Registered: Apr 2004
Posts: 1

I have been 'ploughing' my way through NKS for the past couple of weeks and am currently two thirds through reading it. I found the first chapters absolutely 'enthralling', but now find the text pondorous and repetitive.

I have counted about fifty or more back references to cellular automatons of one kind or another (almost at every opportunity) and I have lost count of the number of times that 'it is my strong belief' or similar wording has come up in the text, to the point of distracting from the content of the text.

The section on randomness and its origin and related to 'systems' is extremely thought provoking .

I found the section on networks and space strained and quite frankly I do not find the propositions believable. I also do not believe that the physical universe is reducable to simple equations and concepts. Am I alone in this?

I also found the section relating to quantum theory how can I put it 'incomplete and cursory'.

The concept of multi-universe and the basic physical problem of the 'Youngs slit experiment' with photons and electrons was not investigated (conspicuous by its absence) in the 'NKS' realm.

I really didn't get what was trying to be said about gravity, that may be me. Crack the conundrum of gravity and 'Young's experiment' and you will probably understand most of physics!

What I really found impressive was the obvious correlations between sea-shells' pigmentations and the 3D figures produced by the various automata. I felt that the depostion of shell material and the potential tie-up to automata could have been investigated deeper as this (so far) seems to be the most poignant visual piece of evidence.

I was also extremely interested in the fluid dynamics analysis conducted with automata, as this has close relationships to the work I am undertaking, and has very real potential benefits in all sectors of science. However there was no further details behind this important topic, so I felt left 'empty'.

Obviously I have a third of the book still to read, and I am unsure of where this it is all leading. I was hoping to read something like a modern 'Principia' mixed with the 'Origin of Species', but at the moment do not feel it coming together. May be I've got it totally wrong, or had to high aspirations? Perhaps the last 'third' will provide this.

Report this post to a moderator | IP: Logged

Registered: Not Yet
Posts: N/A

You won't be able to understand gravity from reading Wolfram's book because physicists do not yet have enough experimental data.

Currently, for describing the "classical" gravity all around us, theorists are not able to show that GTR is clearly superior to VSL (variable speed of light cosmology) or MOND (modified Newtonian dynamics) or maybe even some other theory I am not aware of.

However, this Monday the Gravity B probe will be launched, and within months there could be data from its new and important test of GTR.

As for the double-slit experiment, it is one of the greatest scientific experiments ever because it is simple, easily replicable and profound, and I think I read once that Richard Feynman thought that wave-particle duality is the most fundamental aspect of quantum mechanics.

You can try to imagine what the physical origin of wave-particle duality is or what quantum gravity could be, but doing so might be premature in case the Gravity B probe finds something significant and surprising such that you have to discard your earlier speculations.

You may want to look at

http://www.wolframscience.com/coverage.html

because it has a few well written reviews and criticisms of the NKS book and you can find here the reviews written specifically for the fields that interest you.

Report this post to a moderator | IP: Logged

Registered: Aug 2003
Posts: 712

On fluid dynamics with CAs, look at the attached notebook Richard Phillips provided in the following thread -

http://forum.wolframscience.com/sho...s=&threadid=272

That may help you investigate CA fluids further, if that is of interest.

As to whether the physical world can be "captured" (really, described or modeled) by equations or formal models, that is simply what scientists do - particularly physical theorists. Of course there are different ideas about what sort of equations will do it - the standard model in QFT being the basic one today. That too is an attempt to capture physical reality with equations. The issue being explored in the physics chapter of the NKS book is whether there might be discrete underlying generators giving rise to those results.

That is certainly a hard problem and a speculative one. Nobody claims it has yet been successful. Wolfram is not the only person looking for such underlying generators for QM - though others have their own approaches. A thread on some of them - with links to papers, websites, and such, can be found here -

http://forum.wolframscience.com/sho...s=&threadid=180

I hope this helps.

Report this post to a moderator | IP: Logged

Registered: Oct 2003
Posts: 69

In his lead-off post in this thread, Roland Heap writes:

I also do not believe that the physical universe is reducable to simple equations and concepts. Am I alone in this?

Comment:

No, you are not alone! – but there are few theoretical physicists who both (a) understand the reason why it is NOT so reducible and (b) have the guts to concede the point.

The reason for (a) is not lack of mathematical brains as distinct from the purely analytical kind with which the intellectually mature Einstein was endowed, as reflected, inter alia, in the implicit distinction which Einstein drew between his mature and immature self in this respect in an exchange between Heisenberg and himself, as reported by the former:

“But you don’t seriously believe,” Einstein protested, “that none but observable magnitudes must go into a physical theory?”

“Isn’t that precisely what you have done with relativity?” I asked in some surprise. “After all, you did stress the fact that it is impermissible to speak of absolute time, simply because absolute time cannot be observed; that only clock readings, be it in the moving reference system or the system at rest, are relevant to the determination of time.”

“Possibly I did use this kind of reasoning,” Einstein admitted, “but it is nonsense all the same. Perhaps I could put it more diplomatically by saying that it may be heuristically useful to keep in mind what one has actually observed. But on principle, it is quite wrong to try founding a theory on observable magnitudes alone. In reality, the very opposite happens. It is the theory which decides what we can observe.” (In ‘Physics and Beyond – Encounters and Conversations’, Harper Torchbooks, 1972, p. 63.)

As told in his autobiographical ‘My Philosophical Development’, it was only late in life that Bertrand Russell could bring himself “very reluctantly” to admit that mathematics is a pragmatic human rather than an eternal divine creation – although he still remembered his youthful delight in the contrary belief, he wrote, he now viewed it as nonsense.

Indeed, he was now persuaded that all mathematics is “tautology” as exemplified by the proposition that “a four-footed animal is an animal”. The curious thing about all this is why it took Russell so long to recognize and come to terms with the obvious – or so it had seemed to Wittgenstein as he parted philosophical ways with Russell decades earlier, and so it seemed to me soon after my initial encounter with the epistemological issues involved in the mid-1970s.

In this respect, it is morally certain that Russell was familiar with and must have reflected on the issues raised by Einstein in his 1921 statement on the heart of the matter which Jon Awbrey cited in his ‘All Liar, No Paradox’ thread some time ago as follows:

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. It seems to me,” Einstein added, “that complete clearness as to this state of things first became common property through the new departure in mathematics which is known by the name of mathematical logic or ‘Axiomatics’. The progress achieved by axiomatics consists in its having neatly separated the logical-formal from its objective or intutive content.”

Three years earlier, on the occasion of Max Planck’s sixtieth birthday in 1918, Einstein had emphasized that, in attempting to reduce the physical universe to simple equations and concepts, “the physicist has to limit himself very severely; he must content himself with describing the most simple events which can be brought within the domain of our experience; all events of a more complex order are beyond the power of the human intellect to reconstruct with the subtle accuracy and logical perfection which the theoretical physicist demands. Supreme purity, clarity, and certainty at the cost of completeness. But what can be the attraction of getting to know such a tiny section of nature thoroughly, while one leaves everything subtler and more complex shyly and timidly alone? Does the product of such a modest effort deserve to be called by the proud name of a theory of the universe?” (In ‘Ideas and Opinions’, Dell/Laurel Paperback, 1976, p. 221.)

The modern quest for a Theory Of Everything, I submit, is predicated on (a) the mistaken belief that mathematics is NOT a form of human language and, as such, differs from the verbal kind only in the precision of its tautological propositions, and (b) the identification of “Everything” with that subset of Everything “which can be brought within the domain of our experience” in the manner of experimental science.

A whiff of epistemological clarity would remedy (a) – a prospect which would seem to be alluded to by Prospero in Act IV, Sc. i of Shakespeare’s play, ‘The Tempest’:

“…And, like the baseless fabric of this vision, The cloud-capp’d towers, the gorgeous palaces, The solemn temples, the great globe itself, Yea, all which it inherit, shall dissolve And, like this insubstantial pageant faded, Leave not a rack behind.”

The record shows that the intellectual myopia associated with (a) is not terminal; it is a different matter with the hubris which once made Stephen Hawking proclaim that the object of contemporary physical science was to make Man “master of the universe”.

Gunnar

Report this post to a moderator | IP: Logged

Registered: Dec 2003
Posts: 175

Gunnar,

I enjoyed your post, thanks!

Report this post to a moderator | IP: Logged

Registered: Oct 2003
Posts: 157

Originally posted by MikeHelland
Gunnar,

I enjoyed your post, thanks!

__________________
Tony Smith, Melbourne, Australia
Independent researcher
TransForum developer

Report this post to a moderator | IP: Logged

Registered: Not Yet
Posts: N/A

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” - Einstein

Gunnar, doesn't this depend upon how one 'defines' the ideas of "mathematics" and of "reality"? No, I am not trying to waste your time with the President Bill Clinton evasive trick "That depnds on what your definition of "is" is." :-) Actually, here are two examples of what I mean:

1) What is the most fundamental or basic mathematical structure that can still yield the wide diversity of mathematics?

Some answers that are currently being suggested are the theories of named sets (aka fundamental triads), or n-categories, or simple primitives (ala Wolfram), and perhaps some others that I am not aware of. It would take some time to see how these various ideas are related and if there are any non-trivial discrepancies.

2) Even without any reference to math, "reality" can be uncertain enough that it may have hidden certainty or order, e.g. consider hypothesis A:

A: The vast preponderance of biological evolution has been due to the combination of random mutations and natural selection.

Then would it be that if to the extent that synchronicity, simultaneity and/or parallelism have occured or appear to have been required in the history of evolution then hypothesis A is more and more difficult to accept?

Also, if we put our human math in base 2 notation then it might be decipherable and meaningful to some kind of ET intelligence even though the ETs are not "divine".

“…And, like the baseless fabric of this vision, The cloud-capp’d towers, the gorgeous palaces, The solemn temples, the great globe itself, Yea, all which it inherit, shall dissolve And, like this insubstantial pageant faded, Leave not a rack behind.”

So is your philosophical conclusion that since everything in the universe seems to decay, die and go extinct that the only "meaningful" choice is to try to enjoy the ride while we still can?

The ole Bard himself wanted me to remind you that there is more to Heaven and Earth than dreampt of in your philosophy :-)

Report this post to a moderator | IP: Logged

Registered: Oct 2003
Posts: 69

Charlie:

Let me address your key points in reverse order.

1. "So is your philosophical conclusion that since everything in the universe seems to decay, die and go extinct that the only "meaningful" choice is to try to enjoy the ride while we still can?"

No!

As I understand it, Shakespeare's point is one with that of George Berkeley a hundred years later, namely, that our "common sense" concept of "reality" is that of Plato's cave-dwellers.

In turn, that is an epistemological point which Samuel Johnson sought to "refute" by kicking a stone to establish the evident "reality" of its existence.

And, speaking of the Bard, in Act I, Sc. v he lets Prince Hamlet reflect on the boundary between the stone-kicking state of Denmark and the New World that is the Prospero-Berkeley platonic view of "reality" as follows:

Remember thee! Ay, thou poor ghost, while memory holds a seat In this distracted globe. Remember thee! Yea, from the table of my memory I'll wipe away all trivial fond records, All saws of books, all forms, all pressures past, That youth and observation copied there; And thy commandment all alone shall live Within the book and volume of my brain, Unmix'd with baser matter....

So does the Prince of Denmark mark the passage of his ghostly stone-kicking self across the intellectual boundary which separates Plato's Cave from Miranda's "Brave New World" (Act V, Sc. i of 'The Tempest').

"Brave", because it takes guts to let go of youthful illusions - "New", because its very existence is not dreamt of in our stone-kicking philosophies!

Hence Prospero's wry response: "'Tis new to thee."

2. Re. Einstein's statement, “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

You ask:

Gunnar, doesn't this depend upon how one 'defines' the ideas of "mathematics" and of "reality"?

Yes!

I addressed related issues in my earlier posting on "Einstein's Unfinished Revolution", two sections of which are reposted below - insofar as the cause of epistemological clarity in physical science is concerned, I submit that the appropriate definition is reflected in Hermann Weyl's concept of "realistic mathematics".

Extract begins.

MIND-SPACE AS THEORY FRAME

The General Theory of Relativity represents “the natural simplicity of things” by a set of “concepts and fundamental principles” whose internal relations specified in logico-mathematical form give LOGICAL UNITY to the theory in any observer’s Mind-Space. This construction is IMPLICIT in Einstein’s comments in a London Times article in 1919: “The chief attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up; to modify it without destroying the whole structure seems to be impossible.” (‘What Is the Theory of Relativity?’, reprinted in ‘Ideas and Opinions’, p. 227)

As far as I know, however, Einstein never arrived at an EXPLICIT conceptualization of the subject matter along the above lines.

Yet, the fact that the problem of the now “worried him seriously” late in life AND that he readily conceded that the axiomatic premises of the General Theory of Relativity might not be tenable (see my post ‘Einstein’s “Scientific Testament”’) indicates very strongly, to the point of near-certainty, that Einstein’s thinking was moving towards explicit embrace of the concept of ‘Mind-Space as Theory Frame’ as defined above.

While the concept has been part of my intellectual ‘tool kit’ for years, the following statement thereof by Ludwig von Mises impresses me as exceptionally lucid:

“Logic and mathematics deal with an ideal system of thought. The relations and implications of their system are coexistent and interdependent. We may say as well that they are synchronous or that they are out of time. A perfect mind could grasp them all in one thought. Man's inability to accomplish this makes thinking itself an action, proceeding step by step from the less satisfactory state of insufficient cognition to the more satisfactory state of better insight. But the temporal order in which knowledge is acquired must not be confused with the logical simultaneity of all parts of an aprioristic deductive system. Within such a system the notions of anteriority and consequence are metaphorical only. They do not refer to the system, but to our action in grasping it. The system itself implies neither the category of time nor that of causality. There is functional correspondence between elements, but there is neither cause nor effect.” (‘Human Action: A Treatise on Economics’, 1949, Part I, Ch. V, Section 1, The Foundation for Economics Education, 1998. My thanks to George Giles for posting extracts from von Mises’ statement to the NKS Forum.)

If Mind-Space is the appropriate “frame” for the General Theory of Relavitivity, then an imaginary EXTERNAL Spacetime Continuum is “an ill-chosen frame” within which to address the theory’s meaning. Indeed, the conventional construction of the field equations of general relativity – “Spacetime geometry tells matter how to move; matter tells spacetime geometry how to curve.” – is at once incoherent and eloquent testament to “the metaphysical barbarism” of twentieth-century theoretical physics.

Therein lies the crux of the matter insofar as “the problem of the now” is concerned – as “free inventions of the human intellect”, which aid in our mental construction of a representation of “events” in the “realm of science,” neither “time” nor “space” are attributes of that “permanent possibility of perception” – that NOW or PERMANENCE – which is the Cosmos “just outside the realm of science” itself.

“REALISTIC MATHEMATICS”

In turn, this conclusion implies that “the realm of science”, while co-extensive with the domain of what Hermann Weyl termed “realistic mathematics”, is not “the one REAL world” as he supposed. “It is impossible to discuss realism in logic without drawing in the empirical sciences,” Weyl suggested. “… A truly realistic mathematics should be conceived, in line with physics, as a branch of theoretical construction of the one real world and should adopt the same sober and cautious attitude towards hypothetic extensions of its foundation as is exhibited by physics.” (‘Philosophy of Mathematics and Natural Science’, 1949, Appendix A, “Structure of Mathematics”, p. 235)

The identification of the domain of “realistic mathematics” with “the realm of science” lays bare the root cause (superior and, hence, infuriating intuition and intellectual integrity) of Einstein’s painful isolation within the physics community of which Max Born wrote as follows: “He has seen more clearly than anyone before him the statistical background of the laws of physics, and he was a pioneer in the struggle for conquering the wilderness of quantum phenomena. Yet later, when out of his own work a synthesis of statistical and quantum principles emerged which seemed to be acceptable to almost all physicists, he kept himself aloof and sceptical. Many of us regard this as a tragedy – for him, as he gropes his way in loneliness, and for us who miss our leader and standard-bearer. I shall not try to suggest a resolution of this discord,” Born continued. “We have to accept the fact that even in physics fundamental convictions are prior to reasoning, as in all other human activities.” (‘Einstein’s Statistical Theories’, in ‘Albert Einstein, Philosopher-Scientist’, p. 163)

That is, “Einstein is completely cuckoo,” as J. Robert Oppenheimer put it in 1935.

The record indicates that Einstein’s early command of the epistemological aspects of science did not match his intuitive grasp of the essence of “realistic mathematics” as reflected in the following two statements made in 1918 and 1933, respectively: (1) “The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction.”; and (2) “I am convinced that we can discover by means of purely mathematical constructions the concepts and laws connecting them with each other, which furnish the key to the understanding of physical phenomena.” (‘Ideas and Opinions’, p. 221 and p. 267)

The first statement defines the task of theoretical physicists in “the realm of science” (mis-labeled ‘Cosmos’) and the second expresses the intuitive conviction of scientists of first rank from Kepler, Galileo, and Newton to Planck and Einstein that, as Newton observed with respect to Newton’s Rule, “we are not to recede from the analogy of Nature, which is wont to be simple, and always consonant to itself.”

In the context, Newton’s “Nature” is synonymous with Einstein’s “realm of science” alias the “empirical contents” of Wittgenstein’s “World” introduced at the outset of his ‘Tractatus Logico-Philosophicus’ as follows: 1. The world is all that is the case. 1.1 The world is the totality of facts, not of things. 1.11 The world is determined by the facts, and by their being all the facts. 1.12 For the totality of facts determines what is the case, and also whatever is not the case. 1.13 The facts in logical space are the world. 1.14 The world divides into facts.

In other words, the World denotes “our experiences” transformed by Intuition into “concepts and fundamental principles” and “[brought] into a logical system” in Mind-Space by Reason.

With respect to the World so defined, Wittgenstein’s following statements hold true: 3. A logical picture of facts is a thought. 3.001 ‘A state of affairs is thinkable’; what this means is that we can picture it to ourselves. 3.01 The totality of true thoughts is a picture of the world. 3.02 A thought contains the possibility of the situation of which it is the thought. What is thinkable is possible too. 3.03 Thought can never be of anything illogical, since, if it were, we should have to think illogically. 3.031 It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not say what an ‘illogical’ world would look like. 3.032 It is as impossible to represent in language anything that ‘contradicts logic’ as it is in geometry to represent by its coordinates a figure that contradicts the laws of space, or to give the coordinates of a point that does not exist.

Here is my own, less formal, short-hand expression of the like view, born of research in theoretical physics and economics in the 1970s: Theory is an axiomatic structure of thought based on some given set of axioms which are consistent, coherent, and complete for the purpose at hand.

That is to say, “theory” is a UNITARY structure in Mind-Space such that “A perfect mind could grasp [it] all in ONE thought,” as noted by von Mises. Therein, I suggest, lies the mystery of INTUITION in the work of path-breaking scientists such as Kepler, Galileo, Newton, Planck, and Einstein. For, as Pascal remarked in mid-17th century: “The thing must be seen all at once, at a glance, and not as a result of progressive reasoning, at least up to a point.” (‘Pensées’, Penguin Books, 1975, p. 211)

Extract ends.

Gunnar

Report this post to a moderator | IP: Logged

Registered: Not Yet
Posts: N/A

Gunnar, there may be some truth to what you write but it is not so clear to me. At least one consequence of the ANKS book is that it has inspired me to ask questions for which I am not sure about the answer.

For example, should the theory of recursion be viewed as part of mathematical logic or as part of the theory of algorithms?

I don't even know what the formal difference is between the computational complexity of a universal Turing machine vs. a universal cellular automaton.

Report this post to a moderator | IP: Logged

Registered: Oct 2003
Posts: 69

Charlie,

Sorry for my belated response - I was on an overseas trip.

You write:

For example, should the theory of recursion be viewed as part of mathematical logic or as part of the theory of algorithms?

Comment:

I think of "mathematical logic" as that which gives coherence to some given set of axiomatic premises such as those of Euclidean Geometry - such coherence resides in the fact that, absent failure in deductive reasoning, we can always call to mind any and all aspects of what, for ease of reference, I call "the structure of thought" which is implied by any such set of axiomatic premises.

In turn, "recursion" or "algorithm" is the means whereby we call to mind any and all such aspects.

In this respect, both Blaise Pascal and Ludwig von Mises made the point that an omniscient mind would not operate by means of recursive steps - it would grasp all at once the logic of any given axiomatic structure of thought.

Gunnar

Report this post to a moderator | IP: Logged