Registered: Mar 2005
Posts: 6

Dear friends,
I would like to present to this forum my commentary on Stephen Wolfram's book "A New Kind of Science"

http://www.geocities.com/spatlavskiy/ComStephenWolfram.pdf

Best,
Serge Patlavskiy

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Registered: Aug 2003
Posts: 712

"A" goes to "A" is simple and symmetric enough that it does nothing interesting.

Something will be complicated enough to do something interesting.

Ergo, there is some continuum from dead simple to complicated, after which the behavior gets as complicated as you please.

The sole question is how soon it happens.

If one categorizes solely on the outcome, then one can call anything that produces a complex output, complex. But this is assuming a conclusion or playing with words.

If instead one categorizes on the form of the rule, then one can speak of simple rules leading to complex behavior or not doing so. The question simply cannot arise otherwise.

In the first third of the book, Wolfram strips away candidate after candidate for the supposed magic component that effortlessly produces arbitrary complexity from little. There isn't one - each special bit of 2 color CAs is removable, without the formal phenomena disappearing. How far you have to push to find it differs at the margin for register machines vs CAs, etc, that is all.

The specific hang up of this review seems to be symmetry. He notices that in the ECAs, the most complex behaviors come from the non-symmetric rules, and that is true. It is clearly easier to arrive at a complex behavior non-symmetrically, since symmetric anything effectively has fewer bits of distinguishable behavior to play with.

But the totalistic CAs have symmetry, and show all the complexity one could ask for, very quickly.

My personal favorite in impressive complexity combined with a symmetry I find beautiful, is a bit farther out in the rule variety tree. All the way out at 3 colors, and outer totalistic. You don't really have to go that far, and I'll give an ECA example below. But the result is to me prettier and the complexity more staggering, this extra bit out. If one isn't interested in finding an exact threshold or first, it is enough.

It is outer totalistic 3 color CA number 8640199.


JasonsRule = 8640199;
Partition[IntegerDigits[JasonsRule,3,15],3]


Notice, all 3 colors occur 5 times in its rule table. The behavior for any given outer total is always symmetric between 0 and 2. Outer total 2 always leads to 2, ignoring the previous center cell value.

To appreciate it, start with at least 400 steps of evolution. (I've studied the center of the pattern to 50000 steps, and it stays spectacular).


ArrayPlot[
 CellularAutomaton[{JasonsRule, {3, {3, 1, 3}}, {1}}, {{1}, 0}, 
  400, {All, All}], 
 ColorRules -> {0 -> Yellow, 1 -> Red, 2 -> Black}, 
 PixelConstrained -> 2]


Symmetric? Yes. Makes it quite pretty, too. Simple? No.

Don't want to push to 3 colors or outer totalistic? OK. Look at rule 182, which appears to be simple. Now look at it with a periodic background, made of block {0,0,1,1,1}. Put a single 1 between tiles of that block.


ArrayPlot[
 CellularAutomaton[
  182, {{1}, {0, 0, 1, 1, 1}}, {{1, 400, 2}, {-400, 400, 2}}], 
   PixelConstrained -> 4]


Now, let's look at the effect of moving the "defect" 1 by phase one, aka the difference between a repeating background of {0,0,1,1,1} vs. one of {0,1,1,1,0}. Using the fact those two background are IntegerDigits[7,2,5] and IntegerDigits[14,2,5], you get this -


With[{data2 = 
   CellularAutomaton[
      182, {{1}, IntegerDigits[#, 2, 5]}, {200, All}] & /@ {7, 14}}, 
 ArrayPlot[data2[[1]] - data2[[2]] + 1, PixelConstrained -> 2, 
  ColorRules -> {0 -> Yellow, 1 -> Red, 2 -> Black}]]


Symmetric? Yes. Simple? No.

I hope this is interesting...

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Registered: Mar 2005
Posts: 6

[Jason Cawley]
>The specific hang up of this review seems to be symmetry. He
>notices that in the ECAs, the most complex behaviors come
>from the non-symmetric rules, and that is true. It is clearly easier
> to arrive at a complex behavior non-symmetrically, since
>symmetric anything effectively has fewer bits of distinguishable
>behavior to play with.

[S.P.] The cognitively independent entity has no immanent properties. No entity possesses an immanent property to be complex (or simple). It is the subject of cognitive activity (say, the human) who assigns such or other property to the given entity during the process of cognition, and thereby transforming that entity into the object of cognition. So, every rule (as an object of cognition) has an assigned property to be complex (or simple). The complexity (simplicity) is not an objective feature of the given rule: what seems complex for one person may seem simple for another person. Therefore, before talking about complexity and simplicity, Stephen Wolfram had first to establish some objective criterion by which the complex rules can be unambiguously distinguished from the simple ones. (The objective criterion presumes determination of complexity in comparison with simplicity, and necessarily within the set of homogeneous elements, here, rules). But, instead of suggesting a criterion, the author perfunctorily calls all 256 rules simple.

Now then, in my commentary I have firmly proven that those 256 rules can be divided into the complex and simple ones by applying a strict, objective criterion of the presence or absence of the mixed (negative+mirror) transformations. Using this criterion we can predict with 100 percent of confidence whether the distribution will be complex or simple just by looking at the very rule. Thereby, those entire 256 rules can be unambiguously (or objectively) divided into the simple and complex ones (note, that they are complex and simple in comparison with themselves, but not with some other rules that are not the elements of that 256-rules-set). As we may easily check, the simple rules produce simple distributions, while the complex ones produce complex distributions (it would be contra-factual to state that the simple rules produce complex distributions). So, WHERE IS A DISCOVERY here? For me, it is not a discovery, but statement of the self-evident facts. Would it be a discovery to learn that it is cold in winter and hot in summer in Northern hemisphere? Maybe, it really is a discovery, but on the level of some private person (like a one-year-old infant, or an African first-year student of the Moscow University), but not on the level of the learned scientific community. And what "new kind of science" the author is talking about? Maybe, he means a science that will already be based not on scientific (objective) discoveries, but on subjectively perceived revelations?

I would much like to hear the author's personal opinion concerning the expressed critical arguments (if he feels it important to pick up this gauntlet, of course). It is an obvious fact that the author has totally overlooked the possibility to divide the rules into the simple and complex by applying some strict objective criterion. This fatal omission at the very start puts into a big question the validity and importance of the whole author's (life-long) work. It is the same as to go fishing, and to take a broom instead of a fishing-rod -- in this case the outcome of fishing is predictable.

As one may judge from my 2005 year post to this forum (NKS Way of Thinking: "Roads to Reality... but only without incorrect criticism."), I am very tolerant as to the new ideas and approaches. Yes, we need the new kinds of science, the new paradigms, the new appropriate explanatory frameworks (especially for formalization of consciousness-related phenomena and artificial intelligence), the new meta-theoretical systems, but, whatever they could be, they cannot be grounded on omissions, and they cannot violate the criteria of scientific correctness.

[Jason Cawley]
>It is outer totalistic 3 color CA number 8640199.

[S.P.] Yes, I agree, it would be interesting to investigate whether the objective criteria for determination of complexity and simplicity can be established for other sets of rules too. But, it is already a task for the WolframResearch staff. I see my task (provided there will be the author's interest) rather in examining whether his ideas, taken in toto, can be considered as some new all-sufficient meta-theoretical system which is able to replace the presently dominating purely materialistic and reductionistic one, and whether it can be investigated for compatibility with other authors' new meta-theoretical systems.

Best,
Serge Patlavskiy

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I don't think you quite understand the NKS argument.
"But, instead of suggesting a criterion, the author perfunctorily calls all 256 rules simple."
What Wolfram is looking at is the behavior of simple programs and trying to see if just because the programs rules are simple if that necessitates a simple output. But according to NKS if one looks at for example Rule 30 one gets quite rich behavior from relatively simple rules. Or take rule 110, where it used to be thought that universality was something that was hard to achieve, Rule 110 shows that the entry level to universality is far lower then originally thought. You also may recall the Wolfram classifies CA into different classes 1-4 where Rule 30 would be Class 3 and 110 would be Class 4, the classifications divide the rules from simple to complex by the type of output.

Now it would be incorrect to focus to much on CA since this misses the broader point of NKS, that is, that the abstract study of simple programs is a valuable thing. That one can find all manner of interesting behavior can be found simply be searching for it. Also that complexity does not imply complex rules to get complex output, one can have simple rules, and yet one can get far more complex output then input.

"Maybe, he means a science that will already be based not on scientific (objective) discoveries, but on subjectively perceived revelations? "

This kind of statement may be merited if you understood the NKS argument and had a cogent argument to counter it, but as it is you do not. You seemingly paid no attention the general direction of NKS argument and got lost in some well understood snares.

Further if you ever manage to accomplish what Wolfram has accomplished you could make your argument that NKS is trash based on this poor criticism, but you have not. Whether NKS is correct or not is up for debate but the debate is relegated to those who understand the argument and understand science in general. This would exclude you from said debate.

Wolfram never claims NKS to be all sufficient, in fact if you read the book and listen to some of his speeches you will see he believes it to be an extension of current science allowing us to do things in science that he believes we have not been able to do.

Please do everyone a big favor and educate yourself and a little humility goes a long way when critiquing the works of others.

Thanks

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Registered: Mar 2005
Posts: 6

[tomjones] wrote:
“I don't think you quite understand the NKS argument.”

[S.P.] The basic NKS argument that the simple programs can produce complex distributions won’t wash. What we have in real is that the simple rules produce simple distributions, while the complex rules produce complex distribution. Where is the discovery here?

[tomjones] wrote:
“This kind of statement may be merited if you understood the NKS argument and had a cogent argument to counter it, but as it is you do not.”

[S.P.] Please, read my commentary (if you haven’t read it yet).

[tomjones] wrote:
“Please do everyone a big favor and educate yourself and a little humility goes a long way when critiquing the works of others.”

[S.P.] A shallow argument, I must admit. The case is that to assess the ideas expressed in the NKS book, it is by no means sufficient to be a grad student in mathematics -- it necessarily requires an interdisciplinary approach. What we need is to investigate the NKS for compatibility with the meta-theoretical system of some other author. Unlike [tomjones], I have my own meta-theory constructed, and unlike [tomjones], I do not worship the NKS, but conduct scientific investigation.

Best,
Serge Patlavskiy

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Well, excuse me, and allow me to bow before your incredible intelligence. And I am sorry for merely shedding light on your ill conceived ignorant commentary which is of little value to anyone.

Perhaps one day when you are intelligent enough to skip straight to graduate studies without any undergrad work, you can talk down to me. But thankfully you and I are not on the same intellectual level, no, you could spend the rest of your life studying and I will still have forgotten, and learned more in my 22-years then you will learn in your lifetime.

Now if your quite finished being stupid please do me the favor of reading and comprehending my post, then posting back with intelligent response.

"[S.P.] A shallow argument, I must admit. The case is that to assess the ideas expressed in the NKS book, it is by no means sufficient to be a grad student in mathematics -- it necessarily requires an interdisciplinary approach. What we need is to investigate the NKS for compatibility with the meta-theoretical system of some other author. Unlike [tomjones], I have my own meta-theory constructed, and unlike [tomjones], I do not worship the NKS, but conduct scientific investigation. "

I never claimed to agree with NKS, in fact I don't, merely that your argument fails to disprove it. And thanks for the interdisciplinary idea, but I think I have that well covered. Of course I have no theories of my own being a poor stupid mathematician unlike you, the great and magnificent amateur thinker/ bozo that you are.

But it will delight you to know that I have in-fact many of my own theories, and all of them superior to the best you have to offer. How can I be sure of this for the same reason your sure that I don't. And since were on the topic of stupidity, lets examine your arrogance in assuming that you have any idea of what I think. Well, maybe not, that could only be a waste of valuable seconds.

So go back to your poor deluded, foolish, ignorant ideas and leave the thinking to those who have minds.

Bottoms up...

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Registered: Mar 2005
Posts: 6

[tomjones] wrote:
"But thankfully you and I are not on the same intellectual level, …"

[S.P.] That's right!

[tomjones] wrote:
"But it will delight you to know that I have in-fact many of my own theories, and all of them superior to the best you have to offer."

[S.P.] I have commented on dozens of books and papers from the fields of consciousness studies and artificial intelligence, and I will readily look into any manuscript with sober ideas. The case is that in those fields the satisfactory paradigm is not established yet, and no one worth to be regarded as an impeccable authority. So, anybody's thoughts are of equal importance.

Best,
Serge Patlavskiy

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Registered: Mar 2005
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I would like to explain the idea ones more. The case is that we can determine simplicity only in reference to complexity. Let us formulate the following axiom here: if the system of homogenous elements is full, then it cannot be called simple (or complex). This axiom may be reformulated in such a way: no strict criterion for objective determination of simplicity (or complexity) can be found in reference to a system of homogenous elements which is full.

If we have a system which consists of homogenous elements, and if that system is full, then a strict criterion can be found only for division of the elements of that system into the simple and complex ones, and those elements will be simple and complex only in reference to each other. And this is exactly what I have proven in my commentary: the strictly determined simple rules produce simple distributions, while the strictly determined (using the same criterion) complex rules (as the elements of the same full system of rules) produce complex distributions.

Now then, Stephen Wolfram has formulated his discovery in such a way: simple rules can produce complex distributions. He clearly refers here to the set of the 256 rules. But, the set of those 256 rules is full; therefore no strict criterion can be found so that to determine objectively that full set of rules as simple (or complex).

I do not discuss a question whether Stephen Wolfram has or hasn't made a discovery. I just state that the wording of that (possible) discovery is not correct. In fact, the appeal of the given by him formulation is based on the interplay of words "simple-complex". So, I would suggest to replace the improperly used term "simple" into "elementary mathematical", and the term "complex" into "unpredictable". Then we may reformulate that (possible) discovery in such a way: elementary mathematical rules can produce unpredictable distributions. Yes, the suggested formulation loses its appeal (and I can't still say whether it is a discovery, or just a statement of the self-evident facts), but instead it already contains no "playing-with-words". Hope, the idea is clear.

Respectfully,
Serge Patlavskiy

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Registered: Sep 2007
Posts: 20

Hi all, (specifically tomjones and SP):

Can we please settle down a bit? Passionate disagreement is all well and good, but let's not resort to flaming. Let's keep the din to a gentle roar.

Thanks!

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