Thanks for the explanation, are you saying that there are 3 time dimensions but beings like us, cannot travel in more than one? That's not so hard to understand. Oh, and what on earth are zero-point fields?

And no, Jason Tesser is not a charecter in the book.

<font size=-1>[ This Message was edited by: p9107 on 2002-01-29 02:13 ]</font>

Hawking explains the idea of imaginary time in his recent popular-audience book "The Universe in a Nutshell" as an additional 2-vector at right angles to true (Greenwich) time. I don't understand a darned thing about how he's using the concept, but it obviously creates a sort of 3-D time.

Anybody know more about this? Could it be used to understand the many-universes version of quantum decoherence, with each possible history propogating along a unique 3-vector of one real + two imaginary time dimensions?

Don Stahl

<font size=-1>[ This Message was edited by: DStahl on 2002-01-29 04:18 ]</font>

In A Wrinkle in Time the characters "tesser," but that has nothing to do with Jason Tesser, right?

That's right. I read the book when I was a small boy. It is quite good actually. See for yourself:

Thanks for finding the link by the way.

http://www.uky.edu/~engjlg/hon202/coltharp.htm

Here is a link to a net of a 4-dimensional 'hypercube'. I thaught for a minute and wondered how do we know there are more or less than 3 dimensions? How can we prove that things can exist in more or less than 3 dimensions. Take for example a 2D shape, lets say a square drawn on a piece of paper. That, when layed flat it still is a 3D shape. The hieght of the ink on the page. Also, how do we know there are 4 dimensions.
____
| |
|____|
| |
____|____|____
| | | |
|____|____|____|
| |
|____|

Above is a net of a 3D cube. It is 6 squares, which when folded make a cube. In the link, there are 8 cubes which in theory 'fold' together to make a 'hypercube'. How do we know this? Is it just made up, or has it been proved?
I hope you can answer this for me...

<font size=-1>[ This Message was edited by: p9107 on 2002-01-30 12:28 ]</font>

<font size=-1>[ This Message was edited by: p9107 on 2002-01-30 12:35 ]</font>

It is made up, just like Newton's laws, and the laws of thermodynamics.

"How can we prove that things can exist in more or less than 3 dimensions?"

If there were more than 3 large-scale physical dimensions in OUR universe then distance-dependant forces like electromagnetism and gravity would not allow stable configurations like the solar system or a hydrogen atom. (See page 88 of "Universe in a Nutshell" by Hawking for one explanation of this idea.)

--Don Stahl

On the other hand, it is hypothesized that the reason gravity is so weak in comparison with the other forces is that it extends into other dimensions.

__________________
Everything I need to know I learned through Googling.

I just would like to point out here (since I've never done it anywhere else) that the idea that gravity is so much weaker is not a very well-defined concept.

Typically, the ratio of gravity strength to electromagnetic strength is computed by comparing the sizes of the forces between two electrons. The ratio is an incredibly small number, of course. The ratio is larger if you use an electron and a proton. If you do the comparison with a couple of protons, the ratio is a million times larger--but still, a very small number.

Now, what if you do it with neutrons?

I don't know - what happens...?

I would assume that the electromagnetic force between neutrons would be nil, so that in that case the gravitational force would be infinitely stronger. Kind of an unfair comparison, but then (as GoW points out), so is the electron example, since an electron is at the other extreme and is almost nothing but charge.

__________________
Everything I need to know I learned through Googling.

One cannot deny the existence of something simply because they cannot fathom it.

A single dimensional creature cannot comprehend a dual dimensional universe. They example is a point sitting on a plane. If the point looks forward on it's plane, and something intersects that plane at a right angle, the point "sees" a line of points on it's plane. It cannot comprehend something in the plane above, nor below.

A two dimensional creature cannot comprehend a 3 dimensional universe. Something intersecting two planes at a right angle (something we can obviously see and understand) looks like a moving line or moving set of points.

A three dimensional creature cannot comprehend a 4 dimensional universe. If "time" is the true 4th dimension to our existing 3, then a 4 dimensional creature could move forward and backward in time as easily as we move in our 3 dimensions. We obviously cannot comprehend that. Thought we labor intensely to do so.

A very good explanation of this is given in the book "Tertium Organum."

I once had a vision of a 4-dimensional sphere. It flashed through my mind. And surely, just as I had heard would happen, it leaves you, you cannot describe it to someone else, nor could you draw it or for that matter or prove it. The only thing I remember is it took into account something called the "long body of time."

The key is to not dismiss something. It is written in every language in every way that a lower cannot see a higher. As above, so below, goes my response to that.



<font size=-1>[ This Message was edited by: DJ on 2002-02-01 11:15 ]</font>

I just purchased that book, because of this. Where does he discuss it?

Aw, jeez, I'm at work and don't have the book with me. The index surely has listings for "time, imaginary?" I hope you aren't disappointed that the book is truly for a popular audience and not a mathematically sophisticated one. At least the illustrations in the book are gorgeous, whatever their explanatory value.

Don Stahl

Yep, thanks. I wasn't sure what he called it, but I see that that is exactly what you'd called it. I'm not nearly that lazy, just impatient.

Grapes of Wrath, is your name taken from a book by John Steinback? If not, why...

Hmm... I think I have an argument for stating that the forces in our universe only extend through three dimensions:
The Inverse-Square law.

Lemme see if I can write this without making a total fool of myself. The inverse-square law is true because, if energy (say light) is radiating in a sphere from it's source (say the sun)...

Okay, if I keep writing, I'm going to make a total fool of myself. Just think about how the density of energy decreases as the sphere expands. Now imagine how it would decrese if the sphere were 4-dimensional instead of 3.

I hope you guys can extract some sense from this jumble. It honestly does make sense in my head. [img]/phpBB/images/smiles/icon_wink.gif[/img]

Well, even if you CAN make sense of it, all it proves is that energy doesn't interact 4-dimensionally.

If the universe is truly just 3 dimensional, then the universe is the same as at first cause, only expanded to ludicrous dimenions. In this scenario, Time is a stretching of the original singularity to the dimensions we see today. Everything just seems further apart because of the dilation. In essence, the .00000000001mm (or whatever the size of the original singularity) is today equal to 10^16 light years. That's a pretty big equivalence factor.

Four dimensions allows us to express movement independent of original conditions and allows one to understand great distances. This is much closer to observation.

I believe Hawking once put it best: 3 dimensions are the minimum required for life. He used an example with a dog's digestive tract... from mouth to butt. If only 2 dimensions, the top half of the dog would not be attached in any way to the bottom half.

<font size=-1>[ This Message was edited by: DJ on 2002-02-08 16:14 ]</font>

Yes, I remember reading that. It fails to take in to account that life-forms do exist with a one-opening digestive tract. Or none at all; look at amoebae. [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

Fine, maybe advanced life can't exist in two dimensions.

Anyway, in my (muddled) example, I was talking about four dimensions in space, not three in space and one in time. I really do have to learn the language necessary to make these things clear. My bad.

Sort of. It was the name of many of my old softball teams, which were named after the hovel I lived in--which was named by my roommate. I'm not sure that it was Steinbeck's novel, but it could have been. Of course, Steinbeck got his phrase from the Battle Hymn of the Republic, so that's probably it, ultimately.

ObBABB: I'm half-way through Hawking's book. I've only found a few errors. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Hey, Grapes, we're up to 5000.

On page 107, he mentions hidden variable theories and says that they are not in agreement with observation. That is not true. Observations are not in agreement with so-called "local" hidden variable theories, but non-local hidden variable theories haven't been contradicted. I think the hidden variable theories were pretty much non-local anyway.

The Chronology Protection Conjecture (defined p.202 as the idea that the laws of physics conspire to prevent time travel by macroscopic objects) is listed in the index as appearing on pages 64, 153, and 160, but I can't find it near page 64. On page 153 he also defines his Chronology Protection Conjecture and says that the probability of time travel is zero. But he also mentions there his bets with Kip Thorne and says that he can't bet about time travel with Thorne because they're on the same side, and he wouldn't bet with anybody else because they might be from the future and would already know that time travel works.

On page 170, he claims that within two decades, you'll be able to build a computer as complex as the human brain for a thousand dollars.

Fig. 4.1, page 103, has a nice illustration of the retrograde motion of Mars and why it occurs, but the numbers at the top are mis-matched. The 3 and the 4 should be switched. On the next page, the text talks about a butterfly in Tokyo causing rain in Central Park, and refers to Fig. 4.3, but the figure shows a butterfly in New York.

On page 159, he claims that if you stacked all the new books being published next to each other you'd have to go ninety miles an hour to keep up. Although he talks there about the large number of articles that might someday appear in his field (ten per second), he's referring toall of the copies of books in that example (later, page 165, he says that there are 200,000 new books being published each year). If you place the books flat and end to end, and assumed they averaged a foot, ninety miles an hour is still over four billion books per year. Probably an exaggeration.

On page 188 he discusses the possibility that missing mass in the universe is contained in "shadow" universes, that might contain shallow humans wondering about their shadow stars in their shadow galaxies. Maybe he meant "shadow" instead of "shallow" but I'm betting that one is on purpose.

REALLY {no longer a BrKEYlee fan after BSD}
anyway heres my revisit of today MODIFIED
RESTART;
lambda := 1;
t0 := 0;
tmax := 5;
c0 := 1;
h := 0.1;

t := array(t0..tmax); # page 78 see RED Maple book Room 110 DC

c := c0 * exp(-lambda*t);

plot( c(t), t = t0..tmax) ;
??????????????????????????
anwy? I think it will work as is /Maple
v1 at 10:11 was my tranxlation of a MatLab version
as there exist some subtile differences in syntax
it took ME a long while ( and several different coloed books to arive at
c(t) rather than t,c but alass i made It.. 10:36 am
{link 2 B4 may go here some day &amp; maye_not 2}

Thanks for the bump; surely, someone else has read/is reading this book?

WHooo... things sure seam to go Fast around here these days
{let me say first though I seam to have been DEbuged} =D>
now back to an hour {ok 10 minutse ago today..}
RESTART;

lambda := 1;
t0 := 0;
tmax := 5;
c0 := 1;
h := 0.1;

t := vector(tmax/h,t0..tmax);

c := c0 * exp(-lambda*t);

plot( c(t), t = t0..tmax);
title = `exponential decay, decay const = 1`;
-------------------------------------------------------
so I changed my t:=
from array
to vector
===========
I could not see 1 speck of difference? Maybe I was not LOOKING
at the graphic right? \_ {oh well} back to the book {page 100}?