A tale of two points

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Posted by: stak
Posted on: 2008-09-17 22:27:06

If you have a point, you probably won't even realize it's just a point. It just is, because that's all you have, and you have nothing to compare it to. But then, if you encounter a second point, you realize that what you had was a point too. If you think about it a bit, you can figure out the variable that distinguishes the two points, and from that extrapolate a line full of points.

But then you have a line, and probably won't even realize it's just a line. Sure, you could come across some other point or line and extrapolate a plane, but is it possible to extrapolate the plane from just those two initial points? What about 3-D space? And if it's possible, how much meta-thought does it take to do that?

Mmmm... going meta. Oh so confusing, and yet oh so fun.

Posted by Fai at 2008-09-23 23:11:20
From 2 points, how do you distinguish the meta-line from the meta-plane?
I think you could if you can easily find another variable that could be different, but that happens to be the same in your 2 points. But I think you'd have to be aware of the existence of 3d space in a different set of points/lines.
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Posted by stak at 2008-09-24 00:00:48
Ah, but that's precisely my question. Is it possible to do without being aware of the existence of 3-D space? If you extrapolate a line and then realize what you just did, can you start twiddling with other things just to see what happens?
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Posted by peiran at 2008-09-24 23:09:54
I say sure, why not?

As long as the two points share more than two attributes, and have different values for those attributes.

Example, in (x,y,z), points (1,2,3) and (2,3,4), or
London, 1 Jan 1970 and New York, 2 Jan 1970, or
The front page of the globe and mail and the script of hamlet. (If you happen to consider words, sentences, narrative to be features of your points.)

It depends on how closely you examine your two points, I guess. And you can take into consideration as many dimensions as you wish.
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Posted by stak at 2008-09-25 08:01:25
The hard part is figuring which things are attributes. You may not realize something is variable until you actually see it.. variated.
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