| Topic: |
Science > Physics |
| User: |
"mimus" |
| Date: |
06 Sep 2005 11:17:50 AM |
| Object: |
Can You Have Infinity Without Eternity? |
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
But does this prove that the Universe is eternal as well as infinite?
--
In the beginning, there was nothing, which exploded.
< Pratchett
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| User: "Brian Fletcher" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 05:23:48 PM |
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"mimus" <tinmimus99@hotmail.com> wrote in message
news:apq3uk6d08tr$.1wdeg14keieb1$.dlg@40tude.net...
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
But does this prove that the Universe is eternal as well as infinite?
--
In the beginning, there was nothing, which exploded.
< Pratchett
In the beginning "you" were "one cell". Then looked what happened.
When the mind finds its way to the edge of infinity via "proof" it has
nowhere else to go.Then look what happens.
BOfL
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| User: "" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 05:30:12 PM |
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Cybernetically, there are just two infinities, the potential infinity
and the actual infinity. This lets you get on with solving real-world
problems rather than debating forever.
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| User: "Wordsmith" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 02:00:36 PM |
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All the items you mention are, or at least seem to be (hedging my
bet!), potentially infinite, but I'm dubious as whether they're
acutally infinite.
The idea of an exploding nothingness stirs my poetic self.
W : )
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| User: "Publius" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 01:33:51 PM |
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mimus <tinmimus99@hotmail.com> wrote in news:apq3uk6d08tr$.1wdeg14keieb1
$.dlg@40tude.net:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
But does this prove that the Universe is eternal as well as infinite?
No. Equations, fields, etc., are conceptual constructs, and may be infinite
because they are defined that way.
Whether the universe is infinite or eternal is an empirical question, and
must be answered by observation. The evidence suggests it is not.
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| User: "Sam Wormley" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 11:37:40 AM |
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mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
But does this prove that the Universe is eternal as well as infinite?
Number of points on a circle.
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| User: "Mark Fergerson" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 12:12:45 PM |
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mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
Well, yes and no. "Infinity" is a convenient boundary condition
to assume because it allows the use of (relatively) simple
continuous functions. Experimentally, you can measure the field due
to an electron's charge out to the sensitivity limit of whatever
apparatus you're using, but that's a hardware-dependent issue that
doesn't necessarily verify the theoretically infinite spatial extent
of its field.
OTOH at some distance its field will vanish into the "noise
floor" of zero-point fluctuations. If you look at continuum
mechanics closely enough it smacks into QM, at which point you trade
one set of infinities for another.
But does this prove that the Universe is eternal as well as infinite?
No. Why do you think there's a connection?
Mark L. Fergerson
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| User: "mimus" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 12:54:17 PM |
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On Wed, 07 Sep 2005 10:12:45 -0700, Mark Fergerson wrote:
mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
Well, yes and no. "Infinity" is a convenient boundary condition
to assume because it allows the use of (relatively) simple
continuous functions. Experimentally, you can measure the field due
to an electron's charge out to the sensitivity limit of whatever
apparatus you're using, but that's a hardware-dependent issue that
doesn't necessarily verify the theoretically infinite spatial extent
of its field.
THE POINT IS, you have four different fundamental equations, borne out in
daily phenomena, experiment and practice, and all four have no boundary
conditions on the distance to which they're defined, and would be rather
different with boundaries defined.
That is the evidence; what counter- evidence is there that these unbounded
distances, and equations, are false?
--
In the previous number, the cattle rustlers (post-
Hegelian dogma) had trapped Professor Dewey in an
abandoned mine shaft (Jamesian pragmatism) and had
ignited the fuse leading to a keg of dynamite
(neo-Newtonian empiricism).
< S. J. Perelman
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| User: "PD" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 01:43:17 PM |
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mimus wrote:
On Wed, 07 Sep 2005 10:12:45 -0700, Mark Fergerson wrote:
mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
Well, yes and no. "Infinity" is a convenient boundary condition
to assume because it allows the use of (relatively) simple
continuous functions. Experimentally, you can measure the field due
to an electron's charge out to the sensitivity limit of whatever
apparatus you're using, but that's a hardware-dependent issue that
doesn't necessarily verify the theoretically infinite spatial extent
of its field.
THE POINT IS, you have four different fundamental equations, borne out in
daily phenomena, experiment and practice, and all four have no boundary
conditions on the distance to which they're defined, and would be rather
different with boundaries defined.
Really? Boundaries typically affect the *solutions* to equations, not
the equations themselves. The solutions are what's matched up to
experiment, and if the boundaries are too far away to have an effect on
the solution, then the agreement with experiment may be sufficiently
close (though perhaps not *absolutely, exactly* dead-on) that we say
our application of the equations is warranted.
That is the evidence; what counter- evidence is there that these unbounded
distances, and equations, are false?
Be careful about using math to drive the reality. We apply the math to
see if it matches reality over the domain we can measure. It's entirely
possible to apply math that assumes infinity to a reality that does not
contain infinity, and not have the agreement blow up cataclysmically.
A good example is radioactive decay. The exponential function *never*
goes to zero. A radioactive sample *always* eventually disappears.
PD
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| User: "Mark Fergerson" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 03:18:56 PM |
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mimus wrote:
On Wed, 07 Sep 2005 10:12:45 -0700, Mark Fergerson wrote:
mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
Well, yes and no. "Infinity" is a convenient boundary condition
to assume because it allows the use of (relatively) simple
continuous functions. Experimentally, you can measure the field due
to an electron's charge out to the sensitivity limit of whatever
apparatus you're using, but that's a hardware-dependent issue that
doesn't necessarily verify the theoretically infinite spatial extent
of its field.
THE POINT IS, you have four different fundamental equations
Which four "basic physical field equations" did you have in mind?
You mentioned electric, magnetic, gravitational, and "quantum
mechanical" as if they were four separate "basic physical" entities.
They are not. For starters, Maxwell used four equations just for the
electromagnetic field, which is one thing not two. BTW, you left out
the weak force, probably because it doesn't go to infinity. But
notice that it's what you might call a special case of the
electromagnetic force (actually, the electroweak force) which makes
it at least "basic". Oh, and don't forget that what we used to call
separately electricity, magnetism, and the weak force are now
inclusively described by Quantum Electrodynamics, which rather badly
blurs your arbitrary lines.
borne out in
daily phenomena, experiment and practice, and all four have no boundary
conditions on the distance to which they're defined, and would be rather
different with boundaries defined.
Pay attention; the _defined_ boundary for EM and gravity is
INFINITY, because of the 1/r^2 function. That function is _defined_,
not extracted from experimental observations.
That is the evidence; what counter- evidence is there that these unbounded
distances, and equations, are false?
The electroweak field may have a finite bound (if the charge
carrier in question is a W or Z) or infinite if the charge carrier
is an electron.
Did you gag on my mention of the field from an electron vanishing
into the ZPF?
Now, what did you mean by "false"?
Mark L. Fergerson
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| User: "mimus" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 06:02:57 PM |
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On Wed, 07 Sep 2005 13:18:56 -0700, Mark Fergerson wrote:
Pay attention; the _defined_ boundary for EM and gravity is
INFINITY, because of the 1/r^2 function. That function is _defined_,
not extracted from experimental observations.
Gosh, and the equations even work . . . .
--
In the previous number, the cattle rustlers (post-
Hegelian dogma) had trapped Professor Dewey in an
abandoned mine shaft (Jamesian pragmatism) and had
ignited the fuse leading to a keg of dynamite
(neo-Newtonian empiricism).
< S. J. Perelman
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| User: "Henry Lemington-Wholeflavors" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 11:27:54 AM |
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mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
They don't extend out to infinity, because the universe isn't
infinitely old, and c is finite.
But does this prove that the Universe is eternal as well as infinite?
No.
--
http://cherenkov-radiation.blogspot.com/
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| User: "1Z" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 09:14:11 AM |
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Henry Lemington-Wholeflavors wrote:
They don't extend out to infinity, because the universe isn't
infinitely old, and c is finite.
http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2
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| User: "mimus" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 11:33:52 AM |
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On 6 Sep 2005 09:27:54 -0700, Henry Lemington-Wholeflavors wrote:
mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
They don't extend out to infinity,
Take a look at "r" or "(x,y,z)" in those equations again . . . .
There's no boundary condition(s) imposed.
because the universe isn't
infinitely old,
You just begged my damned question.
and c is finite.
Yes, but that has nothing to do with the extent of the alternating electric
and magnetic waves involved . . . .
Indeed, it has nothing to do with the question at all.
But does this prove that the Universe is eternal as well as infinite?
No.
OK . . . .
--
In the previous number, the cattle rustlers (post-
Hegelian dogma) had trapped Professor Dewey in an
abandoned mine shaft (Jamesian pragmatism) and had
ignited the fuse leading to a keg of dynamite
(neo-Newtonian empiricism).
< S. J. Perelman
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| User: "PD" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 02:51:32 PM |
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mimus wrote:
On 6 Sep 2005 09:27:54 -0700, Henry Lemington-Wholeflavors wrote:
mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
They don't extend out to infinity,
Take a look at "r" or "(x,y,z)" in those equations again . . . .
There's no boundary condition(s) imposed.
Ah, but see, you're imposing a Euclidean geometry on the universe,
which has axes that run to infinity in all directions. That is probably
not warranted.
The geometry that runs on the surface of the Earth is definitely
non-Euclidean, and you'll note that it doesn't have infinite extent on
either longitudinal or latitudinal coordinates, and for good reason.
because the universe isn't
infinitely old,
You just begged my damned question.
and c is finite.
Yes, but that has nothing to do with the extent of the alternating electric
and magnetic waves involved . . . .
Yes it does. You assume that a charge has an electric field of infinite
extent. If the charge had a birth at some point in the past, then its
field does not have an infinite extent. There is nothing, in fact, that
requires that an electric field *must* have infinite extent.
Indeed, it has nothing to do with the question at all.
But does this prove that the Universe is eternal as well as infinite?
No.
OK . . . .
--
In the previous number, the cattle rustlers (post-
Hegelian dogma) had trapped Professor Dewey in an
abandoned mine shaft (Jamesian pragmatism) and had
ignited the fuse leading to a keg of dynamite
(neo-Newtonian empiricism).
< S. J. Perelman
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| User: "Brian Fletcher" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 05:35:03 PM |
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"PD" <TheDraperFamily@gmail.com> wrote in message
news:1126036292.271403.96330@g44g2000cwa.googlegroups.com...
mimus wrote:
On 6 Sep 2005 09:27:54 -0700, Henry Lemington-Wholeflavors wrote:
mimus wrote:
All of the basic physical field equations, electric, magnetic and
gravitational, as well as the quantum mechanical wave equations, are
defined and extend to infinity, and are borne out daily in phenomena,
experiment and practice.
They don't extend out to infinity,
Take a look at "r" or "(x,y,z)" in those equations again . . . .
There's no boundary condition(s) imposed.
Ah, but see, you're imposing a Euclidean geometry on the universe,
which has axes that run to infinity in all directions. That is probably
not warranted.
The geometry that runs on the surface of the Earth is definitely
non-Euclidean, and you'll note that it doesn't have infinite extent on
either longitudinal or latitudinal coordinates, and for good reason.
**You havn't had the experience of running around in circles???
**Of course you have! Joining two circles together and calling it infinity
is a step in the right direction.
BOfL
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| User: "mimus" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 03:30:24 PM |
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On 6 Sep 2005 12:51:32 -0700, PD wrote:
There is nothing, in fact, that
requires that an electric field *must* have infinite extent.
The equation is defined for all values of "r" . . . .
--
In the previous number, the cattle rustlers (post-
Hegelian dogma) had trapped Professor Dewey in an
abandoned mine shaft (Jamesian pragmatism) and had
ignited the fuse leading to a keg of dynamite
(neo-Newtonian empiricism).
< S. J. Perelman
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| User: "Richard Herring" |
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| Title: Re: Can You Have Infinity Without Eternity? |
12 Sep 2005 09:15:46 AM |
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In message <1mztgpmpc3wog.1k93jm0reswdn.dlg@40tude.net>, mimus
<tinmimus99@hotmail.com> writes
On 6 Sep 2005 12:51:32 -0700, PD wrote:
There is nothing, in fact, that
requires that an electric field *must* have infinite extent.
The equation is defined for all values of "r" . . . .
The *solution* of the equation is undefined until you specify a boundary
condition. Where's the boundary?
--
Richard Herring
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| User: "PD" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 05:09:22 PM |
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mimus wrote:
On 6 Sep 2005 12:51:32 -0700, PD wrote:
There is nothing, in fact, that
requires that an electric field *must* have infinite extent.
The equation is defined for all values of "r" . . . .
Being mathematically defined does not mean physically relevant.
SU(5) is a perfectly well-defined mathematical symmetry that breaks
down into SU(3)xSU(2)xU(1); however, nature does not appear to exhibit
SU(5) symmetry.
--
In the previous number, the cattle rustlers (post-
Hegelian dogma) had trapped Professor Dewey in an
abandoned mine shaft (Jamesian pragmatism) and had
ignited the fuse leading to a keg of dynamite
(neo-Newtonian empiricism).
< S. J. Perelman
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| User: "Henry Lemington-Wholeflavors" |
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| Title: Re: Can You Have Infinity Without Eternity? |
06 Sep 2005 04:44:01 PM |
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mimus wrote:
On 6 Sep 2005 12:51:32 -0700, PD wrote:
There is nothing, in fact, that
requires that an electric field *must* have infinite extent.
The equation is defined for all values of "r" . . . .
You're trivially wrong, even without resorting to non-Euclidean
geometry.
Think of a simple Big Bang with just the creation of a single electron.
The universe is expanding, and the electron just got created. Both of
these mean that there is a time varying electric field present. The
"news" of this electron's existance (its electric field) will therefore
travel at c.
15 billion years later, its electric field will extend 15 billion
light-years in every direction. 15 billion light-years isn't infinity.
Get it?
--
http://cherenkov-radiation.blogspot.com/
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| User: "Wordsmith" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 11:18:57 AM |
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Henry Lemington-Wholeflavors wrote:
mimus wrote:
On 6 Sep 2005 12:51:32 -0700, PD wrote:
There is nothing, in fact, that
requires that an electric field *must* have infinite extent.
The equation is defined for all values of "r" . . . .
You're trivially wrong, even without resorting to non-Euclidean
geometry.
Think of a simple Big Bang with just the creation of a single electron.
The universe is expanding, and the electron just got created. Both of
these mean that there is a time varying electric field present. The
"news" of this electron's existance (its electric field) will therefore
travel at c.
15 billion years later, its electric field will extend 15 billion
light-years in every direction. 15 billion light-years isn't infinity.
Get it?
I do. Infinity is just too big a concept (reality?) to get one's mind
around.
W : )
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| User: "tadchem" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 03:45:18 PM |
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"Wordsmith" <wordsmith@rocketmail.com> wrote in message
news:1126109937.775010.36570@f14g2000cwb.googlegroups.com...
<snip repost>
I do. Infinity is just too big a concept (reality?) to get one's mind
around.
The mind of a *mathematician* has no trouble dealing with infinities.
It is the observable (physical) universe that isn't big enough for an
infinity.
Good physicists are also mathematicians, but they also recognize the
necessity for *empirical* constraints.
Tom Davidson
Richmond, VA
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| User: "Henry Lemington-Wholeflavors" |
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| Title: Re: Can You Have Infinity Without Eternity? |
07 Sep 2005 09:45:10 PM |
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Wordsmith wrote:
Henry Lemington-Wholeflavors wrote:
mimus wrote:
On 6 Sep 2005 12:51:32 -0700, PD wrote:
There is nothing, in fact, that
requires that an electric field *must* have infinite extent.
The equation is defined for all values of "r" . . . .
You're trivially wrong, even without resorting to non-Euclidean
geometry.
Think of a simple Big Bang with just the creation of a single electron.
The universe is expanding, and the electron just got created. Both of
these mean that there is a time varying electric field present. The
"news" of this electron's existance (its electric field) will therefore
travel at c.
15 billion years later, its electric field will extend 15 billion
light-years in every direction. 15 billion light-years isn't infinity.
Get it?
I do. Infinity is just too big a concept (reality?) to get one's mind
around.
Even stranger, is the idea of different infinities.
The number of natural numbers (0, 1, 2 ....) is infinite, and is equal
to the number of integers (..... -2, -1, 0, 1, 2....).
However, the number of real numbers (such as pi) is also infinite, but
it's a bigger infinity than that mentioned previously. This can be
mathematically proved quite easily.
--
http://cherenkov-radiation.blogspot.com/
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| User: "Sleepyhead" |
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| Title: Re: Can You Have Infinity Without Eternity? |
08 Sep 2005 04:41:46 AM |
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This can be mathematically proved quite easily.
Maybe it can, but if infinity means "don't stop counting" rather than
"a very big number - much too big to comprehend" then the analysis is
entirely bogus.
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| User: "Henry Lemington-Wholeflavors" |
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| Title: Re: Can You Have Infinity Without Eternity? |
08 Sep 2005 10:45:19 AM |
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Sleepyhead wrote:
This can be mathematically proved quite easily.
Maybe it can, but if infinity means "don't stop counting" rather than
"a very big number - much too big to comprehend" then the analysis is
entirely bogus.
Nope, it's not bogus. There is no bijection (one to one countability)
between real numbers and natural numbers.
This can be shown using the diagonal slash procedure (IOW, when you try
and match up a set of natural numbers with a set of real numbers, you
can always show that you've missed a real number) and it means that the
infinite set of natural numbers has to be less than the infinite set of
reals.
--
http://cherenkov-radiation.blogspot.com/
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| User: "Sleepyhead" |
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| Title: Re: Can You Have Infinity Without Eternity? |
08 Sep 2005 12:56:26 PM |
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Yes, but only if the word "Infinite" is taken to mean "A number too
large to comprehend". If you simply never stop counting it doesn't make
any difference which set of numbers you're counting because
(ex-hypothesi) you'll never reach the end.
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| User: "DBLEXPOSURE" |
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| Title: Re: Can You Have Infinity Without Eternity? |
08 Sep 2005 04:36:15 PM |
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"Sleepyhead" <simonharpham@usa.net> wrote in message
news:1126202185.982669.166390@z14g2000cwz.googlegroups.com...
Yes, but only if the word "Infinite" is taken to mean "A number too
large to comprehend". If you simply never stop counting it doesn't make
any difference which set of numbers you're counting because
(ex-hypothesi) you'll never reach the end.
Alright. I am stepping into a realm wear I am surely to be bludgeoned to
death. I am neither a physicists nor a mathematician, I just find it all
very interesting.
Is not Infinity a mathematical dead ender? You cannot apply any mathematical
operator to it. It can't be divided, multiplied, added to or subtracted
from. Doesn't this tell us that either it is impossible or that our
understanding of mathematics is flawed. Perhaps the universe is not
Infinite. I can better understand absolute nothing better than, or more
easily than infinity or a never ending universe. Could it not be that the
universe slowly fades away to a point where matter cannot exist. That
space time itself is a gradient and behaves differently at it's edges than
it does at the center? To me this seems more comprehendible...??
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| User: "Proginoskes" |
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| Title: Re: Can You Have Infinity Without Eternity? |
08 Sep 2005 05:36:36 PM |
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DBLEXPOSURE wrote:
"Sleepyhead" <simonharpham@usa.net> wrote in message
news:1126202185.982669.166390@z14g2000cwz.googlegroups.com...
Yes, but only if the word "Infinite" is taken to mean "A number too
large to comprehend". If you simply never stop counting it doesn't make
any difference which set of numbers you're counting because
(ex-hypothesi) you'll never reach the end.
Alright. I am stepping into a realm wear I am surely to be bludgeoned to
death. I am neither a physicists nor a mathematician, I just find it all
very interesting.
Is not Infinity a mathematical dead ender? You cannot apply any mathematical
operator to it. It can't be divided, multiplied, added to or subtracted
from.
Which infinity are you talking about? One of the points needed for the
2-point compactification of R? The size of the set {1,2,3,...}, i.e.,
cardinals? Ordinals?
You can compute with cardinals; for instance aleph_0 * aleph_0 =
aleph_0. (Aleph_0 is the cardinality of {1,2,3,...}.) You can also do
arithmetic with ordinals:
(w + 2) + (w + 3) = 2 w + 5. (w is the first infinite ordinal.) You
can't subtract cardinalities, but you can subtract ordinal numbers
(provided you're working with surreal numbers).
And (+infinity) + (+infinity) = +infinity.
Doesn't this tell us that either it is impossible or that our
understanding of mathematics is flawed. Perhaps the universe is not
Infinite.
That's not the point, though.
--- Christopher Heckman
I can better understand absolute nothing better than, or more
easily than infinity or a never ending universe. Could it not be that the
universe slowly fades away to a point where matter cannot exist. That
space time itself is a gradient and behaves differently at it's edges than
it does at the center? To me this seems more comprehendible...??
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| User: "DBLEXPOSURE" |
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| Title: Re: Can You Have Infinity Without Eternity? |
08 Sep 2005 07:29:14 PM |
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"Proginoskes" <CCHeckman@gmail.com> wrote in message
news:1126218996.703959.6830@g47g2000cwa.googlegroups.com...
DBLEXPOSURE wrote:
"Sleepyhead" <simonharpham@usa.net> wrote in message
news:1126202185.982669.166390@z14g2000cwz.googlegroups.com...
Yes, but only if the word "Infinite" is taken to mean "A number too
large to comprehend". If you simply never stop counting it doesn't make
any difference which set of numbers you're counting because
(ex-hypothesi) you'll never reach the end.
Alright. I am stepping into a realm wear I am surely to be bludgeoned to
death. I am neither a physicists nor a mathematician, I just find it
all
very interesting.
Is not Infinity a mathematical dead ender? You cannot apply any
mathematical
operator to it. It can't be divided, multiplied, added to or subtracted
from.
Which infinity are you talking about? One of the points needed for the
2-point compactification of R? The size of the set {1,2,3,...}, i.e.,
cardinals? Ordinals?
You can compute with cardinals; for instance aleph_0 * aleph_0 =
aleph_0. (Aleph_0 is the cardinality of {1,2,3,...}.) You can also do
arithmetic with ordinals:
(w + 2) + (w + 3) = 2 w + 5. (w is the first infinite ordinal.) You
can't subtract cardinalities, but you can subtract ordinal numbers
(provided you're working with surreal numbers).
And (+infinity) + (+infinity) = +infinity.
Doesn't this tell us that either it is impossible or that our
understanding of mathematics is flawed. Perhaps the universe is not
Infinite.
That's not the point, though.
--- Christopher Heckman
I can better understand absolute nothing better than, or more
easily than infinity or a never ending universe. Could it not be that
the
universe slowly fades away to a point where matter cannot exist. That
space time itself is a gradient and behaves differently at it's edges
than
it does at the center? To me this seems more comprehendible...??
told you I would be bludgeoned to death... Way out of my league dude! I
thought a cardinal worked at the church and wore a funny hat :-) And I
thought I was ordinal ??
I guess I think of infinity as most common men do, Never ending. Now, with
my limited knowledge of your mathematical language, it seems to me you are
treating Infinity as a whole and it's real size is meaningless. Is that not
just a trick to make it possible to perform mathematical operations on it.
You can take this whole and cut it in half, mathematically, and you .5
whole but if you can't quantify the whole how can you quantify the half?
Please, excuse my ignorance... And please do, dumb it down some... :-)
I would like to here a response to my amateurish hypothesis..
I can better understand absolute nothing better than, or more
easily than infinity or a never ending universe. Could it not be that
the
universe slowly fades away to a point where matter cannot exist. That
space time itself is a gradient and behaves differently at it's edges
than
it does at the center? To me this seems more comprehendible...??
.
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| User: "Proginoskes" |
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| Title: Re: Can You Have Infinity Without Eternity? |
09 Sep 2005 02:16:15 AM |
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DBLEXPOSURE wrote:
"Proginoskes" <CCHeckman@gmail.com> wrote in message
news:1126218996.703959.6830@g47g2000cwa.googlegroups.com...
DBLEXPOSURE wrote:
"Sleepyhead" <simonharpham@usa.net> wrote in message
news:1126202185.982669.166390@z14g2000cwz.googlegroups.com...
Yes, but only if the word "Infinite" is taken to mean "A number too
large to comprehend". If you simply never stop counting it doesn't make
any difference which set of numbers you're counting because
(ex-hypothesi) you'll never reach the end.
Alright. I am stepping into a realm wear I am surely to be bludgeoned to
death. I am neither a physicists nor a mathematician, I just find it all
very interesting.
Is not Infinity a mathematical dead ender? You cannot apply any mathematical
operator to it. It can't be divided, multiplied, added to or subtracted
from.
Which infinity are you talking about? One of the points needed for the
2-point compactification of R? The size of the set {1,2,3,...}, i.e.,
cardinals? Ordinals?
You can compute with cardinals; for instance aleph_0 * aleph_0 =
aleph_0. (Aleph_0 is the cardinality of {1,2,3,...}.) You can also do
arithmetic with ordinals:
(w + 2) + (w + 3) = 2 w + 5. (w is the first infinite ordinal.) You
can't subtract cardinalities, but you can subtract ordinal numbers
(provided you're working with surreal numbers).
And (+infinity) + (+infinity) = +infinity.
Doesn't this tell us that either it is impossible or that our
understanding of mathematics is flawed. Perhaps the universe is not
Infinite.
That's not the point, though.
--- Christopher Heckman
I can better understand absolute nothing better than, or more
easily than infinity or a never ending universe. Could it not be that the
universe slowly fades away to a point where matter cannot exist. That
space time itself is a gradient and behaves differently at it's edges than
it does at the center? To me this seems more comprehendible...??
told you I would be bludgeoned to death... Way out of my league dude!
That's what happens when you post about infinity in sci.math. 8-)
I
thought a cardinal worked at the church and wore a funny hat :-) And I
thought I was ordinal ??
I guess I think of infinity as most common men do, Never ending. Now, with
my limited knowledge of your mathematical language, it seems to me you are
treating Infinity as a whole and it's real size is meaningless.
It's treated as an object with certain properties. One property that
seems to be in common with all the definitions is that infinity is
larger than any positive integer. Some systems don't allow infinity
minus 1 (because if you say infinity is the "smallest" object grater
than all integers, then you get a contradiction if you assume infinity
minus 1 exists), some say it's also infinity (cardinality in set
theory; take the set of integers -- which has cardinality aleph_0 --
and remove the element 0; the resulting set has cardinality alpeh_0 as
well), and some say that infinity minus 1 is okay (surreal numbers).
Different properties for different models of infinity.
Is that not
just a trick to make it possible to perform mathematical operations on it.
You can take this whole and cut it in half, mathematically, and you .5
whole but if you can't quantify the whole how can you quantify the half?
Your argument seems to say that since no real number is equal to
infinity, no real number is equal to half of infinity. That is
perfectly acceptable, because if
r = infinity/2, then 2*r = infinity, and 2*r is a real number. So if
infinity is not a real number, infinity/2 can't be, either.
Simiarly, the square root of -1 doesn't exist in the actual world (does
it?), but mathematicians can still say things like it's half of the
square root of -4.
Please, excuse my ignorance... And please do, dumb it down some... :-)
Check out these links:
Infinity: http://mathworld.wolfram.com/Infinity.html
Cardinal numbers: http://mathworld.wolfram.com/CardinalNumber.html
Ordinal numbers: http://mathworld.wolfram.com/OrdinalNumber.html
Surreal numbers: http://mathworld.wolfram.com/SurrealNumber.html
I would like to here a response to my amateurish hypothesis..
Go forth to yonder links and seek knowledge!
--- Christopher Heckman
I can better understand absolute nothing better than, or more
easily than infinity or a never ending universe. Could it not be that the
universe slowly fades away to a point where matter cannot exist. That
space time itself is a gradient and behaves differently at it's edges than
it does at the center? To me this seems more comprehendible...??
.
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| User: "Autymn D. C." |
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| Title: Re: Can You Have Infinity Without Eternity? |
11 Sep 2005 02:11:31 AM |
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DBLEXPOSURE, stop misspelling its. And go look up Riemann sphere.
Infinity and zero are together; they are or aren't numbers together.
.
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