Principle of Computational Equivalence (PCE) - A Future Theosophy?

At the Singularity Summit 2011, noted mathematician Stephen Wolfram outlined his views about the future and the principles that will govern the onset of that future. One of those being the Principle of Computational Equivalence, which he explains as:

Now, we might have thought that as we make the underlying rules for a system more complicated, the computations it ends up doing would somehow become progressively more sophisticated.

But here’s the big claim of the Principle of Computational Equivalence: that isn’t true. Instead, after one passes a pretty low threshold—and one has a system that isn’t obviously simple in its behavior—one immediately ends up with a system that’s doing a computation that’s as sophisticated as anything.

Should that be true, will it become an underlying principle to evaluate all our past teachings, several of those with great reputation about the level of their sophistication?  Stephen Wolfram, a little further down the address tells us about his vision for the future:

I think computational irreducibility has something to say here. I think it implies that there at least exists a sort of endless frontier of different purposes that can be built on one another. In a sense, computational irreducibility is ultimately why history is meaningful. For if everything was reducible, one would just always be able to jump ahead, and nothing would be achieved by all those steps of history.

But even though new purposes and new history can be built, will we choose to do so?

It is hard to know. Perhaps for all practical purposes, history will end.

You know, I have a strange guess about at least part of this. My guess is that when in a sense almost anything is possible, there’ll be an almost religious interest not in the future but in the past.

Even more significantly, he concludes that computational irreducibility can solve the problem of free will vs. determinism:

And at for example a philosophical level, I think it finally gives an explanation of how there can be both free will and determinism.  

Full text of this fascinating address can be read here.

Does PCE qualify to be a Future Theosophy?


Views: 420

Replies to This Discussion

In his address, Stephen Wolfram speculates that someday an algorithm could be devised which will allow each of us to create our own universes.The ancient Indian text Yoga Vasishtha postulates, "manodrsyam idam sarvam", implying universe is the object of the mind. Or, the universe exists as perceived by the mind.

Could this be the reason Wolfram feels that someday future will become redundant and we will be compelled to look at the past?

  Hi, friends!

 You have given us a lot to think, Anand!!! :-)

 I have followed the link and the link into the link ;-)  ... until they have told me I have to register and allow cookies into the PC I use to keep on reading :-(

 I think that PCE can be an useful element of XXIst century theosophy (hehehehe please notice that I have not used the word "future", nor capital letters for theosophy hehehe :)  The idea is so good that I'm happy to use it against his creator: if the PCE is true, then the ancient Chinese I-Ching is as sophisticated as all scientific computers and methods, and there's room for astrology, too. Good news indeed!!!

 Good news because I-Ching and astrology are much cheaper than all the stuff scientists like Stephen Wolfram need to work and to believe they are superior to the "primitive animistic".

 This idea of computational irreducibility... one step at a time, and the only way to reach step 5000001 is through  5000000 steps, is good, too, but I don't think it's so new.... a journey of ten thousand miles starts with one small step.

 I don't trust scientists when they speak about history and even less when they speak about philosophic questions... I mean scientists who have not studied history and philosophy, too. For what I have read, his historical frame is of about 400 years(Galileo, Newton) . People have been living in my hometown by the Mediterranean sea since about 3000 years, we have some archeological rests of minor importance that date from before the Romans. Your frame, Anand, is much broader than mine... so, it seems that people who are in their "before500th step" sometimes tend to think they are the first and only ones to walk the path hehehehe.

 I don't think Stephen Wolfram will be remembered in history because of his contribution to the philosophic question of the free will, but the idea of working through small steps (does anyone know if Wolfram likes reading the Chinese classics?)  well, "relatively simple programs", to use today's word, with today's technology will bring very good results.

 And, well, the guess that when in a sense almost everything is possible people will turn their interest, almost religiously, to the past is like when in the first pages of his book A New Kind of Science writes about not-needing a supernatural or supersophisticated creator, a symptom that a human being needs, to be wholesome, to resolve the religious question.  Maybe we could offer him some relatively simple programs to do so, but I think he is too busy a man. 






Thanks Ferran.

I don't think anyone ever considered I-Ching as less sophisticated in comparison to any other system. But the point really is to not make such comparisons as they all could be the outputs of very simple code at the core.

And, computational irreducibility is not only about taking one step at a time, but actually about inability to see the result of a program before actually running them, i.e. inability to arrive at a result just on the basis of a theory. Practical results have to be evaluated. This of course, will not go down well with the traditional philosophical thoughts where everything is proven or dis proven by arguments alone.

Another practical example of this would be the various mixture of humans and other life forms that happened as described in the Anthropology of the Theosophical literature. These would perhaps be the result of "bugs" in the program used to create them. Until the creators worked out the simple code. That does not mean that the present program humanity v1.0 is perfect. Far from it, there are in-numerous bugs still to sort out, progressively in Humanity v2.0 and Humanity v3.0 and so on.

Philosophy is changing like everything else. It would not really be fair to judge the emerging thoughts by old standards or distrust merely because it comes from a scientist or economist or a politician. That will be taking too narrow a view. More than whether he would be remembered in history or not, I think it is important to realize that he is leading us to think in unconventional ways. That may be a departure from rote based learning pattern of spiritualists but who knows, the way forward maybe.

Wolfram may not be the first to propose it, but simplicity has been an idea associated with not only spirituality but also philosophy of science.

 Thanks to you, Anand! :-)

 The fact, as you have probably guessed, is that Wolfram has offended me:

 "You know, there are expressions like “the weather has a mind of its own”. And one might have thought that that was just some primitive animistic point of view."  

 I take offence because of his use of the word "primitive" in this sentence.  

 I cannot quote the sentence in A New Kind of Science in which Wolfram wrote about not needing a supernatural supersophisticated creator of the universe because I have not registered in his web, so I'm not allowed to read again.

 I take offence because of this mention of a "god", too. Yes, I do. I am crazy, remember?

 Why don't scientists stick to their business, the one they have been trained in and practiced but go speaking about history, philosophy and theology as if they were experts? Why do people appreciate their opinions more than the opinions of historians, philosophers and theologians? 

 Wolfram is not an anthropologist, so his use of the word "primitive" is not a technical one but a valorative one. He's comparing himself and his ideas to the primitive and his ideas, and feeling so proud of his superiority.

  I did not start any comparison, he does. So I use his PCE idea against his superiority. I love doing so!!!

 He presents his ideas as new ones, and to me he is showing his ignorance of cultural human traditions that are outside of his specific field of studies. What I think when reading him is that scientists have moved one step forwards becoming reflexive, but many more steps are needed.

 If scientists from Newton and Descartes on used to think that theory alone allows anyone to reach results, or, maybe more precisely said, to predict which results are possible and which are impossible, it's their problem, their illusion born of fear of controlling nature's forces. If they're beginning to see now that it's not so, it's good news. We are barely still in time to save the ecosystem.

 The word "theory" was introduced by Plato, with a quite different meaning from the usual one nowadays. When Plato tried to put his theory into practice, which means politics, the result he got was that he was sold as a slave... quite a lesson on unpredicted results, isn't it?  

 Philosophers have not proven anything along history. Anywhere a philosopher says "a", another one will say "b". It's been like this since ancient Greece. They have spoken a lot about proving and about how to prove or disprove, and even pretending to prove and disprove, etc... I got my degree in Philosophy just as a mean to defend my integrity as a crazy man, hehehehe, to make my insanity impossible to prove hehehehe ;-) 

 Saint Nietzsche wrote that "any valuable thought is a thought you have walked ", against lazy people who believe they can know everything without leaving their chair, just by looking, reading or thinking.

 Anyone like you, my friend, would not consider the I-Ching less sophisticated than anything else, but the fact is that the I-Ching comes from "primitive animistic" times and, belonging to a living tradition as it does, it is still used today. My opinion is that it works because animism is not at all an inferior idea of reality than mechanicism.

 The trouble I find in contemporary science and technology is 1) that the equipment needed is too expensive, so only a few privileged people (the "best" ones in their class, the ones who win the competition) can have access to the funds to practice it, to investigate. Is this fair?  ... and 2) it is soulless, irreflexive, has provided insane people with massive destruction weapons that have been used to kill millions of defenceless people, has given a lot of comfort to some, but has not been able to feed the hungry of the world, although the means to do so are there.  

 Wolfram does not say anything about feeding the hungry when he speaks about the future... I dare say he's not looking in the good direction. (Or maybe he has written about this somewhere else, if so please give me the link, I'll be happy to change my opinion.)

 This said, the method of working through relatively simple programs and observe what happens is, in my opinion, a really important and useful idea for XXIst century.

 Have a good day today, everyone! :-)







Thank You Ferran.

Kindly permit me to seek forgiveness from you for the hurt that Wolfram has caused. In a way that was intended. Not the hurt, but the challenge which led to that hurt.

I would be interested in learning what or whose Philosophy considers Science to be different (other than the Christian Church's) from Philosophy. That division - is it artificial or real? If Philosophy has not been able to prove anything why such high expectation from Science? Are the Philosophers looking up to Science to provide answers to them? And if the Science comes up with different kind of answers, should that cause hurt?

Perhaps, you may be aware but in ancient India, Science was taught to students under Philosophy. The Nyaya Vaiseshika system of Indian Philosophy is a good example.

Which Philosophical System has been successful in feeding the hungry? And if there is any success why there are so many hungry people still on this earth. And by your own assertion of strict separation of domains, leave that to the Political Scientists or the Economists. If Scientists cannot talk about Philosophy, why Philosophers should be permitted to talk about social issues?

By no means am I proposing that what Wolfram says is correct. I am only curious whether there is any substance worth considering in his propositions.

Why the idea that we all could be simple programs created by someone who has it figured out and someday we will be able to create our own if we manage to figure it out, so offensive? Had it been less offensive if he said that we could be very complex (sophisticated) programs which are undecipherable?

Hi, Anand! :-)

Well, I don't think I'll have the time to finish with your questions right now, but I can't help answering some now.

 Generally speaking, Continental philosophy, considers that science and philosophy are different business. Hehehehehehe :-) The idea that philosophy's business is to clarify and generalize science, its methods and language, is usually associated to the philosophy branche that started in modern times with Locke and Hume, continued with Bertrand Russell, and so on. It's a philosophical opinion, as good as any other.


 I think that science and philosophy are different business, games or jobs, different activities with different rules.  


 Science is powerful, that's the reason why people expect so high from it. I don't know if scientific and technological development in the last centuries has caused more suffering or well-being to the people of this world up to today, I give this to anyone to ponder... but the fact of so many atomic bombs ready to destroy all life in this planet so many thousand times gives me a hint on what to expect... if Stephen Wolfram had remembered this fact and said "and maybe, just maybe, we'll find a way to neutralize atomic bombs and the effects of nuclear accidents with this New Kind of Science that seem impossible from our present point of view", I'd become a fan of him!!! It's his selective memory on the side effects of his business on people that offends me.


 Yes, answers or whatever, some philosophers have even made a religion from science, like A. Comte did.   


 It's not about any "should", philosophers have not made atomic bombs... it's a fact that atomic bombs hurt.   

 Sorry, time over, we'll continue. ;-) Have fun today, everyone!

 Hi, friends!

 I'm continuing with Anand's questions in the post above. ;-)

 I am thankful because there is no question about Indian Philosophy.


 Well, the ideal of many philosophers along history has been to build a Philosophical System, but these are not my favourite ones hehehehe... the word "System" goes well with Hegel, the "philosophical father" of K. Marx, so yes, horrible things have been done in the name of "feeding the hungry".... I'm just a crazy fellow who uses philosophy to resist against the system, so maybe I'm not the best person to ask about Philosophical Systems. I did not assert any strict separation of domains, I just asked "Why?"  and the key part of the question is "as if they were experts" and I don't mean that anyone has to be an "expert" or anything before speaking... I just asked "why?" ... anyone is permitted to talk about anything, so replies (and by the way, any literary resource:) are part of the game.  


 The idea is not at all offensive, I think it is a step on the right direction. Yet, I see it more as losing the old idea of "complication= sophistication" than realizing the simplicity beyond words of the laws of life. What is offensive is to resolve a philosophic or theologic question as a kind of side-effect of a scientific investigation... it's just that I'm tired of seeing scientists doing this in their books adressed to the general public, and I have seen it one more time.

 What is offensive is the pride of these who believe they are superior to the animistic... animistic "technology" has not succeed in solving the issue of human needs, neither have science and technology in the usual meaning of the word, and from what I've read of Wolfram's ideas about next years, his New Kind of Science forgets about this issue... so I take offence because I don't find any human meaning there, and I'm happy to use PCE idea idea to kill his pretension of superiority, to make his computers and the I-Ching "computationally equivalent" hahahahahaha which is quite a pleasure in itself hahahahahahahahaha!!!

 Have fun today, friends!!!

Thanks Ferran.

Let us consider even more fundamental questions. What is Philosophy? Should there be a defining definition that everyone must strictly adhere to? Can there be a single line of inquiry?

Is Philosophy subject to evolution where like everything else the form and content will have to change?

The author of the ancient Indian text "Yoga Vasishtha", Valmiki, was a highway robber before he became a saint. Should he have been banned from thinking?

Can there be only one process to get a product?

If Philosophers feel incapable of grasping subjects like Mathematics, Physics, Biology etc., let them honestly admit so, why introduce turf battle into it? Why deflect the question by bringing "superiority" or "inferiority" into it?

Of course the topic deserves a full fledged discussion on its own merits.

Embrace, Compare, Explore is the mantra for this century. Please allow the future to modify the past.

I must confess that Wolfram always loses me. He is incredibly talented.

He is so wrapped up in Cellular Automata that I think he believes it can explain the entire reality of the universe. Anyway - that is how I currently view him. The foundational principles of his "new" field have lacked some rigor - I do not believe any program can be written to produce a priori a given particular need/result/function. Hence - it is usually a shot in the dark.

To get an example of cellular Automatum that actually creates things that seem physical, you should take a look at Conway's "Game of Life". I remember playing that a lot in the mid-70's. It is entirely local, 4 rules involving only the touching cells of the 4 neighbors. Strange things happen on a global scale. (wiki has some evolution clips).

The CA theory is very popular and powerful for emergent technology/phenomena. It appears to be the system used by complex social insects. (ants, bees etc). The Military likes these types of systems, since communication is irrelevant for the success and survival of a group/system.

So - I do not know the answer.

It is totally deterministic. Free will does not exist, unless you get to tweak the rules. However any small tweak of the rules yields a mammoth change that is often more worthless than not. Natural evolution may work this way. (??). It fails to explain correlated items separated by distance. If anyone understand where he gets free will from - I'd like to hear it. (seriously).

As to philosophy - it consumes everything. I decided a long time ago that any discussion will end up in a philosophical argument. If it doesn't, either you are asking the wrong questions, or not asking enough questions. People with Doctorates in Physics, Math, Chemistry, Biology etc. traditionally all received the same degree - Doctor of Philosophy. (i.e. PhD). The Arts and Sciences at that level were all considered Philosophy. I agree with that idea and viewpoint.

as an aside - the Conway I referred to above is the same Conway from the "Strong free Will Theorem".


Search Theosophy.Net!


What to do...

Join Theosophy.Net Blogs Forum Live Chat Invite Facebook Facebook Group

A New View of Theosophy


Theosophy References

Wiki Characteristics History Spirituality Esotericism Mysticism RotR ToS

Our Friends

© 2023   Created by Theosophy Network.   Powered by

Badges  |  Report an Issue  |  Terms of Service