Re: Questions (Space)
- From: Tina.Hall@xxxxxxxxxxxxxxxxx (Tina Hall)
- Date: Sat, 15 Sep 2007 20:04:00 mez
Jonathan L Cunningham <spam@xxxxxxxxxxxxxxxxxxxx> wrote:
Tina Hall <Tina.Hall@xxxxxxxxxxxxxxxxx> wrote:
Jonathan L Cunningham <spam@xxxxxxxxxxxxxxxxxxxx> wrote:
[a^2+b^2+c^2=d^2][doesn't have to be true]
No, as far as I know it's the _only_ option, and you say there is
_more_ than one option. I ask what that other option is.
I thought it was obvious.
I wouldn't keep asking for it, then, would I? That _is_ the question,
after all.
You said: a^2 + b^2 = c^2 (for a right-angled triangle, except I
don't remember if you mentioned the right-angled triangle).
I asked a couple of times or so whether it is a right-angled triangle
because I couldn't remember.
I said that was Euclidean geometry.
I still don't know what that is, and I think the term is just confusing
the issue. (You're not defining what that is.)
Another possibility is that:
a^2 + b^2 > c^2 (greater than)
This is Riemannian geometry.
That's an example (look at that post from you about themes). It doesn't
tell me what you're talking about. (It may be that my reply to your post
there about serial and, eh, the other learners hasn't arrived in Usenet
yet because the node I sent it to is offline. In any case, what you said
about these serial learners sounded very true to me, applying not only
to that but this thread, too.)
In any case, I don't know how a flat triangle with three straight lines
could be calculated by that formula. That still needs to be explained.
Any other shape than that, and we're not talking about a^2+b^2=c^2, and
I don't see why you point out that other shapes are calculated
differently. (That's kind of obvious. It's like saying when a dog wags
its tail it's friendly, you say that doesn't have to be true, and then
give cats as examples. Well, cats aren't dogs.)
Another possibility is that:
a^2 + b^2 < c^2
This is hyperbolic geometry (it's also named after some famous
mathematician, but I can't spell his name without looking it up.
Lobachevsky I think.)
Your terms for whatever geometry aren't helping, they just add confusion
because I don't know what you mean by any of them.
I'm sure there are other geometries too. But those three kinds are a
tidy set of possibilities.
Explain how they apply to a flat, 2D triangle, then.
If you can tell me why you believe it is true, I can say where the
explanation depends on some "fact" which is incorrect.
What fact?
Part of your explanation of why you believe it is true.
You're the one who claims it doesn't have to be true. You said that to
the raw formula that describes how to calculate the length of a straight
diagonal from one corner of a cube to the opposite corner. I assume you
know what I meant, as you were adressing it with a statment.
If you're now asking what I meant, I wonder how much your statement
could possibly apply.
Just for interest, though, it may depend on what is often called
"the parallel postulate" which I will call PP. This can be stated
approximately as:
(1) Draw a straight line
(2) Mark a point somewhere off to the side (not on the line).
then
(PP) you can draw *exactly one* other line, so that it goes
through the point from step (2) but never crosses the line from
step (1) in either direction.
That's parallel, nothing to do with triangles.
It's about straight lines. Triangles are made out of straight lines.
Not out of parallel straight lines.
The connection is not simple, but requires many steps.
Well, I don't see it.
Many mathematicians, over about two thousand years, spent large
parts of their life trying to prove that statement (PP) must be
true.
Huh? What's there to prove? If it isn't parallel, they cross
somewhere. You can draw one line on either side of (1), and that's
it.
No, that isn't it, because it's not true. It just looks that way.
That's just a claim. No explanation in it.
They failed, because it doesn't have to be true.
There's that again. Why wouldn't it have to be true?
Because it isn't? Why doesn't 2+2=5? You ask impossible questions.
No, you make statements, and I ask you to explain them.
Well, if I draw a triangle (I think it's a right-angle triangle, but
am still not sure) on the table here in my one room with kitchen
corner, it's true.
No, alas, it isn't. It's only approximately true. The error is
smaller than you can measure, but it's not true.
Another statement without explanation.
I started out thinking you might offer something interesting, but right
now I plain don't believe you. You even ask what I meant, so I don't
think you're talking about the same thing as I.
Trouble is, if they calculate it *that* accurately, it's no longer
true, because "space" (the space we live in) isn't that shape. Real
circles differ (a bit) from the calculated value.
It's either a circle (flat) or it's not.
Ok, if you want to look at it that way, it's impossible to draw a
flat circle, because the space we live in isn't flat.
Space doesn't enter into it. As soon as you add curves, you aren't
talking about the same thing as I anymore.
--
Tina
WIP: Space: 2666 words
WISuspension: Seasons & Elements trilogy | Magic Earth series
Posted to Usenet newsgroup rec.arts.sf.composition.
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