[NKS, Science, and Economics] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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NKS, Science, and Economics
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Posted by: Gunnar Tomasson
My following message addressed to a fellow-Gang8 member (see www.creditary-economics.org) on issues relating to Stephen Wolfram's A New Kind Of Science was re-posted to the University of Colorado's PKT (Post Keynesian Thought) list of economists around the world today.
FYI.
Thanks for posting Wolfram's interesting comments - 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."
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 [two other researchers] - 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.
Posted by: Jason Cawley
It seems to me there are a couple of issues here, that we would do well to separate. I don’t think Humean skepticism is critical to the subject matter, but its introduction can confuse that subject matter. To clear it out of the way, I will explain the reasons I am not a Humean skeptic. This is tangential to NKS, which is quite open to those of that persuasion and those not of that persuasion.
The main issue arises after that. It concerns method and social science, whether method can be imported from beyond the social sciences and if so what method, whether similar issues arise even within the hard sciences, and a related bundle of questions. This issue is about a distinction, where the proper place is to make that distinction, what it really consists in. And here NKS has something to say, which I think is essentially new. Though bits of it could be seen earlier.
Very briefly, so you can see where I am headed, previous distinctions between “nature” and “history” or between theoretical and practical knowledge are (in a definite context or problem, only) replaced by a distinction between computationally reducible and computationally irreducible systems. Which can and almost certainly do arise on either side of those previous distinctions. Popper spoke about this as the problem of “clocks and clouds”.
First to clear the ground of method problems related to Hume and skepticism. To me it adds little to put an extra pair of doubt brackets around all my thoughts. If anything met some standard of certainty it might be important that other things don’t. But when one tells me there is a standard of certainty, A, such that nothing satisfies it, I conclude that A isn’t a useful standard, not that nothing is known. Reason begins when we make a distinction. Distinctions one side of which are empty aren’t very informative; as distinctions they leave something to be desired.
It seems to me the extra set of doubt brackets are something of a survival from dogmatic days and the search for infallibility. I know a speaker’s statements are fallible because his lips are moving. Not having met any infallible gods, the notion that fallible mortals do not possess the certainty of infallible gods does not rivet my attention.
Someone can prepare himself for all his substantive comments eventually being proved incorrect by conceding beforehand that after all, they aren’t certain. This does not however redound to his intelligence, because try as he might he can’t arrange to be wrong about the matter. Nor does his love of his extra notational brackets imply any greater courage to admit his substantive mistakes once those are established and shown to him. He concretely admits he was wrong when his concrete errors are shown, or he does not.
All the interesting stuff happens inside the brackets. If things moved outside or inside of them, they’d be substantive. But since the area outside Humean skepticism is claimed to be empty, they are a notational extra. I can understand every substantive claim a Humean skeptic makes without them, and he can understand every substantive claim I make by adding them mentally himself, without his insisting I do so, or my insisting he does not. He lives in a world of doubt, I live in a world of provisional conviction. But the worlds are in their internal structure quite precisely the same. Those with the extra pair of brackets can go around congratulating each other on their humility if they like, and look down their noses at unsophisticated provisional conviction people without them. But it is not on the surface a particularly humble thing to do, and it certainly does nothing to establish actual error in any of the particular, substantive claims advanced by said provisional conviction people.
The method question is something else. It has to do with actual distinctions, with claims not that “all is x”, but that some things are x and others are y. In one classic formulation, that the methods appropriate to the “realm of nature” are not those appropriate to the “realm of history”, because there is an essential difference in their subject matter, what can be known about it, and how. Von Mises made this case, for example. Or one can speak of what is known theoretically, perhaps in accord with some postulated formal structure, as distinguished from what is known practically, perhaps only by experience. Perhaps calling one a science and the other an art. (There might be a scientific law of supply and demand, but only an art of central banking, for example). A third formulation of the issue, due to Popper, is to speak of clocks and clouds. Meaning in both cases physical systems, but one appearing to common sense as regular and predictable, and the other appearing as complicated and unpredictable.
Before getting to all of these and the new version of them I see coming from NKS, it may be worth pausing briefly to notice that this question really is distinct from the previous Humean skepticism discussion. A skeptic may notice that it is difficult to apply an inductive scheme to clouds and figure out from it what they will look like. But he also claims it is unjustified to apply that inductive scheme to clocks. Nothing he has told us illuminates the specific difference between them. If you like, he is unsurprised by a failure of induction in clouds. He is, if not surprised, made to spin a bit sophistically at its seeming non-failure with clocks. But he is not the one who makes much of the distinction between them. He has only put both alike in the same “uncertainty” brackets.
Back to the actual distinctions. They are all trying to capture the same phenomenon - an inability to predict some systems, as we are in fact able to predict some others. Some trace the problem to human valuations or psychology, or to a posited human freedom. Others to an inability to know initial conditions perfectly, combined with the presence of what amounts to amplifiers in some systems. Others might think the problem stems from some epistemological gap between our formal theories and the empirical realities they are trying to describe.
Those all amount to different theories about why the problem arises, but it is the same problem. And the first thing to notice is that it can arise even in purely formal systems. Even from simple initial conditions, exactly known because exactly specified. Even with laws that aren't provisional guesses about a natural system, but are fully known rules we've laid down ourselves.
All of the alleged cut points of these rival theories can be missed, and the phenomena still crops up. You can't tell me the million and tenth center cell of rule 30 for 1 black cell without just running it for a million and ten steps. You certainly can tell me the million and tenth center cell of rule 250 - since a million and ten is even, it is white. One of these things is not like the other.
Can the other explanations sometimes give rise to other forms of unpredictability? No doubt, under the right conditions for each of them. But the crux of the problem is simply that some systems are irreducibly complex, while others just aren't. This difference can arise in any area, in any field. And it means that the world just is not exhaustively predictable. Though it can be extensively modeled. You can get one without the other, as soon as models become as hard to predict as many systems. Indeed, an accurate model of an irreducibly complex system will itself show complexity.
When Wolfram writes on page 9 about NKS in the social sciences, that it will take time before it becomes clear -
when general theories are possible, and when one must instead inevitably rely on the details of judgment for specific cases.
He means some aspects of social systems must be expected to prove irreducible, while others may be tractable with NKS methods. It is possible the traditional mathematical formalisms tried in past social science theory building are unsuited to many of the phenomena they deal with. It is possible the simple programs idea may succeed in areas where those formalisms have not. But one should not expect NKS methods to create predictive models of all social science systems.
NKS tells us that there are many systems that simply aren't predictable beforehand by quick, shorthand methods. It is quite likely the reason the social sciences have resisted predictive formalization in the past is simply because such behaviors are common in their areas. When prediction fails, we still have much to learn from models. A model of the economy may not tell us where it will be in ten years, but might well tell us why answering that question is hard.
In the area of practice, however, when predictive science fails we must carry on. We fall back on an experimentalist's toolkit, and on pragmatism. We want as much familiarity with the systems we are dealing with as possible, from models and from practical responsibility. That is what Wolfram was talking about when he spoke of details of judgment for specific cases. It is part of living with the reality of irreducibility.
I hope this is interesting.
Posted by: Gunnar Tomasson
Re. the following:
All the interesting stuff happens inside the brackets. If things moved outside or inside of them, they’d be substantive. But since the area outside Humean skepticism is claimed to be empty, they are a notational extra. I can understand every substantive claim a Humean skeptic makes without them, and he can understand every substantive claim I make by adding them mentally himself, without his insisting I do so, or my insisting he does not. He lives in a world of doubt, I live in a world of provisional conviction. But the worlds are in their internal structure quite precisely the same. Those with the extra pair of brackets can go around congratulating each other on their humility if they like, and look down their noses at unsophisticated provisional conviction people without them. But it is not on the surface a particularly humble thing to do, and it certainly does nothing to establish actual error in any of the particular, substantive claims advanced by said provisional conviction people.
Comment:
At the present stage of the game, several important things need to be worked out with respect to NKS – not surprisingly, for as detailed in the Publisher’s Summary:
“Wolfram uses his approach to tackle a remarkable array of fundamental problems in science, from the origins of apparent randomness in physical systems, to the development of complexity in biology, the ultimate scope and limitations of mathematics, the possibility of a truly fundamental theory of physics, the interplay between free will and determinism, and the character of intelligence in the universe.”
Within this array of problems – unresolved issues - Humean skepticism is concerned with “the character of intelligence in the universe” as manifested at the level of Man and its implications for “the possibility of a truly fundamental theory of physics”.
In other words, Humean skepticism concerns the epistemological aspects of physical science of which Einstein wrote late in life, “Science without epistemology is – insofar as it is thinkable at all – primitive and muddled.”
And, as it happens, Einstein’s view is firmly rooted in historical fact.
For the non-Humean construction of Newtonian Mechanics advanced by the Marquis de Laplace and embraced by his nineteenth-century peers with conviction was shown by century’s end to have been built on the intellectual quick-sand of wishful thinking.
Moreover, it remained an unresolved issue for Einstein whether he had been on firm ground in writing of Newton’s “great and lucid ideas” that they “will retain their unique significance for all time as the foundation of our whole modern conceptual structure in the sphere of natural philosophy.” (‘What Is the Theory of Relativity’, London Times, November 28, 1919; reprinted in Ideas and Opinions, Dell Publishing Co., Laurel Paperback, 1976, p. 227)
For, as Einstein wrote in 1954, “I concede, however, 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.” (Letter dated August 10, 1954, in Einstein – A Centenary Volume, Harvard University Press, 1979, p. 269)
Again, as it happens, it is not only “quite possible” but certain that, contrary to the conviction/provisional conviction of theoretical physicists from Newton’s time to our own, the continuous-field hypothesis cannot be valid for the universe as a whole.
For the path of a photon of light – or fireball – propagating through the solar field which appears straight to observers located within the field will appear curved to outside observers with respect to which the solar field is in rotational motion.
This implies that the “great and lucid ideas” which Newton applied to the Earth-Moon System in Principia are local and not universal in reach – that “the foundation of our whole modern conceptual structure in the sphere of natural philosophy” is defective.
Gunnar
Posted by: Jason Cawley
If I break a lance or two against skepticism, bear with me. I do think there is more to what you are saying than to that position, and there is more that NKS has to say about epistemological questions. Frankly the skepticism discussion is about my own notions, not about NKS, which I will get to I promise. Please understand at the outset that I think epistemology useful. I just don't equate it with skepticism or Hume.
First a few mere sallies. Because Laplace had a theory and was wrong, and Einstein had a theory which may be doubted, any theory we have now is not knowledge but opinion. Is this an argument against heroic induction or an instance of it?
You suggest that we all ought to admit that the only thing we know is that we know nothing. It is a venerable saw. But I claim we know no such thing.
When one has shot a theory down on the substance, shown it is inadequate to the phenomena, then one may say that theory was opinion. One may out of humility choose not to advance any claim beyond opinion for any of one's own views. But claiming somebody else doesn't know something, when you haven't yet shot his theory down on the substance, is "just jawing". If you can show it, show it. If you can't, claiming you nevertheless know it can't possibly be simply true, is not humility but the opposite.
I claim to know that the center column of rule 250 from a single black cell at step n is given by n mod 2. On the basis of this rule, I claim to know that the million and tenth step's center cell is white. I've never done the experiment. I'll give you 100 to 1 odds. You won't take the bet.
If you like, you may place my belief in the matter in a set of doubt brackets, and say it is not knowledge. I won't quibble about words and will agree to call it kerfluffle, and will agree that kerfluffle is not Humean certitude. But you won't bet against my kerfluffle in the matter, whatever brackets you put it in. You therefore recognize something, whatever you choose to call it.
If we replace the rule in question with number 30, I claim no kerfluffle in the matter. On condition that the experiment has not yet been done by either party, I predict that neither will give even 10 to 1 odds to the other, in favor of any prediction that said cell is black rather than white.
No laws of nature have changed. No rules of logic have been suspended. No necessarily approximate theory of an empirical system is involved. There are no unknown continuous quantities. There is nothing stochastic in underlying mechanism in the evolution of the systems under review. The scheme is the same, and the logical cut points previous epistemologies have emphasized are all on one side. Hume would lump both together. So would plenty of other people. Nevertheless, with one there is kerfluffle and no one willing to bet against it, and with the other there is not.
One is reducible and the other is not. The difference is real. A theory of knowledge either can account for this difference or it cannot. If it cannot, then it is either wrong or simply unilluminating.
It is of course possible for failures of prediction to arise for other reasons. Other claims - those of Popper about unknowable initial conditions or paradoxes of self-prediction, or of Mises about unknowable human valuations - may apply in this or that other instance. But they are not a general cause of unpredictability. It can arise without the conditions they posit being met. Whatever they have managed to explain, it is not necessary to unpredictability arising in a system.
There is unpredictability within purely formal systems, above a certain complexity threshold. A theory of knowledge either deals with this or it does not. It is not dealing with it to lump rule 250 in with rule 30, and everything else. You cannot explain a phenomenon by abstracting from it.
I do not wish to saddle you with arguments that may be less useful than your own views. Humean skepticism is too powerful an argument - by aiming at too much, it misses too many critical distinctions, and so leaves them unilluminated. But some of your comments went beyond "all is x" and advanced substantive points about current theories.
If someone could make a theory of physics that involved no continuous quantities, and that featured an absolute notion of time, then the current understanding of relativity would presumably shift. Equivalence in various frames would have to arise as an emergent property, rather than being laid down beforehand. It might appear for many cases but not for all.
Laying down such principles beforehand let physicists look for natural laws in terms of the symmetries that must hold if the principle is strictly true. Everyone involved ought to be aware that this is a search for rules, and inside of an "if". No model has to keep this principle, a priori. Nothing is exempt from criticism and therefore possible revision - one does not need any commitment to skepticism to understand that principle.
A theory must be adequate to the phenomena, and must stick its neck out and say what it expects of them - what it needs internally in order to do so is its own affair, and in principle "free". In practice it is not at all easy to account for observed phenomena without something like this principle (invariance of laws), or some underlying formalism that gives rise to it, at least "usually". There is a sketch in the NKS book of some formal ideas that might allow relativity to arise as an emergent property of a causal network. See pages 516-524. It is too early to say where this may go.
The two issues should not, however, be confused. Inability to predict due to irreducibility can and does arise without any need to invoke hypothetical variation in natural laws in different frames of reference. It is not like the reason one can't predict rule 30 is the rule being used changes every 1000 steps. Even when it doesn't, the problem arises.
Applied to economics, there could be simple rules that generate various economic phenomena and are stable through time, without it implying that economies are predictable. For an economy to be predictable, more would be required. Its rules would have to be reducible, in addition, and there is no reason a priori to assume they must be. Economies might be modeled, successfully, even without reducibility. The models would just exhibit complexity, just as real economies appear to do.
I hope this is interesting.
Posted by: Gunnar Tomasson
Jason:
First a few mere sallies. Because Laplace had a theory and was wrong, and Einstein had a theory which may be doubted, any theory we have now is not knowledge but opinion. Is this an argument against heroic induction or an instance of it?
Comment:
Neither - the concept of “provisional conviction” has about it the oxymoronic flavor of “doubtful certainty” – to equate a “working hypothesis” with “conviction”, however qualified, conveys to me a wrong impression of the place of hypothesis in science.
Jason:
You suggest that we all ought to admit that the only thing we know is that we know nothing. It is a venerable saw. But I claim we know no such thing.
Comment:
I agree with Hume’s view on the limitations of modern physical science –
“While Newton 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.” –
and disagree with Hawking’s “provisional conviction” that the structure of physical reality and our minds are such that “a complete theory” may be within our reach –
“…if we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason – for then we would know the mind of God.” (‘A Brief History of Time’, final paragraph)
As for the structure of physical reality – that something “out there” which generates the impressions on our senses and technical instruments which are the raw data of physical science – the Humean No answer to the question whether we will ever know its “ultimate secrets”, I submit, reflects a view of Mind and its relation to Science which I summarized in a 1980s working paper on Economic Science as follows:
1. All knowledge is axiomatic.
2. Hence, knowledge relates to a state of mind.
3. A state of mind is either clear or confused, coherent or incoherent, logical or illogical.
4. A claim to knowledge is a claim to a clear, coherent, and logical state of mind.
5. Hence, a claim to knowledge is distinct from a claim to opinion, whose validity is beyond any conceivable refutation on grounds of clarity, coherence, and logic.
6. A claim to knowledge derives from the perception that one's mind is clear, coherent, and logical in holding such claim to be beyond dispute by any other mind equally clear, coherent, and logical.
7. Hence, a claim to knowledge can only be refuted by minds satisfying the requirements of clarity, coherence, and logic.
8. A claim to axiomatic knowledge is a claim to a state of mind marked by clarity, coherence, and logic in its grasp of propositions beyond relative time and space.
9. The art of economics addresses policy issues within relative time and space in light of the axiomatic propositions of economic science itself.
The above concept of knowledge accords perfectly with the definition offered
in 1922 by Keynes [my working paper continued]:
"The Theory of Economics does not furnish a body of settled conclusions immediately applicable to a policy. It is a method rather than a doctrine, an apparatus of the mind, a technique of thinking, which helps its possessor to draw correct conclusions." [Extract from working paper concluded.]
In 1949, Einstein penned a scathing ‘Reply to Criticisms’ on issues relating to Mind and that something “out there” in the field of Quantum Mechanics as follows:
“Roughly stated [my] conclusion is this: Within the framework of statistical quantum theory there is no such thing as a complete description of the individual system. More cautiously it might be put as follows: The attempts to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems. In that case the whole “egg-walking” performed in order to avoid the “physically real” becomes superfluous. There exists, howerver, a simple psychological reason for the fact that this most nearly obvious interpretation is being shunned. For if the statistical quantum theory does not pretend to describe the individual system (and its development in time) completely, it appears unavoidable to look elsewhere for a complete description of the individual system; in doing so it would be clear from the very beginning that the elements of such a description are not contained within the conceptual scheme of the statistical quantum theory. With this one would admit that, in principle, this scheme could not serve as the basis of theoretical physics.” (‘Albert Einstein, Philosopher-Scientist’, The Library of Living Philosophers, Cambridge University Press, Third Edition, 1988, pp. 671-672)
In an apparent response to the thrust of Einstein’s acerbic remarks, Hawking wrote in ‘A Brief History of Time’ on related issues as follows:
“In order to talk about the nature of the universe and to discuss questions such as whether it has a beginning or an end, you have to be clear about what a scientific theory is. I shall take the simple-minded [read: the Humean – insert] view that a theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make. It exists only in our minds and does not have any other reality (whatever that might mean).” (Bantam Books, 1988, p. 9)
In subscribing to the Humean concept of scientific theory as the product of interplay between (a) impressions on our senses and measuring instruments generated by a something “out there”; (b) our imaginative and intuitive faculties; and (c) our reasoning faculty, Hawking’s elliptical comments on “any other reality” in effect concede Hume’s point that:
“[Nature’s] ultimate secrets [were “restored” by Newton] to that obscurity in which they ever did and ever will remain.”
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