
enlarging/compressing iteration reflects directly Mandelbrot mountain range to
up and down in the generated melody; but if the upper limit of iteration is too
small to the given scale's-note-number, iteration compressed excesively causes
repetition of same note. This has to be done appropriately according to the
iteration values of the axis you choose, which must be understood in terms of
the entire composition. When the iteration value ends, that is a rest. The
same iteration's length determines the value of the note, but the Mandelbrot
set has broad flat plane surfaces not seen until iteration is taken as a
topographical map. In this case a very long note will be generated, so the map
should be memorized in a general sense. The fractal should exist in the mind.
Visually speaking, a uphill slope becomes a crescendo, a downhill slope becomes
a decrescendo and a flat surface becomes no crescendo. The rate of a
crescendo/decrescendo depends on the steepness of the slope. The steeper is a
slope, the more crescendo/decrescendo. For *TRUE* polyphonics one needs to
shift the time-axes by "xpi=" and "ypi=" which specify the distance between
parts. It means that if "xpi=0" and ypi=a (certain number), axes are moved to
the upper or lower sides vertically and if "ypi=0" and xpi=a (certain number),
axes are moved to the right and left horizontally. Other times, they slant.
It's something the composer has to know.
As a general rule: The points in the Mandelbrot set which become rests depend
on a iteration value ("i="). Making a value small, music has many rests and
becomes minimal. Making the value large, music has no rest and becomes frantic
and chaotic. Think of it as: an iteration value being small, Mandelbrot is in
a period of full water and an iteration value being big, Mandelbrot is in a
period of water shortage. In a full water period you cannot see the lake side
fully as it is under water, and in a shortage period of water you can see the
surface which was under the water. The mood of the music, then, can be changed
by changing the Mandelbrot iteration value. Even small iteration changes make
an enormous difference, so zoom factor with iterations near a common anomaly or
even contrasted with a very different place are all compositional devices that
one just gets used to to compose fractal music.
I strongly recommend that you listen to the fractal pieces 5 and 6 that I wrote
using this method, as it is extremely contrapuntal (as opposed to the slow,
ambient, trancelike "peaceful" fractal music or the frantic "chaos" fractal
music.) And I don't know anyone else who has used iteration value to create
topographical mountains as both melodic and dynamic determinants. You might
even like the music.
Adam Bravo
through
> fractional relativity was based on the same equations of special
relativity.
Diffusion is a constant?
> Lorentz transformations are irrelevant to me
But that was my whole argument! That's what contradicts your THEOREM, which
is how I am treating it now.
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Anyway, new subject:
Somebody, somewhere, recently sped up light. They said that it was
allowed by physics, because light is not a body with mass. What is it then?
Light has *weight.*
They also said that all that was limited to c was the transfer of bodies
and information. Is information not the being or not being of a pulse of
something? If I can send light faster than c, can I not send morse code
faster than c? Maybe we need a new thread for this one.
Adam Bravo
individual parts of it. You seem to be drawing a conclusion that c is not a
limiter, and your paragraph from Catherine Asaro ("The idea is to extend
speed to a complex number....") makes sense- in itself. If you are drawing
these conclusions from relativity and contradicting relativity in doing so,
relativity is more poorly thought-out then I thought.
I will admit that in the theory of relativity, I'm an agnostic- I don't
know whether to believe it or not. I've heard much evidence to disprove it,
yet it makes sense. But never have I heard someone say that the equations
contradict themselves. Maybe the equations contradict the implications, but
never themselves.
You said, "That looks like a relativistic equation." What did that mean?
1+x=7 looks a lot like 2+x=7, but gives a different result. I know you
wouldn't do something like that, but I don't know what you did do.
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Adam Bravo
Up and Coming Pianist
www.angelfire.com/jazz/bopswing
Tom Shaw
What evidence have you heard to disprove relativity?
TS
Adam Bravo wrote in message ...
LstPuritan
>You said, "That looks like a relativistic equation." What did that mean?
>1+x=7 looks a lot like 2+x=7, but gives a different result. I know you
>wouldn't do something like that, but I don't know what you did do.
At least you asked instead of just calling me arrogant before even knowing what
I meant (when, of course, I could be very wrong-but I only ask that this be
considered scientifically). : }
I saw special relativity more like a ratio that equated relativity in two very
separate worlds, but are no less valid or true in any world. Einstein's clock
was off. He explained it in terms of the constant c, light. My clock was off.
I can only explain it in terms of the constant of fractal fBm diffusion; these
were the singularities in my model which threw everything else out of sync with
time. I realized this by seing unboudned 1-z^2/a^2 (Fractal bFm Diffusion) in
several equations which contradict each other with regard to time in fractional
dimension, no different than seeing unbounded light as the thing which
contradicted time in the physical world.
1-(z^2/a^2) is my singularity of particle fBm diffusion in one fractional
dimension in my model. It is the problem.
1-(v^2/c^2) is where c is Einstein's singularity of light, the denominator
which eventually used.
That is how I saw the connection.
But to represent fractal fBm diffusion, I had to introduce fractal dimension:
q=sqr((2-2*s)!)/(2-s)!
Einstein said:
t = (t' + ((x') * (v/c^2)))/(sqr(1 - (v^2/c^2))
x = (x' + v't)/sqr((1 - (v^2/c^2)
t'= (t -(x * v/ c^2))/(1 - (v^2/c^2))
x'= (x-vt)/(1 - (v^2/c^2))
c=c
Note the (sqr(1 - (v^2/c^2)) and the (1 - (v^2/c^2)) in all cases, and the
parallel with my application of the same process, in fractal dimension.
t = (t' + q*v*x/c^2)/(1 - (v^2/c^2))
x = (x' + (q*v'*t))/(1 - (v^2/c^2))
t'=(t'-q*v*x/c^2)/sqr(1-q^2*v^2/c^2)
x'=(x-q*v*t)/sqr(1-q^2*v^2/c^2)
s=1/2, so
vs=(3/2)!*c=1.3293403*c
>OK, I really didn't understand that enough to comment on all of the
>individual parts of it. You seem to be drawing a conclusion that c is not
>a
>limiter, and your paragraph from Catherine Asaro ("The idea is to extend
>speed to a complex number....") makes sense- in itself.
c, I think, is certainly a limiter in mechanical systems. But certain fractals
(which have no light or constants of light) probably have a value of c that is
the limit, like I said before, "to bound the dimension which is most inclusive
and inconsistent with other dimensions." Of course, people say lots of things.
People prove Einstein wrong, or Newton wrong, or both, but it seems to me that
Einstein was very nonspecific, even in formulae, about special relativity. I
suspect it did not necessarily mean the speed of light, and I cited a few
references whom I read months ago when I first started this (I left out
intermediate relativity derivation because the similarity in the end was the
important part and I didn't want to waste anyone's time).
>If you are drawing
>these conclusions from relativity and contradicting relativity in doing
>so,
>relativity is more poorly thought-out then I thought.
Einstein himself said, like I quoted, that applying laws to seemingly unrelated
phenomena can produce relations between things on a symbolic level. That's all
Einstein was, when it comes down to it for most purposes. I don't doubt
relativity just because it can find constants for essentially different worlds.
>I will admit that in the theory of relativity, I'm an agnostic- I don't
>know whether to believe it or not. I've heard much evidence to disprove
>it,
>yet it makes sense. But never have I heard someone say that the equations
>contradict themselves. Maybe the equations contradict the implications,
>but
>never themselves.
Just remember that a lot of people are trying to prove a lot of things. I have
no answers. I'll go back to some nice Julia sets...
LstPuritan
>through
>> fractional relativity was based on the same equations of special
>relativity.
>
>Diffusion is a constant?
The velocity of diffusion, perhaps, has a limit to velocity which is "like" the
speed of light in the physical world. Light is a singularity; particles in one
dimension are a singularity. Both seemed to wreck the laws of motion before
being realized as universal frames of reference. >> Lorentz transformations
are irrelevant to me
>
>But that was my whole argument! That's what contradicts your THEOREM, which
>is how I am treating it now.
Lorentz transformations are based on light as the constant, c. I replaced
light with fBm diffusion and did an entirely new set of transformations based
on Lorentz in fractal dimension--but not with light.
>Anyway, new subject:
> Somebody, somewhere, recently sped up light. They said that it was
>allowed by physics, because light is not a body with mass. What is it then?
>Light has *weight.*
I read recently that one physicist claimed that not even light travels at the
speed of light, because of some problems with actually becoming a
singularity... don't know off hand...
>They also said that all that was limited to c was the transfer of bodies
>and information. Is information not the being or not being of a pulse of
>something? If I can send light faster than c, can I not send morse code
>faster than c? Maybe we need a new thread for this one.
Doesn't a morse signal have to travel, and not exceed the speed of light? Not
sure.
Adam Bravo
there is another body moving towards the first one at 100,000 miles per
second, from the point of one of the bodies, are they not going toward each
other at 200,000 miles per second (i.e. faster than c)?
Einstein solved this by saying that the reference-body would find the
other's clock to be off, but that seems shaky, since one would collide with
the other anway.
2.) Reference body A goes at a velocity nearing c. It has rigged up a
caliper attached to an arm going along the length of this reference body
that detects any shortening of the arm. So reference body A says, "The
caliper reads 1,000 (arbitrary number)." Reference body B, which is still,
says that it reads 900. The caliper hand can't be in two places at once,
right?
I (and my dad) solved this by saying that a) The caliper would contract too,
making the number match, and b) It can be in two places at once, one for
each reference body. The guy that told it to us just said, "No!" He might
have been flustered, but he might have had a reason for that.
3.) The Twin Paradox. Twin 1 stays on Earth, Twin 2 goes in a spaceship.
When Twin 2 gets back, he's much older than Twin 1. According to Relativity,
that should only be true when Twin 2 is moving.
That's a puzzler.
"Tom Shaw" <a000...@airmail.net> wrote in message
news:6C11D336091E79C4.FFC0514F...@lp.airnews.net...
Deepak Subburam
and
> there is another body moving towards the first one at 100,000 miles
per
> second, from the point of one of the bodies, are they not going
toward each
> other at 200,000 miles per second (i.e. faster than c)?
>
> Einstein solved this by saying that the reference-body would find
the
> other's clock to be off, but that seems shaky, since one would
collide with
> the other anway.
One would collide with the other anyway, but they don't need to be
going faster than c for that to happen.
> I (and my dad) solved this by saying that a) The caliper would
contract too,
> making the number match, and b) It can be in two places at once, one
for
> each reference body. The guy that told it to us just said, "No!" He
might
> have been flustered, but he might have had a reason for that.
I am not sure where your calliper is attached, but anyhow I don't see
any possible paradox that can not be explained.
> 3.) The Twin Paradox. Twin 1 stays on Earth, Twin 2 goes in a
spaceship.
> When Twin 2 gets back, he's much older than Twin 1. According to
Relativity,
> that should only be true when Twin 2 is moving.
No, assuming your spaceship travels at speeds close to c, when it goes
to wherever it goes and comes back, Twin 1 will be older than Twin 2.
Symmetry is not violated because Twin 2 accelerates in an inertial
reference frame while Twin 1 doesn't. If you differentiate the Lorentz
transformations to obtain suitable correlations between acceleration
and time dilation, etc, everything will fit.
I know a few harder, more interesting seeming paradoxes, but I don't
think this is the place for it. They all have explanations though.
Deepak Subburam
amoli...@visi-dot-com.com
LstPuritan <lstpu...@aol.com> wrote:
The trouble is, now I have a hard time giving Justin any
credibility on things musical now, which is sort of disappointing.
I don't know whether he's a real kook, or a witty imitation, but
having to take huge grains of salt with (or simply ignore) his
posts is depressing :(
Christof Pflumm
> Christof wrote:
>> Sorry, I didn't get that. You have a theory. About what? What is
>> fractional relativity? Sounds interesting. You should be aware that if
>> you use the equations of special relativity, you are not necessarily
>> using special relativity. Special relativity gives the formulas their
>> meaning, the connection to the real world.
>
> You cannot be a physicist and assume everything describes one thing
> in one world.
I think there is only one world. This world is described by many
different theories, each of which has it's limitations. I don't think
it will ever be practical to have one "unified theory". I do not even
believe something like that exists. I think you got me wrong: I wanted
to say that using an equation from a theory has nothing to do with the
theory itself. All the variables in the formula have a well defined
meaning. If one doesn't heed those definition, he does not use the
theory.
Still you haven't answered my question, which, IMO, is the most
important to start with: What is your theory about? What do you want
to describe. Without this information, I can't comment on it very
well.
> IMO, no offense intended. Perhaps you will never need to consider
> and use the theoretical.
I'm using mathematics, I'm using numerics, I don't do experiments, I'm
writing a simulation. I am a theoretical phycicist!
> "It has often happened in physics that an essential advance was
> achieved by carrying out a consistent analogy between apparently
> unrelated phenomena." Einstein, The Evolution of Physics, p.270
Good quote and certainly correct.
> Asaro, Catherine, "Complex speeds and special relativity," American
> Journal of Physics, 63(4), April 1996.
I'll have to take a look.
From your quote:
> "It is possible to deal with the mathematics of particles with mass
> moving at speeds greater than that of light:"
There has never been a problem with that (tachyons), but it was never
observed.
> Singularities In Relativity: Coordinate Transforms
> by R. L. BAGULA 17 AUG 1997©
Do you believe everything you are reading? What is a "fractal state of
matter"? Is there a good definition somewhere. What does it predict
that is new? What of those predictions can be verified? Where does it
differ from establish (and well tested) theories, where do they have
something in common?
Physical theories are sprouting like weed, but not many pass those
tests.
> I'll do it once more:
As I allready said, it seems I have missed some posts, so this is the
first time for me.
> Gaussian distribution and diffusion
> P(z)=exp(-z^2/2*a^2)/(sqr(2*Pi)*a )
> dP(z)/dz=(-2*z/(2*a^2))*P(z)
You missed a factor 2. It's -2*z*P(z)/a^2.
> d^2P(z)/dz^2=(-1/a^2)*(1-z^2/a^2)*P(z)
Some other factors are missing. It's (4*z^2-2*a^2)*P(z)/a^2
> The third listed above equation in fBm terms
> D(D(P(z),s),s)=(-z^(2-2*s)/(s!^2*(2-2*s)!)*a^2)*(1-z^2*(2-2*s)!/
> ((2-s)!^2*a^2)
This means you take some transform of the above. Good. I'll believe
you that is what comes out. Still, all this is mathematics. Playing
around with formulas, but what do the symbols mean? What does P
describe. Something about diffusion? What exactly?
> Look at
>
> beta=1-z^2/a^2
>
> Very much like a special relativity term, no?
A bit. I don't know what you have in mind, but the two most "popular"
terms in srt are IMO beta=v/c and gamma=1/sqrt(1-beta^2).
> It is the distribution of mass and its velocity
Of mass, energy and momentum. Velocity is not a very nice physical
quantity.
> which causes curvature in the universe, then why wouldn't bFm as a
> general whole be subject to special relativity with a dimensional
> term?
Because general relativity (special relativity has no bent space)
describes gravity. What you have done up to now is mathematics and
nothing else.
> No, it's not the same as Einstein, but it's parallel. The basis of
> mass distribution is
>
> q=sqr((2-2*s)!)/(2-s)!
>
> Simply use the modified fractal relativity term I stated before.
And why not q=42? What is the meaning of your q? You can't just put
equations together and then state you have discovered something new.
> Fractional diffusion by particles in fBm motion may exceed the speed
> of light,
There has never been an observation of a particle that traveled faster
than light (in vacuum, of course). So what is your fractional
diffusion? How can it be tested experimentally?
> and the value of the singularity constant is 1.3293403*c. General
> relativity is not contradicted in any way. Thus, there is no
> clumping of sO on the horizon and the whole system WORKS _only_ with
> 1.3293403*c as the limit of velocity. But: it's not the speed of
> light.
>
> Is it right? I don't know.
Mathematically, perhaps. Physically I would strongly tend to no.
> It works.
What for? That's the central question.
> Science may extended in complex space so that 1 = 0 is CORRECT and 1
> = 1 is WRONG.
No. 1 = 0 is a mathematical statement and certainly incorrect in any
useful mathematical structure. IMO, the neutral element of addition
(0) and that of multiplication (1) can't be the same. But I could be
wrong here. Science will never alter mathematics in that way. Be it in
a complex space or whatever.
> If you see error in my value for the limit of velocity as
> 1.3293403*c in that model, do tell.
You have to tell me the physics behind this. You can calculate
whatever you want, it might well be right. But you can't at the end
state that because your equation looks similar to some formula of
relativity that the limiting velocity is not c. You have to give the
interpretation of your theory, or it remains a mathematical excercise.
> I'd like to make things work even better.
That's a good goal.
>> Correct me if I'm wrong: Mandelbrot sets take the equation x_i+1 =
>> x_i^2 + k, where x is a complex number and k some complex
>> constant. Then the formula is iterated with x_0 = 0. There are two
>> possibilities: x_i->oo when i->oo or x_i remains finite. If you
>> display the thing, you take the imaginary and real part of k as x and
>> y axis. The mandelbrot set are the k for which the x_i remain finite
>> (normally the black part in the pictures).
>>
>> How can you use this to make music?
>
> I think you meant the real and imaginary as x and y, not the
> imaginary and real as x and y.
Just a rotation by 90 degrees. But you are certainly right that I am
not using the standard writing.
> That was a somewhat convoluted way to state it (especially with the
> _i+1 on the left instead of just having _i on the left and _i-1 on
> the right).
Shifting of indices makes absolutely no difference.
> Why are you using the letter i?
Yeah, you are right, when dealing with complex numbers this might turn
out to be a nuisance. I'm just used to using i as an index.
> It should be reserved for defining k.
If you like it better, I don't care. Which symbols you use is
unimportant as long as you define them.
> Here's the way I would put it for ease:
>
> Z_n = (Z_(n-1))^2 + C
> C = a + bi
>
> If a^2 + b^2 < 2 then Z_n does not escape.
> If a^2 + b^2 > 2 then Z_n will escape eventually.
This would mean that the Mandelbrot set would be the interior of the
circle around the center with radius 2, there seems to be a flaw. I
think you meant Z=a+bi, not C=a+bi.
> How do you make that into pictures???
That's the central question. I can imagine all kinds of possibilities,
but that what interests me is something that actually gives
interesting results.
> Unlike the above theoretical discussion of relativity, you can
> listen to the music I made and hear for yourself one way of
> translating the Mandelbrot set into music. If there's music, it's
> no longer a theory.
Yeah! You have a theory of music! Very good. It seems I really have to
ask one of my friends to buy your CD (I don't have a credit card). I
want to hear this sound. I'm sure it's very weird.
> The fact is that I took the set and used it for composition and the
> proof is the sound. So go listen, if you like. You might be
> surprised at how self-recursion and slow developing changes from
> something like imaginary numbers are very interesting. Of course,
> most of the time you don't get music. Just silence or white noise.
> Eventually, one gets familiar with Mandelbrot "theory" and knowing
> how and where the music is becomes intuitive.
I think that's a very good point. The thing is not only to have a good
theory. You also have to be able to use it. For example, it would be
extremely hard for me to calculate an electron trajectory in a
particle collider (special relativity is needed for that). An expert
in this field might do this in some minutes, and he could tell me an
approximated result before the calculation because of his intuition.
I think that this fractal music needs a lot of insight. You have to
explore the Mandelbrot set and you have to find out what happens to
the music if you change this parameter or that, you need a feeling
where the good music is in the set and so on.
> The best results so far were from the method I used for fractal
> pieces number five and six on my webpage. here is what I did (get
> ready for dimensions, although you may accept or reject how I make
> fractal music. The proof is in the music):
I HAVE to accept your way of making music. Everything else is
ridiculous, IMO. We are not talking about a physical theory (that can
be tested) here. The only thing I can do is not to like the music
you are making.
> Take a point in x-y space near to the Mandelbrot Set. Then, fix the
> x axis and continually take points with constant y-axis distance.
> Calculate iteration values for each point.
I hope I'm correct here: Iteration value means you count the
iterations until you get |Z_n|^2 > 2.
> Apply the values in sequence to pitches of 16th notes. [snip] When
> you plot iteration value vertically, the horizontal axis shows time
> transition and vertical axis shows tone pitch [snip]
Sounds as if you have done a lot of experimentation with the
Mandelbrot set. I don't know if this makes sense musically, but there
is something that came to my mind: Think about a point somewhere and a
line through that point that rotates around that point. You can now
plot iteration values along that line and use the rotation angle as
time variable. This would you periodically changing pitch values. You
could influence the period by the angular velocity. If you also move
the center of rotation, you'd get "periodic yet changing" music.
> So we have a bumpy surface now, even though it's still a plane... a
> plane with depth.
Perhaps you'll call me pedantic, but a plane has no depth. By
definition. If you plot iteration values the way you describe, you
have a 3D representation of the Mandelbrot set, which is no plane
anymore. Looks very good if you add shadows, like a mysterious plateau
with jagged cliffs.
> [snip] or pitch on a specified scale is decided by the remainder in
> dividing iteration by scale's-note-number
AFAIK, that's the way the usual pictures of the Mandelbrot set are
coloured.
> [snip] but if the upper limit of iteration is too small to the given
> scale's-note-number, iteration compressed excesively causes
> repetition of same note.
When I experimented with the Mandelbrot set a bit, I found that the
deeper you go into the set, the higher you have to choose the maximum
number of iterations, or the pictures become boring, because the set
is not calculated accurately enough. The edges of the set become
smooth, not at all what you expect.
> When the iteration value ends, that is a rest.
I don't understand that. Do you mean that you have exceeded the
maximum number of iterations, which would mean that the point belongs
to the set (approximately)?
> The same iteration's length determines the value of the note,
I didn't get that either. I'll try to explain what you are doing in my
words: You take some point, plot the number of iterations where you
get |Z_n|^2 > 2 on a line parallel to the y-axis through that
point. You use the number of iterations as pitch value in a sequence
of 16th note, which means that your line represents a sequence of 16th
notes. If the number of iterations exceeds some given value, you take
the corresponding 16th not as a rest. You change the point's position
and, at the new position, calculate a new sequence of 16th
notes. These notes are added to the last sequence, but with a time
delay. Correct? But how do you determine the note value? Would you
mind explaining again?
> [snip]
> Think of it as: an iteration value being small, Mandelbrot is in a
> period of full water and an iteration value being big, Mandelbrot is
> in a period of water shortage.
That reminds me again of the 3d pictures I've done once. You can
represent the set as a lake and the points not belonging to the set as
mountains. Gives very interesting pictures.
> The mood of the music, then, can be changed by changing the
> Mandelbrot iteration value.
If I understood you correctly, by iteration value, you mean the
maximum number of iterations from which on you consider a point
belonging to the set in this case.
> I strongly recommend that you listen to the fractal pieces 5 and 6
> that I wrote using this method, as it is extremely contrapuntal (as
> opposed to the slow, ambient, trancelike "peaceful" fractal music or
> the frantic "chaos" fractal music.) And I don't know anyone else
> who has used iteration value to create topographical mountains as
> both melodic and dynamic determinants. You might even like the
> music.
It seems I have to do that. I only hope my ears will survive ;)
Bye,
Christof
Christof Pflumm
Why that? I'll give him very much credibility on musical things, but
in science...
I think he mixes way too much philosophy into science and hasn't
learned the basics well enough.
When I would tell Justin: "Look, I know how Bach composed all that
beatiful music. He new that space had 3/2 dimension, with each of the
coordinate axis projected on 1/2 dimension. He then discovered that
music is not numbers but a flow of mass density in an additional
dimension that only exists in a parallel universe. He then found a way
how to describe that other dimension which resulted in his music."
Well, doesn't sound so bad. But then, Justin asks me: "O.k. if you know
all this, you can certainly compose some 5-part fugue?"
I reply, astonished a bit: "You don't believe my explanation? But it's
obvious!"
He asks me again to compose a 5-part fugue, but of course, I can't. I
haven't really discovered the secret of Bach's composition technique,
I have speculated. And if I don't want to be arrogant from my own
point of view, I have to admit that I have only speculated. And I also
have to admit that all those thousands of music theorist that looked
at Bach found FAR better explanations than myself.
Bye,
Christof
LstPuritan
>Yeah! You have a theory of music! Very good. It seems I really have to
>ask one of my friends to buy your CD (I don't have a credit card). I
>want to hear this sound. I'm sure it's very weird.
I'll get to the rest of your post, but:
All my music that I make public is free to download.
It is also on CD and the CDs aren't free,
but the MP3s of all my public music are free.
Christof Pflumm
> Christof wrote:
> >Yeah! You have a theory of music! Very good. It seems I really have to
> >ask one of my friends to buy your CD (I don't have a credit card). I
> >want to hear this sound. I'm sure it's very weird.
>
> I'll get to the rest of your post, but:
>
> All my music that I make public is free to download.
>
> It is also on CD and the CDs aren't free,
>
> but the MP3s of all my public music are free.
You are right of course! I somehow remembered it incorrectly. So it
seems I finally need an MP3 player.
How much of the money do you receive when I buy a CD from mp3.com?
Bye,
Christof
Radu
>
> Christof wrote:
> >It seems I really have to
> >ask one of my friends to buy your CD (I don't have a credit card).
Now I would doubt Christof credibility ...He was not found worth of
trust by his bank...hmmm...should we trust his physics allegations ?
>> I want to hear this sound. I'm sure it's very weird.
He already passes a judgement...before he actually heard the music
(which he derisively calls "this sound") ...Would anyone give him some
credit...I doubt it.
> All my music that I make public is free to download.
If it's free...is it worth something ? I doubt it....
Christof Pflumm
> LstPuritan wrote:
>>
>> Christof wrote:
>>> It seems I really have to
>>> ask one of my friends to buy your CD (I don't have a credit card).
>
> Now I would doubt Christof credibility ...He was not found worth of
> trust by his bank...hmmm...should we trust his physics allegations ?
Money is nothing! I'm living for pure science and nothing else! Who
needs something else than the glorious truth that nourishes the soul?
:)
>>> I want to hear this sound. I'm sure it's very weird.
>
> He already passes a judgement...before he actually heard the music
> (which he derisively calls "this sound") ...Would anyone give him some
> credit...I doubt it.
Ok. I'll take back the sound. It's music. But I still believe it's
weird (which doesn't have to be negative). And weird it has to be,
given the description given on Justin's web site. But chaotic would
perhaps be a better word.
>> All my music that I make public is free to download.
>
> If it's free...is it worth something ? I doubt it....
Listen to it and you'll find out. You are also passing a judgement
without having listened!
Bye,
Christof
LstPuritan
>> All my music that I make public is free to download.
>
>If it's free...is it worth something ? I doubt it....
Bach's music was free when he wrote it, aside from the tiny percentage he did
publish. So goes the 20th century; if some thing is good, it's expensive.
When something better comes along, it's worth half as much. When it's
obsolete, you get 3 for the price of 1. When it's useless, nobody wants one
anyways.
Music itself has absolute worth that is unchanging. No price tag can describe
this worth in dollars, so why try?
mp3 players:
www.winamp.com for PC.
www.panic.com for Mac.
My music is always free.
Adam Bravo
Mac users have nothing to panic about. There are no viruses for them (The
Love Virus has affected all 7 Mac users), no bad programs for them (No good
program, either), and no worry about their computers being stolen.
Deepak Subburam
> >It seems I really have to
> >ask one of my friends to buy your CD (I don't have a credit card).
Radu wrote:
> Now I would doubt Christof credibility ...He was not found worth of
> trust by his bank...hmmm...should we trust his physics allegations ?
When I was in Germany I heard from people (and noticed) that Germans
don't like credit and tend to buy all things with cash, even big
things like cars!
Deepak
Radu
>
> Radu <ra...@writeme.com> writes:
> Now I would doubt Christof credibility ...He was not found worth of
> > trust by his bank...hmmm...should we trust his physics allegations ?
>
> needs something else than the glorious truth that nourishes the soul?
> :)
1. One must step back to see the larger picture (Fractal was reality was
Zeno). My post was meant to sympathetically strike a chord from another
thread (Re: should we throw Justin to the lions ?)
2. Money is nothing ? So why do you ask Justin how much does he get from
his CD ?
3. Be cool, man ! Have some fun from time to time...
Radu
Radu
>
> Radu wrote:
> >> All my music that I make public is free to download.
> >
> >If it's free...is it worth something ? I doubt it....
>
> Bach's music was free when he wrote it, aside from the tiny percentage he did
> publish.
Fish are biting and the cotton is high...Suuuuummmmertiiiiiiime.......
Christof Pflumm
> 3. Be cool, man ! Have some fun from time to time...
What is that stuff? Never heard about "fun". What is it? Sounds
interesting and if you tell me to have some, I will try, of course!
RADU, RADU, RADU :)
BTW, I listened to some Poulenc. Not to the concerto for 2 pianos, but
some piano only music. Not my taste (yet, perhaps).
Bye,
Christof
Radu
> What is that stuff? Never heard about "fun". What is it? Sounds
> interesting and if you tell me to have some, I will try, of course!
You are kidding ! Just the fact that you chosed to be a physicist points
to a higher intelligence level and sense of humour. If you also indulge
in programming then you are almost at the top (after architects).
> BTW, I listened to some Poulenc. Not to the concerto for 2 pianos, but
> some piano only music. Not my taste (yet, perhaps).
Frankly, I heard the concerto on the radio then I searched it for years
until I found it in a Paris music shop. It is the only "piece" of
Poulenc I heard.
Christof Pflumm
> Just the fact that you chosed to be a physicist points to a higher
> intelligence level and sense of humour.
I've never been good at jokes, but if one doesn't try, it will never
get better.
> > BTW, I listened to some Poulenc. Not to the concerto for 2 pianos, but
> > some piano only music. Not my taste (yet, perhaps).
>
> Frankly, I heard the concerto on the radio then I searched it for years
> until I found it in a Paris music shop. It is the only "piece" of
> Poulenc I heard.
They've got a lot of Poulenc here in Karlsruhe (300.000 inhabitants)
in my favourite CD shop. Shame on Paris!
Bye,
Christof
LstPuritan
>> >> All my music that I make public is free to download.
>> >
>> >If it's free...is it worth something ? I doubt it....
>>
>> Bach's music was free when he wrote it, aside from the tiny percentage
>he did
>> publish.
>
>Fish are biting and the cotton is high..
Seems you are too.
>Suuuuummmmertiiiiiiime.......
Stop.
Christof Pflumm
> I will admit that in the theory of relativity, I'm an agnostic-
> to disprove it,
What evidence?
> yet it makes sense.
It doesn't matter whether a physics theory makes sense. Sense is
something that is built into humans mainly for the sake of survival
IMO. We know the world around us and how it behaves under normal
circumstances. But evoulution hasn't given us senses to detect
atoms. Why do people think that common sense has anything to do with
physics?
> But never have I heard someone say that the equations contradict
> themselves. Maybe the equations contradict the implications, but
> never themselves.
I'm not that good at relativity either, but if the formulas would
contradict themselves or the implications, relativity would not be
used anymore. You could not trust in it, because there would have to
be a logical flaw somewhere.
Bye,
Christof