Möbius strips and differential equations
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Möbius strips and differential equations
1–10 of 25 posts
Re: Möbius strips and differential equations
#2Here's the reason you need enginners in the universe. Yes, the strip has non-orientability. Howwever, just introduce spin about the center, as you would a wheel, and you get all the same benefits of orientation as long as you're not in a completely empty void in space. Upside sees constantly changing, inside sees the other side of the strip.
Re: Möbius strips and differential equations
#3I enjoyed reading this. I have been making my way through Needham's Visual Complex Analysis (https://global.oup.com/academic/product/visual-complex-analy...) book which takes a similar visual-focused view of teaching all of complex analysis. Chapter 2 in particular covers multivalue functions and branch points to make a similar point about how some paths will yield different values at same points.
Re: Möbius strips and differential equations
#4Here's the reason you need enginners in the universe. Yes, the strip has non-orientability. Howwever, just introduce spin about the center, as you would a wheel, and you get all the same benefits of orientation as long as you're not in a completely empty void in space. Upside sees constantly changing, inside sees the other side of the strip.
I think you are saying something interesting. Could you elaborate a little though because I am not quite getting you yet hooked to understand what you are saying.
Re: Möbius strips and differential equations
#5Here's the reason you need enginners in the universe. Yes, the strip has non-orientability. Howwever, just introduce spin about the center, as you would a wheel, and you get all the same benefits of orientation as long as you're not in a completely empty void in space. Upside sees constantly changing, inside sees the other side of the strip.
I think you are saying something interesting. Could you elaborate a little though because I am not quite getting you yet hooked to understand what you are saying.
Spin gets you centripetal force. You know where inside and outside are globally because the forces will be opposite depending on which "side" you're standing, which directly contradicts their statement "..globally you cannot label one side as up and one side as down. If you try to label one side as up, and then you move continuously around the Möbius strip, you'll end up labelling that same side as down!"
Re: Möbius strips and differential equations
#6Earlier quoted context omitted.
I think you are saying something interesting. Could you elaborate a little though because I am not quite getting you yet hooked to understand what you are saying.
Spin gets you centripetal force. You know where inside and outside are globally because the forces will be opposite depending on which "side" you're standing, which directly contradicts their statement "..globally you cannot label one side as up and one side as down. If you try to label one side as up, and then you move continuously around the Möbius strip, you'll end up labelling that same side as down!"
Got you.
Re: Möbius strips and differential equations
#7Earlier quoted context omitted.
I think you are saying something interesting. Could you elaborate a little though because I am not quite getting you yet hooked to understand what you are saying.
Spin gets you centripetal force. You know where inside and outside are globally because the forces will be opposite depending on which "side" you're standing, which directly contradicts their statement "..globally you cannot label one side as up and one side as down. If you try to label one side as up, and then you move continuously around the Möbius strip, you'll end up labelling that same side as down!"
I get what you're saying, but with the spin you need to introduce the notion of movement, mass and force. It adds complexity you might not be able to afford, especially since typically you want to investigate a whole bunch of shapes, not just one strip.
Also, since everything on your model is continuous, there must be a point on the strip where the centrifugal force is 0. Is that point inside or outside?
Re: Möbius strips and differential equations
#8Earlier quoted context omitted.
Spin gets you centripetal force. You know where inside and outside are globally because the forces will be opposite depending on which "side" you're standing, which directly contradicts their statement "..globally you cannot label one side as up and one side as down. If you try to label one side as up, and then you move continuously around the Möbius strip, you'll end up labelling that same side as down!"
I get what you're saying, but with the spin you need to introduce the notion of movement, mass and force. It adds complexity you might not be able to afford, especially since typically you want to investigate a whole bunch of shapes, not just one strip. Also, since everything on your model is continuous, there must be a point on the strip where the centrifugal force is 0. Is that point inside or outside?
>introduce the notion of movement, mass and force
Hence my statement about not being in a void.
>Is that point inside or outside?
Depends on which foot is inside and which is not. That's the beauty of reality. It's fully deterministic at the marco level.
Re: Möbius strips and differential equations
#9Earlier quoted context omitted.
I get what you're saying, but with the spin you need to introduce the notion of movement, mass and force. It adds complexity you might not be able to afford, especially since typically you want to investigate a whole bunch of shapes, not just one strip. Also, since everything on your model is continuous, there must be a point on the strip where the centrifugal force is 0. Is that point inside or outside?
>introduce the notion of movement, mass and force Hence my statement about not being in a void. >Is that point inside or outside? Depends on which foot is inside and which is not. That's the beauty of reality. It's fully deterministic at the marco level.
Ah. I think it's better we don't discuss this topic from a mathematical perspective and agree you can indeed do a lot of different things with a lot of different outcomes.
Re: Möbius strips and differential equations
#10Earlier quoted context omitted.
Spin gets you centripetal force. You know where inside and outside are globally because the forces will be opposite depending on which "side" you're standing, which directly contradicts their statement "..globally you cannot label one side as up and one side as down. If you try to label one side as up, and then you move continuously around the Möbius strip, you'll end up labelling that same side as down!"
I get what you're saying, but with the spin you need to introduce the notion of movement, mass and force. It adds complexity you might not be able to afford, especially since typically you want to investigate a whole bunch of shapes, not just one strip. Also, since everything on your model is continuous, there must be a point on the strip where the centrifugal force is 0. Is that point inside or outside?
Note that for a particle there is no discrepancy.