Re: infinity
brian a m stuckless
Once upon a time (before time, actually), BEFORE CREATiON,
GOD lived in VACUUM, He *HAD* to CREATE a life for Himself.!!
$ SiMPLE ATHESiM
ATHEiSM is the SiMPLE, virtual, OBjECTiFiCATiON of GOD.!!
But jUDiSM is the COMPLEX virtual OBjECTiFiCATiON of GOD.!!
And jUDAEO CHRiSTiANiTY more virtual OBjECTiFiCATiON of GOD.!!
But, jESUS CHRiSTiANs say NO virtual OBjECTiFiCATiON of GOD.!!
* VACUUM vs CREATiON.!!
VACUUM is a MENTAL state or condition, ..in the mind or out.!!
(VARiOUS vacu ONLY exist in SQUEEZED Swiss-cheese-LiKE minds.)
* No iNFiNiTY
There NEVER ever WAS, yet, even ONE (1) iNFiNiTY.!!
There never EVER will BE ..even ONE (1) iNFiNiTY.!!
VERY sincerely u c,
```Brian
>><> >><> >><> >><> >><>
Dirk Bruere at Neopax
> $ BEFORE creation and SUBsequent evolution
> Once upon a time (before time, actually), BEFORE CREATiON,
> GOD lived in VACUUM, He *HAD* to CREATE a life for Himself.!!
>
> $ SiMPLE ATHESiM
> ATHEiSM is the SiMPLE, virtual, OBjECTiFiCATiON of GOD.!!
> But jUDiSM is the COMPLEX virtual OBjECTiFiCATiON of GOD.!!
> And jUDAEO CHRiSTiANiTY more virtual OBjECTiFiCATiON of GOD.!!
> But, jESUS CHRiSTiANs say NO virtual OBjECTiFiCATiON of GOD.!!
And we Heathens say STFU you YHVH ass kisser.
--
Dirk
The Consensus:-
The political party for the new millenium
http://www.theconsensus.org
Ron Baker, Pluralitas!
"Dirk Bruere at Neopax" <dirk....@gmail.com> wrote in message
news:3ptiaeF...@individual.net...
> brian a m stuckless wrote:
You misspelled his name. It is "Stuck Brainless".
<snip>
Autymn D. C.
-Aut
donsto...@hotmail.com
principles ruing all. Science and religion become one. No local
system/global system fallcies to face; all is consistent and complete.
Godel turns over in his grave. All knowledge becomes available to a
properly cleansed mind, cleansed of falsehoods leaned during one's
upbringing. What more could one ask for???????? Its groovey.
brian a m stuckless
ATHEiSM the VERY most SiMPLE virtual OBjECTiFiCATiON of GOD.!!
PANTHEiSM the SiMPLE virtual OBjECTiFiCATiON of His SYNONYM.!!
jUDiSM more COMPLEX virtual OBjECTiFiCATiON of THAT one GOD.!!
jUDAEO cHRiSTiANs MOST virtual OBjECTiFiCATiON EVER, of GOD.!!
jESUS CHRiSTiANs say "NO virtual OBjECTiFiCATiON of IAM He".!!
* CREATiON vs VACUUM.!!
VACUUM is a MENTAL state or condition, ..in the mind or out.!!
(VARiOUS vacu ONLY exist in SQUEEZED Swiss-cheese-LiKE minds.)
$ BEFORE creation and SUBsequent evolution
Once upon a time ( ..before time, actually), BEFORE CREATiON,
GOD lived in VACUUM; He *HAD* to CREATE a Life for Himself.!!
* NO iNFiNiTY at all.!!
There NEVER ever WAS, yet, even ONE (1) iNFiNiTY.!!
There never EVER will BE, even ONE (1) iNFiNiTY.!!
VERY sincerely u c,
```Brian
Autymn D. C.
brian a m stuckless
ATHEiSM the VERY most SiMPLE virtual OBjECTiFiCATiON of GOD.!!
PANTHEiSM the SiMPLE virtual OBjECTiFiCATiON of His SYNONYM.!!
jUDiSM more COMPLEX virtual OBjECTiFiCATiON of THAT one GOD.!!
jUDAEO cHRiSTiANs MOST virtual OBjECTiFiCATiON EVER, of GOD.!!
jESUS CHRiSTiANs say "NO virtual OBjECTiFiCATiON of IAM He".!!
* CREATiON vs VACUUM.!!
VACUUM is a MENTAL state or condition, ..in the mind or out.!!
(VARiOUS vacu ONLY exist in SQUEEZED Swiss-cheese-LiKE minds.)
$ BEFORE creation and SUBsequent evolution
Once upon a time ( ..before time, actually), BEFORE CREATiON,
GOD lived in VACUUM; He *HAD* to CREATE a Life for Himself.!!
* NO iNFiNiTY at all.!!
There NEVER ever WAS, yet, even ONE (1) iNFiNiTY.!!
There never EVER will BE, even ONE (1) iNFiNiTY.!!
VERY sincerely u c,
```Brian
'*:-.,_,.-:*'``'*:-.,_,.-:*'``'*:-.,_,.-:*'``'*:-.,_,.-:*'
____ _ _ _ _
| _ \ | | ___ _ __ | | __ | | | |
| |_) | | | / _ \ | '_ \ | |/ / |_| |_|
The BiG | __/ | | | (_) | | | | | | < _ _ _
|_| |_| \___/ |_| |_| |_|\_\ (_) (_) (_)
.-:*'``'*:-.,_,.-:*'``'*:-.,_,.-:*'``'*:-.,_,.-:*'``'*:-.,
>><> >><> >><> >><> >><>
Autymn D. C. wrote:
>
> Universe != God
Tony Orlow
metaphysics to the universe which is eternal and unchanging? Are these your
"cybernetic" principles? Science and religion should become more integrated for
sure. Where do you get your ideas? Oh, and what does this have to do with
mathematical infinity, and what is your opion of set theory, and are you
involved in information science in any sense? Just wondering.
--
Smiles,
Tony
tadchem
Tony Orlow wrote:
> donsto...@hotmail.com said:
> > I worship the Universe. Pantheism. Universe = God. With cybernetic
> > principles ruing all. Science and religion become one. No local
> > system/global system fallcies to face; all is consistent and complete.
> > Godel turns over in his grave. All knowledge becomes available to a
> > properly cleansed mind, cleansed of falsehoods leaned during one's
> > upbringing. What more could one ask for???????? Its groovey.
> >
> >
> Sounds pretty groovy, Don. But, have you considered that there is an underlying
> metaphysics to the universe which is eternal and unchanging?
Being a physical scientist, I cannot help but observe daily that there
is an underlying *physics* to the universe which is eternal and
unchanging.
I start every day by testing gravity even as I get out of bed. ;-)
It is a simple thing; it works the same at all times, in all places,
and on all things. It has all the power, immanence, justice,
immortality, fairness, mercy, and attention to detail that one could
expect from a deity.
Tom Davidson
Richmond, VA
Tony Orlow
> Universe != God
>
>
god->universe->life->god
--
Smiles,
Tony
brian a m stuckless
Ross A. Finlayson
universe and the tachyon universe. The Big Bang, measured to be so
many years ago, is actually infinitely many years ago, and as we learn
more about it we'll discover ever longer spans. As entropy increases,
it goes towards a state where entropy's infinite and the tachyon
universe is a point. Then it becomes the Big Bang of the tachyon
universe, the tachyon universe becomes the regular universe, and round
and round and round she goes.
sci.physics_20050608.rtf:The universe is infinite where functions
between physical objects are physical objects, and infinite sets are
equivalent. ZF is inconsistent, etcetera.
sci.physics_20050610.rtf:If you're really interested on arguing about
the transfinite cardinals, you can find many friends on sci.math and
sci.logic. I argue that infinite sets are equivalent, because of
induction. I use that to discuss mappings between the naturals and
reals, and things like the infinitesimals necessarily in a variety of
nonstandard models of the real numbers. That is for some
considerations of analytic results on discrete point sets. Then, I go
off about the null axiom theory, and various implications of
completeness of any theory. That leads me to refer to modern technical
philosophers and their works to help explain the paradoxes in your
theories.
sci.physics_20050612_b.rtf:I discuss this on sci.math, I think it's
about nonstandard real numbers that are at once the complete ordered
field as determined from any depth-first traversal and partially
ordered ring from any breadth-first traversal, with the same elements
in either case but equation or identity within the one or the other.
It's about well-ordering the real numbers and necessary conclusions
about the real numbers. From their continuity, there are only real
numbers between zero and one, and a combination of Cantor's first and
the transfer and well-ordering principles lead to basically the proof
that iota values exist among the reals, in the sufficiency of
infinitesimals.
sci.physics_20050613.rtf:There are a variety of nonstandard models of
the reals with these various considerations. For example, in Newton's
reals iota is basically the first fluxion, the fluxion to the unit. In
Leibniz's reals, it's dx. In the modern theories of surreal numbers,
there's basically a limit infinitesimal of sorts, in a similar way as
to how there are limit ordinals like zero and infinity, but differently
as I don't know anybody else who calls them that. The hyperreals are
similar to the Newtonian reals and basically admit a first fluxion or
iota value. Other nonstandard models of the reals, and numbers in
general, besides Robinso(h)n's and Conway's exist.
sci.physics_20050613.rtf:On the quantum level, and in terms of
dimensionality, the cumulative hierarchy of ordinals, and so on, on the
quantum level I believe there are a variety of parallels to be drawn
between various point particles and various infinitesimals, both on the
line and not. In terms of dimensionality and why there are three
apparent space dimensions that has to do with extensions of the null
axiom theory, which is the only possible theory that can be strong,
consistent, complete, and hopefully concrete, in terms of mathematical
logic.
sci.physics_20050613.rtf:The universe is infinite and infinite sets are
equivalent.
sci.physics_20050613_b.rtf:About the universe being infinite, that is
about a set-theoretical, or logical, or categorical or type based, or
here physical universe, and the unbounded extent of objects in that
universe via unrestricted comprehension. Say there are two point
particles and gravity. The first, second, ..., n'th derivative of
motion are each a physical object, like a proton/electron pair is 1
amu, having to do with units. While that might be simply an instanton,
with regards to the singular and plural, it is yet not. All the other
functions between those mathematical objects are as well mathematical
objects, or here physical objects, as are theirs ad infinitum, so there
are infinitely many of them. As are theirs, where the number of
functions would be a greater "cardinality", then there is basically the
set-of-all-sets being its own powerset as the physical universe,
including thoughts and other ephemera, via identity the powerset is not
indistinct from the set. Infinite sets are equivalent.
sci.physics_20050613_b.rtf:About three dimensions, and this is rather
vague, I think it has to do with one scale and then the scale
infinitely large and the one infinitely small and just how they are
adjacent in that sense, each is appreciable. That has to do with my
conceptions of "scalar infinities" and "scalar infinitesimals."
sci.physics_20050614.rtf:Where these "point" particles are discussed,
on the quantum level everything is as well a "wave", there is the
"particle/wave" duality. Is that still held true? I think the physics
can show us something about the mathematics. That's where I think a
point particle on the (1-d) line is a point, and the discrete point in
the n-space is the n-sided point, towards re-Vitali-ization of
infinitesimals in measure theory.
sci.physics_20050614_c.rtf:That's a digression from some considerations
of the real numbers as basically the best or most accessible example of
a continuum, although there was Spinoza who saw the natural numbers of
a continuum of sort. I'm a non-traditionalist in terms of the natural
numbers and reals because I think there can be a function one-to-one
and onto between the naturals and in the most utilitarian way the unit
interval of the real numbers. That's counter to the status quo's
opinion that that is not possible as a result of Cantor's theorem(s).
I extend Cantor's first theorem to support the existence of a least
positive real, or iota-value, and infinite sets are equivalent via
induction. Something like the infinitesimal analysis, also known as
the integral calculus, works very well where dx is the unit iota value.
So, not all aspects of my systems are novel, in this case they just
reflect a return to the basically post-classical, pre-"standard",
infinitesimals. It might be of use to further investigate Schmieden
and Laugwitz pre-Robinsonian infinitesimals, where they have the reals
as a partially ordered ring with a "rather restricted" transfer
principle, I have the reals being complete ordered field as closure and
partially ordered ring as contiguous, sequential points.
sci.physics_20050618_b.rtf:When I get to thinking about the infinite
and why infinity equals negative one, it's something along the lines of
"infinity is greater than everything" being the same thing as
"infinity is less than nothing" to "infinity is less than zero."
sci.physics_20050618_b.rtf:So, "negative absolute temperature" being
"greater (not less) than any finite temperature" is similar to
"negative one" being "infinity."
sci.physics_20050618_b.rtf:It seems easy to point out that this is a
fallacious argument. Infinity is obviously greater than zero, for it
to be as well less than zero would appear to violate trichotomy of
numbers, that x is exclusively one of less than, equal to, or greater
than y. It seems that the trichotomy only holds in given regions of
various sizes, and the region containing zero and infinity in this
non-trichotomous way is just those two elements.
sci.physics_20050618_b.rtf:Some people have that the infinite set of
finite integers necessarily contains infinite integers, or an infinite
integer, which is the same conclusion.
sci.physics_20050618_b.rtf:ZF is inconsistent. The universe is
infinite and infinite sets are equivalent.
Virgil
Tony Orlow <ae...@cornell.edu> wrote:
> Autymn D. C. said:
> > Universe != God
> >
> >
> god->universe->life->god
TO going in circles again.
Ross A. Finlayson
quarks etcetera and possible consideration of further depths of
organization of "point" paradigm, as opposed to basically little
segments of continua, I get to thinking that there is currently around
a hundred orders of decimal magnitude between the largest and smallest
objects of the current theories, from galactic structures of the
universe to quarks and leptons and tau neutrinos, where basically I
think the universe is infinite and where physical objects are
mathematical objects and functions between physical objects are
physical objects the universe is infinite and infinite set are
equivalent, with the universe basically equating to the ur-element,
that leads via duality to the consideration of a "tachyon universe",
which I just reread about in Gordon Dickson's "Time Storm", via
duality. I digress. At the extrema of the scale of these structures,
I expect that the physical phenomena are going to reflect some funny
features of infinity and its reciprocal and inverse the infinitesimal.
In no small part, that's due to the exact accuracy of infinitesimal
analysis, the integral calculus, in the meso-scale, defined and
defining the infinital micro- and macro- scales.
Nick
creation how is this
atheism?
Infinity is a concept.
I say the only thing that is infinite is the future.
Ross A. Finlayson
No.
Do you have a mathematical statement about (insert your favorite
synonym for infinity here) that is relevant to the foundations of
mathematical logic as practiced?
If not, in general, no.
Ross
brian a m stuckless
THERE is ALREADY some, quite a lot actually,
THERE is ALREADY, too, MUCH gone, in fact.!!
VERY sincerely u c,
```Brian
Lloyd Parker
Lloyd Parker
>universe and the tachyon universe. The Big Bang, measured to be so
>many years ago, is actually infinitely many years ago,
No it is not.
> and as we learn
>more about it we'll discover ever longer spans.
Wrong again.
>As entropy increases,
>it goes towards a state where entropy's infinite
3rd strike. You're out.
>and the tachyon
>universe is a point.
Is that where the Borg live?
Tony Orlow
Is this related to mass being the product of light speed on a massless
particle? Can a particle actually go faster than light? I am not sure about
this, theory about neutrinos notwithstanding. In terms of infinite and
infinitesimal analysis, I agree that it is bound to help with problems
regarding zeroes and infinities, such as speed of light, masslessness, absolute
zero, event horizons, etc, as well as on the spatially smallest and largest
scales. I also like the mention of the "segments of continua". We may not be
too different in some of our thinking, Ross, although I obviously don't
consider all infinite sets the same. So many fences to choose sides of, we all
end up alone in our own yard if we do any of our own thinking. :D
--
Smiles,
Tony
Ross A. Finlayson
OK.
Then I wonder, what was there "before" the Big Bang? If all matter and
energy of the universe comprised some protoplasmal point at the Big
Bang, and the universal stopwatch started ticking, well, I am not very
familiar with the current cosmological models of the nature of space
and time at the Big Bang.
What if the Big Bang of our universe took place in basically some
region of a still larger cosmiverse, and there are other universes, in
terms the entire region and all contents as from a Big Bang? Basically
that's consideration of larger structures than bordered by the
wavefront of light from the Big Bang formation event of our universe.
Why do some galaxies appear to be going in directions that do not seem
to match their apparent age and formation? Where did they come from?
Maybe at the Big Bang, the tachyon universe was infinite, in extent and
entropy, and as the universe goes flat the tachyon universe goes to a
point?
A tachyon is basically saying, there's a mathematical object that is
basically the opposite of a photon, but it goes faster than light so it
can't be in the universe, so it's in the tachyon universe. They might
be purely mathematical, but to them so are the photons. It's kind of
like the projection of an instanton to all dimensions.
I wonder about basically whether time scales vary in cosmological terms
pointing to the Big Bang.
About point particles as infinitesimals, the more exactly the mass of
point particles is measured, the smaller they get. Is that not so?
There've only been predicted and experimental masses of the quarks for
some thirty years, or perhaps longer I don't know, and over that time
they've decreased considerably.
Ross
Ross A. Finlayson
although his laws are excellent approximations for many systems
perceptible on the unaided human scale, and so has the integral
calculus. While that is so, where in its formation the integral
calculus was, and in many ways is, the infinitesimal calculus, where
the integral with its summand notation, the integral bar is an S for
summation, is exactly the same thing as the area of point widths, the
fluents and fluxions, stopping at the first one and calling it iota the
least positive real number, in establishing that system, it may be
possible to apply associated considerations of the continuous and
discrete to physical entities that match those properties.
sci.physics_20050518.rtf:I hope to introduce to you some mathematical
reasonings that would agree with that statement. Over the past few
years I've spewed forth a variety of considerations of the mathematical
logic of infinity.
sci.physics_20050518.rtf:Is that really so? Is negative temperature
really infinite? That seems somewhat counterintuitive.
sci.physics_20050519.rtf:Anyways, I think that's kind of funny. In set
theory, it's like considering infinity, or perhaps more technically
Ord, the order type of all ordinals. Ord is greater than anything
else, so it's less than nothing. One method of constructing the
ordinals is that nothing, or the empty set, is zero. So, infinity is
less than zero, but only by itself, where it is greater than any finite
ordinal including zero, where "inclusion" may well make it mean a
non-zero ordinal.
sci.physics_20050521.rtf:The universe is infinite and infinite sets are
equivalent. Any theory of everything is necessarily a logical theory
of everything, and ZF is inconsistent. The electron and photon are
point particles, but so are the other particles. There is not a
theoretical smallest particle, except for any of those. That's a
similar consideration to that the reals, nonstandardly, have a smallest
positive real number.
sci.physics_20050523.rtf:A funny thing happened on the way to the
infinite.
sci.physics_20050531.rtf:In real numbers with a scalar infinitesimal,
Vitali's result does not hold and all sets of numbers are measurable.
ZF is inconsistent.
sci.physics_20050531_b.rtf:That's about infinitesimals, I'm trying to
understand particles in terms of infinitesimals instead of Planck, the
discrete and continuous etcetera. If you know of things for which that
is true, I'm interested in hearing about that.
sci.physics_20050602.rtf:I got to examining the real numbers and the
difference between a point on a line and a point in space. Basically
the point on the line is "one-sided", it is defined, in a way, as the
next bead on the string, but in a blur. I consider rephrasing that.
So anyways, the contiguous sequence of points in a line leads to that
the point, with point width, has only one side. Then, the discrete
point in space, in a one-dimensional space, basically is two-sided.
It's still point width, but it can be defined from the positive or
negative side, or rather, it represents an endpoint, with basically a
difference between endpoints and non-endpoints of a line, in one
dimension. In two-dimensions then there is geometric consideration of
basically the geometric mutation of the circle or regular polygon in
the infinitely large and in this case moreso the infinitesimally small.
David R Tribble
> Then I wonder, what was there "before" the Big Bang?
Indeed.
> About point particles as infinitesimals, the more exactly the mass of
> point particles is measured, the smaller they get. Is that not so?
No, it's not. The current limit of anything physical is the Planck
scale, 10^-35 m. The conclusion is that the universe has a smallest
distance, below which you can't get anything smaller. Particles are
not, in fact, zero-width points, even though a lot of physics up until
the last 20 years or so modeled them as such.
Very little of this, though, has anything to do with the mathematics
of set theory and infinity.
mme...@cars3.uchicago.edu
>Ross A. Finlayson wrote:
>> Then I wonder, what was there "before" the Big Bang?
>
>
>
>> About point particles as infinitesimals, the more exactly the mass of
>> point particles is measured, the smaller they get. Is that not so?
>
>scale, 10^-35 m.
No, it is not. That's coffee table book stuff.
> The conclusion is that the universe has a smallest distance, below
>which you can't get anything smaller.
No, again, there is no such conclusion.
Mati Meron | "When you argue with a fool,
me...@cars.uchicago.edu | chances are he is doing just the same"
Autymn D. C.
Autymn D. C.
> Being a physical scientist, I cannot help but observe daily that there
> is an underlying *physics* to the universe which is eternal and
> unchanging.
>
> I start every day by testing gravity even as I get out of bed. ;-)
>
> It is a simple thing; it works the same at all times, in all places,
> and on all things. It has all the power, immanence, justice,
> immortality, fairness, mercy, and attention to detail that one could
> expect from a deity.
all wrong rubbish
Ross A. Finlayson
quantum mechanics and relativity representing ultimately micro- and
macroscale essentially combinatoric and continua-based ramifications of
very large or small numbers or "infinity", my naive perception is that
that is what those things are. About the consideration of the
continuum in nature, if there are straight lines then there are circles
and if there are circles then there are irrational quantities. A
raindrop is a droplet.
sci.math_20050211.rtf:If so, then the universe has infinitely many
physical objects.
sci.math_20050212.rtf:I forgot explicitly the principle of induction.
Ah, transfinite induction: plain induction is plenty, thank you, for,
for example, that a process with infinitely many steps can trisect the
arbitrary angle with edge and compass. Then again, a circle is
approximated by the regular polygon as the number of sides goes to
infinity.
sci.math_20050212.rtf:If so, the universe has infinitely many physical
objects, and, infinite sets are equivalent.
sci.math_20050213.rtf:When I consider that, I consider relations of
concrete physical objects to be concrete physical objects, and thus: a)
there are infinitely many concrete physical objects, and b) infinite
sets are equivalent.
sci.math_20050213.rtf:When I do consider the relations among concrete
physical objects to be concrete physical objects, that doesn't disagree
with my set theory, where any and every thing's a set. That's both
"each thing is a set" and "everything is a set". Where that's so that
set of all sets is its own powerset. It's rigorously been shown that
that leads into either a: contradiction with the powerset result in
that it doesn't apply to all sets, or b: some nullification of the
powerset result. It's conceivable for that to be the same source of
cognitive dissonance as Burali-Forti and model extensions, and to be
honest I'd be surprised that not more have reached the notion of
conflating infinity and the void, except that that's a philosophical
tenet of humanity since probably before recorded history.
sci.math_20050214.rtf:You talk about V and ordinals alpha, that's the
same thing as talking about N and natural integers. There's an ivory
tower cottage industry of stacking finitely many elements towards
infinity and relabelling the relevant concepts many times over, if you
want some insight it would seem more rational to address the actual
explanation of these things as themselves, intensionally.
sci.math_20050214.rtf:I suggest discarding all the non-logical axioms
and just theorizing from tautology the axioms of ZFC besides
regularity. That's about a vague notion that infinite sets can not be
regular, well-founded.
sci.math_20050215.rtf:I got to thinking about the atomic particles,
say, point masses, for simplicity's sake, molecular atoms. Then,
there's a gravitational force between each pair of those in the
universe. If there are countably infinitely many point masses, then
there would be basically N^N functions, or NxNxNx..., and each one of
those mappings or pairs represent a vector of gravitational force, and
there would be uncountably many of those.
sci.math_20050215.rtf:Thus the consideration of elements of the
physical universe leads to similar considerations of elements of the
universe of logical discourse: U, the universe, the set of all sets.
Where that is so, then in a real or concrete way there is evidence a)
the universe is infinite, and b) infinite sets are equivalent.
sci.math_20050215.rtf:Then again, I already think the universe is
infinite and that infinite sets are equivalent so I'm biased in my
preconceptions, but that does agree with this rationale, as does that
the set of all sets is its own powerset.
sci.math_20050215.rtf:Here's something for correction if I'm wrong:
there's no theoretical limit on the number of subatomic particles of
the neutron in the standard model. Where that's so in the large and in
the small the universe is infinite.
sci.math_20050215_b.rtf:Infinite sets are equivalent. I think the
actual infinite _is_ necessary for the explanation of the physical.
hanson
news:1128145016....@f14g2000cwb.googlegroups.com...
> all wrong rubbish
>
[hanson]
hmmm... "rubbish"?.... not "deity" like?.....hhmmm... OK, then,
listen hogie: Instead of making such a short quasi intellectual
discourse into own "rubbish" just demonstrate to us a convincing
counter proof. Go up to the fifth floor, open a window and do
step out. When you arrive at and encounter the close proximity
of the electromagnetic cushion of the calcium-silico aluminate atom
network, kindly do report back with your exiting findings, of how
you convinced/managed/overpowered the deity-like properties
of gravity to act otherwise.
Good luck on your voyage down!
Tom Davidson, I like your very nice (original?) take on the issue,
illustrating how much interwoven physics and psychology really is.
Like has been said so many times before: "Physics is a social
enterprise", a fact that was beautifully highlighted here by her
dyslexic "rubbish" comment.
ahahaha.... ahahaha... ahahahanson
Autymn D. C.
> [Dyslexia]
[lysdexia]
> > all wrong rubbish
> >
> [hanson]
> hmmm... "rubbish"?.... not "deity" like?.....hhmmm... OK, then,
> listen hogie: Instead of making such a short quasi intellectual
> discourse into own "rubbish" just demonstrate to us a convincing
> counter proof. Go up to the fifth floor, open a window and do
> step out. When you arrive at and encounter the close proximity
> of the electromagnetic cushion of the calcium-silico aluminate atom
> network, kindly do report back with your exiting findings, of how
> you convinced/managed/overpowered the deity-like properties
> of gravity to act otherwise.
> Good luck on your voyage down!
http://egroups.com/message/free_energy/18907
http://groups.google.com/group/alt.sci.physics/browse_frm/thread/ed2d7581f100f250/186cbbc223bd6856?q=Autymn+arbitrary+advancedphysics&rnum=1#186cbbc223bd6856
http://groups.google.com/group/sci.physics/browse_frm/thread/1dd958603e069763/d2cf56b39252dc4c?q=Autymn+arbitrary+advancedphysics&rnum=2#d2cf56b39252dc4c
PD
One of the things that you're presuming is that time is an axis that
extends to minus infinity. That is, you're presuming that every event
has a "before". Modern cosmology doesn't presume that.
Ross A. Finlayson
>
> One of the things that you're presuming is that time is an axis that
> extends to minus infinity. That is, you're presuming that every event
> has a "before". Modern cosmology doesn't presume that.
>
It's kind of like: say the entire universe of everything physical
began with the Big Bang. Then, it seems consensus currently has there
not being a Big Crunch, instead towards heat death of the universe, or
cold death. Then, somehow, that becomes another Big Bang, because,
when everything is all together then that's the same in some sense as
there being nothing anywhere, because of short circuits in logic, and
the Liar paradox.
That's like saying in the context of infinity that infinity, ... is
zero, or infinity, is negative one.
It's similar in consideration to the rationalization of temperature, in
terms of negative temperature, degrees Kelvin. There is no such thing
as less than absolute zero, right? That would seem to be the intuitive
notion, what with that all temperatures are measured in terms of
positive degrees Kelvin, compared to absolute zero, the cessation of
random-walk Brownian motion of particles., if I use those words
correctly. Where that might seem to be the case, there is the notion
among physicists I hear that negative temperatures are actually hotter
than any finite positive temperature.
It's like the notion that there is no first point on a circle. Select
one, the origin is anywhere. It's like the projectively extended
reals, with a point at infinity that is negative infinity.
Why are there three space dimensions? What did Feynman mean by that?
So, just like modern cosmological models might not have moments
"before" the Big Bang, there aren't temperatures below absolute zero or
naturals less than zero. Yet, in some senses, it's possible to
rationalize why there are.
Good day,
Ross
hanson
>> tadchem aka Tom Davidson wrote:
>>> Being a physical scientist, I cannot help but observe daily that there
>>> is an underlying *physics* to the universe which is eternal and
>>> unchanging.
>>> I start every day by testing gravity even as I get out of bed. ;-)
>>> It is a simple thing; it works the same at all times, in all places,
>>> and on all things. It has all the power, immanence, justice,
>>> immortality, fairness, mercy, and attention to detail that one could
>>> expect from a deity.
>>
>> > all wrong rubbish
>> >
[hanson]
>> hmmm... "rubbish"?.... not "deity" like?.....hhmmm... OK, then,
>> listen hogie: Instead of making such a short quasi intellectual
>> discourse into own "rubbish" just demonstrate to us a convincing
>> counter proof. Go up to the fifth floor, open a window and do
>> step out. When you arrive at and encounter the close proximity
>> of the electromagnetic cushion of the calcium-silico aluminate atom
>> network, kindly do report back with your exiting findings, of how
>> you convinced/managed/overpowered the deity-like properties
>> of gravity to act otherwise.
>>
>> Tom Davidson, I like your very nice (original?) take on the issue,
>> illustrating how much interwoven physics and psychology really is.
>> Like has been said so many times before: "Physics is a social
>> enterprise", a fact that was beautifully highlighted here by her
>> dyslexic "rubbish" comment.
>> ahahaha.... ahahaha... ahahahanson
>
a) http://egroups.com/message/free_energy/18907 says: "browser is
not accepting our cookies"... [hm... I am not into cookies.]
b)
http://groups.google.com/group/alt.sci.physics/browse_frm/thread/ed2d7581f100f250/186cbbc223bd6856?q=Autymn+arbitrary+advancedphysics&rnum=1#186cbbc223bd6856
says " Forces have been arbitrary" & refers to:
c) http://www.advancedphysics.org/viewthread.php?tid=2154
which complains that "The page cannot be found"... [Sorry about that, Dyslexia]
d)
http://groups.google.com/group/sci.physics/browse_frm/thread/1dd958603e069763/d2cf56b39252dc4c?q=Autymn+arbitrary+advancedphysics&rnum=2#d2cf56b39252dc4c
a post in which
1) Dy states: "Decay the electron by putting it near an event horizon, then
sapping its strength until it becomes a foton and neutrino"....
[Interesting speculation, Dy. Dearly departed Franz Heymann posted long
time ago that the neutrino maybe an electron without its charge.]
2) Dy states: "the foton has a far-field massive pseudoparticle, as they say.
I'd just call it a proxy particle". [... ahahaha... Interesting speculation, Dy.
Now could you express that in very simple and short classical terms without
resorting to pseudos and/or proxys?]
3) Dy states: "A normal time machine that takes its passenger back will only
serve amnesia"... "Or one should try finding a universe-scale time machine,
including one that skips universes so that one could find alternate selves
to molest"... [ahahaha... AHAHAHA... sorry, babe, I am not into neither
finding alternate selves nor into molestations.... ahahaha... but hey, whatever
turns you on... ahahaha...]
4) Dy states: "how to make a tunnel and elevator of arbitrary depth"
5) Dy states:"how to launch into orbit without onboard propellant and costly
drag"
6) Dy states:"how to use less propellant for arbitrary ballistic speeds, that
NASA can't figure out"
7) Dy states:"how to kick NASA and JPL in the arse"
8) Dy states:"how to make a lightsaber"
9) Dy states:" how to accelerate matter to c (five screens down, after the
asterisk)"
10) Dy states:"how to fix maths and write new maths".... [AHAHAhaha...
I think I've just heard one of those alternate selves groan. Big time.....]
11) Dy states:"how to make over the Standard Model"... to which....
>>>Mark Martin wrote:
>>>>> Autymn just got herself banned from advanced physics.org
>>>>> for her doo-doo.
12) Dy states: "No, they got me, Autymn, & banned because they think
losing my contributions is preferable to having to know what they're writing
wrong. And they think that people who correct people's spelling in private
should be kicked off, even though I was also trying to help tutor them with all
the science questions. They harassed me and didn't care. I cared, and
complained, and fixed, so they call me the harasser because they're
cretins"... [AHAHAHA... I wonder why they would that, Dy?... ahahaha..]
(13) Dy states: "my, lysdexia's, profile:"
http://forums.about.com/dir-app/bbcard/profile_center.asp?webtag=ab-physics&uName=lysdexia
But it says here, unfortunately: "The page you are looking for is currently
unavailable." [hm... hm... ahahaha... nobody's home at Dy's, huh?.....]
>
Hey, dudie Dy, it sounds like life's for you a bowl of cherries with its all
its blossoms, but never mind and fuck the pits, right?... ahahaha....
ahahaha... ahahaha... Thanks for all the laughs dudie, I will read all that
wisdom of yours one day, time and fancy depending, because you sure
have the fantasy to drive physics forward. I shall look whether I can find
in your expressions a connection to reality from where I'd like to connect
to your lofty realms. Till then, dear, don't get lost out there, somewhere...
BTW Dy, you still haven't explained "of how you convinced/managed/over
powered the deity-like properties of gravity to act otherwise"....AHAHAHA...
ahahaha... ahahanson
Tony Orlow
--
Smiles,
Tony
brian a m stuckless
ATHEiSM the VERY most SiMPLE virtual OBjECTiFiCATiON of GOD.!!
PANTHEiSM the SiMPLE OBjECTiFiCATiON of His virtual SYNONYM.!!
jUDiSM more COMPLEX virtual OBjECTiFiCATiON of THAT one GOD.!!
jUDAEO cHRiSTiANs MOST virtual OBjECTiFiCATiON ever, of GOD.!!
jESUS CHRiSTiANs say "NO virtual OBjECTiFiCATiON of IAM He".!!
* CREATiON vs VACUUM.!!
VACUUM is a MENTAL state or condition, ..in the mind or out.!!
(VARiOUS vacu ONLY exist in SQUEEZED Swiss-cheese-LiKE minds.)
$ BEFORE creation and SUBsequent evolution
Once upon a time ( ..before time, actually), BEFORE CREATiON,
GOD lived in VACUUM; He *HAD* to CREATE a Life for Himself.!!
$ NO iNFiNiTY at all.!!
There NEVER ever WAS, yet, even ONE (1) iNFiNiTY.!!
There NEVER ever WiLL BE ..even ONE (1) iNFiNiTY.!!
$ by deeds you know them
jESUS CHRiSTiANs say, "IAM.!!" note with OPEN ARMs;
..jUDAEO cHRiSTiANs, "I AM.!!", pointing iNWARD.!!
"IAM hath brought Me onto you.!!"
But note, i tell you this now so you will know then.!!
```Brian
Virgil
Tony Orlow <ae...@cornell.edu> wrote:
Reke thine own rede.
Ross A. Finlayson
as I have claimed for some years in evolving argumentation among from
the very set-theoretically literate to the very set-theoretically
illiterate, that means that I think transfinite cardinals are largely
meaningless and without utility, without foundation, and that other
tools are needed to satisfactorially replace them.
sci.physics_20050321_d.rtf:So anyways, via induction I think infinite
sets are equivalent. Thus, where my primary consideration was that of
a bijective mapping between the naturals and reals, I conjectured the
natural/unit equivalency function, and forthwith discussed various
constructions of nonstandard models of the very real numbers. In terms
of the set of all sets and other constructions that are not even
existent in, say, Zermelo-Fraenkel set theory, those kinds of things
are considerable, and by so doing a theory may be consistent, complete,
and concrete.
sci.physics_20050322.rtf:There's basically a sixty year period from
Cantor to Goedel where most of what is today called set theory is
formulated. Then, in the 1960's and onwards, various schools went
forward towards addresing what are perceived as inadequacies in the
basically finitist, counternomenclaturally (anticladistically),
Cantorian perspective on the infinite. On one hand there are the
basically pure academicians who confound describing the infinite as
cataloging their bowel movements and calling it a transfinite cardinal,
and noticing they occur regularly and calling that progress. Another
school basically went directly to nonstandard analysis and outwards to
keep the 19th century set theory's abhorrence of infinitesimals from
interfering with integral calculus, which has many utilitarian results.
sci.physics_20050323.rtf:Consider the explanation put forth earlier in
this thread that the universe is comprised of infinitely many physical,
mathematical objects and that infinite sets are equivalent.
sci.physics_20050323.rtf:Anyways, infinite sets are equivalent.
sci.physics_20050324.rtf:Talking about everything at once, for example
as was discussed earlier in this thread with regards to the
mathematical, physical universe being comprised of infinitely many
mathematical, physical objects including those defined as functions
among sets of mathematical, physical objects leading to a conclusion
that infinite sets are equivalent as we exist, talking about everything
at once is different than one at a time.
sci.physics_20050428.rtf:If it's a point particle/wave, and we're
talking the continuous and discrete, and the internal and external
structure of those point particles, in the relatively infinitesimally
small, I'd like to know what you can infer about the infinitesimals in
the real numbers from that.
sci.physics_20050510.rtf:Hey I'm writing to again ask your opinion
about the physical universe containing all physical objects, and
functions between physical objects themselves being physical objects,
so the physical universe is infinite and infinite sets are equivalent.
sci.physics_20050510.rtf:I got to thinking more about the "instanton".
The instanton, it is basically about an instance. That is where, as we
were discussing before the system of equations describing the
gravitational force of two point particles in an otherwise empty
Gedanken universe, that it is not as much infinitely many
differentiations but rather one or none, the instanton.
sci.physics_20050510.rtf:In considerations of gravity before, one
notion that came to fore was that the physical universe was surrounded
by infinitely dense infinitely distant more or less spherical shell,
immovable celestial spheres, with a repulsive explanation of gravity,
and blocking mass. That's not completely nonsense. There is possible
consideration of MWI in that, but I think that is not the case.
sci.physics_20050511.rtf:Dirk, maybe you can address this, such
luminaries as the vituperative Bob Kolker have no official opinion
about it: the universe is comprised of physical objects, functions
between physical objects are physical objects, and thus the universe is
infinite and infinite sets are equivalent by a readily verifiable
experiment that you exist.
sci.physics_20050512_b.rtf:If you've discovered a well-ordering of the
reals, which are not just decimals, congratulations, you've solved one
of Hilbert's problems. You haven't actually shown that. I say the
reals as the complete ordered field have as well a partially ordered
ring structure, with the infinitesimals, and integral iota-multiples,
thus that the normal ordering is the natural well-ordering, of the
positive real numbers. A well-ordering of the real numbers exists,
please present one, or all. That totality implied there has to do with
extension of some of Cantor's results. Consider the base, or radix, of
one, or, and infinite radix.
sci.physics_20050512_b.rtf:Consider again the consideration that the
universe is comprised of physical objects, and functions between
physical objects and physical objects are hysical objects. Then, the
universe is infinite, and infinite sets are equivalent.
sci.physics_20050512_b.rtf:There is a somewhat different reasoning
about why infinite sets are equivalent, constructively from that they
are infinite via induction, and also from inference of the necessary
(to avoid paradoxes) dually minimal and maximal ur-element of a theory.
sci.physics_20050512_c.rtf:Those are theories of symbolic logic. At
some level, the necessities leading to the consideration of the
null-axiom theory with dually minimal and maximal ur-element, towards
finally resolving paradox classes in symbolic mathematical logic, may
well lead to further understanding of the number system's formation and
physical applications of the infinite.
sci.physics_20050513.rtf:I'm not much of a physicist, but I think the
Standard Model basically allows infinitely many classifications of
"particles", and that they are related in quite obvious ways, in
various ways of looking at them.
Tony Orlow
not exist before it. That's when the universe began. This is because science
has no evidence of anything, not only before the Big Bang, but before the
release of the microwave background radiation 300,000 years later, when the
density finally became low enough for light to exist in space, separate from
matter. Since we have nothing to work with, science has nothing to do there.
It's still worth pondering and guessing, and perhaps one of the guesses will
lead us in the direction of a test that can confirm it.
>
> What if the Big Bang of our universe took place in basically some
> region of a still larger cosmiverse, and there are other universes, in
> terms the entire region and all contents as from a Big Bang? Basically
> that's consideration of larger structures than bordered by the
> wavefront of light from the Big Bang formation event of our universe.
space bubble comprises the entire multiverse, as some call it. I can conceive
of it beginning, but I cannot cenceive of there being nothing before it which
caused it. It is my belief that the quantities and constants of the universe
are determined by its geometry and expansion, rather than vice versa as is
generally believed, and that the geometrical nature of the universe is caused
by the outside factors that caused it. It goes a bit deeper than that, but I
don't feel like getting into that right now. It does, by the way, involve
infinities in several respects.
>
> Why do some galaxies appear to be going in directions that do not seem
> to match their apparent age and formation? Where did they come from?
accountable for given local masses causing local high velocities which may be
in line with our line of sight, either increasing or decreasing the redshift
(or possibly causing blueshift, especially for closer galaxies).
>
> Maybe at the Big Bang, the tachyon universe was infinite, in extent and
> entropy, and as the universe goes flat the tachyon universe goes to a
> point?
Perhaps by the tachyon universe you mean the primordial infinite-dimensional,
infinite and flat universe where the speed of light is infinitesimal? Maybe. :D
>
> A tachyon is basically saying, there's a mathematical object that is
> basically the opposite of a photon, but it goes faster than light so it
> can't be in the universe, so it's in the tachyon universe. They might
> be purely mathematical, but to them so are the photons. It's kind of
> like the projection of an instanton to all dimensions.
What you are suggesting when you speak of particles that always move faster
than light, in the light of relativity, is a particle of negative mass, isn't
it? With no mass, any mmentum causes light speed. With positive finite mass,
any momentum causes finite speed. To get speed beyond c, it would seem you need
infinite momentum, or negative mass. I can see that particale of positive and
negative mass may need to reside in different places. Not sure. When you say
it's like applying the projection of an instanton to all dimensions, it that
like saying it is a non-point momentary particle? i am not familiar with
instantons.
>
> I wonder about basically whether time scales vary in cosmological terms
> pointing to the Big Bang.
You mean whether time has slowed or sped up? I rather suspect time has slowed
with the expansion, and is determined by it.
>
>
> About point particles as infinitesimals, the more exactly the mass of
> point particles is measured, the smaller they get. Is that not so?
> There've only been predicted and experimental masses of the quarks for
> some thirty years, or perhaps longer I don't know, and over that time
> they've decreased considerably.
Is that true? It would make sense. Take away the time element, and the mass
generated by massless particles at light speed with any momentum is bound to go
away too.
>
> Ross
>
>
Good thoughts!
--
Smiles,
Tony
Tony Orlow
You always seem to be discussing interesting stuff. Yes, we crackpots are very
interesting people. Haha! :D
> sci.physics_20050513.rtf:Physics has come a long way since Newton,
> although his laws are excellent approximations for many systems
> perceptible on the unaided human scale, and so has the integral
> calculus. While that is so, where in its formation the integral
> calculus was, and in many ways is, the infinitesimal calculus, where
> the integral with its summand notation, the integral bar is an S for
> summation, is exactly the same thing as the area of point widths, the
> fluents and fluxions, stopping at the first one and calling it iota the
> least positive real number, in establishing that system, it may be
> possible to apply associated considerations of the continuous and
> discrete to physical entities that match those properties.
> sci.physics_20050518.rtf:I hope to introduce to you some mathematical
> reasonings that would agree with that statement. Over the past few
> years I've spewed forth a variety of considerations of the mathematical
> logic of infinity.
> sci.physics_20050518.rtf:Is that really so? Is negative temperature
> really infinite? That seems somewhat counterintuitive.
This part does seem counterintuitive.I always thought Negative Kelvin would be
a great name for a band, or at least a song about a cold nasty little boy who
goes back in time. In a way, I imagine temperatures below absolute zero as
signifying brownian and other motion, going backwards in time. I am interested
in hearing more about it could be infinitely hot. That would fit with one of
the two perspectives on the real numbers that I see worth entertaining. Oh! I
see there is stuff out there about this. I never imagined! Did I make up
something real 25 years ago? Haha! When you got it, you got it. :D
> sci.physics_20050519.rtf:Anyways, I think that's kind of funny. In set
> theory, it's like considering infinity, or perhaps more technically
> Ord, the order type of all ordinals. Ord is greater than anything
> else, so it's less than nothing. One method of constructing the
> ordinals is that nothing, or the empty set, is zero. So, infinity is
> less than zero, but only by itself, where it is greater than any finite
> ordinal including zero, where "inclusion" may well make it mean a
> non-zero ordinal.
This sounds like the unsigned infinite number circle, which corresponds to the
positive side of the number line wrapped back on itself. The other is the
signed (2's complement) number circle, where +oo and -oo are the same point.
> sci.physics_20050521.rtf:The universe is infinite and infinite sets are
> equivalent. Any theory of everything is necessarily a logical theory
> of everything, and ZF is inconsistent. The electron and photon are
> point particles, but so are the other particles. There is not a
> theoretical smallest particle, except for any of those. That's a
> similar consideration to that the reals, nonstandardly, have a smallest
> positive real number.
One can certainly play successfulyl with that concept.
> sci.physics_20050523.rtf:A funny thing happened on the way to the
> infinite.
> sci.physics_20050531.rtf:In real numbers with a scalar infinitesimal,
> Vitali's result does not hold and all sets of numbers are measurable.
> ZF is inconsistent.
> sci.physics_20050531_b.rtf:That's about infinitesimals, I'm trying to
> understand particles in terms of infinitesimals instead of Planck, the
> discrete and continuous etcetera. If you know of things for which that
> is true, I'm interested in hearing about that.
> sci.physics_20050602.rtf:I got to examining the real numbers and the
> difference between a point on a line and a point in space. Basically
> the point on the line is "one-sided", it is defined, in a way, as the
> next bead on the string, but in a blur. I consider rephrasing that.
> So anyways, the contiguous sequence of points in a line leads to that
> the point, with point width, has only one side. Then, the discrete
> point in space, in a one-dimensional space, basically is two-sided.
> It's still point width, but it can be defined from the positive or
> negative side, or rather, it represents an endpoint, with basically a
> difference between endpoints and non-endpoints of a line, in one
> dimension. In two-dimensions then there is geometric consideration of
> basically the geometric mutation of the circle or regular polygon in
> the infinitely large and in this case moreso the infinitesimally small.
yes, I think 2D infinitesimal geometrical entities can take on a variety of
forms and "shapes". I tend to think of the rectangularly, in line with the
dimensions of the space they're in. Maybe I am not understanding you here.
>
>
--
Smiles,
Tony
Tony Orlow
what you're on, or off, or what you're really trying to say. But, it is clear
to me that you have very little idea of what the "I am that I am" really means.
What really exists primordally, without cause, eternally unchanging? I'll give
you a hint. It's not alive, and it's not physical. Now, go eat a piece of fish,
have a glass of wine, and a piece of essene bread, sit by a stream, and check
out the stars while you think.......
--
Smiles,
Tony
Virgil
Tony Orlow <ae...@cornell.edu> wrote:
> Ross A. Finlayson said:
Tony and Ross make a pair.
Of what no one can be quite sure, but a pair nevertheless.
A match made in ....?
Virgil
Tony Orlow <ae...@cornell.edu> wrote:
> brian a m stuckless said:
> Brian, I am not sure what your random capitlaization is supposed to
> convey, or what you're on, or off, or what you're really trying to
> say.
Brian is a soulmate to TO, in terms of how close to reality they are.
Ross A. Finlayson
Hirsch tells me a superconductor is one big atom. It's not, yet it is.
People toss around words like "infinity" and "atom" quite too
cavalierly if you ask me. The superconductor just has some
dielectric/diamagnetic behavior of the atom. That's what he says.
sci.math_20041113.rtf:Obviously enough the positive infinitesimal has
relative infinitesimals, each non-zero infinitesimal is basically the
same thing. If you query the existence of infinitesimals, a 360 degree
revolution is 2Pi radians.
sci.math_20041113.rtf:My question about the astronomy is if the average
visible light shift of visible objects in the skies was zero. That
might imply: a: no big bang, and b: infinite universe. Where that is
not so, I'm not certain that it disproves those things. A cursory
average of a chart shows a tendency towards red-shift, separation.
It's generally accepted that the universe is infinite in the three
spatial dimensions, but the status quo has that it is toroidal in four
dimensions, but travelling in three dimensions will never lead to a
return to the origin. Now _that's_ some mumbo-jumbo: the origin is
everywhere.
sci.math_20041113.rtf:In that opacity, there do seem to be some issues
that will be resolved by these contemporarily non-standard
considerations of the infinite.
sci.math_20041113.rtf:If there can be determined some means of scaling
multiple dimensions, or rather transforming, then that would be a
thing. Consider the infinitesimals, say you have a two coordinate
system. You take the infinitesimal, perhaps twice, of one coordinate,
and then something along the lines of e2 is e1 i^2. Then, you could
represent those two co-ordinates uniquely with an unordered pair of
scalars, a set. In that sense, one set of real numbers = infinite
dimensional coordinate system, plus every single thing gets its own
ordinal(s).
sci.math_20041114.rtf:J.E., fishfry, I hope that some of the readers of
this and other threads are emboldened to overcome the academic inertia
of the bulwark of transfinite nonsense because there is a lot of
concrete mathematics to do with infinity for which transfinite
cardinals mean nothing and are in some cases contraindicatory. They
can still be there, just out of the way.
sci.math_20041114.rtf:The universe, it's infinite dimensional, and
there are four of those dimensions that matter, your space and time.
About the infinite universe, it being spatially infinite, I have read
about it in the lay news over the last year or so, others agree.
sci.math_20041114.rtf:About the infinitesimals and the multiple
coordinates, infinite sets are equivalent, and the notion is that given
a value, a real number, definite and indefinite in several ways, that
it could represent, say, the coefficient of i, j, or k without further
notation, essentially hiding a number line within the number line,
leaving the original undisturbed.
Ross A. Finlayson
meaningless in physics and for the most parts in theories used to
explain physics, it is ephemera that entails from that most educated
people in mathematics have been exposed to the word and many use it.
That mostly means that's one of the first words they use to describe
the real numbers, because they can't count them. For most of them,
trying to justify mapping the naturals to the reals doesn't enter into
their equations because they have seen their tool of the integral
calculus justified in terms of finite approximations. Newton, Leibniz,
Robinson, and Conway believe in infinitesimals.
sci.math_20041008.rtf:Is not the frequency of light infinitely
variable? It is, because it spins around in a circle, and pi is
irrational.
sci.math_20041008.rtf:In terms of Skolem's paradox, and why math is the
way it is, Skolem basically tells us that infinite sets are equivalent.
sci.math_20041010.rtf:Here's one method: determine the distance between
vertices of regular polyhedra at random, for each finite regular
polyhedron "inscribed" into the unit sphere, extrapolate to regular
polyhedra of infinitely many sides, compare to the result for each unit
sphere "inscribed" into any regular polyhedron.
sci.math_20041011_b.rtf:You're telling me that you can't infinitely
tune a laser, but laser is coherent light of one wavelength and
frequency, uncoherent light is not coherent. My thoughts on the matter
are not particularly coherent.
sci.math_20041011_b.rtf:I would like some example of something in
nature that is infinitely variable. I think the universe itself is
infinite, in space-time.
Tony Orlow
> sci.physics_20050321_d.rtf:When I say "infinite sets are equivalent",
> as I have claimed for some years in evolving argumentation among from
> the very set-theoretically literate to the very set-theoretically
> illiterate, that means that I think transfinite cardinals are largely
> meaningless and without utility, without foundation, and that other
> tools are needed to satisfactorially replace them.
infinities are the same, and yet that is not what you seem to believe. I
suppose it is more a comment on the "countability" issue. In my opinion, when
you are looking at digital representations of the reals, you are not actually
looking that the points on the real number line. You are looking at a symbolic
system with certain properties that allow it to generate an infinite set of
strings, which can represent any enumerable set of values. We use such digital
strings for whole numbers, for real fractions, even for the characters you are
reading now on the computer. So, when you are looking, say, at Cantor's
diagonal proof and the array of digits on your list, you are not looking at the
reals, but at a complete symbolic language, where N=S^L holds. That formula has
nothing to do with real values. For sets of real values, we need to apply
formulas, and for intervals in the continuum there are no formulaic mappings (I
think) from the naturals, so intervals need to be handled somewhat differently,
and yet discretized using infinitesimals.
Meaning all countable?
> sci.physics_20050324.rtf:Talking about everything at once, for example
> as was discussed earlier in this thread with regards to the
> mathematical, physical universe being comprised of infinitely many
> mathematical, physical objects including those defined as functions
> among sets of mathematical, physical objects leading to a conclusion
> that infinite sets are equivalent as we exist, talking about everything
> at once is different than one at a time.
> sci.physics_20050428.rtf:If it's a point particle/wave, and we're
> talking the continuous and discrete, and the internal and external
> structure of those point particles, in the relatively infinitesimally
> small, I'd like to know what you can infer about the infinitesimals in
> the real numbers from that.
I rather see the point as the real, and the wave as the infinitesimal interval
surrounding it, as my parietal lobe ruminates on that. :D
> sci.physics_20050510.rtf:Hey I'm writing to again ask your opinion
> about the physical universe containing all physical objects, and
> functions between physical objects themselves being physical objects,
> so the physical universe is infinite and infinite sets are equivalent.
> sci.physics_20050510.rtf:I got to thinking more about the "instanton".
> The instanton, it is basically about an instance. That is where, as we
> were discussing before the system of equations describing the
> gravitational force of two point particles in an otherwise empty
> Gedanken universe, that it is not as much infinitely many
> differentiations but rather one or none, the instanton.
But maybe an infinite number of instantons? I dunno.
> sci.physics_20050510.rtf:In considerations of gravity before, one
> notion that came to fore was that the physical universe was surrounded
> by infinitely dense infinitely distant more or less spherical shell,
> immovable celestial spheres, with a repulsive explanation of gravity,
> and blocking mass. That's not completely nonsense. There is possible
> consideration of MWI in that, but I think that is not the case.
Not sure what MWI is, but that explanation doesn't sound right to me.
> sci.physics_20050511.rtf:Dirk, maybe you can address this, such
> luminaries as the vituperative Bob Kolker have no official opinion
> about it: the universe is comprised of physical objects, functions
> between physical objects are physical objects, and thus the universe is
> infinite and infinite sets are equivalent by a readily verifiable
> experiment that you exist.
Why does our existence depend on the infinitude of the universe? There is a
leap here I don't quite get. Not that I think the universe overall is finite
mind you....
> sci.physics_20050512_b.rtf:If you've discovered a well-ordering of the
> reals, which are not just decimals, congratulations, you've solved one
> of Hilbert's problems. You haven't actually shown that. I say the
> reals as the complete ordered field have as well a partially ordered
> ring structure, with the infinitesimals, and integral iota-multiples,
> thus that the normal ordering is the natural well-ordering, of the
> positive real numbers. A well-ordering of the real numbers exists,
> please present one, or all. That totality implied there has to do with
> extension of some of Cantor's results. Consider the base, or radix, of
> one, or, and infinite radix.
Yes, you are certainly thinking along some of the same lines as myself.
Infinite radix indeed! :D N=S^L requires either infinite radix of infinite
strings for an infinite language.
Now, as far as I can tell, you are well-ordering the reals in the unit interval
as the mirror of the digital representations of the naturals (finite and
infinite), to the right of the decimal point? That makes sense to me. However,
it does rely on a specific number base and digital representation, and for that
reason, one can perhaps get different sizes of sets of points for the unit
interval, unless one decalres that they are using logx(N) digits for radix x,
which presents its own specificities. However, there is a base-free enumeration
of the reals between 0 and oo which I had showed to Dave Rusin, who said he
hadn't seen such an enumeration, but then dismissed it as irrelevant. Do you
have any such base-free ordering of the reals?
> sci.physics_20050512_b.rtf:Consider again the consideration that the
> universe is comprised of physical objects, and functions between
> physical objects and physical objects are hysical objects. Then, the
> universe is infinite, and infinite sets are equivalent.
Assuming an infinite number of objects, an infinite number of interactions at
any given moment per object, or an infinite number of moments within which at
least one interaction occurs.
> sci.physics_20050512_b.rtf:There is a somewhat different reasoning
> about why infinite sets are equivalent, constructively from that they
> are infinite via induction, and also from inference of the necessary
> (to avoid paradoxes) dually minimal and maximal ur-element of a theory.
> sci.physics_20050512_c.rtf:Those are theories of symbolic logic. At
> some level, the necessities leading to the consideration of the
> null-axiom theory with dually minimal and maximal ur-element, towards
> finally resolving paradox classes in symbolic mathematical logic, may
> well lead to further understanding of the number system's formation and
> physical applications of the infinite.
> sci.physics_20050513.rtf:I'm not much of a physicist, but I think the
> Standard Model basically allows infinitely many classifications of
> "particles", and that they are related in quite obvious ways, in
> various ways of looking at them.
>
>
I'm not sure we need an infinite number of elementary particles. I rather think
there are perhaps two at the point level, or perhaps only one, which takes on
different characteristics depending on how many and which dimensions it
oscillates on.
As always, good ideas. Good to have you in the discussion, Ross. Happy to join
a movement where change seems needed, if not inevitable.
--
Smiles,
Tony
Tony Orlow
> sci.math_20041111.rtf:I search for "J.E." and "physics" and Jorge
> Hirsch tells me a superconductor is one big atom. It's not, yet it is.
> People toss around words like "infinity" and "atom" quite too
> cavalierly if you ask me. The superconductor just has some
> dielectric/diamagnetic behavior of the atom. That's what he says.
> sci.math_20041113.rtf:Obviously enough the positive infinitesimal has
> relative infinitesimals, each non-zero infinitesimal is basically the
> same thing. If you query the existence of infinitesimals, a 360 degree
> revolution is 2Pi radians.
to those of an atom, but it's certainly not a single atom. I do rather suspect
that proper application of infinitesimals will help in understanding
superconductors eventually, though.
> sci.math_20041113.rtf:My question about the astronomy is if the average
> visible light shift of visible objects in the skies was zero. That
> might imply: a: no big bang, and b: infinite universe. Where that is
> not so, I'm not certain that it disproves those things. A cursory
> average of a chart shows a tendency towards red-shift, separation.
> It's generally accepted that the universe is infinite in the three
> spatial dimensions, but the status quo has that it is toroidal in four
> dimensions, but travelling in three dimensions will never lead to a
> return to the origin. Now _that's_ some mumbo-jumbo: the origin is
> everywhere.
Is that the status quo? I have heard that is discussed, but didn't think that
was status quo yet. There is actually very good reason to believe the universe
is the surface of a hypertoroid, rather than a hypersphere as I remember it
being generally describe 25 years ago. If that is the case, there is still no
center to this surface, but there is direction, and not every point is exactly
isomorphic to every other.
> sci.math_20041113.rtf:In that opacity, there do seem to be some issues
> that will be resolved by these contemporarily non-standard
> considerations of the infinite.
> sci.math_20041113.rtf:If there can be determined some means of scaling
> multiple dimensions, or rather transforming, then that would be a
> thing. Consider the infinitesimals, say you have a two coordinate
> system. You take the infinitesimal, perhaps twice, of one coordinate,
> and then something along the lines of e2 is e1 i^2. Then, you could
> represent those two co-ordinates uniquely with an unordered pair of
> scalars, a set. In that sense, one set of real numbers = infinite
> dimensional coordinate system, plus every single thing gets its own
> ordinal(s).
This sounds related to axiom of choice and the representation of coordinates as
sets derived from taking an element from each of the sets of values along each
dimension. This is not restricted to infinitesimals, as I see it.
> sci.math_20041114.rtf:J.E., fishfry, I hope that some of the readers of
> this and other threads are emboldened to overcome the academic inertia
> of the bulwark of transfinite nonsense because there is a lot of
> concrete mathematics to do with infinity for which transfinite
> cardinals mean nothing and are in some cases contraindicatory. They
> can still be there, just out of the way.
Yes, they still look nice on the shelf, next to the phoenician urn.
:D
> sci.math_20041114.rtf:The universe, it's infinite dimensional, and
> there are four of those dimensions that matter, your space and time.
> About the infinite universe, it being spatially infinite, I have read
> about it in the lay news over the last year or so, others agree.
Within this spacetime bubble? I don't think so.
> sci.math_20041114.rtf:About the infinitesimals and the multiple
> coordinates, infinite sets are equivalent, and the notion is that given
> a value, a real number, definite and indefinite in several ways, that
> it could represent, say, the coefficient of i, j, or k without further
> notation, essentially hiding a number line within the number line,
> leaving the original undisturbed.
?
>
>
--
Smiles,
Tony
Ross A. Finlayson
> Ross A. Finlayson said:
> > sci.math_20041111.rtf:I search for "J.E." and "physics" and Jorge
> > Hirsch tells me a superconductor is one big atom. It's not, yet it is.
> > People toss around words like "infinity" and "atom" quite too
> > cavalierly if you ask me. The superconductor just has some
> > dielectric/diamagnetic behavior of the atom. That's what he says.
> to those of an atom, but it's certainly not a single atom. I do rather suspect
> that proper application of infinitesimals will help in understanding
> superconductors eventually, though.
>
He says that, I don't.
http://physics.ucsd.edu/~jorge/giantatom.html
It sounds similar to the skin effect, why square wire has more voltage
at the corners than round wire.
I think that to learn about electromagnetism that a very good source is
Baylis' book "Electrodynamics", with the restatement of the Maxwell
equations with the Clifford Algebra and Grassmanians.
Ross
Autymn D. C.
> It's similar in consideration to the rationalization of temperature, in
> terms of negative temperature, degrees Kelvin. There is no such thing
> as less than absolute zero, right? That would seem to be the intuitive
> notion, what with that all temperatures are measured in terms of
> positive degrees Kelvin, compared to absolute zero, the cessation of
> random-walk Brownian motion of particles., if I use those words
> correctly. Where that might seem to be the case, there is the notion
> among physicists I hear that negative temperatures are actually hotter
> than any finite positive temperature.
Kelvins are not degrees, and what doesn't exist is zero kelvins. The
so-called negative temperatures as used by scientists are an abuse of
mathematics, by not distinguishing between scalars and vectors or
between states and differences. The hotterness of such temperatures
comes from an inverted population, their sign only representing the
extended rate that they diffuse; but their space isn't bijective with
that of negative states.
> Why are there three space dimensions? What did Feynman mean by that?
Which why?
-Aut
Autymn D. C.
> What you are suggesting when you speak of particles that always move faster
> than light, in the light of relativity, is a particle of negative mass, isn't
> it? With no mass, any mmentum causes light speed. With positive finite mass,
> any momentum causes finite speed. To get speed beyond c, it would seem you need
> infinite momentum, or negative mass. I can see that particale of positive and
no, imaginary--do the maths
Autymn D. C.
> [Dyslexia aka Dy]
I'm not Dyslexia.
> a) http://egroups.com/message/free_energy/18907 says: "browser is
> not accepting our cookies"... [hm... I am not into cookies.]
That's too bad, but not for the rest of us.
> c) http://www.advancedphysics.org/viewthread.php?tid=2154
> which complains that "The page cannot be found"... [Sorry about that, Dyslexia]
AP remodelled lately.
http://www.google.com/search?q=site%3Aadvancedphysics.org+force+arbitrary+lysdexia
> 1) Dy states: "Decay the electron by putting it near an event horizon, then
> sapping its strength until it becomes a foton and neutrino"....
> [Interesting speculation, Dy. Dearly departed Franz Heymann posted long
> time ago that the neutrino maybe an electron without its charge.]
may be
I recently found on Wikipedia that scientists have also speculated that
the electron is a black hole, but I wrote about it independently on one
of my subversive treatises years ago.
> 2) Dy states: "the foton has a far-field massive pseudoparticle, as they say.
> I'd just call it a proxy particle". [... ahahaha... Interesting speculation, Dy.
> Now could you express that in very simple and short classical terms without
> resorting to pseudos and/or proxys?]
Energy gains mass when it's absorbed in an electric medium, such as a
superconductor. Energy has nonzero-amplitude tails that trail off
anywhere, interacting anywhere. So it stays interacting, and stays
massive.
> 3) Dy states: "A normal time machine that takes its passenger back will only
> serve amnesia"... "Or one should try finding a universe-scale time machine,
> including one that skips universes so that one could find alternate selves
> to molest"... [ahahaha... AHAHAHA... sorry, babe, I am not into neither
> finding alternate selves nor into molestations.... ahahaha... but hey, whatever
> turns you on... ahahaha...]
I didn't say sexual.
> 10) Dy states:"how to fix maths and write new maths".... [AHAHAhaha...
> I think I've just heard one of those alternate selves groan. Big time.....]
It's not bad. English has a loose meaning for "is", not distinguishing
it with "is in". So a square is a rectangle, but some would expect it
means that a rectangle is a square, substituting the two labels with
any two categories.
> (13) Dy states: "my, lysdexia's, profile:"
> http://forums.about.com/dir-app/bbcard/profile_center.asp?webtag=ab-physics&uName=lysdexia
> But it says here, unfortunately: "The page you are looking for is currently
> unavailable." [hm... hm... ahahaha... nobody's home at Dy's, huh?.....]
It works now.
> Hey, dudie Dy, it sounds like life's for you a bowl of cherries with its all
> its blossoms, but never mind and fuck the pits, right?... ahahaha....
> ahahaha... ahahaha... Thanks for all the laughs dudie, I will read all that
> wisdom of yours one day, time and fancy depending, because you sure
> have the fantasy to drive physics forward. I shall look whether I can find
> in your expressions a connection to reality from where I'd like to connect
> to your lofty realms. Till then, dear, don't get lost out there, somewhere...
> BTW Dy, you still haven't explained "of how you convinced/managed/over
> powered the deity-like properties of gravity to act otherwise"....AHAHAHA...
> ahahaha... ahahanson
It's in the links that you couldn't read.
-Aut
hanson
>> 1) Dy states: "Decay the electron by putting it near an event horizon, then
>> sapping its strength until it becomes a foton and neutrino"....
> hanson wrote:
>> [Interesting speculation, Dy. Dearly departed Franz Heymann posted
>> long time ago that the neutrino maybe an electron without its charge.]
>
Dy states:
> I recently found on Wikipedia that scientists have also speculated that
> the electron is a black hole, but I wrote about it independently on one
> of my subversive treatises years ago.
>
[hanson]
That's an old, old one, known since the days of Bohr/Hartree, almost a
century ago. Here's the equation and the numbers for the electron m_e
and the proton m_p as a function of being black holes... and similarly
one can construct the entire mass spectrum of the elementary particles:
m_p = [c^2/2G]*[sqrt(hG/(2pi*c^3)]*[I_H/(f_L*F)]*(3*pi^2)*sqrt(2a)
=1.67E-24 gr
It says: The Hydrogen nucleus (m_p) is a black hole with [***]
--- the classical Schwartzschild limit or event horizon of (c^2/2G) at
--- a radius of 1 Planck length sqrt(hG/2pi*c^3) and is shrouded in
--- a substance-characteristic Coulomb mantle, being the product of,
--- the H-Ionisation potential multiplier of 13.5
.... [I_H=4pi^4*sqrt(a)/sqrt(6)],
--- the Lyman series frequency limit (f_L), and
--- the Faraday Constant (F, the charge transfer handler),
.... and is further governed by
--- toroidal geometry demands of (3*pi^2) and
--- EM/QM fine structure conditions set by [sqrt(2*a)].
[***] Consider the distance between this event horizon and the larger,
classically measured H-radius as the "nuclear accretion zone" analog.
In case of leptons, here the electron m_e, the e-shell Ionization-potential
considerations do fall away and the situation changes to:
m_e = [c^2/G] * [sqrt(hG/(2pi*c^3)] * [1/(f_L*F)] * a*pi*sqrt(3)/3
= 9.09E-28 gr
It says essentially the same as above, except that as already noted ,
there are no ionization considerations and that the electron's geometry
is spherical (instead of toroidal as in the composite H-atom)
Also, it indicates that the electron may be a rotating Kerr blackhole
type character with the Kerr- [c^2/G] (instead of the Schwartzschild
[c^2/2G]) event horizon.
hanson
Ross A. Finlayson
> >> The universe is infinite, infinite sets are equivalent.
>
> As stated many times before, this is provably false.
>
> >> The universe is infinite. There are three dimensions
> >> in space: why.
>
> Both statements are false. The universe is finite but expanding (but
> the expansion has slowed). Modern physicists believe that there are 10
> space-time dimensions. See:
>
> http://en.wikipedia.org/wiki/Why_10_dimensions
>
> >> Please answer the question: the universe is infinite.
>
> That's not a question; that is a false statement.
>
> Hope that helps.
>
> Jonathan Hoyle
That wasn't the question.
Is your set-theoretic universe infinite?
On FOM recently they are having a difficult time even having the
universe exist.
Do you exist? Do I exist?
That fringe "scientist" Sarfatti is talking about the universe
containing itself.
You want a theory of everything? A complete, consistent, theory of
everything?
About the string theories, thanks for that link, that's interesting.
Some comments, mostly questions:
Where are the mathematical infinitesimals?
Have you ever noticed the observation that the more precisely you
measure the subatomic particles the smaller they get?
Einstein says: he's pretty sure the universe is infinite.
Is the cylinder the sinecosine? Do the reals have a frequency?
Why do Hawking and Feynman say there are infinities in nature?
Zeno tells you: stop.
Skolemize, your model is countable. Ask Bob.
Ross
Jonathan Hoyle
Certainly. It contains 0, S0 (denoted as '1'), SS0 (denoted as '2'),
etc.
>> Do you exist? Do I exist?
If not, who are the 'you' and the 'I' referring to in those questions?
>> You want a theory of everything? A complete, consistent,
>> theory of everything?
Yes, please, with fries to go.
>> About the string theories, thanks for that link, that's
>> interesting.
No problem. You might want to read Hawkings' "A Brief History of
Time". It's a little dated but well written for the non-physicist.
>> Where are the mathematical infinitesimals?
Very interesting field, you might try first looks at:
http://www.metaweb.com/wiki/wiki.phtml?title=Hyperreal_number
Essentially, they are an extension of the reals, usually denoted *R.
The positive infinitesimals have the property that they are greater
than 0 and less than every positive real number (and of course the
symmetrically for negative infinitessimals). Any infinitesimal value
multiplied by a standard finite real (no matter how large), remains an
infinitesimal. Around every real number x, there is a range of
hyper-reals infinitesimally close to x, called its halo. Halos never
overlap, so *x is in the halo of x, it is not in the halo of any other
real number. Ths standard part of a hyper-real is the unique real
number it is closest to.
The hyper-naturals are infinite numbers greater than any natural
number. No matter how many times you add one to a finite natural, you
never get to a hyper-natural; conversely, no matter how many times you
subtract 1 from a hyper-natural, you never get back to the finites.
After these hyper-naturals, you can define hyper-rationals, define
hyper-integers, hyper-algebraic, and of course the hyper-reals.
<Remaining questions snipped.>
Hope that helps.
Ross A. Finlayson
Nope, that doesn't help. The question is where are the mathematical
infinitesimals in physics. Does "comments snipped" mean "I don't
know", "I don't care", "I don't understand", or what? Why don't you,
what do they call that, proffer, offer, venture, an answer to those
questions?
There can be only one theory of everything. That's understandable,
right? If there is a correct (consistent and complete) theory of
everything, then that's the same as any other formulation, right?
Well, if you want a complete and consistent theory, it's the null axiom
theory.
There are a variety of those string theories, with varieties of numbers
of claimed dimensions, pyramidal numbers many of them. While string
theories are so great, I've never heard of anyone verifying them via
experiment.
Have you ever thought that perhaps string theory's compact dimensions
are stuffed in the infinitesimals? How about now?
Fish, or cut bait.
Ross
Tony Orlow
mean in geometic terms?
--
Smiles,
Tony
Jonathan Hoyle
>> mathematical infinitesimals in physics. Does "comments
>> snipped" mean "I don't know", "I don't care", "I don't
>> understand", or what? Why don't you, what do they call
>> that, proffer, offer, venture, an answer to those
>> questions?
I didn't get into those other questions, since I didn't think they were
relevant to the topic. Infinitesimals might have some uses in advanced
physics, but I doubt it. Out typical Euclidean model breaks down once
you get smaller than Planck length (a finite, not infinitesimal, size),
so even the real number line is far more divisible than our physical
universe. Unfortunately, your 19th century view of an infinite
universe and 18th century view of the mathematics of infinity doesn't
play much a roll in the modern physics theory, so I didn't think
anything I would have to say would be of interest to you. Your world
view is, from my perspective, an entirely fictional one (and I suppose
you in turn feel the same way about the work of modern scientists
today).
>> There can be only one theory of everything. That's
>> understandable, right? If there is a correct (consistent
>> and complete) theory of everything, then that's the
>> same as any other formulation, right?
For centuries, the Aristolean model was believed to be the correct
theory of the universe. Along comes Newton to replace it with
Newtonian Mechanics, and that reigned for a couple hundred years.
Einstein showed us that Newtonian Mechanics was merely a special case
of a much broader relativistic system. Modern Cosmologists and Quantum
Theorists are coming closer and closer to truth. Are we there yet?
I'm not sure we'll ever be there completely.
>> Well, if you want a complete and consistent theory,
>> it's the null axiom theory.
A theory that denies the last hundred years of physics and mathematics
is more of a religion than it is a science. The crank.net web site is
filled with a number of these weird world views. My favorite is The
Flat Earth Society [ http://www.talkorigins.org/faqs/flatearth.html ],
which just goes to prove, you can justify almost any favorite pet
philosophy.
>> There are a variety of those string theories, with varieties of
>> numbers of claimed dimensions, pyramidal numbers many of
>> them. While string theories are so great, I've never heard of
>> anyone verifying them via experiment.
>>
>> Have you ever thought that perhaps string theory's compact
>> dimensions are stuffed in the infinitesimals? How about now?
As stated above, the real line is far more divisible than the physical
universe. Once those dimensions shrink below Planck length, we no
longer have a model of what's "really" happening anymore.
>> Fish, or cut bait.
I'm still here, aren't I?
Jonathan Hoyle
Ross A. Finlayson
"String theory explores the implications of strings that are either
open (they have free ends) or closed (they form loops and have no free
ends)."
Why, that sounds like iota, one-sided or two-sided on the 1-D line,
iota, the unit scalar infinitesimal.
If you have iota, and the reals as a sequence of points, then Vitali's
non-measurability criterion falls, and all sets are measurable.
It's the smallest infinitesimal. Infinity is big.
With ten dimensions, is it the five dimensions of Cl(3,2) and then
another five as a "compact dimension" for each of those? (I don't
know.) Speaking of Cl(3,2), why not Cl(4,1)?
So, when you hear string theory, can it not be understood as "points
variously on or off a line theory"?
A physicist's superstring appears to be what a mathematician would call
some form of infinitesimal.
Well-order the REALS.
If you want a complete theory of everything, then it must overcome
Goedel's incompleteness results.
You might want to check your calender it's 2005.
Ross
Jonathan Hoyle
>> either open (they have free ends) or closed (they form
>> loops and have no free ends)."
>>
>> Why, that sounds like iota, one-sided or two-sided on the
>> 1-D line, iota, the unit scalar infinitesimal.
Not sure why you assume infinitesimal. All you need is to be less than
Planck length.
>> If you have iota, and the reals as a sequence of points,
>> then Vitali's non-measurability criterion falls, and all sets
>> are measurable.
Wouldn't that violate Quantum Mechanics, and thus invalidate your use
of String Theory?
>> A physicist's superstring appears to be what a mathematician
>> would call some form of infinitesimal.
Not necessarily. It need only be a specific size for granularity.
>> Well-order the REALS.
Haven't we already done this exercise? How is it related?
>> If you want a complete theory of everything, then it must
>> overcome Goedel's incompleteness results.
You'll have bigger problems with Heisenberg's Uncertainty Principle.
>> You might want to check your calender it's 2005.
Ummm...yeah...I assume you know what that reference is for. Most of us
are not surprised that it's 2005, but hey, it's newsworthy for you to
post, glad to at least see you are on the correct side of the calendar
(if not mathematics or physics).
Jonathan Hoyle
PS: When we were discussing demonstrable differences between countable
and uncountable infinities, would further examples help?
Ross A. Finlayson
Yeah, I would be interested in some further examples.
So far, let's see, you say zero, times Aleph_1, is some finite number
that varies, and I say epsilon-delta only involves countably many
intervals. This is where multiplication is repeated addition.
Would you be interested in further reasoning as to why compact
dimensions' superstrings are mathematical infinitesimals?
I don't understand what Vitali and non-measurable sets have to do with
quantum mechanics. I just have never heard of any relation between
those. I don't use iota to invalidate Banach-Tarski, just note that it
demands revalidation.
The correct side is truth.
Ross
Ross A. Finlayson
Schroedinger's been solved for years.
Well-order the set of reals, and in extension of Cantor's first, nested
intervals, there are adjacent points in the normal ordering of the
reals.
They're infinitesimals because their sum is the correct total.
I never took hard sciences in college except for mathematics,
statistics, and econometrics, when I was in high school there was like
"cold fusion", nowadays called CANR/LENR, high temperature
superconductors, and in chemistry they brought out the
Belousov-Zhabotinsky, B-Z, reaction. Schroedinger was put on the
blackboard as an exercise. Obviously that means little, I'm quite
ignorant.
Visit a Pertti Lounesto shrine:
http://tiki-lounge.com/~raf/lounesto/LounestoShrine.html . His book is
an excellent introduction to Clifford Algebra, and applications.
Look at the particles more closely, they get smaller.
Ross
Ross A. Finlayson
Oh, superstring theory and M-theory is ALL ABOUT mathematical
infinitesimals and infinities.
http://www-dft.ts.infn.it/~ansoldi/Research/FuzzyDimensions/HTML/node5.html
I found that from searching for "poly-brane". The author mentions
Pezzaglia, who I discovered for searching for polydimensional, eg,
polydimensional points on a line.
http://www.clifford.org/~wpezzag/
Excellent.
You still want a consistent and complete theory?
Ross
Jonathan Hoyle
One of my books discusses the possibilities of uncountable versus
countable infinities in the physical universe, so I will get those to
you.
>> So far, let's see, you say zero, times Aleph_1, is some finite
>> number that varies...
Actually, I didn't say this at all. I don't even recall ever making a
reference to Aleph_1. (I have spoken of c, the cardinality of the
continuum, is that what you were thinking of?) Also I never said that
zero times Aleph_1 was any value. What I did say that it was provable
that Uncountable Additivity does not hold in Measure Theory, since
[0,1] is of measure 1, yet it is composed of an uncountable number of
points, each of measure 0.
>> and I say epsilon-delta only involves countably many
>> intervals. This is where multiplication is repeated addition.
I'm not sure your point here. I am saying that Countable Additivity
always holds, whereas Uncountable Additivity does not always hold.
With regard to multiplication as an extension of addition, it therefore
holds only in the Countable case.
>> I don't understand what Vitali and non-measurable sets have to
>> do with quantum mechanics. I just have never heard of any
>> relation between those. I don't use iota to invalidate
>> Banach-Tarski, just note that it demands revalidation.
My point with quantum mechanics is merely that our knowledge of
physical laws breaks down once you get below Planck length, which
although small, is still infinitely larger than an infinitesimal. You
don't need to get that small before things break. Since the universe
is not infinitely dividible (it has a finite sized granularity or
resolution), it would seem to be that infinitesimals are completely
irrelevant. But again, I am not a physicist, and I would be happy to
be corrected on this point.
Jonathan Hoyle
Jonathan Hoyle
If by "solved" you mean using probabilities of quantum mechanics, then
yes.
>> Well-order the set of reals, and in extension of Cantor's
>> first, nested intervals, there are adjacent points in the
>> normal ordering of the reals.
The normal ordering of the reals is not a well-ordering, only a partial
ordering. A well-ordering of the reals would have adjacent point; the
usual partial order does not.
>> They're infinitesimals because their sum is the correct total.
I'm surprised to hear you say this, as it seems to violate your most
precious assumption: that all infinities are equal. If all infinities
are equal, then the number of points in [0,1] and [0,2] are exactly the
same, yet they sum to different lengths. How do infinitesimals help
here?
Jonathan Hoyle
Ross A. Finlayson
Yeah, so in Measure Theory, you have Uncountably Many Zeros is Non-Zero
Additivity? That's a leading question and uses ill-defined terms.
The measure of the unit interval of real numbers is one. Basically, in
Measure Theory, that's not infinitely divisible. Yet, the unit
interval is the union of each set containing a point from the unit
interval. As Zeno knows, it should be infinitely divisible because the
integers are infinite.
In the sense of particle physics, there are a couple things t consider
with regards to mathematical infinitesimals, there are many things to
consider where mathematical infinitesimals are rigorously used to form
correct and useful analytical results. Anyways, the more closely the
subatomic particle is inspected, the smaller it appears. There does
not seem to be some barrier to that, the more energy that is used to
determine the particle's mass, the smaller that value becomes.
As well, it would seem that the more that is learned about the
universe, the larger it would seem to be. I don't know if that's the
case, basically physicists have determined a finite figure for the mass
of the universe. While that is so, do not more accurate experimental
predictions of that value lead to larger values?
Ross
Ross A. Finlayson
I hear Schroedinger's equation was just plain solved. Basically it is
a non-linear system and a variety of today's methods can handle that,
where the mathematical machinery was nascent or non-existent even
twenty years ago.
The point about the Cantor's first is that for some interval of the
reals, the normal ordering is the well-ordering, basically the natural
well-ordering. Where that is so, then instead of the domain being some
well-ordered ordinal cardinally equivalent to the great number that is
the cardinality of the reals, if cardinality is a number or numeric
quantity, then the domain can be the naturals. Where it's not, the
reals are not a set. The reals are complete and gapless, basically as
each point on a line they are the complete ordered field, but there is
no place for non-real infinitesimals "between" them. As each of a
contiguous sequence of the points on a continous line, they are at once
complete ordered field and dually partially ordered ring.
I don't say "infinities are equal", just "infinite sets are
equivalent", equipollent, cardinally equivalent. I think there is a
good reason to think that there are twice as many points on [0,2] than
the unit interval, those of the unit interval and those of f(x)=x+C, in
this case, x+1, or that in the obvious function between them f(x)=2x,
that the two there in that equation implies twice as many. Can you
think of a more simple function between [0,1] and [0,2]? There's a
bijective function between [0,1] and [0,2]. Apparently there is also
between the unit interval and the unit square, encoding two points into
one.
If infinite sets are equivalent, then there's a bijection between the
naturals and unit interval of reals, and, as well, analytical results
besides those readily available from obvious geometric results exist,
and as new tools for a toolbox of analytical methods, a variety of true
statements can be made about the continuum, vis-a-vis the discrete,
only available in non- or post-Cantorian theory.
Consider the search results for "superstring" and "infinitesimal",
Google says there are some 29,000 of them. That's not saying much
except that they appear together in the context very often.
Now, is a physical point a mathematical point? Yes, in many ways it
is.
Now, when I can detail some unprecedented experimental predictions from
analytical results of my null axiom theory, then that would be
something.
Ross
Ross A. Finlayson
compact dimensions, two for each of the three spatial dimensions.
http://www.google.com/search?q=%22six+compact+dimensions%22
I think that means for each spatial dimension, say x, y, z, or e1, e2,
e3, there is a compact dimension for each of the other two for each of
those.
Now, I've been known to say things like infinity = i, a square root of
negative one, so you might understand why my uninformed gropings
towards understanding of superstring theory's compact dimensions would
be unclear.
That's basically about encoding on the real line enough information to
represent more than one point. It's a conception similar to having
having the regular real numbers, then off in infinity encoding another
real number, and back in the infinitesimals encoding the third, and
then, they encode each other in one and thus there are three space
dimensions. The idea is that in a scale or perspective of the real
numbers, there is a way to have three, so there must be three, but
there doesn't need to be more than three, because in the other two it
could be one of those, three spatial dimensions.
Few people would say: multiply the real number 7 by infinity and it's
the complex number 0 + 7i, that doesn't make much sense. As well,
multiplying (7,0,0) by infinity and getting (0,7,0) might also seem
capricious, non-justifiable, and useless.
If there's that kind of notion about space, three spatial dimensions,
then there is again about time. The three spatial dimensions are
Euclidean, to each other, but not to the time-like dimension(s), in the
Minkowskian space-time coordinate space or reference, or, Cl(3,1),
Cl(1,3). Space and time can be plotted in a Euclidean system, eg time
series data, and that is about the space-time pseudoscalar and various
reflections and rotations about which I am ignorant.
There are various models of physics where c, the speed of light, is 1.0
infinity distance units per time unit. Photon: constant speed.
Infinite: non-finite.
Ross
Jonathan Hoyle
>> is Non-Zero Additivity? That's a leading question and uses
>> ill-defined terms.
I don't follow this sentence at all, as it does not seem to correspond
to anything I have said. I did say Countable Additivity holds in
Measure Theory while Uncountable Additivity does not. Which part of
this do you disagree with?
>> The measure of the unit interval of real numbers is one.
Correct.
>> Basically, in Measure Theory, that's not infinitely divisible.
Sure it is.
>> Yet, the unit interval is the union of each set containing
>> a point from the unit interval.
That's certainly true.
>> As Zeno knows, it should be infinitely divisible because
>> the integers are infinite.
It is infinitely divisible, although I don't see how Zeno or the
integers are directly relevant to that.
>> In the sense of particle physics, there are a couple things to
>> consider with regards to mathematical infinitesimals, there
>> are many things to consider where mathematical
>> infinitesimals are rigorously used to form correct and useful
>> analytical results. Anyways, the more closely the subatomic
>> particle is inspected, the smaller it appears. There does not
>> seem to be some barrier to that, the more energy that is
>> used to determine the particle's mass, the smaller that value
>> becomes.
Yes, there is a barrier to that: Planck length, which is 1.6 x 10^-35
m, or approximately 10^-20 times the size of a proton. As I understand
it, length has no meaning below that size. So while the real line is
infinitely divisible, the physical universe apparently is not.
>> As well, it would seem that the more that is learned about
>> the universe, the larger it would seem to be. I don't know
>> if that's the case, basically physicists have determined a
>> finite figure for the mass of the universe. While that is so,
>> do not more accurate experimental predictions of that
>> value lead to larger values?
I don't think we are getting larger values. We can see only as far as
30 billion light years away, and only thanks to universal expansion,
since the universe itself is only about 13 billion years old (without
which we would not see anything further than 13 billion light years
away). Seeing only a tiny fraction of the universe, we don't have a
good handle on its total mass. Worse still, we can only guess what
percentage of the mass that is out there is visible, as opposed to
dark.
Jonathan Hoyle
Jonathan Hoyle
>> it is a non-linear system and a variety of today's methods can
>> handle that, where the mathematical machinery was nascent
>> or non-existent even twenty years ago.
I do not believe what you have written here is at all true. You might
wish to double check this again before repeating it, as you are likely
to be called on it.
>> The point about the Cantor's first is that for some interval of
>> the reals, the normal ordering is the well-ordering, basically
>> the natural well-ordering.
<snip>
This is provably false. The normal ordering can never be a
well-ordering on the reals. Remember your own challenge: "Well order
the reals, I dare you"? It wouldn't be much of a challenge if the
standard ordering worked.
>> The reals are complete and gapless, basically as each point
>> on a line they are the complete ordered field, but there is no
>> place for non-real infinitesimals "between" them. As each of
>> a contiguous sequence of the points on a continous line,
>> they are at once complete ordered field and dually partially
>> ordered ring.
The reals are not (in their standard ordering) "a contiguous sequence
of points on a continuous line", since between any two, there are an
infinite number of others. As for being "gapless", you'll need to
define that better. From a Non-Standard Analysis point of view, they
are certain not gapless.
>> I don't say "infinities are equal", just "infinite sets are
>> equivalent", equipollent, cardinally equivalent.
Doesn't that put the final nail in the coffin of your "well order the
reals" challenge? If you think that all infinities have the same
cardinality, then there ought to be a bijection F between the reals and
the naturals, right? Then the well-ordering operator <= is simply
defined as r1 <= r2 if F(r1) <= F(r2) for all reals r1, r2.
Okay, so now it's my turn to turn it around on you, Ross: If you think
that all infinities have the same cardinality, then well-order the
reals. I dare you. :-)
>> I think there is a good reason to think that there are
>> twice as many points on [0,2] than the unit interval,
>> those of the unit interval and those of f(x)=x+C, in this
>> case, x+1, or that in the obvious function between
>> them f(x)=2x, that the two there in that equation
>> implies twice as many. Can you think of a more
>> simple function between [0,1] and [0,2]? There's a
>> bijective function between [0,1] and [0,2].
You have simply shown that "twice as many" and "the same size" turn out
to be the same thing when dealing with infinite quantities. There are
twice as many points on [0,2] as there are on [0,1]. There is also the
same number of points. This is no contradiction here. The only error
is assuming that doubling the size means increasing it. (It also
doesn't increase it if the size were zero.)
To make the point even more obvious, there is a bijection between (0,1)
and (1,oo): f(x) = 1/x.
>> Apparently there is also between the unit interval
>> and the unit square, encoding two points into one.
Yes, the approach is to interlace the decimal values. You can map
every point (x,y) in the unit square onto some unique point z on [0,1]
in the following manner: Let x be written decimally as 0.abcde... and y
be decimally 0.ABCDE... . Now map (x,y) to the point z =
0.AaBbCcDdEe... For this technique to work, you have to handle the
special cases of certain values with multiple decimal representations,
such as 1/2 = .5000... and as 0.4999..., but still you see the point.
>> If infinite sets are equivalent, then...
<snip>
Unfortunately, all of that is just hopeless fiction.
>> Now, when I can detail some unprecedented experimental
>> predictions from analytical results of my null axiom theory,
>> then that would be something.
It certainly would, Ross, but until you remove your own internal
inconsistencies to your theory, I am not expecting to see any. My
question for you would be: How long are you willing to go with no
results before you at least consider that you are working from a flawed
foundation?
Jonathan Hoyle
Ross A. Finlayson
Have a new Zeno race: a turtle, versus, a rock. The turtle begins the
race. Travelling at its constant speed, the turtle completes the race.
The rock has zero velocity and never moves. You can (infinitely)
divide the turtle's path, into however many non-zero segments you care.
Sum them, and the result is correct.
Add zero together as many times as you want, and the result is zero.
To say a non-empty set has "measure zero", and equate that to the
number zero, leads to incorrect results. For it to have infinitesimal
measure is quite different. Where iota exists in the reals, all sets
are measurable.
The above is as I say it is.
Fine structure constant: variable.
I'm not sure about that. It would take me a while to explain that, and
I might reverse my decision. Perhaps it was some other "constant".
I've seen numbers bounced around of 1/5, 2/3, 4/5, and 9/10 of the mass
being not dark mass. I had some ideas about it with regards to points
on a line.
I'm glad you're beginning to think that the superstrings of the compact
dimensions of string theory are similar to mathematical infinitesimals.
If you're not, I don't care.
Thanks, that's interesting. I'm hoping you can find that book you
mention.
Ross
Ross A. Finlayson
I'm not sure about the Schroedinger non-linear equation with the Psi
and so on. It is almost certain that a variety of members of these
physics discussions will have a more informed opinion about it than I
do today.
Now about Cantor's first, you got it wrong there, the problem is that
it's so.
I've sent to you a variety of considerations about well-ordering the
reals ,and other sets, I encourage you to read them. Jon, you were
away from sci.math for some time, things have changed.
I think I can gather some easy accessible results in the next couple
years.
How long have transfinite cardinals gone? That's a hell of a drought,
considering there hasn't been a first one.
Empirical validation of Finlayson mathematics: existence, immutable
laws of physics.
Ross
Jonathan Hoyle
>> is zero. To say a non-empty set has "measure zero", and
>> equate that to the number zero, leads to incorrect results.
Not necessarily. As long as the number of values you are adding is
Countable, you always get the right answer. It is only when you have
an Uncountable number that you get incorrect results. Measure Theory
is one of the most obvious places where Countable infinities make their
differences from Uncountable infinities.
>> For it to have infinitesimal measure is quite different. Where
>> iota exists in the reals, all sets are measurable.
That's not true either. It's not even true in your sense of "iota", as
you have shown yourself that there are the same number of iotas in
[0,1] as there are in [0,2], yet their sum can't be equal to both 1 and
2 at the same time.
>> I'm hoping you can find that book you mention.
It's been a while, so I may be wrong about it, but the book I think has
it is "Infinity and the Mind" by Rudy Rucker. I seem to recall a
chapter there called "Higher Physical Infinities" or something like
that. You might also try Google searching with the phrases "physics"
and "uncountable infinity".
Hope that helps,
Jonathan Hoyle
Tony Orlow
The current estimate of the age is 13.6 billion years, and we have seen things
just about 13 billion light years away, about half a billion years after the
Big Bang. If you have a reference to any sighting of something 30 billion light
years away, I'd like to see it.
> >
> > Jonathan Hoyle
>
> Have a new Zeno race: a turtle, versus, a rock. The turtle begins the
> race. Travelling at its constant speed, the turtle completes the race.
> The rock has zero velocity and never moves. You can (infinitely)
> divide the turtle's path, into however many non-zero segments you care.
> Sum them, and the result is correct.
>
> Add zero together as many times as you want, and the result is zero.
> To say a non-empty set has "measure zero", and equate that to the
> number zero, leads to incorrect results. For it to have infinitesimal
> measure is quite different. Where iota exists in the reals, all sets
> are measurable.
>
> The above is as I say it is.
>
> Fine structure constant: variable.
>
> I'm not sure about that. It would take me a while to explain that, and
> I might reverse my decision. Perhaps it was some other "constant".
>
> I've seen numbers bounced around of 1/5, 2/3, 4/5, and 9/10 of the mass
> being not dark mass. I had some ideas about it with regards to points
> on a line.
>
> I'm glad you're beginning to think that the superstrings of the compact
> dimensions of string theory are similar to mathematical infinitesimals.
> If you're not, I don't care.
>
> Thanks, that's interesting. I'm hoping you can find that book you
> mention.
>
> Ross
>
>
--
Smiles,
Tony
Jonathan Hoyle
>> away. The current estimate of the age is 13.6 billion years, and we
>> have seen things just about 13 billion light years away, about half a
>> billion years after the Big Bang. If you have a reference to any sighting
>> of something 30 billion light years away, I'd like to see it.
http://www.faqs.org/faqs/astronomy/faq/part9/section-10.html
http://www.physicsforums.com/archive/index.php/t-5715.html
Ross A. Finlayson
Where infinite sets are equivalent, those are not problems. Infinite
sets are equivalent.
sci.math_2005019:
About the cumulative hierarchy, consider it with regards to this
circular ordering with the positive infinite and negative infinite. If
positive infinite is less than any finite negative temperature, where
is negative infinite and any finite positive temperature? I would
actually that negative one there might be twice as much as any finite
temperature, exactly twice as much, with one infinite ordinal for each
positive, finite ordinal, or just one. There are other cases where the
ordinal has dual representation as positive and negative. As well,
consider infinite integers. In a variety of nonstandard models there
are infinite integers.
sci.math_2005019:
If each negative temperature is hotter than any finite temperature,
then as infinite temperatures there are a variety at least as much as
the finite, and not more.
sci.math_2005019:
You know I avoid the transfinite cardinals, and think infinite sets are
equivalent. That is for example with the ubiquitous ordinals where
powerset is order type is successor. There are a variety of theories
with irregular sets equivalent to their powerset.
sci.math_2005019:
ZF is inconsistent. The universe is infinite and infinite sets are
equivalent.
sci.math_20050201:
I think the stumbling block is rather about dual representation. I
seem ridiculous to say that infinity and zero are the same thing.
sci.math_20050201:
I read one of these Feferman papers, deciding.pdf, "Deciding the
Undecidable: Wrestling with Hilbert's Problems". That's some good
stuff. It's telling me things I didn't know, for example one of
Hilbert's problems is to find a well-ordering of the reals. I should
know that, I've read lists of Hilbert's problems before. It also has
some interesting background on Hilbert's tenth problem, about the
integer solutions to Diophantine systems. Brute force is a positive
algorithm, but only when it works, and that's not exhaustive. One
problem I have with the piece is that there does exist the trisection
of the arbitrary angle. I agree with the Hilbert program, and use
"infinity = zero" to coerce it. Fall forward, spring back.
sci.math_20050201:
The theory can only prove itself consistent if it is inconsistent...
how can anything be inconsistent in a consistent way, consistently
inconsistent? Any theory with finitely many (more than zero) axioms is
incomplete. That's about Goedel's second and first incompleteness
results, meaningless indeterminacy or sarcastic inconsistency, and both
and/or neither, or not, and the infinite ghost chain. I discarded
sarcasm long ago. That's about the consideration of the liar
"paradox", and various states of belief. "The theorem is inconsistent
because of its consistency."
sci.math_20050201:
Ta-da, a non sequitur: There's only one free variable, but it's
infinite-dimensional.
Tony Orlow
exactly, but a little more googling and I see estimates of up to 156 billion
light years for the diameter of the universe. It wasn't that long ago I
remember reading that they had detected the farthest object yet, at just over
13 billion light years. Perhaps there is some controversy over this? If the
universe is 13 billion years old, and expanding at the speed of light, it seems
like nothing could be father than that many light years from anything else.
Perhaps the expansion itself, perpendicular to our internal 3-space, moves at
the speed of light, and given the circular or toroidal geometry of the
universe, we would see an overall rate of expansion 2*pi times greater, but can
only see half of it? That first link said the ratio is a little over 3 to 1,
which sounds close to pi. Hmmm.... Thanks again.
--
Smiles,
Tony
Ross A. Finlayson
When you say differences between countable and uncountable, I read that
as differences between inferential (inductive) and non-inferential.
That's a good book, I call it "70's state-of-the-art", and was very
widely read. among books on the subject perhaps the most widely read
book, almost certainly, but it doesn't present any physical predictions
of uncountability that I can recall. I suppose you might turn to
Chaitin and his constant Omega, except there aren't any predictions
from that? Chaitin thinks the universe is digital.
Keep in mind, the universe is infinite. That's because for any two
physical objects, each function between them is as well a physical
object. In ZF set theory, there is no universe.
There are twice as many of the iotas of [0,1] in [0,2] than [0,1].
There are half as many of the elements of N that are even as are in N.
So, the universe is infinite, and infinite sets are equivalent, because
the universe is all of those things. You might try searching for
"universe" and "infinite".
Infinite sets are equivalent.
Ross
Ross A. Finlayson
Anyways, besides that sap, we're talking about infinity here, mostly in
theory potential and actual infinity are equivalent. This thread is on
sci.physics. I'm trying to think of something that's infinite in the
physical universe. My opinion is that the universe is infinite,
although I saw an MWI scenario in a comic book when I was young,
multiple worlds intepretation, it's turtles all the way down. The zero
point projects to all infinite-dimensional polyhedra. What I'm trying
to say with that is that that doesn't matter from our medio-scale
perspective. About alternative philosophy, I understand there are
various meanings of the term objectivist, one of which is not Randian.
Maybe you've heard of that, too, that might make us semi- or
pseudo-objectivists, non-Randian objectivism, and perhaps anti-Randian
objectivism. In terms of logic, effect => cause for all intents and
purposes, although infinitely many consistent theories are
axiomatizable.
sci.math_030921_b:
Let's consider energy "pushing out" on the Universe, with: "condensed
energy". I can only assume you speak of mass. You are trying to say
that the expansive energy of the Universe is more than the mass of the
Universe. Do you know what that means? It means indefinite expansion
of the Universe. You are trying to say that the gravity of mass
"outweighs" the "expansive enery of the Universe". I'll tell you again
how to solve your problem: assume the Univeres is infinite, and
infinitely far away from the next Universe. You may as well assume
that our Universe is the center of a 3x3x3 Multiverse, et-cetera.
Jonathan Hoyle
>> I read that as differences between inferential (inductive) and
>> non-inferential.
I'm not sure what you mean by that, but almost certainly it is not what
I meant. I mean that the "inconsistencies" many ancient mathematicians
found in dealing with infinities had to do with one simple distinction:
in many instances, Countable Additivity holds whereas Uncountable
Additivity does not. Making this distinction sweeps away a number of
problems (whereas ignoring it can put you in a world of hurt).
>> That's a good book, I call it "70's state-of-the-art", and
>> was very widely read. among books on the subject
>> perhaps the most widely read book, almost certainly,
>> but it doesn't present any physical predictions of
>> uncountability that I can recall.
Are we speaking of the same book? "Infinity and the Mind" was released
in the 1990's, if I remember correctly.
>> There are twice as many of the iotas of [0,1] in [0,2]
>> than [0,1].
Then how do you explain the 1-1 mapping between [0,1] and [0,2] with
the function f(x) = 2x. For each and every x in [0,1] there is a
unique y=2x in [0,2], and for each and every x in [0,2], there is a
unique x/2 in [0,1]. No values are missed or ignored.
Jonathan Hoyle
Autymn D. C.
calender -> calendar
donsto...@hotmail.com
infinity and the actualized infinity and do something constructive.
Autymn D. C.
> Keep in mind, the universe is infinite. That's because for any two
> physical objects, each function between them is as well a physical
> object. In ZF set theory, there is no universe.
The universe is not infinite, and the number of functions for any two
objects is not infinite, as there are a finite number of objects and
states. And after some number of transforms, the functions are
dependent. Event horizons are porous.
-Aut
Ross A. Finlayson
Well obviously the reals are a complete ordered field. The book was
re-released.
Hoyle, you have a habit of offering mathematical redemption to those
talking about infinity. I don't have much use for your redemption.
You are having measure theory with uncountable additivity of measure
zero sets. I think that's bullshit. Zero + Zero = Zero. Zero's the
additive identity of the ring, and field, of real numbers.
ZF doesn't have a universe. That's plain and simple. If ZF is the
perspective, the universe is not part of that picture.
Where there is the set of all sets, that is its own powerset.
You mention NBG, initialized von Neumann-Bernays-Goedel, you imply that
it is infinitely axiomatized ZFC with classes, others might disagree in
a pedantic manner. What's the class of all classes? The universe
includes those things, anything, everything.
In a physical theory, the goal of a theory of everything is to have a,
yes, consistent, and complete, theory, of everything, including the
universe of everything.
Perhaps you might see reason to reconsider.
Ross
Ross A. Finlayson
What number of transforms would that be?
It's something to consider that the functions are not always different
than the previous set of functions, in a similar way as to how a
powerset of a set of ordinals contains some of the same ordinals as the
set. That basically gets into infinitely many, and, "countably"
infinitely many, instantons, that reduce back to the objects. For the
functions there are more functions, and in the physical universe
they're objects of the theory, do you get that?
Ask Kolker, he has no opinion.
The universe is infinite. Infinite sets are infinite. Infinite sets
are equivalent.
Ross
Autymn D. C.
> >> There are twice as many of the iotas of [0,1] in [0,2]
> >> than [0,1].
>
> Then how do you explain the 1-1 mapping between [0,1] and [0,2] with
> the function f(x) = 2x. For each and every x in [0,1] there is a
> unique y=2x in [0,2], and for each and every x in [0,2], there is a
> unique x/2 in [0,1]. No values are missed or ignored.
As iotas are limit solutions, mathematical inference proofs are bunk.
For every smallest-interval limit, there are twice as many intervals in
[0,2] as in [0,1]. One cannot go from a finite existence proof (for
each..) to an infinite existence proof (for every; for all..) to
compare the infinite content of two sets.
However, it is true that for each and every x in [0,1] that there is a
2x in [0,2], and the inverse, but the width of x of iota in [0,1] is
doubled to the width of x of iota in [0,2]. As numbers are elements of
spaces, they are made from boundaries of spaces; they dwell in
intervals and not points; there is no such thing as a zero-dimensional
point in any context except a zero-dimensional space. Thus, there are
twice as many numbers in [0,2] than in [0,1], even thouh there are the
same number of points.
-Aut
Down with Cantor! Hail Kronecker!
Autymn D. C.
> What number of transforms would that be?
Divide the volume of the universe by a Planck tetrahedron's volume to
get the number of spaces. Divide the mass of the universe by a
quantum's mass whose wavelength is bounded by the universe's width to
get the number of elements. Divide the life of the universe by a
Planck time's life to get the number of times. As there are a finite
number of particles in any sustem, the freedom of each is limited over
a finite range. As their motions are discrete, over any interval the
finite number of parameters can only generate a finite number of
functions. Besides, there are speed-energy limits.
> It's something to consider that the functions are not always different
> than the previous set of functions, in a similar way as to how a
> powerset of a set of ordinals contains some of the same ordinals as the
> set. That basically gets into infinitely many, and, "countably"
> infinitely many, instantons, that reduce back to the objects. For the
> functions there are more functions, and in the physical universe
> they're objects of the theory, do you get that?
>
> Ask Kolker, he has no opinion.
>
> The universe is infinite. Infinite sets are infinite. Infinite sets
> are equivalent.
Wrong, there are finite objects.
-Aut
Autymn D. C.
> Autymn D. C. said:
> > Tony Orlow wrote:
> > > What you are suggesting when you speak of particles that always move faster
> > > than light, in the light of relativity, is a particle of negative mass, isn't
> > > it? With no mass, any mmentum causes light speed. With positive finite mass,
> > > any momentum causes finite speed. To get speed beyond c, it would seem you need
> > > infinite momentum, or negative mass. I can see that particale of positive and
> >
> > no, imaginary--do the maths
> >
> >
> Oh, okay. Square root of negative (v/c)^2. Gotcha, I think. But, what does this
> mean in geometic terms?
Mass isn't geometric. However, mass-energy-force-space-time is
geometric. Look up my posts where I mention "mass ring" and "charge
dome" for my model of the particle. Also look at my messages for
tunnelling. Reading the "New Model" message also would help. A full
mechanistic model must have two temporal axes and six spatial axes.
For imaginary mass, the mass ring then exists in the next half of axes.
As the fundamental forces add another three interdependent axes to a
particle's description, making eleven axes, a particle existing
"off-shell" no longer is subject to the forces in our space, and
signals thereof may be transmitted at any arbitrary (hmm, tautology)
speed, as well as the speed limit, being medium-dependent, in that
space being arbitrary. But it's another tautology that particles
always travel at their speed limit. Changing the vacuum background
will keep the particle from cutting off when it goes superluminal.
-Aut
Jonathan Hoyle
>> of measure zero sets. I think that's bullshit. Zero + Zero
>> = Zero. Zero's the additive identity of the ring, and field, of
>> real numbers.
No, what I am saying is that Uncountable Additivity does NOT work with
Measure Theory, only Countable Additivity.
>> ZF doesn't have a universe.
I don't know what that means.
>> Where there is the set of all sets, that is its own
>> powerset.
Haven't I answered that question many times already? There are already
non-Well Founded Set Theories that handles this. Look for ZF + ~AF.
>> You mention NBG, initialized von
>> Neumann-Bernays-Goedel, you imply that it is
>> infinitely axiomatized ZFC with classes, others
>> might disagree in a pedantic manner.
"infinitely axiomatized ZFC"? I don't know what that means. NBG is a
small extension on top of ZFC. I'm not sure what there is to disagree
with here.
>> What's the class of all classes?
That's not in NBG. Try the Devlin book I mentioned, it has a Set
Theory including it.
>> In a physical theory, the goal of a theory of everything
>> is to have a, yes, consistent, and complete, theory, of
>> everything, including the universe of everything.
But when it does not correspond to either the truth of mathematics or
the truth of physics, all you have created, Ross, is a consistent, and
complete theory of a fictional universe.
Ross A. Finlayson
Thanks. Please don't call me a crank.
There's additivity of the intervals in infinitesimal analysis, the
integral calculus.
NBG is basically an axiom schema, where for each axiom of ZFC, for each
predicate and each input or set, that is an axiom, the axiom schema is
specialized for each input.
NBG doesn't necessarily contain the concept of a class. That's a
separate notion, added to variously ZF or what-have-you because such
things as the universe, the complete and entire universe, are part of
the domain of discourse. Cantor himself intuited that the universal
set exists, in calling that the domain principle, in a similar way as
to how Zermelo posited the well-ordering principle, and later others
the transfer principle.
http://mathworld.wolfram.com/TransferPrinciple.html
There is basically no difference between ZF and NBG. That's including
ZFC because I notice an ordinal exists for each of ZFC's cardinals,
where those are largely hereditarily finite, basically, yes, the
potential infinite.
Again, I'm not an expert in those theories, I'm not a proponent of
them, I think they're inconsistent besides being incomplete.
There is paraconsistency in the null axiom theory,
dual-self-intraconsistency. The natural numbers are that.
Ross
platopes
Autymn D. C. wrote:
[snip]
>
> As there are a finite
> number of particles in any sustem, the freedom of each is limited over
> a finite range.
Okay, but, and this is *key*, are there a fine looking "bunch" of
hufen-sporting mustics in any sustem? Or is that huperbole? Or what?
p
Jonathan Hoyle
I'm sorry, Ross, I don't mean to offend. But staatements like "ZF is
inconsistent", "all infinite sets are equivalent", "the universe is
infinite", etc., that is how you will be received.
>> NBG doesn't necessarily contain the concept of a class.
I don't think you understand NBG very well. Here is a link you should
read:
http://planetmath.org/encyclopedia/VonNeumannBernausGodelSetTheory.html
The opening reads: "von Neumann-Bernays-Gödel (commonly referred to as
NBG or vNBG) set theory is an axiomatisation of set theory closely
related to the more familiar Zermelo-Fraenkel with choice (ZFC)
axiomatisation. The primary difference between ZFC and NBG is that NBG
has proper classes among its objects. NBG and ZFC are very closely
related and are in fact equiconsistent, NBG being a conservative
extension of ZFC."
>> Cantor himself intuited that the universal set exists
Cantor predated ZFC, which does not contain a universal set of sets.
However, as I have stated ad nauseam, there are other Set Theories that
do. That doesn't make it inconsistent, it merely means that such a
"universal set" is not in the domain of ZFC to talk about.
>> There is basically no difference between ZF and NBG.
>> That's including ZFC because I notice an ordinal exists
>> for each of ZFC's cardinals, where those are largely
>> hereditarily finite, basically, yes, the potential infinite.
I aam not able to follow all of that. But essentially, all the same
ordinals and cardinals exist in NBG that live in ZFC, with the added
benefit that NBG alson contains such proper classes as the class of all
ordinals and the class of all cardinals. "The Potential infinite" (I
assume you mean something like the class of classes?) is not
addressable in NBG either.
For more on non-well-founded set theories, look at:
http://en.wikipedia.org/wiki/Non-well-founded_set_theory
Ross A. Finlayson
That's unfortunate.
I've heard of NBG before without the proper classes. Generally people
say "ZF(C) with classes". GNC, NBG, I thought they didn't have
classes, but instead were based around the axiom schema.
So, you want two kinds of collections, set, and classes, where for one
kind of the collection, the class, you can't quantify over them, and
the other, the set, if you do it's a class, and you can't quantify over
them?
So there's basically an anti-powerclass axiom, an anti-infiniteclass
axiom, anti-emptyclass axiom, anti-unionclass axiom, and so on, for
what holds true for the set does not for the class.
If you have the class of all ordinals, and the class of all sets, and
then some non-empty class of all sets that are not ordinals, besides
that Ord would be an ordinal, those notions denied classes as
collections are trivial theorems.
If Ord would be an ordinal, and a proper class, then the class of
ordinals contains a class and is wrong. Burali-Forti is the same
problem in the theory with classes.
There can only be one proper class.
Then, if you want to talk about the collection of classes, you say to
go to Morse-Kelley, or MK, set theory.
So, to talk about the universe, then ZF, ZFC, or NBG, are unusable?
In the limit, in infinitesimal analysis or the integral calculus, the
area of the section is zero, but it's often non-zero, and the sum is
over the naturals. The integral bar appears to be an S for summation,
with the definite integral super- and sub-scripts basically being range
of the summation.
Ross
Jonathan Hoyle
>> Generally people say "ZF(C) with classes". GNC,
>> NBG, I thought they didn't have classes, but instead
>> were based around the axiom schema.
They are. It's a not mutually exclusive scenario. It is merely a
matter of defining classes. In NBG, all sets are classes, but there
are certain proper classes that are available. Since NBG is
well-founded, it does not have the class of all classes, but it does
have the class of all sets.
>> So, you want two kinds of collections, set, and classes,
>> where for one kind of the collection, the class, you can't
>> quantify over them, and the other, the set, if you do it's a
>> class, and you can't quantify over them?
Essentially, although I think of NBG as really the most watered-down
extension of ZFC that is as close to ZFC as possible. NBG allows your
to formally talk of, say the class of all ordinals, whereas in ZFC you
can't even refer to it in any formal way. To get more interesting
results though, deeper Set Theories are available which allow you to
deal with non-Well Founded sets.
>> If Ord would be an ordinal, and a proper class, then the
>> class of ordinals contains a class and is wrong.
>> Burali-Forti is the same problem in the theory with classes.
Burali-Forti is avoided by virtue of the fact that the class of all
ordinals is itself not an ordinal. In NBG, no proper class is a member
of another class (classes can have only sets as members). You can't
get around Burali-Forti without replacing the Axiom of Foundation.
>> There can only be one proper class.
Actually, no, there re all kinds of proper classes: the class of
ordinals, the class of cardinals, the class of all sets, etc. etc.
Perhaps you meant to say all proper classes are the same "size"? This
is true, for an extended definition of "size". (But remember too that
proper classes to not bijectively map to any ordinal, so it is "the
largest" size anything can be.)
>> Then, if you want to talk about the collection of classes,
>> you say to go to Morse-Kelley, or MK, set theory.
Well, that is an excellent starting point, Ross, but don't limit
yourself just to there. From what I know of your other posts, you'll
probably not be happy until you get a much larger set view, including
non-Well Founded sets. View them as stepping stones. Most of
mathematics will be quite content in ZFC, but there are gems of
knowledge available in other systems.
>> So, to talk about the universe, then ZF, ZFC, or NBG,
>> are unusable?
What universe are you talking about? This is mathematics, not physics.
>> In the limit, in infinitesimal analysis or the integral calculus,
>> the area of the section is zero, but it's often non-zero, and
>> the sum is over the naturals. The integral bar appears to
>> be an S for summation, with the definite integral super-
>> and sub-scripts basically being range of the summation.
I'm afraid I don't know what any of that means.
Ross A. Finlayson
A class can't contain other classes, so there's no class of all classes
in any theory, no?
Yet, the universe is to contain everything.
In non-well-founded set theories, there is not necessarily a need for
classes for Burali-Forti? Every collection of zero and its succesors,
and for each its predecessor, is an ordinal. The problem with Ord, the
order type of the collection of ordinals, as a mathematical object, is
that it's an ordinal.
As an object of the domain of discourse, it's basically the
Ding-an-Sich, which is Kant's description of what he calls a
Thing-in-Itself in his native language. It's the Ouroboros, Ord is
less than nothing.
There are lots of models of the cosmos, ranging from the Norsk Tree of
Life with its remarkable squirrel, Ratatosk, to the Giant Spaghetti
Monster to immobile celestial spheres, which is remarkaby close to
accurate.
Some of the modern ones include having the universe being some packable
regular polyhedron, that a ray on a straight line proceeds in that one
direction and goes out the universe and comes back the other side and
returns to the origin. That's like calling a number line a number
circle of sorts, or projectively extended. It's also rather
ridiculous.
When I say that the physical universe is infinite, it's not necessarily
about no finite number of yardsticks necessary to return to the origin
in a straight line, it's about that objects in the universe, particles
and fields and oranges and puppies and various things, functions
between them as physical objects are also physical objects. Then, so
are the functions between those, and those between those, ad infinitum.
For example, if an orange and a puppy are the only things in the
universe, then gravity draws them together. As it does, then there's
the field gradient and its field gradient and so on ad infinitum.
Obviously that system is a point-wise instanton, yet it is infinitely
diverse along continuous time.
So, where the universe is all things, the totality, then it's infinite.
As well, if the universe contains everything, then that gets into the
dilemma of sorts, which I tend to spell dilemna and believe is the one
true correct spelling, that the universe in a way contains itself, as
it would in a theory adequate to discuss the universe.
To be honest I'm able to able to explain why Yggdrasil is an
illustration, in metaphor, of the null axiom theory, dually the
universal theory.
Ross
--
"I'm thinking about showing that the qabalah and gematria is a
null-axiom set theory with ubiquitous ordinals and ur-element. Is that
not funny?"
Jonathan Hoyle
>> all classes in any theory, no?
Of course you can have a class of all classes. I thought I stated this
many times already, so I apologize that I did not explain it well.
Absolutely you can have a class of all classes, but these occur
(obviously) only in non-Well Founded Theories. In a well founded
theory, you have the Axiom of Foundation which states that no set (or
class) can be members of themselves. A non-Well Founded theory is one
which does not contain the Axiom of Foundation. Again, I suggest the
Devlin book, "The Joy of Sets" but there are many others of course.
>> Yet, the universe is to contain everything.
Again, what universe are we talking about? The universe of set theory
contains only sets (or classes), whereas the phyical universe contains
elementary particles and relationships.
>> In non-well-founded set theories, there is not necessarily a
>> need for classes for Burali-Forti?
Typically, the term "class" is used to describe non-well founded
collections, whereas "set" is typically well-founded collections. In
some books on non-Well Founded Set Theory, they do not bother with the
distinction and call everything collection a "set". This is merely a
matter of terminology. Non-well founded collections have different
behavior than well-founded ones, so the distinction is an important one
to make most of the time. But some authors of non-WF Set Theories do
not wish to call out the distinction, so they do not.
>> Every collection of zero and its succesors, and for each its
>> predecessor, is an ordinal.
Typically, an ordinal is defined only for well-founded sets. So the
class of all ordinals is itself not an ordinal. Non-WF collections
have a "size" but not in the same way WF ones do. For example, the
class X = { X } is infinitely recursed as X = {{{{... ...}}}}. It
seems to have "size" 1 but infinite rank. But what size is the class
of all classes? Cardinality definitions become trickier, and you
should read how the individual theory defines it.
>> The problem with Ord, the order type of the collection of ordinals,
>> as a mathematical object, is that it's an ordinal.
Typically not, as this would give you contains itself as a member, thus
making ordinals not well-founded. However, I think some authors have
actually addressed this as a possibility, extended into non-WF
ordinals, I'm not sure. If you do extend it this way (making the class
of all ordinals an ordinal itself), you would have some interesting
properties.
<remaining philosophy and physics discussion snipped>
I snipped the remaining portion of your post only due to the fact that
it does not seem to speak to the subject at hand. I will say though
that the universe remains finite, and its corresponding Set Theory
would be extremely large (yet still finite) V_n, where n is the number
of elementary particles in the universe.
donsto...@hotmail.com
many times already, so I apologize that I did not explain it well.
******************
Another example of how complex everything is getting. Sure need a
Theory of Complexity pretty soon.
Daryl McCullough
>Typically, the term "class" is used to describe non-well founded
>collections, whereas "set" is typically well-founded collections. In
>some books on non-Well Founded Set Theory, they do not bother with the
>distinction and call everything collection a "set". This is merely a
>matter of terminology. Non-well founded collections have different
>behavior than well-founded ones, so the distinction is an important one
>to make most of the time. But some authors of non-WF Set Theories do
>not wish to call out the distinction, so they do not.
Are you sure about this terminology of set versus class? It
seems weird to me because there are well-founded proper classes,
and also because there is no reason to consider a collection with
one element X = { X } to be a class.
The usual distinction that I'm familiar with between set and
proper class in theories with only one sort of object is that
anything that can be proved to exist is a set, and any other
definable collection is a proper class. More formally, a
formula Phi(x) defines a set if
exists y, forall x, x in y <-> Phi(x)
otherwise, the collection of all x such that Phi(x) is
a proper class. In ZFC, the distinction is one of size:
a proper class is one such that there does not exist a
bijection to any set. In Quine's New Foundations, it's
a little more complicated, but definitely some formulas
such as Phi(x) = x is not an element of x do not define
a set. On the other hand, in NF, the collection of *all*
sets V = { x | x = x } exists, but is non-well-founded.
I thought that typically terminology in NF called V
a set, but still called R = { x | x is not an element of x }
a proper class.
--
Daryl McCullough
Ithaca, NY
Jonathan Hoyle
>> The usual distinction that I'm familiar with between set
>> and proper class in theories with only one sort of object
>> is that anything that can be proved to exist is a set, and
>> any other definable collection is a proper class.
Hi Daryl, I think you may be more accurate about the usage of "set" and
"proper class" within most theories than mine. In NBG however, a
proper classes are defined, so the class of ordinals is "officially" a
class, whereas the class of all classes does not exist in NBG.
I was speaking more from a meta-Theory perspective, that my experience
is that mathematicians typically do not speak of "the set of ordinals"
but rather the "class of ordinals" (whether or not a given theory has
such a concept). Likewise of any other collection that would be
non-well-founded if called a "set". But my experience is not a hard
definition of course, and I think your's may be a better one.
Jonathan Hoyle
Eastman Kodak
Daryl McCullough
>Hi Daryl, I think you may be more accurate about the usage of "set" and
>"proper class" within most theories than mine. In NBG however, a
>proper classes are defined, so the class of ordinals is "officially" a
>class, whereas the class of all classes does not exist in NBG.
Yes, NBG (and also Morse-Kelly set theory) have two sorts of
objects, sets and classes. But the distinction isn't on the
basis of whether it is well-founded or not. In NBG, the class
of all ordinals is well-founded.
>I was speaking more from a meta-Theory perspective, that my experience
>is that mathematicians typically do not speak of "the set of ordinals"
>but rather the "class of ordinals" (whether or not a given theory has
>such a concept). Likewise of any other collection that would be
>non-well-founded if called a "set". But my experience is not a hard
>definition of course, and I think your's may be a better one.
Okay, well the collection of all sets (or the collection of all
ordinals) *would* be ill-founded if it were a set, but since they
are classes (in NBG, anyway) they don't include themselves, and
so are perfectly well-founded. The weird cases allowed with
ZFC - foundation are sets such as
X = { X }
I don't think that the fact that they are not well-founded is a good
reason to not consider them sets. Or maybe you're thinking that the
cumulative hierarchy defines what's a set, and any other collection
is a proper class? I guess that's a viable distinction, but it's not
one I'd heard anyone make before.
Ross A. Finlayson
There's a simple solution to that.
Call them Hoyle classes. Are those Devlin classes?
Heh, hrm. I find that humorous.
If you have to leave first order logic, then as a consequence none of
second, third, ..., order logic are suitable. Similarly, when the
mathematical object is a set, and theory has non-set objects, and sense
is about the relationships and existence of mathematical objects, then
that's a non-sense theory: non-set: nonsense.
Skolemize, in the generic extension there are no new elements.
Mechanistically, any collection of all ordinals would be an ordinal.
That in various guises is called the paradox of Cesare Burali-Forti,
but is basically the same problem as infinity = infinity plus one, or
various concerns about the Socratic, Aristotlean, "potential" versus
"actual" infinity.
An ordinal exists for each cardinal. Well order the reals.
Ross
--
"Particle physics, it is said, is like trying to figure out how a watch
works by slamming two watches into each other at the speed of light and
looking at the pieces that fall out." - Greg "Elmo" Morrow