Some Physics/Geometry I Assume In My Designer Speculations

[Phil153]

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the greatly enhanced, post-singularity David Sklansky of the year 2300 [img]/images/graemlins/wink.gif[/img]

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Ugh, that prospect is enough to create another unabomber.

That said, I like this post, even though all he's really shown is that an extra dimension makes life easier in lesser dimensions. Does any of this make an intelligent designer more plausible? I don't know. I think we're back at square one, looking at the universe and seeing what fits.

Also, if time doesn't exist in the theoretical universe that created us, have we solved the problem of existence, or just made it weirder?

[m_the0ry]

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7. If you live in a place where time is one of the dimensions and it is embedded in a place of even more dimensions, then it is conceivable that moving in a "straight line" timewise gets you back to where you started. So there is no beginning or end.

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It's definitely conceivable but as you said yourself in your first comment this makes the assumption that the manifold (surface) that represents time has positively oriented curvature. If it is negatively curved time diverges away from itself when you traverse it and it is aperiodic (you cannot arrive where you started). If it is not curved it is aperiodic as well. This is why the curvature of spacetime is an incredibly important discussion in physics. If the ultimate fate of the universe is a 'big crunch' where all the matter collapses back into a pre-big-bang-like singularity then spacetime is a positively curved 4-fold and it looks like a 4 dimensional sphere. Returning to our original position by heading off in one direction is theoretically possible. Experimental evidence strongly suggests there will be no big crunch because there is not enough gravitational force to stop the spreading of the universe. That is to say there is a negatively oriented curvature on the 4-fold which makes it look more like a saddle shape. Heading infinitely off in any direction will never return you to your original position.

[Metric]

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Forget two dimensions. Or a designer for the moment. Was my math and physics generally accurate?

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None of the concepts you postulate are obviously wrong. Which elements get incorporated into physically realistic models is, of course, a seperate question. But there is certainly no reason a priori why the universe couldn't have extra dimensions and interesting topology (in fact, the most fashionable theories at present incorporate these ideas in various ways).

[Siegmund]

I do think you've played fast and loose with the difference between 'there exists...' and 'for all...' when you say "it is possible."

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1. If you live on a two dimensional surface that is curved or embedded in three (or more) dimensions, it is possible to move in a "straight line" and arrive back where you started from. Surface of the Earth being an obvious example.


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True: There exist m-dimensional objects embedded in m+1 or more dimensions where moving "in a straight line" (in some sense) returns you to your starting point. (For example, the surface of a sphere.)

False: For any m-dimensional object embedded in m+1 or more dimensions, you can return to your starting point by moving "in a straight line." (Obvious counterexamples, the plane, and the hyperboloid of one sheet.)

This doesn't necessarily mean there is anything wrong with your arguments -- but (without rereading them to check) there is a danger that you've invited your readers to assume something is true of the space we are embedded in, just because it is true in some but not all spaces similar to ours.

If you mean specifically the rest of your points in this post, no sins of this type commited. I think there are some issues (unrelated to the above) with #7, but tend to agree with the conclusion in #8.

[Metric]

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Also, if time doesn't exist in the theoretical universe that created us, have we solved the problem of existence, or just made it weirder?

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These kinds of things by themselves don't solve the problem of existence -- they merely expand the space of possible scenarios by which the problem of existence might be solved (which is a good thing, since understanding the physics of our universe alone doesn't appear sufficient to solve the problem of existence).

[David Sklansky]

I didn't mean to say it always will be possible. Poor choice of words.

[Piers]

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I'm going under the assumption that the following things are basically true and/or reasonably possible.

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Fine, so what’s the plot of your story? I always enjoy good Sci Fi.

[arahant]

It's not clear to me that 5) or 8) are true. Flatland was not exactly rigorous.
To the extent they are, the 'higher' dimensions would seem to be observable of neccesity, though I haven't thought it through. The piece of paper analogy is cute, but when you try and actually create a truly lower-dimensional space and play around with it, you come up with some problems. Any sick topology PhD's around here?

[disjunction]

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6. Time is thought to be a dimension.


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Well, ok, if you define it as so. Other dimensions on other axes include my age, shoe size, and the number of times they say "pitchy" on American Idol.

The math is a set of assumptions you make and all the theorems that follow from those axioms. Physics is not derived, it is a model, it is just an assignment to that math that happens to describe the data well. Yes?

Thus, is there evidence that the statement below fits a good model?

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7. If you live in a place where time is one of the dimensions and it is embedded in a place of even more dimensions, then it is conceivable that moving in a "straight line" timewise gets you back to where you started. So there is no beginning or end.


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[Bork]

Good question, I would phrase it like this:

What makes you think time is a dimension, further even if it is a dimension what makes you think it is relevantly similar to spacial dimensions such that it can loop?

Certainly from our perspective time seems to have some very important differences from spacial dimensions. Why lump it with them and conclude it has (most of/exactly) the same properties?