PKT message, On Wolfram's 'New Kind of Science'

My following message of today's date to a fellow-Gang8 member may be of interest to PKT.

Gunnar

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Thanks for posting [Stephen] Wolfram's interesting comments [in A New Kind Of Science] - let me make a few brief comments.

1. I strongly agree that:

"If theoretical science is to be possible at all, then at some level the systems it studies must follow definite rules."

This is how Albert Einstein put the like point in 1949:

"Science without epistemology is - insofar as it is thinkable at all - primitive and muddled."

2. I also agree that:

"(Some) systems are computationally irreducible - so that in effect the only way to find their behaviour is to trace each of their steps, spending about as much computational effort as the systems themselves."..."So this implies that there is in a sense a fundamental limitation to theoretical science." (p.6)

As I see it, the "fundamental limitation to theoretical science" is manifested across the board in modern physical science, whose leading practitioners have put aside as irrelevant all epistemological considerations which may imply that modern "theoretical science" is "primitive and muddled" - science which permits us to do engineering feats of astonishing precision not because their epistemological foundations are sound, but because Nature's Laws are invariant with respect to time and space.

For some reason - Pride? - most modern scientists abhor the Socratic view that all we can ever know is that we know nothing - that, as David Hume wrote with respect to Newton, "while [he] seemed to draw off the veil from some of the mysteries of nature, he shewed at the same time the imperfections of the mechanical philosophy; and thereby restored her ultimate secrets to that obscurity in which they ever did and ever will remain."

In this respect, my own research in theoretical physics has persuaded me that Einstein was spot on with his final words on related issues written to a friend a few months before his death:

"I concede that it is quite possible that physics cannot be founded on the concept of field - that is to say, on continuous elements. But then, out of my whole castle in the air - including the theory of gravitation, but also most of current physics - there would remain almost nothing." (Italics in original.)

3. The fact that the marvels of modern physical science are rooted in the invariance of Nature's Laws and not on their epistemological coherence has long been lost on physics-envying economists and psychologists, as indicated by Wolfram's comments:

"From Economics and psychology there has been a widespread if controversial assumption - no doubt from the success of the physical sciences - that solid theory must always be formulated in terms of numbers, equations and traditional mathematics...."

4. In this respect, I would go a step further than Wolfram does in the following insofar as the 'possibility' of "general theories" is concerned:

"....But it will take time before it becomes clear when general theories are possible and when one must instead inevitably rely on the detail of judgement for specific case." (p.9)

Insofar as "general theories" are "possible", they must reflect invariance of Nature's Laws as follows: Given A, B, and C, doing such and such will yield X, Y, and Z.

It strikes me as self-evident that, insofar as Economics concerns Man-made "systems", it is folly of the highest degree to apply to one's study thereof a modus operandi predicated on the invariance of Nature's Laws.

5. Finally, re. your comments:

"A possible application of this theme to "Creditary Economics" would be the importance of making particular observations of results of different money systems, rather than just trying to draw logical conclusions from theoretical considerations based on questionable or certainly questioned definitions."

As indicated on earlier exchanges on Gang8, I am persuaded that "logic" has its place in our analysis of the Man-made "system" with which Economics is concerned - a place occupied by mathematical logic since the advent of neo-classical economics (see "folly in the highest degree" in 4. above) in the last third of the nineteenth century.

The "place" is Money and the "logic" of Monetary Relations is the foundation of Creditary Economics - a conclusion arrived at independently in the 1980s by Geoffrey, Chris, and myself along three wholly different paths of analysis.

I discern the same concern with the "logic" of Monetary Relations in the work of Dieter Braun and Wes Burt - and, when all is said and done, I would not be surprised to find that five wholly different paths of analysis have led to conclusions with respect to the "logic" of Monetary Relations which are substantively identical.

For such "logic" is akin to the invariant Laws of Nature and Man-made Engineering Systems.

Gunnar