Re: Questions (Space)

Tina Hall <Tina.Hall@xxxxxxxxxxxxxxxxx> wrote:

Jonathan L Cunningham <spam@xxxxxxxxxxxxxxxxxxxx> wrote:
Tina Hall <Tina.Hall@xxxxxxxxxxxxxxxxx> wrote:
Jonathan L Cunningham <spam@xxxxxxxxxxxxxxxxxxxx> wrote:

I believe that would be misleading, because I think Tina would say
that a sphere is three dimensional.

Wasn't the thing a^2+b^2+c^2=d^2, as in 'three dimensions', too?

Yes, but it's nothing to do with the surface of a sphere.

Surface? You said three dimensional.

Yes. That's my point. I'm talking about a surface. I think that
mentioning spheres would be confusing.

As Tina (correctly) said in an earlier post, the surface of a cone
is not curved.

I did?

You did.

What did I say to sound like saying that?

I can't remember the details. You gave two examples.

Oh dear. Because I don't think it's what I meant (and didn't use those
words).

But I'm not going to re-read all your posts over the last two weeks:
there are too many of them. And I can't remember enough specific
keywords to do a google search.

Hm. That?

"(Btw, the net with the ball in that's often depicted to show how space
is curved doesn't work for me, because the net is flat, dent or no,
while space is 3D.)"

Perhaps. If you just meant the net is 2D, then I misunderstood you.

I'll change what I said: "A Tina didn't say in an earlier post, the
surface of a cone is not curved." :)

More precisely, it has a curvature of zero. The demonstration of this is
to take a flat piece of paper, and (with the help of scissors and glue)
to make a cone. It's possible. You can't smoothly cover the surface of a
ball with a flat piece of paper.

Euclidean geometry is the one you've learned.

How do you know what I've learned? I know there are things about shapes
that I haven't learned (missed them), and I doubt that's what you mean.

Two reasons: (a) Euclidean geometry is "ordinary" geometry, and is what
gets taught in schools, (b) you said a number of things which sound like
you learnt some (ordinary) geometry, but you've said nothing that sounds
like you've learnt about any other kinds of geometry.

That's sufficient evidence for me, for now.

(Hyperbolic is one of those words I'm trying to attach to a picture
still. It's improving but I'm better off checking the dictionary.
... The definition gives me an image of an uneven ellipse - the
opposite curves, along the longer axis, aren't identical, one is
more the other less curved. Or in other words, the thing is
egg-shaped.)

Another image is of a saddle: it curves down across the saddle, and
curves up from front to back.

The dictionary definition is that of a flat thing. If you take a one
dimensional slice of egg from top (small end) to bottom (big end), you
have that hyperbole thing. (Actually, it's describing the surface you
get if you slice a cone almost horizontally.

You are thinking of a hyperbola (and maybe a parabola as well). They are
the names of certain shapes. There's a connection with the name
"hyperbolic" but it would be easier if you just think of it as a name
for a different kind of geometry, rather than ask about the connection,
The answer involves equations (which you don't like).

It's not particularly useful as an image, except that if you try to
draw a circle on the saddle, the line you draw (circumference of the
circle) will be more than pi times its diameter.

It also isn't a circle. It will still be 'saddle'-shaped.

It's the nearest you can get to a circle drawn on a saddle.

There's another way to picture it: one way to draw a circle is to use a
pair of compasses. Another way is to stick a pin in (to a piece of
paper), make a loop of string, hook the string onto the pin, stick a
pencil into the loop of string, then pull it tight (sideways), then draw
a line keeping the string tight. You'll draw a circle.

Now do the same thing on a saddle. You'll draw a shape, which is as
close to a circle as you can manage on a saddle.

If you don't want to call it a circle, that's up to you. But I'd call it
a circle because I don't have a better word. It's not confusing, because
you *can't* draw a flat circle on a saddle. So if I talk about a circle
on a saddle, everyone will know what I mean.
It *is* possiblel to explain how a "curved space" can act as an
attractor, but the only explanation I've read was by Eddington. (He
talked about trying to walk in a straight line on the side of a
mountain.)
</rant>

That's a nice image. If I only knew what it explained. :)

Gravity! :)

:)

Except it doesn't fit into the open slot that wonders how gravity works.

The first theory of gravity was "things fall down".

The second theory of gravity was "things fall towards the centre of the
Earth".

The third theory of gravity was "Everything in the universe attracts
everything else according to <some formula>. Closer things attract more
strongly than distant things, and heavier (more massive) things attract
more strongly than light (less massive) things. The Earth is big and
close, so it attracts us more than anything else.

The fourth theory of gravity was Einstein's, and is called General
Relativity.

If your "how gravity works" slot is looking for an explanation based on
the third theory, then telling you about the fourth theory can only
confuse. Curved space is an explanation of gravity in the fourth theory.
It doesn't help in explaining where gravity comes from in the third
theory (which doesn't have an explanation: it "just is".)

Jonathan

--
"There's many a best seller that could have been prevented
by a good teacher." Flannery O'Connor
.

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