#Rudy's Here
11 messages in this thread
Rudy:
Good to see you on line. My wishes/ideas:
** CA Lab: **
A slicker interface, especially for CA. Don't remove the ability to
play RC "like a color organ", though.
Higher resolution for RC woud be nice, although perhaps that just means
adding RC-like controls to CA.
Maybe cell shapes other than rectangular? This one isn't too high on my
list, but it could be fun (cf. the hexagonal cells in Wolfram's September 84
Scientific American article).
Keep the manual's present format and style – don't let it get "homogenized".
I'd like to read more about mathematical "irreducibility" and how CAs bear
on it. You mention such things in the manual and in "Mind Tools", but both
descriptions are tantalizingly brief.
** CHAOS: **
This idea may sound a bit weird, but I'd like to see a module/graphical
tutorial/on-line primer on topology. After reading a few layperson's books
on chaos theory, I have something of a feel for how strange attractors and
other chaotic systems work, but I don't really understand their connection
to the underlying topological ideas.
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I don't really care for the physical format and layout of CHAOS's manual.
CA Lab's paperback-sized manual is ideal in my opinion: it gives one the
inviting sense of being a book (which it is in many ways), and it's easy to
tuck into a knapsack or briefcase without consuming a lot of space. I know
that oversized pages with oodles of whitespace and every command sequence
spelled out in excruciating detail are the current fashion, but such tomes
are a curse for those of us who schlep them around with us on BART,
airplane, bicycle, foot, or other means of conveyance.
** ALIFE: **
Will Rudy's ant farm be included?!
I dimly recall some reports not too long ago about an a-life and/or CA model
which mimicked proteins or DNA bases organizing themselves into chains –
that would be interesting to play with. Sorry I don't remember the details
– all I recall are a bunch of short horizontal bars of different colors on a
computer screen.
Doyne Farmer pointed out that the study of artifical life should in some
sense be prior to that of articial intelligence, since living systems are
simpler than intelligent systems: "Let's see if we can even grasp the basic
principles that keep a bacteria (sic) going". Whatever you do with a-life,
that seems like the right sort of compass to follow.
– Mark M.
>>This idea may sound a bit weird, but I'd like to see a module/graphical
>>tutorial/on-line primer on topology. After reading a few layperson's
books >>on chaos theory, I have something of a feel for how strange
attractors and >>other chaotic systems work, but I don't really understand
their connection >>to the underlying topological ideas.
Wow, you don't ask for much, do you? <g> I think that's a great idea.
Very sophisticated and very hard, though …
James:
>> Very sophisticated and very hard, though …
Yeah, I figured it would be. A good afternoon programming project for John
Walker, perhaps? <g>
– Mark M.
I don't think it'll be so hard as a programming task.
The main problem would be to write a primer (graphically oriented) reducing
the amount of math to something the user can follow. (Do you know of anybody
who has read and understood the mathematical sections of the chaos manual,
besides me <g>?) Topology is pure math.
Dietmar
Dietmar:
> Do you know of anybody who has read and understood the mathematical >
sections of the chaos manual, besides me <g>?
Well, no. <g> But then I haven't spoken to too many people about it,
either.
> Topology is pure math.
If you mean the mathematics of formal notation (algebra, calculus, etc.)
I'm not so sure that needs to be true. Certainly it's *a lot* of math, but
given that topology is descended from geometry, there's got to be a visual
element to it that might help some people get a handle (or is that a donut
hole?) on the subject. James Gleick points out that Mandelbrot's great
genius in his early years depended upon his being able to visualize and
manipulate a problem geometrically.
– Mark M.
Mark,
> topology is descended from geometry
Well, that's exactly the problem. As you know from CAD, everything's easy as
long as you stay in 2D. The same is true in topology. In just two dimensions
you can draw sets as regions with holes in it, draw lines connecting
arbitrary points a.s.o.
Unfortunately there are only very few things in chaos that are 2D, even the
Lorenz attractor is 3D and many other things are 2.something D <that's
fractal, you know <g>>.
What exactly do you want the user to learn from this topology primer? Can
you give me some examples?
Dietmar
Dietmar:
Trying to make me contradict myself, eh? <g> If I knew exactly what I
wanted someone to learn from a topology primer, I wouldn't need it myself!
Yes, visualizing spaces of dimensions higher than 3 is a challenge, but
there often are lower-dimension analogues that can help someone "see" what's
happening (Roger Penrose uses this technique well in "The Emperor's New
Mind").
It's been a while since I've thought much about this subject, but I recall
after reading Gleick's book and another by Ian Stewart that I went looking
for a topology book which would provide something beyond the "intelligent
layperson's" approach, but not up to the university level. I'm not afraid
of equations or calculus, but I can't follow page upon page of differential
equations. Often a *picture* of an equation helps fix it in my mind.
Here's one example: As I understand it, many attractors (e.g., the Henon
attractor) are (2D) Poincare sections of 3D orbits. A primer might show the
equations of motion for the orbits (with some likely account of why a
particular equation generates a particular type of orbit), animate the
orbit, and then let the user place a plane somewhere to generate the
Poincare section.
Another example (although I don't know whether this is part of topology):
There are lots of *descriptions* of how the Mandelbrot set is generated, but
why not let the user pick different values for c, and then *show* the
iterations in action?
– Mark M.
Good points,
I specially like the second one (Mandelbrot). You just want the user to grab
with his hands (i.e. eyes <g>) HOW the nice pictures are comming to the
screen.
In the Mandelbrot case it ought to be possible to click on two screen
coordinates (i.e. Cs) and draw a simple two dimensional graph with n in X
direction and abs(xn) in Y direction and then show how the two iterations
vary. Must not be so difficult to implement (Rudy, are you listening?).
As it goes to attractors, I don't see an easy way to make visible what you
want to see. The attractor itself is used as a graphical aid because it IS
the easiest way to see what's going on (if I understand that correctly).
Dietmar
Dietmar:
>> The attractor itself is used as a graphical aid because it IS the easiest
>> way to see what's going on (if I understand that correctly).
I don't know whether it's the easiest way or not. Again, in the case of the
Henon attractor, I think the image represents a section through a
3-dimensional orbit. Seeing the orbit might help someone understand how the
attractor is generated and what relationship it bears to the original
equations. Of course much of this is conjecture on my part….
– Mark M.
Well, seems to be time for Rudy and James to step in. <grin>
No, to be serious: I understand that you refer to the figure at the
beginning of the Henon description in James' book. (I have the german
translation, so pagenumbers are of little use.) There you have a three
dimensional curve which is cut at a specific plane, specified by an angle A
in the XY plane. It might be useful to have this 3D curve presented on the
screen, but it will be very crowded. It'll be very time consuming, too,
because you'll have to calculate x' (which is the distance in the XY plane)
and y' (which is the Z value) for every angle A running from 0 to 2*pi.
Then you want to place the cutting plane interactively by rotating the plane
around the Z axis. As a graphical aid this might help. I don't know. In fact
you can do what you want right now by changig the B (Chaoticy) parameter in
the Henon dialogue box. Since A is B*(pi/4), you'll rotate the cutting plane
to the angle A of interest.
I hope this is correct and I would be glad if someone (Rudy?) could confirm
it.
Dietmar