Mobius Strip

[Gaerin]

I love the ItTD video yet have specific point to argue.
The video said something to the effect that a flat-lander traveling a Mobius Strip would appear to not exist once reaching the point of origin after traveling once around the strip.

I think the analogy of a 2-Dimensional land likened to a piece of paper was taken a little too far to be accurate.

I don't think a 2-D being would be aware if it was traveling across a surface.
That would suggest that a 2-D being would know where 'down' was, which would be awareness of the 3rd dimension (given that a 2-D being is conceiving only of left, right, forward, and backward, yet not up or down).

Here is what I think a 2-D being would see if their friend walked all the way around a Mobius Strip:
They would see their friend arrive from the opposite direction than which they departed, yet their friend would be backwards with the friend's right and left reversed, which would probably be disturbing.
If using a piece of paper as an analogy, I would say that the 2-D flat-lander would travel through the paper, not on it's surface.

Not that this makes any difference to the entirety of the video (which I love), I'd just hate to misrepresent anothers' existence (the flat-landers that is).

[Michel]

Welcome to the forum, Gaerin and ... I agree with you. But, knowing myself as a 3D being, I can't know how a 2D being will experience.

If there is a possibility to construct a mobius strip in a fourth spacial dimension, and matter was to move along it, perhaps we would see it "through the strip" as ... anti-matter. Or even black matter. I don't know. What do you think?

Cheers,
Michel

[Rob Bryanton]

Hi Gaerin, welcome to the forum, and thanks for your kind words. Here's a video and blog you might enjoy, called "What Would a Flatlander Really See?"
http://imaginingthetenthdimension.blogs ... y-see.html

You wrote:

The video said something to the effect that a flat-lander traveling a Mobius Strip would appear to not exist once reaching the point of origin after traveling once around the strip.

Hmm, I don't see where you got the idea that the flatlander doesn't exist once he's completed the loop, clearly there has been a misunderstanding here. The analogy is more like what happens to we 3D creatures if we follow the equator - we feel like we're traveling in a straight line, and eventually we find that we're right back where we started.

I don't think a 2-D being would be aware if it was traveling across a surface.
That would suggest that a 2-D being would know where 'down' was, which would be awareness of the 3rd dimension (given that a 2-D being is conceiving only of left, right, forward, and backward, yet not up or down).

Yes. The flatlander thinks he is traveling within the plane of his 2D world, and is completely unaware that he is actually twisting and turning in the dimension above.

Regarding the left-right flip, are you saying if I start traveling in the "left lane" of a mobius strip, by the time I arrive back where I started I'll be in the "right lane"? I just tried it. I made a mobius strip, started drawing a line, by the time my line met back up with itself (in other words my line was now on both sides of the paper) I was still in the "left lane". There was of course, the half way point where I didn't see my line yet but knew it was on the other side of the 3D paper, but within the no-thickness 2D plane my line was traveling within, I wouldn't have been able to see somebody standing at the point where I started then because they were separated by the additional third dimension my 2D plane was looping through.

I do like science fiction stories of people being lifted out of their dimension and plopped back in with their symmetry reversed though, I understand how this could happen to a 2D flatlander if he were lifted off of his 2D plane. And in his book "Physics of the Impossible" Michio Kaku has a section about the extreme difficulty one would have in describing left/right to an alien species via long-distance communication. You could send them all sorts of pictures and descriptions, but until they finally showed up here and you said "let's extend our right hands (or whatever appendage this alien might have ) for a handshake", you could never be sure if the information had been interpreted correctly.

Interesting things to ponder.

Thanks for writing,

Rob