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Author  Topic: Mathematics and Nature  
RAZD Member Posts: 19811 From: the other end of the sidewalk Joined: Member Rating: 10.0 
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. we are limited in our ability to understand by our ability to understand RebelAAmerican.Zen[Deist
 
Son Goku Member (Idle past 69 days) Posts: 1120 From: Ireland Joined: 
No, thatâ€™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.
 
cavediver Member (Idle past 1748 days) Posts: 4129 From: UK Joined: 
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?
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.
Back to the philosophy, but I really have lost interest now. I will finish by restating 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, 12182005 05:11 AM
 
RAZD Member Posts: 19811 From: the other end of the sidewalk Joined: Member Rating: 10.0 
is a mathematical concept.
 
Son Goku Member (Idle past 69 days) Posts: 1120 From: Ireland Joined: 
And?
 
RAZD Member Posts: 19811 From: the other end of the sidewalk Joined: Member Rating: 10.0 
On a forum where anything over integration is esoteric maths.
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?
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.
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.
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. we are limited in our ability to understand by our ability to understand RebelAAmerican.Zen[Deist
 
RAZD Member Posts: 19811 From: the other end of the sidewalk Joined: Member Rating: 10.0 
 
Son Goku Member (Idle past 69 days) Posts: 1120 From: Ireland Joined: 
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".
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.
 
Son Goku Member (Idle past 69 days) Posts: 1120 From: Ireland Joined: 
The mobius concept is a topology! The concept is a topological one. How can compare a topological concept to topology itself?
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.
 
cavediver Member (Idle past 1748 days) Posts: 4129 From: UK Joined: 
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.
quote:
I have been saying that the paper loop on its own is not the mobius strip.
Describe how the rotations of the apple are an abstraction.
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.
I'm glad you have reality so well sown up to be able to claim this. I wish I had your insight.
Let me know when you start working in the real world of subnuclear 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, 12182005 08:57 AM
 
RAZD Member Posts: 19811 From: the other end of the sidewalk Joined: Member Rating: 10.0 
Where this started:
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. we are limited in our ability to understand by our ability to understand RebelAAmerican.Zen[Deist
 
Son Goku Member (Idle past 69 days) Posts: 1120 From: Ireland Joined: 
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.
 
Dr Jack Member (Idle past 210 days) Posts: 3507 From: Leicester, England Joined: 
 
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Brad McFall Member (Idle past 3138 days) Posts: 3428 From: Ithaca,NY, USA Joined: 
quote: www.evcforum.net/cgibin/dm.cgi?action=msg&f=11&t=219&m=89#86 >www.evcforum.net/cgibin/dm.cgi?action=msg&f=11&t=219&m=89#86">http://www.evcforum.net/cgibin/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" 3D? 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" geoMETREE (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 enumbers 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 This message has been edited by Brad McFall, 12192005 10:23 PM



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