Hello Wilson:

Prof. Alan Guth was a guest lecturer for a class I took almost a decade ago
on general relativity at Harvard Extension School taught by Edwin F. Taylor
(an amazing course, general relativity for a general audience, but the
school did not support the class because it was not a cash cow, the only
animals allowed to stay in their stable of courses). I asked him if
virtual particles were an intermediate mathematical step to the final
correct calculation. Since there are often several ways to go from one
place to another, that may be why the particles are virtual. He replied
"That sounds vague enough to be true." That was a much better answer than
the question I asked :-)

Based on the article, it sounds like Peter Lynds is avoiding the specifics
of the math. From my reading of the article, he does sound vague enough to
be true. It is only the mathematical nuts and bolts of implementing the
transitory nature of time into the tools of math that will have a big
payoff.

For the last month, I have been developing programs that treat time
dynamically, because that is what time is, a dynamic object. Take as a
starting place the static complex plane with three points in it, shown by
periods below:

| yj
|.
----- t
.|
. |

This is known as the Argand plane, and was promoted by Gauss (although also
developed independently by Wessel). What bothers me about this
representation is that it looks the same three years later, so time, the
core of change, is drawn statically.

Notice that neither axis is infinite in how it is represented. This led to
a thought: what if I create a ten second universe that is 10 y units wide?
Then I could animate the Argand plane like so:

seconds 0-2
. |
seconds 2-4
.|
seconds 4-6
|
seconds 6-8
|.
seconds 8-10
|

This is the same information as in the Argand plane, but is represented
with time as a dynamic variable. Time looks more like we expect it to
look, which is different as time moves on.

I have been working with an obscure field of numbers called quaternions for
the last few years. A quaternion has three complex numbers as subfields,
which all share the same scalar. I could imagine a second complex number
for times and position along x:

| t
|.
----- xi
| .
| .

or dynamically:

seconds 0-2
| .
seconds 2-4
| .
seconds 4-6
|
seconds 6-8
|.
seconds 8-10
|

The x's can take any value, but there has to be three events, one each in
the time slots of 0-2, 2-4, and 4-6. Now the animation will involve a
dynamic plane of information:

seconds 0-2
| yj
|
----- xi
|
| .
seconds 2-4
| yj
|
----- xi
| .
|
seconds 4-6
| yj
|
----- xi
|
|
seconds 6-8
| yj
|.
----- xi
|
|
seconds 8-10
| yj
|
----- xi
|
|

A third complex plane for time and z can be used to determine just how big
the dot is: if z is small, the dot looks big, if z is large, the dot gets
small.

I have written a few programs that can take a stream of real, complex, or
quaternion numbers, and generate an animation. One thing that has been a
huge amount of fun is seeing basic trig functions of quaternions. It just
looks like a looping circle, but is much more amusing that the infinite sea
of camels in the traditional representation.

I have to go now and code in the ability to create animations of binary
operators, but a preliminary set of slides is available if anyone is
interested in this specific way of representing time.


doug
quaternions.com

http://sdm.openacs.org/wp/display/1238/