We Start with a Point

To read along go to http://imaginingthetenthdimension.blogspot.com/2008/12/we-start-with-point.html
This video blog starts with the "point-line-plane postulate" which uses very similar logic to the original Imagining the Tenth Dimension animation to show a way to imagine any number of spatial dimensions. This is an important key - when physicists talk about extra dimensions, they are indeed talking about spatial dimensions, not dimensions that are somehow "imaginary".

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[levlobotomy]

@4:30 only true for non-hyperbolic spaces innit

[10thdim]

What do you think about the idea that the hyperbolic description of spacetime as a Minkowski space is really revealing the additional degree of freedom afforded by an additional dimension, as our 4D curves through 5D?

[levlobotomy]

i dont know if its so, certainly is alluring and simple. isn't a hyperbolic plane 2-dimensional. but do/can they even exist in reality the way they do in mathematics? i tend to think not (much like points don't actually exist due to planck length limitations). and is the degree of freedom really a degree of freedom? a plane remains a plane. the freedom only exists from the viewpoint of the higher(s) dimension. holographic or not, we're assuming even and flat euclidian dimensions here or not?

[10thdim]

We're assuming that while you're confined to the topology of a space, you are unable to perceive the additional "bending" that is happening unless you go to the next dimension up. So Euclidean concepts make sense for our universe until we get out to the really big picture, where things like the curvature of spacetime become a factor.

[swordofisis]

Start with a point, two is a line.. isn't that from the Pythagoran mysteries?

[10thdim]

I've been talking about the point-line-plane postulate a lot lately, you can look that up in wikipedia.

Hadn't come across the term "Pythagorean Mysteries" before, though. I see that it's an ancient school of mysticism based on points, lines, planes and solids, and the number 10. Fascinating connection! Thanks for pointing it out.

Rob

[thefailguy]

I got lost on "Hi."

[telamascope]

you don't need to "reach" zero for the limit to equal zero. If you divide something an infinite amount of times you are making the limit statement lim as a->infinity of n / (2^a) where n is any number. There IS a definite answer to this limit, and that is zero.

[DocsDota]

@jeffaquarius If you were smart enough to hear what his explanation is, it would make sense. He said: "there is only 1 electron with no dimensions, going back and forth in time to be "all" the electrons", which is not something us 4-D creatures can see with our eyes, but if you think about it.

[jeffaquarius]

At 2:41 he quoted someone said that "the reason why electrons look the same is because there is only one electron in the universe". Is that some kind of a joke?

[levlobotomy]

what i couldn't add was that i do agree its a useful model because it seems like spacetime, at least, does turn out to be flat on a large scale. and it does suggest itself that time would be the fourth dimension imho. intriguing how 10 dimensions would self-evidently result if feynman is right.

[levlobotomy]

of course we can.

[017renegade]

You should remember that the question is not the result of the division process but rather the number of divisions you would have to complete ... and this is as you statet a = infinity ... So the third example is just the same as the others! There is no need to describe any limit that you won't be able to reach. You CAN NOT reach 0 by dividing any number by 2!

[telamascope]

This.

The theory presented here is very elaborate yet conceptually easy to understand. Unfortunately, there's little science behind this... just a combination of euclidean geometry and the most basic principles of string theory.