[Star trails, instants, and instances] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

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Star trails, instants, and instances
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Posted by: Lawrence J. Thaden

NASA’s Astronomy picture of the day web site (http://antwrp.gsfc.nasa.gov/apod/ap050413.html) recently had an item promoting Astronomy Day (4/16/2005).

It shows star trails, those curved streaks of starlight caught by a camera set up in timed exposure mode. You know, the ones that explain the spin of the earth.

The picture reminded me of the discussion on this forum by Mike Helland and others about the meaning of an instant with respect to time (http://forum.wolframscience.com/sho...d=2812#post2812).

Or perhaps in this case I should say an instance.

Aside from the philosophical positions expressed, I find the discussion stimulating because it makes you think about things in a different way.

Tony Smith from Melbourne (tic-toc) seems to have a similar ability: stimulating people to think in a different way. By the way, I haven’t seen any posts recently from down under. Is everything OK?

And isn’t this what NKS is all about? Thinking about science in a new way?

Well, I shouldn’t shake the stick at my Australian friend. I haven’t had much to say on the forum lately.

I’ll close these ramblings with one more interesting example of the CAs that have kept me occupied in recent months.

This shows a pair of localized triangular structures that move from upper right to lower left. They are not passing information to the new location so much as they are passing themselves to the new location. It happens nine times within the cycle. At each new location they are shifted left four cells relative to the previous location.

Halfway through the cycle there is a single row that has nothing to do with the rest of the CA. It is as though its only function is to let the CA sync itself so that it can continue doing the same thing.

The last step also has nothing to do with the rest of the CA except that it produces the initial conditions. So it also allows the CA to continue doing the same thing by beginning the cycle once more.

The CA graph is the “star trails”, but I do not know what corresponds to the “spin of the earth” in this case. That is, I do not know what behavior is being simulated. Although it seems that the discrete reappearance of the image offset four cells to the left is a clue to remember.

Getting back to the notion of instant, in this example time is partitioned into thirty four rows per frame. That is how many rows it takes to contain the pair of localized triangular structures. In all there are nine frames of time. Call each one an instance.

So to use the star trail analogy, it is like viewing the star trails on nine successive nights. They won’t be in the exact same locations each night. But the changes in location will point in a single direction.

Similarly the CAs partitions can be viewed as nine repeated wrappings of a torus, each offset by four cells to the left which come back to start after the ninth wrapping. It would follow the trajectory of a solenoid.

Here are the particulars.

Algebraic rule number 4755: Mod[(1 + p)s + q(2 – r + s), 3]

Initial conditions: {2,0,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,2,1,0,1,2,0,0,2,0,1,2,0,2,1,0,1}

Neighbors: p and q are left next nearest and nearest neighbors;
r and s are right nearest and next nearest neighbors.

The updated value of a cell is found by evaluating the rule once substitutions for p, q, r, and s have been provided by the neighbors. Notice that the previous value of a cell does not enter into the calculation of its new value.

Posted by: Tony Smith

Tony Smith from Melbourne (tic-toc) seems to have a similar ability: stimulating people to think in a different way. By the way, I haven’t seen any posts recently from down under. Is everything OK?

Thanks, ;-(

I guess I've fallen into a loop of starting more things than I ever get close to finishing, which sounds less like a good place to be every day older I get.

Right now I'm not even game to try to list all my on-topic sticking points here, save at least for a few recent returns to the evolution of reasonably compact starting configurations in Conway's Life, a project which still seems able to turn up surprises in true Class 4 fashion.

And isn’t this what NKS is all about? Thinking about science in a new way?

There was a post here recently which, though it did not say it, reminded me that we are talking about "A New Kind of Science" a.k.a the science of simple programs and should not get ourselves too caught up with the idea that it might serve as a replacement for older science as much as a doorway to new knowledge and another source of checks and balances on our understanding of the world.

Rereading the above, nobody would suspect that I'm also considerably distracted by the challenge of parsing and marking-up prose in a way that may allow facts and context to be extracted from stories with the help of computer software.

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