Registered: Jan 2004
Posts: 16

Stephen Wolfram asks in A New Kind of Science: Open Problems and Projects(pg. 10); "What might history have been like if cellular automata had been investigated in antiquity?"

It may be that cellular automata were at least encountered in antiquity. As a student of yoga, I have long wondered about the similarity between aspects of yogic philosophy and NKS. The most obvious connection is that yogis hold that the universe is a manifestation of "Cosmic Mind" and that the underlying foundation of reality is consciousness; from here it is a short jump to what Jason Cawley refers to as the "digital philosophy/digital physics movement" where computation is the foundation of the universe.

This is just the start; a common concept in different yogic philosophies is that the universe is the resultant interplay between consciousness (shiva) and "energy" (shakti). Shakti is nothing more than the aggregate name for three theoretical principles, the static principle (tamah guna), the mutative principle (rajah guna), and the sentient principle (sattva guna). All three principles are always present in varying degrees in all structures within the universe. This would be analogous to the idea that the universe is a class 4 CA and that local regions of class 4 CAs often appear to be comprised solely of class 1, 2, or 3 CAs. The static principle corresponds nicely with the idea of class 1 CAs where change ceases; yogis maintain this is responsible for the mental feeling of "I have done". The mutative principle corresponds to class 2 CAs where change continues on indefinitely but without variation and leads to the feeling of "I do". The sentient principle is held to give rise to consciousness due to its reflective and self- referential nature; this corresponds to class 3 CAs and is at the heart of the sense of "I".

I am certainly not suggesting that the ancient yogis received this information by divine revelation, but suggest that they were the original "hackers" using mediation to explore the ultimate basis of the mind. The question is if someone had the discipline and wherewithal to become aware of the ultimate computational basis of the mind, would they encounter the four classes of cellular automata? Isaac Newton is said to have devoted more time to proving the triune nature of God than in exploring science and mathematics; I certainly wouldn’t suggest that he had encountered cellular automata. Anyone who has looked at Ramsey theory will understand the inevitability of spurious patterns in the universe. A wonderful example of this phenomenon takes place in the movie "A Beautiful Mind" where Russell Crowe and Jennifer Connelly are gazing at the stars and Crowe displays the ability to find patterns of stars resembling arbitrary objects. Prior to the publication of Wolfram's work on CA I has noted a correspondence between the three yogic principles of energy and the three types of structures in structured programming; sequential, conditional, and iterative structures.

Daniel Geisler

Report this post to a moderator | IP: Logged

Registered: Sep 2003
Posts: 5

I think that one of the very few points Wolfram gets wrong in his view of science history is when he speculates on whether NKS might have been invented before calculus-based science (OKS, for my purposes here). I don't think this might ever have been the case.

Wolfram himself stresses that what made it possible to make NKS experiments in a reasonable scale is that computing power became available and that a computer language/environment (Mathematica) was invented to access the computational world.

Of course one can imagine a Babylonian king having hundreds of slaves drawing steps of rule 110, but it's hard to think of any historical context in which this might have happened. Personally, I can't even imagine NKS being developed within a procedural compile-and-debug environment.

So it's hard to imagine this kind of stuff being done before our time. And if one thinks of all those scientists that still use Fortran, or, worse, of physicists like Weinberg who don't even understand what computers are capable of in terms of modeling, than one has to acknowledge that the NKS paradigm is, still, ahead of our time. It would have taken a few decades for things to get going had Wolfram not been around.

So my point is: in order to have NKS you need something like Mathematica; in order to have something like Mathematica you need digital computers with a certain amount of computing power. And in order to have digital computers you need engineering, which is OKS-based. And OKS emerges out of people using calculus-based math to describe computationally reducible natural phenomena. So, no NKS before OKS, period.

I concede that this argumentation is shamelessly ex post, since I'm just sticking to things the way they happened. But I can't think of any other possible developments.

Fred

Report this post to a moderator | IP: Logged

Registered: Oct 2003
Posts: 38

To have computers, i agree that OKS is pretty crucial, for among other things it allowed us to master electricity.

But I think one can probably get pretty far without computers, if one had sufficient creativity. Because the rules are so simple, it presumably becomes more easy to implement them mechanically.

And one can imagine a history of computers born from ever-more-sophisticated devices for working with the simple programs. Although it would have its own bizzare and arcane details, one might imagine a computer of such orgin would be fundamentally cleaner and more efficient.

In terms of historical context, there are several routes one can imagine.

First of all, there is a pretty long tradition of people spending their entire lives doing the most bizzare and tedious things. I could certainly imagine some priest spending his entire life calculating automata. Im sure one could get through many thousands of rules by hand. If someone did that and published a short book full of pictures of them, im sure that would have been a great start for NKS.

Another possibility is that NKS could have arisen in art, particularly in weaving and floor tilings.

In terms of the development of actual computers, one probably needs a good application of NKS or some general purpose need for computation. One of the best applications of NKS, at least in the ancient world, would probably been for prophesy. Surely someone could make a living interpreting the complex patterns emerging from the simple rules. Presumably one can encode a question in the initial conditions.

One can also imagine NKS arising in games using simple devices.

Finally, one can certainly imagine concepts like cellular automata arising from the study of physical systems, since some of these systems are actual cellular automata. If fibonacci had found some good clean automata model of something, im sure things would have been much different.

__________________
Everything is an expression.

Report this post to a moderator | IP: Logged

Registered: Oct 2003
Posts: 69

Re. the following:

Stephen Wolfram asks in A New Kind of Science: Open Problems and Projects(pg. 10); "What might history have been like if cellular automata had been investigated in antiquity?"

Comment:

Right or wrong, ancient sages viewed the world we live in as the product of what, shorthand-style, may be termed Mind.

It is not clear how the ancients could have squared the concept of "cellular automata" with their view of Mind's role in Creation.

Report this post to a moderator | IP: Logged

Registered: Jan 2004
Posts: 3

"We always knew that Archimedes was making a step in the direction leading to modern calculus. What we have found right now is that, in a sense, Archimedes was already there. He already did develop a special tool with which you can sum up infinitely many objects and measure a volume."
-- Reviel Netz


Could it be that in the time of Archimedes, where he was already working with calculus toolsets, there were others working within the NKS style of thought?

I believe this is true but we have lost the documents to back this claim up so it remains pure speculation and it is save to say that Calculus came first... and later on NKS.





***
NARRATOR: A breakthrough because Archimedes had come up with a set of rules for dealing with infinity. He'd worked out a system for calculating the value of each slice and then adding up an infinite number of them.

REVIEL NETZ: Well, I was totally shaken. I was exhilarated and surprised when I saw this argument. And I definitely had the sense that without my knowing yet what the argument is, what this argument represents in terms of the mathematical interest of Archimedes which we didn't know about, it represents something very important, something very deep for the history of mathematics.

NARRATOR: It was clear that Archimedes had a made a huge leap beyond ancient mathematics toward a modern understanding of infinity.

REVIEL NETZ: Infinity is central to the history of Western mathematics because the history of Western mathematics was determined by a very Greek problem, the problem to which Archimedes contributed more than anyone else: how to calculate the properties of curved objects. The theorem of the wedge is the first time that we see any Greek mathematician doing something with infinity, actually producing an argument using infinity. That's something which we simply thought could not happen.

NARRATOR: Even today infinity is a concept that mathematicians can struggle to deal with.

DR. CHRIS RORRES: Humans are finite creatures, and to talk about infinity in any context, whether it's in a religious context or in a mathematical context, has always caused us problems. Possibly the fact that we can even think about infinity, about the concept, even come up with the concept, involves that we have some kind of a, a passport to God. Now I'm getting very religious here, but whenever you talk about infinity you almost have to confront religious issues. Will we live for infinity? Will the universe last for infinity? Where did the universe come from? Is infinity something that exists only in our minds and has no reality in basis.

NARRATOR: It was Archimedes' work with infinity that ultimately led him to the beginnings of calculus. The new findings reveal that Archimedes was a more sophisticated thinker and closer to modern science than anyone had realized. It's amazing to think that a branch of mathematics so crucial to progress and human advancement was first begun by a man who died over 2,000 years ago.


REVIEL NETZ: We always knew that Archimedes was making a step in the direction leading to modern calculus. What we have found right now is that, in a sense, Archimedes was already there. He already did develop a special tool with which you can sum up infinitely many objects and measure a volume.

NOVA | Infinite Secrets | PBS[
A battered manuscript turns up after 1,000 years, revealing the mind of the Greek Genius Archmimedes

Report this post to a moderator | IP: Logged

Registered: Jan 2004
Posts: 16

Let me briefly reiterate my point. My question is whether the similarities between a small portion of yogic philosophy and the four classes of cellular automata might be a result of certain yogis witnessing the computational basis of the mind. I am doubtful myself because I don’t believe that CA are the computational building blocks of the universe, but I also don’t believe in throwing data away because it doesn’t fit a cherished theory. As to Archimedes, while I think it is possible that he was the greatest intellect to every walk the Earth, I don’t see the connection between Archimedes and the possible history of CAs, beyond the obvious fact that Archimedes was a historical figure. I’m sure Archimedes would have been enchanted with CAs, but does any part of his work involve anything similar?

Report this post to a moderator | IP: Logged

Registered: Jan 2004
Posts: 3

.
Let me briefly reiterate my point. My question is whether the similarities between a small portion of yogic philosophy and the four classes of cellular automata might be a result of certain yogis witnessing the computational basis of the mind.

Maybe, using different words to describe the same concept. The difference is that with CA’s we are able to implement the four states into machinery and doesn’t stay reclusive in the human mind.

I am doubtful myself because I don’t believe that CA are the computational building blocks of the universe

Me too. CA gives us much deeper insight of the concept information (Data) [1] itself while Calculus gives us an understanding of action (in the form of matter) and energy. But I believe that it would go to far to label it as the computational building blocks of the universe (reality) itself [2]. CA’s gives us a better understanding of how Data is intertwined with energy and matter which is still sourly lacked in current day human intellectual structures (like economics).

, but I also don’t believe in throwing data away because it doesn’t fit a cherished theory. As to Archimedes, while I think it is possible that he was the greatest intellect to every walk the Earth, I don’t see the connection between Archimedes and the possible history of CAs, beyond the obvious fact that Archimedes was a historical figure. I’m sure Archimedes would have been enchanted with CAs, but does any part of his work involve anything similar?

As far as I know the answer is negative. But the question was if there already was an intellectual New Kind of Science structure before Calculus and what we know of the past the answer is negative.

J.


[1] The conventional view is that matter is primary, and that information, if it exists, emerges from matter. But what if information is primary, and matter is the secondary phenomenon! After all, the same information can have many different material representations in biology, in physics, and in psychology: DNA, RNA; DVD's, videotapes; long-term memory, short-term memory, nerve impulses, hormones. The material representation is irrelevant, what counts is the information itself. The same software can run on many machines.

Information is a really revolutionary new kind of concept, and recognition of this fact is one of the milestones of this age.

-- Gregory Chaitin, VII. Mathematics in the Third Millennium? --- The Unknowable, 1999


[2] Two complexity perspectives:

“Perhaps the best way to explain the difference is to say that he (Stephen Wolfram) is looking at "hardware" complexity, and I'm looking at "software" complexity. The objects he studies have complexity less than or equal to that of a universal computer. Those I study have complexity much larger than a universal computer. For Wolfram, a universal computer is the maximum possible complexity, and for me it is the minimum possible complexity.”

-- Gregory Chaitin, On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility, 2002

Report this post to a moderator | IP: Logged