What definition of "dimension" are you using here. Because it is my understanding that the only scientific definition does not preclude time, for example, being one.
On a side note, c'mon black caps, what are you doing!
Extraordinary claims require extraordinary proof
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What definition of "dimension" are you using here. Because it is my understanding that the only scientific definition does not preclude time, for example, being one.
On a side note, c'mon black caps, what are you doing!
Reality Check
Penultimate Amazing
E.g. "F = ma" vs "the acceleration of an object is proportional to the force applied, and inversely proportional to the mass of the object".
sol invictus
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You're still failing to understand the most basic point in this discussion after being told it multiple times. A strip of paper with a half-twist is NOT an "actual" Mobius strip. A Mobius strip is a TWO DIMENSIONAL surface. It is an abstract mathematical concept, like the number 5.
It's the paper model that fails to represent the Mobius strip, not the other way around.
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sol invictus
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No it isn't - what are you talking about? That's woo talk. Don't you know that tables are made of atoms, and atoms have tons of space between them? Tables don't have a surface at all, that's just abstract mathematical BS.
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Yes, when I realised that I started to call a strip of paper with a half twist a mobius band (not strip). In my experience, most (virtually all) people describe the paper model as a mobius strip, not a model of the math. Confusion is bound to result.
I’ve always thought that math works best when used to abstractly model reality, not the other way around. Of course math can come first as a predictive tool, but if the prediction isn’t ultimately validated by reality, does it have any credibility or value? What value does mobius strip math have if it can’t be validated by reality? It’s interesting that you say that it’s the reality that’s failing and not the math. When did math become god?
I think the purpose of this thread is questioning whether or not the current predictive math of the universe (extraordinary claims to some) is validated by the reality of the universe (extraordinary proof).
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sol invictus
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Those people should be more precise.
A Mobius strip is one of the simplest non-trivial examples of what mathematicians call a fiber bundle. Fiber bundles play an absolutely central role in physics (although physicists don't usually think of things in that language). Without them we wouldn't understand anything about the three forces of particle physics, or the Pauli exclusion principle, or many other essential phenomena of nature. So "Mobius strip math" is extraordinarily well validated by reality. Note that the types of Mobius strips involved there are not physical objects - they are configurations of fields, for example, or of groups of symmetry transformations.
It’s interesting that you say that it’s reality that’s failing and not the math. When did math become god?
I didn't say anything of the sort. I just said that a paper strip with a half twist is not the same thing as a Mobius strip.
Do you only believe in things you can make with paper? What about justice? The number 5? A true flat surface?
Absolutely correct! The only really non-abstract things are whatever the smallest things are that can’t be divided (elementrons?). All things that are formed by combinations of these things are just abstractions. Or is it that the universe is the only “pure” thing and divisions of it are just abstractions?
Your post #303 - "It's the paper model that fails to represent the Mobius strip, not the other way around."
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Perhaps that's because a paper model of a Mobius strip is only an approximation of a real Mobius strip?
sol invictus
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Yes, and? I said the piece of paper is not a Mobius strip, and to you that means reality is failing and math is god?
Do you believe in the number 5? If so, please provide a physical model for it.
What's that? You can't? I guess we'd better throw it out as a concept then. That's going to make it a little hard to run an economy, isn't it? Back to the stone age we go, all because of ynot...
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The mobius strip mathematical model has no actual existence. It’s not real. The paper model is the thing that’s real.
“It's the paper model that fails to represent the Mobius strip”
If this isn’t a specific statement then perhaps you’re one of “those people” that needs to be “more specific”.
5 has no actual existence but it abstractly exists as part of an abstract mathematical system and language. The digits of my hand are a physical model for 5.
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sol invictus
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I honestly have no idea what you're on about. The paper model is not a Mobius strip - it's a model, and not a perfect one. So?
Right - and not a perfect one. For example, suppose you cut yourself and lose a little of one finger. Is what remains attached to your hand still a good model for 5? Clearly there's a problem, but that doesn't mean we should abandon 5, or that it doesn't make sense...
Anyway, I'm getting less than nothing out of this exchange, so I'm ending it.
Abstract mathematical models may or may not accurately represent actual reality. The abstract mathematical models themselves are only abstract realities, not actual realities.
All I’m saying is if a mathematical model can’t be validated by actual reality, what credibility or use does it have? If a mathematical model can be validated by actual reality it is credible and useful. I’m not throwing out the baby with the bathwater as some seem to suggest.
See?
Reality Check
Penultimate Amazing
In general "mathematical models" are created to model actual reality. Therefore they have both credibility and usefulness.
Mathematicians though do not just do mathematical physics. The mathematical models used to describe reality are just a small part of mathematics. Thus there are things in mathematics that can’t be validated by actual reality because they do not occur in actual reality.