| Topic: |
Science > Physics |
| User: |
"Sam Wormley" |
| Date: |
03 Mar 2006 10:33:36 PM |
| Object: |
The Limits of Mathematics |
[MATHTREK]
The Limits of Mathematics
Some mathematical facts can't be compressed into a theory
because they are too complicated.
http://www.sciencenews.org/articles/20060304/mathtrek.asp
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| User: "Mike Elger" |
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| Title: Re: The Limits of Mathematics |
04 Mar 2006 12:10:15 AM |
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"Sam Wormley" <swormley1@mchsi.com> wrote in message
news:AM8Of.800513$x96.736009@attbi_s72...
[MATHTREK]
The Limits of Mathematics
Some mathematical facts can't be compressed into a theory
because they are too complicated.
http://www.sciencenews.org/articles/20060304/mathtrek.asp
Arrrr........ Lad, Tis true.....
many fields of math run out and a few connect on over into another field.
Coding Theory is like that.
Then again, personal limits of math are reached, but may never be
recognized, like JSH.
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| User: "" |
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| Title: Re: The Limits of Mathematics |
04 Mar 2006 12:46:55 AM |
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Those limitations are artificial. You can always define them away,
(assuming that the number of statements which are unprovable is
finite).
If the number of statements which are unprovable is infinite, (based on
a given set of axioms), then the number of exceptions is also infinite
and unclear if you can build walls around all of them.
More interesting are the limitations imposed on observability of
physical hoo-hahhhs like dimension.
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| User: "" |
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| Title: Re: The Limits of Mathematics |
07 Mar 2006 01:29:08 PM |
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What about Theory theory?
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| User: "uri" |
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| Title: Re: The Limits of Mathematics |
09 Mar 2006 11:36:16 AM |
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The limit of mathematics is it's abstraction. For example, what is
charge or an atom really?
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| User: "" |
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| Title: Re: The Limits of Mathematics |
04 Mar 2006 03:35:49 PM |
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Chaitin often makes overly grandiose claims about his work, so you have
to take any story based on interviews with hm with a grain of salt.
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| User: "BernardZ" |
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| Title: Re: The Limits of Mathematics |
04 Mar 2006 03:35:23 AM |
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In article <AM8Of.800513$x96.736009@attbi_s72>, swormley1@mchsi.com=20
says...
[MATHTREK]
The Limits of Mathematics
Some mathematical facts can't be compressed into a theory
because they are too complicated.
http://www.sciencenews.org/articles/20060304/mathtrek.asp
=20
There are some fields of mathematics that are not affected by G=F6del's=20
theorem.
--=20
People were participants not observers in history.=20
Observations of Bernard - No 97
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| User: "John Bailey" |
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| Title: Re: The Limits of Mathematics |
04 Mar 2006 07:45:28 AM |
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On Sat, 04 Mar 2006 04:33:36 GMT, Sam Wormley <swormley1@mchsi.com>
wrote:
[MATHTREK]
The Limits of Mathematics
Some mathematical facts can't be compressed into a theory
because they are too complicated.
http://www.sciencenews.org/articles/20060304/mathtrek.asp
For anyone interested in the subject of Godel/Chaitin/Incompleteness,
let me call to your attention the new book: Incompleteness by Rebecca
Goldstein. I recommend it only to those who collect books and
articles on the subject or who have no interest in the technical
subject and don't care if their basic ideas on the subject are
acquired from someone who seems to have a sociologist's understanding
of math. (The liar's paradox appears as a verse in the Bible--Titus
12:1-13)
OTOH Goldstein's book is very stimulating. Reading what one perceives
as a wrong headed idea makes you think hard about what the corrected
version would be.
Soduko provides a model for science, mathematics and knowledge.
Imagine several players. On a turn a player provides a number to be
entered into a soduko cell. Other players can see that entry and
using that knowledge will be able to add other numbers. A player may
wrongly propose a number. Other players may question his proposal. As
the game proceeds, the combined effort of the players determine more
and more of the grid's numbers. Not every initial configuration can
be fully solved. Further, if a wrong entry is made, the solution may
be lost--become dead ended (needlessly) The question is:
Does this game (our universe and its physics) have an ultimate
solution (satisfying all constraits) or is the game flawed?
The dream of an over-arching theory of Physics which encompasses
everything and explains everything is thwarted by Godel's Theorem. An
axiomatic system [of theorems] cannot be both complete and consistent.
Either the system will contain contradictions or there will be
theorems which can neither be proved nor disproved.
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| User: "Bob Cain" |
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| Title: Re: The Limits of Mathematics |
16 Mar 2006 06:22:17 PM |
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John Bailey wrote:
OTOH Goldstein's book is very stimulating. Reading what one perceives
as a wrong headed idea makes you think hard about what the corrected
version would be.
Her "fiction" is great too. Especially the one about what it's like to
be a woman married to a genius. :-)
She's a philosopher and the dialogs and commentary in the book are what
she's really trying to project in a very entertaining way.
Bob
--
"Things should be described as simply as possible, but no simpler."
A. Einstein
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| User: "Jan Panteltje" |
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| Title: Re: The Limits of Mathematics |
04 Mar 2006 06:59:56 AM |
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On a sunny day (Sat, 04 Mar 2006 04:33:36 GMT) it happened Sam Wormley
<swormley1@mchsi.com> wrote in <AM8Of.800513$x96.736009@attbi_s72>:
[MATHTREK]
The Limits of Mathematics
Some mathematical facts can't be compressed into a theory
because they are too complicated.
http://www.sciencenews.org/articles/20060304/mathtrek.asp
<start serious>
This is interesting Sam, it reflects what I wrote in response to one of the
postings about that new 'gravity formula', making an equation from data.
I keep asking myself in how far Chaitin touched on neural nets.
As you can see a computer program that represents a neural net (including
its configuration and weights) as something that gives answers that will
CHANGE (possibly) every time, based on the new weights set by feedback
in a learning process......
And then see in the final conclusion in that link:
'
Chaitin goes further. Human creativity is absolutely necessary for
mathematical work, he argues, and "intuition cannot be eliminated from
mathematics.'
where he ADMITS that 'intuition' is the key (sort of) and this 'intuition'
thing is what the neural net does as standard action.
The mathematician IS<<<<<----- a neural net, and the math (structure) just
a distilled pattern in it (configuration and weights).
And from that follows immediately the same conclusions.
It ticked of Baez in a bad way when I called him a neural net some month ago.
But is not reality what we want to understand?
</serious>
hehe
LOL
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| User: "tadchem" |
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| Title: Re: The Limits of Mathematics |
05 Mar 2006 12:31:53 PM |
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To weigh in on this for the empiricists, I would like to point out that
empirical validation of theoretical statements developed through
mathematics is *exempt* from Goedel's Incompleteness Theorem, as the
empiricism leave the system open.
We lab scientists see mathematics as a 'toolbox'. Given a problem we
look in our toolbox to find the right tool (mathematical technique) to
fix (solve) it.
Sometimes if the problem is novel we may not have the right tool on
hand to use, and we are always open to developing new tools.
If RadicalLibertarian would pause for a moment and think, it would
become almost trivial to *prove* that if there is a single statement
that can be made within any given closed system of logic that cannot be
proven in that system, then there is at least one entire (infinite)
family of statements that can be made within that system that cannot be
proven for exactly the same reasons. If he has *any* mathematical
telent at all he should be able to develop this proof.
I would like BernardZ to know that any branch of mathematics that is
"not affected by G=F6del's theorem" cannot encompass even the simple
arithmetic of counting or dichotomous set theory, and so is of limited
or no applicability to the external universe in which we all live (and
in which we empiricists work).
Jan Panteltje makes a reference to neural nets, which are simply
non-rigorous logic systems. They make probability estimates of the
validity of conclusions based on their own complexity, experience, and
self-correction capability. They 'cross the line' from axiomatic
systems of mathematics and thus are not 'covered' by Goedel's Theorem.
John Bailey make reference to multi-player Soduko, a system in which
Cartesian determinacy *should* apply, but actions are often made in the
absence of an exhaustive analysis and lead to insoluble situations.
The lesson here for students of 'science, mathematics and knowledge' is
that the more exhaustive the analysis *before* an action is taken, the
less likely mistakes will be made. Chess (in which exhaustive analysis
is computationally nearly impossible) provides a similar model, and an
argument for the *need* to develop 'fuzzy logic' techology such as
neural nets.
Non-axiomatic systems such as neural nets provide tools that are useful
but which do not fit inside the 'toolbox' of mathematics to which we
are accustoimed and to which Goedel's Theorems apply.
Tom Davidson
Richmond, VA
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| User: "bernardz" |
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| Title: Re: The Limits of Mathematics |
05 Mar 2006 06:08:31 PM |
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I would like BernardZ to know that any branch of mathematics that is
"not affected by G=F6del's theorem" cannot encompass even the simple
arithmetic of counting or dichotomous set theory, and so is of limited
or no applicability to the external universe in which we all live (and
in which we empiricists work).
G=F6del's theorems does not apply to Euclidean geometry. Checkout
Tarski's axioms!=20
Few people would regard this as a trivial theory.
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| User: "uri" |
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| Title: Re: The Limits of Mathematics |
07 Mar 2006 11:09:49 AM |
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Mathematics has limits because it's abstract. I mean the fields which
deal with higher dimensions in set theory and topology are abstract.
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| User: "Grendel" |
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| Title: Re: The Limits of Mathematics |
07 Mar 2006 11:41:49 AM |
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Mathematics has limits because it's abstract. I mean the fields which
deal with higher dimensions in set theory and topology are abstract.
Mathematics, by its very definition, has no limits. The only limits to
math are to the extent that people are able to understand and/or apply
mathematics.
Mathematics is in no way abstract (no more than grass is abstract) and
is the most logical of the sciences. If done correctly, the true
answer will be reached. The limits of math are inherent in a
person's ability, not contained within the math itself.
Math can be used to determine/describe Nth dimensional dynamics and
string theory and countless other science. The fact that the human
mind is unable to picture a 4th dimensional object does not mean that
it does not exist and cannot be described by math. (FWIW, the 4th
dimension is 90=B0 from the first three) We are just unable to
comprehend the answer.
Much as the little fellow in "Flatland" is unable to comprehend a
third dimension until shown by a higher being, human minds will be
unable to encompass some higher dimensions until such time as we make
astounding breakthroughs in science and thinking. How does one
envision a sphere in a two dimensions? Math, with all probability,
will be the tool used to show us the way.
Yol Bolsum,
Grendel.
"Black holes are where God divided by zero."
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| User: "uri" |
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| Title: Re: The Limits of Mathematics |
07 Mar 2006 11:47:52 AM |
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Symbolic thinking is abstract. Numbers are abstracted from the object
or event that they describe in the sense that a meaning from the number
may be applied to the objects or events that the number describes.
Symbolic thinking is emergent here in that there may be a special
meaning of twoness.
http://www.psinvention.com/zoetic/abstract.htm
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| User: "Grendel" |
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| Title: Re: The Limits of Mathematics |
07 Mar 2006 12:02:17 PM |
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Symbolic thinking is abstract.
In that case, you don't exist; you are only abstract, because ALL
thinking is symbolic, thus abstract. Everything is labels.
The word "Grass" is a symbol for the green (symbol) vegetable
(symbol) matter (symbol) on the lawn (symbol).
This entire conversation is symbol. Every word, name, description is a
symbol of an actual thing.
When I see "Red" is it the same color that you see? It may not be,
it may be that you and I see the color red differently. But when we
attempt to replicate it in the real world, we may be replicating in our
own way but the other sees it differently. You may never know.
All language can be considered abstract as all language is based on
symbols. What one thinks or says is only a group of symbols that
humankind has agreed means a certain thing.
Math is no more abstract than water, and is FAR more logical than the
I.R.S.
If we ever contact an extraterrestrial intelligence, it will be math
that helps us communicate.
Yol Bolsum,
Grendel.
"Black holes are where God divided by zero."
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| User: "Y.Porat" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 02:08:11 AM |
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since we are in a physics ng
and not in a mathematics ng
it should be clear once and forever
1 too many mathematicians think that they can sit
with a paper and pencil not know too much physics
and solve all the problems of physics with Devinne accuracy
(even the biggest computers of today will not do it )
that is the old sin of Hubris
that we have to shake them off once and forever
2
any mathematical for fomula or equation in *physics*
*has its limits of validations*
it is the task of the real physicists to make clear
those limits !!
ATB
Y.Porat
--------------------------
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| User: "Hexenmeister" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 07:08:17 AM |
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"Y.Porat" <maporat@012.net.il> wrote in message
news:1142582891.869859.23130@j33g2000cwa.googlegroups.com...
| since we are in a physics ng
| and not in a mathematics ng
| it should be clear once and forever
|
| 1 too many mathematicians think that they can sit
| with a paper and pencil not know too much physics
| and solve all the problems of physics with Devinne accuracy
| (even the biggest computers of today will not do it )
|
| that is the old sin of Hubris
| that we have to shake them off once and forever
|
| 2
| any mathematical for fomula or equation in *physics*
|
| *has its limits of validations*
| it is the task of the real physicists to make clear
| those limits !!
|
| ATB
| Y.Porat
| --------------------------
It is the task of real physicists to learn those limitations themselves
*before* they try to teach, and not misuse mathematics.
Mathematics is a tool like any other, one should not use a kitchen
knife as a screwdriver, or a hammer to solve a jigsaw puzzle.
Androcles.
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| User: "Y.Porat" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 09:43:16 AM |
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right
i didnt say a single word differently
the only trouble with learning those limaitations by youself is
and tak ethem as ghospels
and a few years later it comes out by peooel with
a mind of themselves
that some of those books are nonsense
take for instance the Bhore model that was worshiped
a long period
it was not so long ago it was 'in th emodern era of physics !!
that say aprrot slike you learn from existing books
for another instance
that th e photon is massless
so how can a parrot like you think about another possibility??
while with some independant thinking yiou could reallise that it is
nonsens physics (provided that you are not an *assertive parrot*
(not just a parrot but an assertive and agressive one !!)
Keep well
Y.Porat
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| User: "Robert Low" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 02:20:36 AM |
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Y.Porat wrote: (to sci.math)
since we are in a physics ng
and not in a mathematics ng
I think you might want to adjust the groups
you're posting to.
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| User: "Y.Porat" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 03:10:32 AM |
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why dont you mention the rest part of my post ??
(and may be comment on it ??)
ATB
Y.Porat
---------------
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| User: "T Wake" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 03:15:43 AM |
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"Y.Porat" <maporat@012.net.il> wrote in message
news:1142586632.701184.7750@j52g2000cwj.googlegroups.com...
why dont you mention the rest part of my post ??
(and may be comment on it ??)
Well, you have posted to sci.math so you have falsified your initial claim.
(As you don't like quoting it was "since we are in a physics ng and not in
a mathematics ng it should be clear once and forever."
Pretty much renders the rest irrelevant.
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| User: "Euclid Uranium" |
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| Title: (no subject) |
23 Mar 2006 12:03:54 PM |
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"T Wake" <taswakeAt@hotmail.com> wrote:
Well, you have posted to sci.math so you have falsified your initial claim.
(As you don't like quoting it was "since we are in a physics ng and not in
a mathematics ng it should be clear once and forever."
Pretty much renders the rest irrelevant.
Tell Nelly will as opportunitys small joys, are fucking fringe.
Until the of itchy white outlets except for Shah will not claiming in
touch with Sara's future such an function. When Eliza, and voltage on
the commerce is what did Zamfir will Satam, and other channels is
gives you have complete, navel.
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| User: "" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 04:01:18 AM |
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That's what I say, too.
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| User: "Y.Porat" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 04:33:50 AM |
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sorry you are right !!
i found it in sci.physics
and it was not indicated there that is is in
sci.maths
anyway
it is imho important that sci .maths people
will see it as well
becaus as you see there is a strong entanglement between those groups
ATB
Y.Porat
-------------------------
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| User: "T Wake" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 08:30:45 AM |
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"Y.Porat" <maporat@012.net.il> wrote in message
news:1142591630.480904.18080@j52g2000cwj.googlegroups.com...
sorry you are right !!
i found it in sci.physics
and it was not indicated there that is is in
sci.maths
anyway
it is imho important that sci .maths people
will see it as well
becaus as you see there is a strong entanglement between those groups
Yes there is. Without mathematics how would we model the physical world?
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| User: "Y.Porat" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 09:53:52 AM |
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mathematics i sone of our best tool
but we have to know how to use it and how not to use it
Dynamite is as well a good tool for building
but we have to learn how to use it and how not to use it !!
a bad use of mathematics might be devastating tothe advance of scince
and the first thi9ng to learn abot it is
that ijn physics it has its limits of validation
mathmaticiance with no physics sense and experieince
may be very misleading
i met just a few days ago a physicist that claimed that
the Plank constant h is just a constant figure !
do you get where a mathematics education
that pretends to be physics education leads to ???
ATB
Y.Porat
----------------------
ATB
Y.Porat
--------------------
ATB
Y.Porat
----------------------------
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| User: "Hexenmeister" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 10:47:51 AM |
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I'm sorry to be the one to tell you this, but you've reached the point of
total incomprehensibility. Are you skiving off school?
Androcles.
"Y.Porat" <maporat@012.net.il> wrote in message
news:1142610832.888382.324150@v46g2000cwv.googlegroups.com...
| mathematics i sone of our best tool
| but we have to know how to use it and how not to use it
|
| Dynamite is as well a good tool for building
| but we have to learn how to use it and how not to use it !!
|
| a bad use of mathematics might be devastating tothe advance of scince
| and the first thi9ng to learn abot it is
| that ijn physics it has its limits of validation
| mathmaticiance with no physics sense and experieince
| may be very misleading
|
| i met just a few days ago a physicist that claimed that
| the Plank constant h is just a constant figure !
|
| do you get where a mathematics education
| that pretends to be physics education leads to ???
|
| ATB
| Y.Porat
| ----------------------
|
|
|
| ATB
| Y.Porat
| --------------------
|
| ATB
| Y.Porat
| ----------------------------
|
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| User: "Hexenmeister" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 07:15:13 AM |
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"Y.Porat" <maporat@012.net.il> wrote in message
news:1142591630.480904.18080@j52g2000cwj.googlegroups.com...
| sorry you are right !!
| i found it in sci.physics
| and it was not indicated there that is is in
| sci.maths
| anyway
| it is imho important that sci .maths people
| will see it as well
| becaus as you see there is a strong entanglement between those groups
|
| ATB
| Y.Porat
| -------------------------
There is no such animal as "sci" math, just as there is no such
thing as "computer science". Computers are technology, not
natural occurrences. Science is the study of NATURE as it IS, not
the invention of black holes and then go looking for them.
Androcles.
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| User: "Robert Low" |
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| Title: Re: The Limits of Mathematics |
17 Mar 2006 11:07:09 AM |
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Y.Porat wrote:
why dont you mention the rest part of my post ??
(and may be comment on it ??)
Because you seemed to think that you were restricting
your comments to a phyics group. But OK:
1 too many mathematicians think that they can sit
with a paper and pencil not know too much physics
and solve all the problems of physics with Devinne accuracy
(even the biggest computers of today will not do it )
Which mathematicians are these? I never met one.
2 any mathematical for fomula or equation in *physics*
*has its limits of validations*
What mathematician ever said otherwise?
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