Registered: Feb 2004
Posts: 172

Back in the days of DOS I used to go into a directory with hundreds of files. I would type 'dir' on the command line and then sit back and watch as the screen would scroll vertically with thousands of characters...
I wasnt looking for a file- Just playing around and letting my eyes take it all in.... I could let my imagination run free and I would essentially see patterns in the scrolling of the screen. Of couse my mind was sort of filtering and 'blurring' what I was looking at...

Anyway, you could do the same with a text file by directing it's content to the screen. Depending on the content (and length of the file) you could create something that would produce interesting patterns on the DOS prompt.

So is that emergent complexity from simple rules? I do not know. I saw patterns that appear to be complex so maybe you could say 'yes it was'. But ... it is the same type of thing that happens when i look at the NKS images and perceive complexity....

What about when you watch a tire rotate: as the speed changes it gets to the point where your eye sees a reverse rotation pattern.... ??

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Registered: Feb 2004
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What about when you watch a tire rotate: as the speed changes it gets to the point where your eye sees a reverse rotation pattern.... ??

Only on TV or a movie (see aliasing).

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Registered: Feb 2004
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(not really refering to aliasing of images in playback systems.)

My mountain bike rests up on a stand. I can turn the wheel and let it spin freely. As I watch the treads, I notice that eventually the spin rate drops to a point where my eyes perceive a reverse direction spin. As the tire begins to slow it's spin even further, my eyes see the direction go back to normal.

My eyes see this change of direction and my mind assumes some kind of complexity or emergent behaviour...

So just because my eyes see something that looks complex it doesnt mean that it really is.

Also: what if the complexity produced by NKS is misperceived simplicity? I can look at a weeping willow tree and say upon first glance that it is very complex structurally. But the more I look at it the more I my mind filters it to see simple structures. This leads us to NKS, etc. But what if there really wasnt any complexity in the first place? Open up a can of warm Coke and pour it into a tall glass. The carbonation appears complex. But I say it is not complex. It perhaps abides by NKS, etc. Even if that is the case I still say it is not complex because it can be broken down into processes. Complexity is something that cannot be broken down into simple pieces (my own brand of definition). NKS is simple pieces so it is not in the business of complexity (as i define it). Perhaps true complexity is not going to ever surrender to dissection.
Of course if something cannot be broken down into simple pieces then it would have to be proven to prevent people from wasting time trying to find those pieces.
Random thought: paradoxes are the only true complex thing that i can think of .... you can not take the one side away from the other....

(i am no expert... just experimental thinker so I welcome any refutation, correction, etc.)

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Registered: Aug 2003
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I can illustrate why I think your understand of NKS systems and complexity is off base, with a concrete problem.

Tell me the sequence of center cell values of rule 30 from a single initial "1", steps 1000 through 1009. Your answer should be a series of 10 1s or 0s, like 0001011001 or 0111100111. These are to be the values of the same location in the pattern, but on successive steps.

If you just guess, you will have only about one chance in a thousand of getting the right sequence.

The elements are very simple, each just a 1 or a 0. Each depends on only the rule and that single initial "1", in some abstract sense. Immediately speaking, the first one will depend on the three center cells at step 999. Which will depend on 5 cells back on step 998. Etc.

I claim the fastest way you will find to get the right answer, is to calculate the color of every cell in the pattern down from the top. I only want 10 little 1s or 0s. And the quickest way to the right answer involves first figuring out around half a million other ones.

(Mathematica will do it with a very short bit of code. Executing that code will take quite a number of logic operations internally, however).

I call that complex. If you think it is simple, give us the answer, and please show your work. Can you see the answer straight off? Can you do it in your head? Can you do it by hand with pencil and paper? Can you do it without a full general purpose computer? Are you confident you can do it even with one, if you have to write the software to do it yourself, from stratch? Me, I couldn't do it without Mathematica, not rapidly. If I really had to I could write my own c code to do it, but I wouldn't want to bet very much that I wouldn't include some bug that would get it wrong.

My point is not to be confrontational, far from it. I think as soon as you dive in to a concrete example and see how interconnected the question winds up being, how each value winds up depending on a host of others, which depend on a host of others in turn, you will see why we call it complex. If you find it hard, it will be for the best of reasons. It is hard.

That it has elements does not make it simple. That each of those elements is simple still doesn't make it simple. That it is a problem of pure logic does not make it simple. The dependence of each little element on hosts of other elements, in ways that are not easily compressed into a single formula (that don't just add, for example), is quite sufficient to make it far from simple. A big part of the point of NKS, is that it takes far less to make something far from simple, than people thought.

I hope this helps.

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Registered: Feb 2004
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Thanks for the reply. I dont take it to be confrontational. Before I study it further, I should explain my thinking a bit more (will keep it short).

If Stephen W. had found the rule 30 pattern before finding the algorithm which produced it, then perhaps he would have immediately recognized it to be a 'complex' pattern. Let us pretend that only a few days later he found the corresponding algorithm which surpisingly was quite simple. Well now the complexity is sort of abstracted away from the pattern and the 'complexity' of the pattern is not respected in the light of what is it's fundamental foundation- the simple algorithm. (this is not to say that the pattern is no longer complex.. just that it is harder to respect the complexity knowing that what produced it was so simple.)

Just a thought....

Thanks!
Philip

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Registered: Feb 2004
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I respect (definately) the fact that rule 30 requires a run in order to find the solution to step xxxxx. This definately makes it complex. But the same is true with something like addition. We still have to execute the algorithm. Fundamentally the two are similar in respect to algorithmic process. Am I missing something on this point?

Thanks....

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Registered: Aug 2003
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Suppose I ask the same question about rule 250 instead of rule 30. Do I have to calculate a half million cell colors to get the answer? Here is my answer and my work.

The center column at step 1 is 1, at step 2 is 0, then alternates. Therefore a formula exists for the center cell at step n. It is Center250[n] = n mod 2. 1000 is even, i.e. 1000 mod 2 is 0. (I can tell very easily because its last base 10 digit is 0 and 10 is divisible by 2). So the answer is 0101010101. That is all my work. Didn't take a half million calculations, did it?

I could have calculated every step, and I'd get the right answer. The existence of a slow way to get the right answer does not suffice to make the problem complex. Since a fast way also exists, the problem is not complex. With rule 30, it is not the existence of the slow way that makes it complex. It is the non-existence of a fast way.

With addition, I can add 567 and 345 together with this slow algorithm -

567 minus 1 is 566. 345 plus 1 is 346. Continue until the first register reaches zero. Then return the value in the second register. This takes twice as many steps as the value entered in the first register. Does this make it complex?

Well, here is another way instead. 7 plus 6 is 13. Enter 3, carry 1. 6 plus 4 plus 1 is 11. Enter 1, carry 1. 5 plus 3 plus 1 is 9. Enter 9. Return 913. But ah, you will say, using facts like 7 plus 6 is 13 includes a subcalculation. Fine. I still reduce the number of operations to around 40, down from 1134. Addition is normally well behaved.

Not all seemingly simple mathematical operations are, though. The 3n+1 problem is an example of one that isn't. Factoring large integers can be hard enough to form a basis of practical encryption schemes. Chapter 4 is full of such examples.

Complexity is a formal phenomenon, not an observational one or some artifact of our deficient knowledge of something. It is true there can be cases at the margins, where something appears complex at first, but after hard analysis work we manage to find a "crack" (figuring out what is going on, in some simplified way) that produces a general formula.

Or we may see complexity in one scheme or representation, while we can find simplicity in another. (For example, the Golden Ratio in decimal expansion is pretty complicated, but in a continued fraction expansion it is 1,1,1,1,1,1...). Any choice of representation may present a few problems as simple.

But others will always remain complex. And scads of formal problems with simple statements but no simple solution will arise for which there is no apparent "crack". Even e.g. in integer Diophantine equations in number theory, undecidability will crop up in practice, and can be proved to be ineradicable in theory.

What this repeated phenomenon is telling us is simply that formal complexity is real, does not depend on point of view or basis of representation, and does not require elaborately specified problems or complex rules or constraints, nor does it depend on any underlying stochastic externals or "inside-outside gap", observational limitations. Instead, the onset of complexity is "early and often", purely formally.

I hope this is interesting.

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(not really refering to aliasing of images in playback systems.) ...
My mountain bike rests up on a stand. I can turn the wheel and let it spin freely. As I watch the treads, I notice that eventually the spin rate drops to a point where my eyes perceive a reverse direction spin.

It's still almost certainly aliasing. Am I right in thinking you're looking at the treads under artificial light (most probably a fluorescent strip light or similar)? You get the backward-spin effect because of the 60Hz light source strobing.

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Registered: Feb 2004
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That is a good point! The light sure has an effect. I do, however, remember seeing lots of these effects while outside in average daylight.

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Registered: Mar 2004
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Forgive my abrubt arrival here, this is my first post.

Guys, the same perceptual phenomenae that allows movies to work also mitigates the "reverse motion" perception without any intervening "sampling" or strobe imposed by a light source. The variable sacchade where the retinal data gets integrated in the cortex....part of why the "picket-fence" phenomenae can precipitate seizure....we can look up specifics in the neurology of this, but causally, I just thought I should bring up the 20 to 30hz basal rate that seems to mitigate all such perceptions. So even though fluorescents and such can cause some weirdness in this department, it is important to remember that visual perception is not seamless but like many neural functions is dependent on these synchronized sacchades of cells working together, hence a point at which we are confounded and rapid discrete events appear seamless to us.

It is also the reason why rapid events purposefully "de-sychronized" to these sacchades are invisible, as they occur between the "polling cycle" of the cortical structures. There are a lot of studies of this type covered in Patricia Smith Churchland's "Neurophilosophy". Sorry for my sketchy description, I loaned my copy to a colleague.

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