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Author Topic:   Mathematics and Nature
RAZD
Member
Posts: 19811
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 10.0


Message 76 of 90 (270398)
12-17-2005 8:28 PM
Reply to: Message 75 by Son Goku
12-17-2005 7:42 PM


Re: Confusions of Topology = 1 math for another
However no sequence of atoms can arrange themselves into the shape of August Mobius.

or his strip. we haven't even gotten down to the molecular level of what the model really is in comparison to what the mathematical concept of what it should be.

you are still talking about a mathematical abstraction, now look at the strip of paper with the tape holding it together.


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This message is a reply to:
 Message 75 by Son Goku, posted 12-17-2005 7:42 PM Son Goku has responded

Replies to this message:
 Message 77 by Son Goku, posted 12-17-2005 8:37 PM RAZD has responded

  
Son Goku
Member (Idle past 69 days)
Posts: 1120
From: Ireland
Joined: 07-16-2005


Message 77 of 90 (270401)
12-17-2005 8:37 PM
Reply to: Message 76 by RAZD
12-17-2005 8:28 PM


Re: Confusions of Topology = 1 math for another
you are still talking about a mathematical abstraction, now look at the strip of paper with the tape holding it together.

No, that’s my point. It doesn't matter, the Mobius strip is a topological property which something can either posses or not.
I can't make a piece of paper which posses this property, only one that comes asymptotically close to the property.
However I can have energy levels and boundaries which posses this topology.
This message is a reply to:
 Message 76 by RAZD, posted 12-17-2005 8:28 PM RAZD has responded

Replies to this message:
 Message 79 by RAZD, posted 12-18-2005 8:00 AM Son Goku has responded

  
cavediver
Member (Idle past 1748 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 78 of 90 (270444)
12-18-2005 4:10 AM
Reply to: Message 74 by RAZD
12-17-2005 6:39 PM


Re: Confusions of Topology = 1 math for another
1.b. Of or relating to that which is known by a restricted number of people.
2.a. Confined to a small group: esoteric interests.

We are already discussing mathematics, so I can only assume you a referring to some subset of the mathematically literate as your "small group" or "restricted number of people". What subset is this? Any that excludes you?

While you guys are busy patting yourselves on your backs about the various...

This is what I find insulting. MrJack and I are two mathematicians discussing some exceptionally basic concepts. We are not discussing personal choice or philosophy here. You seem to have a problem with being corrected over a definition, and then bring up Wikipedia to defend your position.

As I have mentioned before, you seem to value your own amateur "expertise" over a consensus of professionals, and seem to take umbridge when you are presented with new information. I have not once detected an ounce of interest in any new concepts presented (and I am talking about accepted facts about reality, not my own esoteric ideas), other than to attempt to deride or ridicule them from your position of skeptism and, more importantly, ignorance. I find this immensely disheartening and is why I am losing patience discussing anything with you... You sound more and more like Randman as time goes by.

You still do not have a real mobius strip, but just a poor approximation that is good for demonstrating the concept. The model is not the concept.

Back to the philosophy, but I really have lost interest now. I will finish by re-stating my point that it is not the paper loop itself that is my mobious strip; in the same way that I point to not the apple but rotations of the apple as the realisation of the group SO(3).

This should continue with SGs comments in his last post becasue that is far more pertient: is Mobius behaviour (or any other mathematical concepts) exactly realised by fundemental particles?

This message has been edited by cavediver, 12-18-2005 05:11 AM


This message is a reply to:
 Message 74 by RAZD, posted 12-17-2005 6:39 PM RAZD has responded

Replies to this message:
 Message 81 by RAZD, posted 12-18-2005 8:24 AM cavediver has responded

  
RAZD
Member
Posts: 19811
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 10.0


Message 79 of 90 (270460)
12-18-2005 8:00 AM
Reply to: Message 77 by Son Goku
12-17-2005 8:37 PM


Re: Confusions of Topology = 1 math for another
topological property

is a mathematical concept.


This message is a reply to:
 Message 77 by Son Goku, posted 12-17-2005 8:37 PM Son Goku has responded

Replies to this message:
 Message 80 by Son Goku, posted 12-18-2005 8:06 AM RAZD has responded

  
Son Goku
Member (Idle past 69 days)
Posts: 1120
From: Ireland
Joined: 07-16-2005


Message 80 of 90 (270461)
12-18-2005 8:06 AM
Reply to: Message 79 by RAZD
12-18-2005 8:00 AM


Re: Confusions of Topology = 1 math for another
Yes, it is.
And?
This message is a reply to:
 Message 79 by RAZD, posted 12-18-2005 8:00 AM RAZD has responded

Replies to this message:
 Message 82 by RAZD, posted 12-18-2005 8:26 AM Son Goku has responded

  
RAZD
Member
Posts: 19811
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 10.0


Message 81 of 90 (270462)
12-18-2005 8:24 AM
Reply to: Message 78 by cavediver
12-18-2005 4:10 AM


Re: Confusions of Topology = 1 math for another
We are already discussing mathematics,

On a forum where anything over integration is esoteric maths.

You seem to have a problem with being corrected over a definition, and then bring up Wikipedia to defend your position.

Which does show a common definition, does it not? There are other sources of the same definition, but why bother if you so readily dismiss anything that doesn't match your "high" level of understanding eh?

I will finish by re-stating my point that it is not the paper loop itself that is my mobious strip;

Funny, I don't remember you saying this particular point in just this way before.

What you are really saying here is that the model is not the concept of the mobius strip.

in the same way that I point to not the apple but rotations of the apple as the realisation of the group SO(3).

And deal with a mathematical abstaction of the apple instead.

This has been my point all along - you keep looking at mathematical abstractions instead of the real object.

Back to the philosophy, but I really have lost interest now.

It's not philosophy but reality intruding on your philosophy. I deal everyday with making my involved, technical, esoteric mathematical approximations of reality work in the real world and take into account the fact that the math is not the reality to make it work.

The mobius strip is just one example of this reality. One that most people can see.

Enjoy.


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we are limited in our ability to understand
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... to learn ... to think ... to live ... to laugh ...
to share.


This message is a reply to:
 Message 78 by cavediver, posted 12-18-2005 4:10 AM cavediver has responded

Replies to this message:
 Message 83 by Son Goku, posted 12-18-2005 8:38 AM RAZD has not yet responded
 Message 85 by cavediver, posted 12-18-2005 8:53 AM RAZD has responded

  
RAZD
Member
Posts: 19811
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 10.0


Message 82 of 90 (270463)
12-18-2005 8:26 AM
Reply to: Message 80 by Son Goku
12-18-2005 8:06 AM


Re: Confusions of Topology = 1 math for another
and so is the mobius strip concept, so comparing the topology to the mobius concept is comparing two concepts, not a concept to the reality of the model.
This message is a reply to:
 Message 80 by Son Goku, posted 12-18-2005 8:06 AM Son Goku has responded

Replies to this message:
 Message 84 by Son Goku, posted 12-18-2005 8:46 AM RAZD has not yet responded

  
Son Goku
Member (Idle past 69 days)
Posts: 1120
From: Ireland
Joined: 07-16-2005


Message 83 of 90 (270464)
12-18-2005 8:38 AM
Reply to: Message 81 by RAZD
12-18-2005 8:24 AM


Re: Confusions of Topology = 1 math for another
When we do Fluid Dynamics, to pick a random area of physics, nobody thinks that there literally is a Stress Tensor sitting at every point in the fluid, a 3 x 3 matrix that literally sits there and takes values.

The Stress Tensor can describe the fluid. It is a series of nine values and Stress on the fluid is a combination of nine independant "directions" of Stress.

Thats it, we know they aren't "real".

This has been my point all along - you keep looking at mathematical abstractions instead of the real object.

What does this mean?
To be honest it sounds like you have a vague idea of what we do and it amounts to us sitting around all day appreciating mathematics and laughing at laymen.
We study physics, just once more that word is physics, the science that studies the laws governing the natural world, the real world.
We do it because we love reality and how it works. If we liked mathematics so much we would have been mathematicians.
However when you start digging nature behaves more and more like our most abstract mathematical systems. This is why we talk in terms of mathematics, not to make ourselves seem smart or aloof, but because we need it. Nature behaves mathematically.
End of story, that is it.
This message is a reply to:
 Message 81 by RAZD, posted 12-18-2005 8:24 AM RAZD has not yet responded

  
Son Goku
Member (Idle past 69 days)
Posts: 1120
From: Ireland
Joined: 07-16-2005


Message 84 of 90 (270465)
12-18-2005 8:46 AM
Reply to: Message 82 by RAZD
12-18-2005 8:26 AM


Re: Confusions of Topology = 1 math for another
and so is the mobius strip concept, so comparing the topology to the mobius concept is comparing two concepts

The mobius concept is a topology! The concept is a topological one.
How can compare a topological concept to topology itself?

not a concept to the reality of the model.

What reality? We aren't applying it yet.
If you want me to compare it to reality, then the boundaries of junction ladders in conformal field theory can be compared to the concept of a mobius strip topology and found to behave the same.
So the boundaries of junction ladders in conformal field theory have a mobius strip topology.
This message is a reply to:
 Message 82 by RAZD, posted 12-18-2005 8:26 AM RAZD has not yet responded

  
cavediver
Member (Idle past 1748 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 85 of 90 (270466)
12-18-2005 8:53 AM
Reply to: Message 81 by RAZD
12-18-2005 8:24 AM


Re: Confusions of Topology = 1 math for another
Which does show a common definition, does it not? There are other sources of the same definition, but why bother if you so readily dismiss anything that doesn't match your "high" level of understanding eh?

Mathematics is fortunately not defined by popular consent of internet references. Dictionaries and encycolpedias of mathematics and physics are full of inaccuracies, and they need pointing out. I do this regularly with one of the UKs best selling dictionaries of science, as an assistant editor.

Funny, I don't remember you saying this particular point in just this way before.

quote:
But in the context of your definition of a Mobius Strip (and as you brought up the term, I have been at fault in immediately substituting my understanding for your understanding without adequately making this clear), you are quite correct. But given that your definition is essentially just an idealisation of a real object: Mobius' first piece of paper "cellotaped" into a loop with a twist, it is not too surprising that you say that my loop cannot possibly satisfy your definition, because it is not idealised. I am happy to concede this rather obvious point

What you are really saying here is that the model is not the concept of the mobius strip.

I have been saying that the paper loop on its own is not the mobius strip.

And deal with a mathematical abstaction of the apple instead.

Describe how the rotations of the apple are an abstraction.

This has been my point all along - you keep looking at mathematical abstractions instead of the real object.

I am looking at something different to what you think of as the "real object". But what I am looking at appears to be equally real to me.

It's not philosophy but reality intruding on your philosophy.

I'm glad you have reality so well sown up to be able to claim this. I wish I had your insight.

I deal everyday with making my involved, technical, esoteric mathematical approximations of reality work in the real world and take into account the fact that the math is not the reality to make it work.

Let me know when you start working in the real world of sub-nuclear to Planck scale physics and we will see how long your hard and fast ideas of reality last.

This message has been edited by cavediver, 12-18-2005 08:57 AM


This message is a reply to:
 Message 81 by RAZD, posted 12-18-2005 8:24 AM RAZD has responded

Replies to this message:
 Message 86 by RAZD, posted 12-18-2005 1:52 PM cavediver has not yet responded

  
RAZD
Member
Posts: 19811
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 10.0


Message 86 of 90 (270505)
12-18-2005 1:52 PM
Reply to: Message 85 by cavediver
12-18-2005 8:53 AM


Re: Confusions of Topology = 1 math for another
cavediver, msg 63 writes:

it is not too surprising that you say that my loop cannot possibly satisfy your definition, because it is not idealised. I am happy to concede this rather obvious point


cavediver, msg 74 writes:

I will finish by re-stating my point that it is not the paper loop itself that is my mobious strip;

Where this started:

razd, msg 31 writes:

We could argue about the concept of a plane as a surface, but let's cut to the quick and take {the still simple yet one level more complex concept of} the mobius strip: no such thing exists in reality.

Are we in agreement then? The mobius strip is a mathematical concept, the topological (mathematical) relationship that is mentally {visualised\extracted} from the paper model is also a mental concept and both are separate from the paper model.

AND that the paper loop is not a mobius strip but a model of one.

This really has nothing to do with understanding the maths at any esoteric levels, but with the relationship between the concepts and the reality of the models.


www.evcforum.net/cgi-bin/dm.cgi?action=msg&f=14&t=1157&m=1>Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

we are limited in our ability to understand
by our ability to understand

RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.


This message is a reply to:
 Message 85 by cavediver, posted 12-18-2005 8:53 AM cavediver has not yet responded

Replies to this message:
 Message 87 by Son Goku, posted 12-18-2005 2:13 PM RAZD has not yet responded

  
Son Goku
Member (Idle past 69 days)
Posts: 1120
From: Ireland
Joined: 07-16-2005


Message 87 of 90 (270512)
12-18-2005 2:13 PM
Reply to: Message 86 by RAZD
12-18-2005 1:52 PM


Re: Confusions of Topology = 1 math for another
AND that the paper loop is not a mobius strip but a model of one.

The paper loop has the mobius strip as a topology.
Of course the paper loop is not a mobius strip.
Just as an apple isn't the colour green, it is coloured green.
The paper has a mobius strip topology, it is not the mobius strip.

The boundaries of junction ladders in conformal field theory also have a mobius strip topology.


This message is a reply to:
 Message 86 by RAZD, posted 12-18-2005 1:52 PM RAZD has not yet responded

  
Dr Jack
Member (Idle past 210 days)
Posts: 3507
From: Leicester, England
Joined: 07-14-2003


Message 88 of 90 (270678)
12-19-2005 4:31 AM
Reply to: Message 69 by RAZD
12-17-2005 7:41 AM


Re: Confusions of Topology = 1 math for another
RAZD when someone refers you to a technical site giving a formal definition of a concept, refering to a popular site giving a popular definition isn't an answer. That's just as absurd as when Creationists argue back to Evolutionist citing The New York Times in answer to an article from Nature.
This message is a reply to:
 Message 69 by RAZD, posted 12-17-2005 7:41 AM RAZD has not yet responded

  
AdminNWR
Inactive Member


Message 89 of 90 (270694)
12-19-2005 8:32 AM


Lets get back on topic
I think the diversion on moebius bands has just about played out. How about a return to the main topic, as defined in the OP.


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  • Replies to this message:
     Message 90 by Brad McFall, posted 12-19-2005 10:02 PM AdminNWR has not yet responded

      
    Brad McFall
    Member (Idle past 3138 days)
    Posts: 3428
    From: Ithaca,NY, USA
    Joined: 12-20-2001


    Message 90 of 90 (270954)
    12-19-2005 10:02 PM
    Reply to: Message 89 by AdminNWR
    12-19-2005 8:32 AM


    Re: Lets get back on topic
    quote:
    the concept of a plane as a surface, but let's cut to the quick

    www.evcforum.net/cgi-bin/dm.cgi?action=msg&f=11&t=219&m=89#86 -->www.evcforum.net/cgi-bin/dm.cgi?action=msg&f=11&t=219&m=89#86">http://www.evcforum.net/cgi-bin/dm.cgi?action=msg&f=11&t=219&m=89#86

    What if one had a "surface" that was not made of thingees but where the parts were equal to the whole and it had enough incidence geometry properties to logically fullfill the place planes are in Spain, mainly, but could it contain topological properties but not "look" 3-D?

    I have always wondered if THIS was what I was looking at when I visualize a "snake" eating its' tail. It seems that one might work out a lot of "Euclid" geo-METREE (as in Euclidean geometry) with this inclination or declination but the point and the line and the line and the plane and the plane and the space, would just not have the relation of whole and part that Euclid had.

    It seems to me that this can be done without philosophy necessarily involved, but if I had wanted to refine Cantor e-numbers into this scene I might have just added enough math philosophy (due to the philosophy that Cantor himself reclined to have taught) that that would curtail me criticizing RAZD if he really spoke with Frege's vocity that Russel preferred over Cantor's marginal and thus marginalized notes, to the big Bertrand. Since types seem not to have any much applied streches(certainly none in supramolecular chemsitry that I know of), I blame the failure to get beyond the philosophical point to be merely a lack of will rather than any dynamic difference of attraction and repulsion. That is all because math at its most esoteric level is really simple, if it does not bring in the philosophically unresolved analytic vs synthetic difference, as it can be verified and remains if true, for anyone and everyone- with common sense etc.

    But can a the snake in stripping off its skin do so in a mobiously conditioned topological reality?

    GeoMETREE would be pure even if the further abstractions of Cantor's work or later set theorists (avoiding BR's focus on classes) was simply pure not yet applied.

    ( The speckled King Snake here
    http://www.evcforum.net/cgi-bin/dm.cgi?action=msg&f=14&t=1168&m=3#3
    started to bite and remain attached to its tail when feeding and even chewed a bit on it after it entered what I guess in snake years was "retirement" age. The snake never formed a loop head-to-tail when young. I thus attribute the oUrobORos
    http://www.crystalinks.com/ouroboros.html
    to some early observation of "elderly" snakes that never learned to eat softer foods after they "got dentures" and to thusly have no substance infintely, except through the actual life and death of snakes etc).

    This message has been edited by Brad McFall, 12-19-2005 10:23 PM


    This message is a reply to:
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