Tuesday, May 20, 2008
John Horgan on "Can Chaoplexology Save Economics?"
Attending the conference I hosted at JMU over the weekend was the former Scientific American editor, John Horgan, who also wrote the bestselling _The End of Science_ a bit over a decade ago. Among the things he blasted in that book was what he called "chaoplexology," or what most of us would call complexity, including in economics, although more broadly. Anyway, I invited him to attend "Transdisciplinary Perspectives on Economic Complexity," and he did, providing a lively and interesting gadfly role. For those who are curious, he has reiterated his skepticism along with a lively report of the conference on his blog. He is currently a professor of scientific communication at the Stevens Institute of Technology.
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18 comments:
Actually in his book he calls it "chaoplexology," but in his posting on his blog he calls it "chaoplexity." Sorry about the goof.
Barkley
I found John Horgan's article to be quite confused. He begins by asking the question: " Can economics get a better grip on the world by cribbing ideas from catastrophe theory, chaos, complexity, physics, biology, other fields? "
And then he appears to answer his own question later in the piece: "economies are fantastically complicated " and " economies vary tremendously across space and time.."
Which lead a reader like me to conclude: Well, yeah. The understanding of a complex system will be enhanced by drawing upon other fields of knowledge.. like ergh.. the field of 'complexity'.
Then halfway through the article Mr Horgan says: "First, there is the stark historical fact that economics keeps lurching faddishly from one approach to another rather than converging on a single paradigm the way that more successful scientific fields such as nuclear physics or molecular biology do. . .
Perhaps John Horgan can explain why these fields are 'successful' and under what 'paradigm'?
R. Buckminster Fuller: "We are in an age that assumes the narrowing trends of specialisation to be logical, natural, and desirable. Consequently, society expects all earnestly responsible communication to be crisply brief. Advancing science has now discovered that all the known cases of biological extinction have been caused by overspecialisation, whose concentration of only selected genes sacrifices general adaptability. Thus the specialist's brief for pinpointing brevity is dubious. In the meantime, humanity has been deprived of comprehensive understanding. Specialisation has bred feelings of isolation, futility, and confusion in individuals. It has also resulted in the individual's leaving responsibility for thinking and social action to others. Specialisation breeds biases that ultimately aggregate as international and ideological discord, which, in turn, leads to war.."
Dont' worry, Barkley; your not alone.
"When amused, ['x'] did not
smile so much as grimace.…his already protuberant eyes bulged still farther from their sockets, and his lips peeled back to expose twin rows of brown, piglike teeth stained by countless cigarettes
and espressos (both of which he
consumed during our meeting). His
vocal cords, cured by decades of exposure to these toxins, yielded a voice as rich and resonant as a basso profundo’s and a deep, villainous snicker...
Guess who that is?
Brenda,
I tried to post a long list of Horgan's slams on folks that appeared in a book review I commissioned of his book, but somehow it did not get up here. Spent a good half hour on it.
Anyway, I do not know about the villanous snicker, but the protuberant eyes bulging from their sockets belonged to the famous chaotician, Mitchell Feigenbaum, who discovered the period-doubling transition to chaos.
I did not expect Horgan to post a blog, but given that he did, I am not surprised that he demonstrated what one reviewer called "a wicked eye for detail."
Barkley
Brenda,
John Horgan apparently tried to post a comment here in response to you without success. He has asked me to do so. Here are his remarks (and I have been having problems posting comments).
"Brenda you're right about the confusion in my post, which sort of conflates economics with complexity. But I think my message got across. You seem to question my remarks about the difference between economics on the one hand and physics and molecular biology on the other. Tell me; Has economics so far, or will it ever, produce something with the explanatory power of general relativity, quantum electrodynamics, or the DNA-based genetic code? YOu and I both know the answer to that question. Re my descriptions of scientists such as Feigenbaum and Barkley himself, they are not meant to be ad hominem attacks but merely descriptions, to give others a sense of what it's like to be in the presence of these brainiacs. You guys are not rational robots, your're human beings, often larger than life ones, and I like to remind my readers of that."
[John Horgan, transcribed by Barkley]
Another commentator on John Horgan's blog has replied to both me and Brenda, Andrei Kirilyuk, available at andrei.kirilyuk@gmail.com. The message is really too long to reproduce entirely, but he has extended remarks on John Horgan's blog on this matter.
To really shorten it, he has proposed a more general definition of complexity, which can be accessed at http://arxiv.org/find/quant-ph.gr-qc.physics/1/au:+Kirilyuk/0/1/0/all/0/1. He also describes qualitative results for his approach at http://hal.archives-ouvertes.fr/hal-00008993, along with comments he has made on John Horgan's blog. He is a physics professor in Kiev, Ukraine.
Barkley
Part One (of two)
I've spent some time today reading John Horgan's and Andrei Kiriyuk's responses today.
I have a number of observations.
- Both writers appear to assume that I have a more extensive knowledge of the state of complexity science than I actually possess.
- Mr Kiriyuk and Mr Horgan have expanded the topic of the debate beyond those small points that I have addressed. Really, my response to Mr Horgan's article was to pinpoint that 'confusion' in the way the subject of his writing was expressed. And to ask him to justify his judgement made that other 'sciences' were more 'successful' with some reasoning (and hopefully some real world examples).
Mr Horgan says: "Tell me; Has economics so far, or will it ever, produce something with the explanatory power of general relativity, quantum electrodynamics, or the DNA-based genetic code?
Aren't you quite deliberately choosing a handful of (unstated) questions in order to justify your assertion here?
And does one have to know what the question is in order to engage in a scientific study in the first instance?
Could you explain, Mr Horgan, why these particular 'sciences' have 'explanatory power' and give the reason you have explicitly chosen them to the exclusion of others such as, for example, 'ecology', 'astrology', 'immunology', 'toxicology', 'neurobiology', 'psychology', 'meteorology'?
You said, in your article, that the study of economics suffered from faddishness (moving from one approach to another), that it didn't converge on a single paradigm. You implied, in that same article, that other fields of scientific endeavour were more 'successful' because the objects being observed were more 'stable' and were not 'subject to influence' by the observer.
Just because the task of observation and study of particular phenomena is easier to perform does not necessarily imply its 'success'.
Because the process of breaking down an entity to something simpler, in order to make the phenomena under observation more predictable or stable, less liable to influence from the observer. Well it is conceivable that such a process can nullify the usefulness and even the validity of the study. Limit the understanding that comes from it.
Part Two
Andrei Kiriyuk says: "There are no results in chaoplexity after years of efforts, despite statements to the opposite..."
I really haven't been following the progession of the science of complexity and theories of chaos. But I have done some reading on both topics and found the books very helpful in assisting me to comprehend and explain (in particular ways) the behaviour of complex systems. Certain concepts presented appear to be helpful tools to describe a dynamic. For instance, 'phase transition', 'learning in noise', 'basins', 'attractors', 'autocatalytic set', 'cellular automata' etc.
What is the purpose of science, then; if not to explore different ways of comprehending and explaining elements of the world?
Andrei Kiriyuk says:"Complexity scientists should be guided by provably best results rather than by any ‘personal’, subjective preferences and interests."
What are 'provably best results'? Could you give some examples of where chaos and complexity theory specifically fall down here?
PS
I note that Andrei Kiriyuk has mentioned 'Hamiltonian systems' on Mr Horgans website and I can't comment on this debate because my knowledge of this science is insufficient.
(So, please disregard the final paragraph of the last posting.)
Hamiltonians are certain classes of differential equations that describe the dynamic patterns of certain kinds of systems. This is why Andrei's definition is not as general as he claims, and does not apply at all to most computational definitions of complexity.
Barkley
I must correct myself. I have in several places in print and in the blogosphere, including here, labeled the term that John Horgan coined as "chaoplexology." It is not. This is apparently my own accidental neologism. John Horgan's own term was and is "chaoplexity." I admit and recognize my error and stand corrected.
Barkley
as for horgan, i personally don't buy the idea that economics has any worse record than genetics, or even maybe QED. genetics is good at predicting things like hardy weinberg equilibrium; get beyond 2 alleles, and in many ways you are as lost as physics. economics i think equally is fairly reeasonable at prediciting some microeconomic behavior (e.g. Bushonomics and its critics, of whether a pentagon toilet seat plus pen is worth $100 or $100,000).
QED applies to what are in many ways 'noncomplex' systems (electrons and photons) but, like computer aLGORITHMS, in large numbers, so then you have to use old calculus to get approximations which are quite complex. They can't really derive 'molecular structure' (eg DNA from first principles, but alot of
'quantum chemnists' have tried---'hartree-fock'. I'm not even sure there is a rigorous derivation of H^2 or helium, or try H20.). Economics may be as good as cosmology, in other areas, or turbulence.
Regarding Kriyluk, he has quite a web presence, but seems to be cited only by 'peers', being himself (similar to my own Oeuvre, except i don't even permit myself to cite or critique my own works, because of lack of qualifications---i'm without peer, due to paranoia about the 'schrodinger cat' problem).
K (is that a german named franz?) seems to a)make some pretty big claims about say
QED->civilization's eigenvalues
which surpass even what say 'R. Thom' or Prigiogine might have argued, not to mention the apparent resolution of 'quantum mysteries' which even Einstein found worrisome.
K's resolutions, as well as the rest of his theory, looks apparently at least 50% generic (in the sense the entire formalism is fairly well known though written in a semi-private appearing 'obfuscationism' language suited for specialized journals; dress for sucess and getting through peer review.).
(I am unsure about what the 'dynamic multivalued' part means, and am very skeptical it means anything other than what you would expect and hence is not new; maybe one day i'll look more closely. (I find the papers fairly unreadable. I do like the 'hamiltonian' parts though. Now, thats ebonics.)
When he references others beyond himself, the references while relatively few and more obscure seem also basically 'standard english' (or science).
(It is probably unlikely this formalsim is taught in economics, thogh I have seen several econophysics papers which appear to use it; hence to try to compare results for 'complexity' would be like speaking russian for me. Its wack. The only known complexity measure is based on standardidzed (metric system) angel and pinhead units: h=c=/=c=/=h, 0=1.)
(The fact K appears to have 1 publication in a fairly well knwon peer reviewed journal I don't think means much; alot gets through the border. His others are more obscure to me.)
On his basic points (apart from claims to having anything new or unique) i would tend to agree. There may be an issue of whether he really has a 'Hamiltonian', but I think like 'American citizen' (propertied white male) over time this term has a changing definition. In my book, you can have a hamiltonian for anything, and you can define a copmplexity measure for it (probably several different kinds---whether there is one particular one from which the others can be derived is a question left altruistically as an excercize for the reader. Damn!!! a confeernce!!!)
Fo rexample, if I recall, a well known paper by Feynman from 1984 in J. Stat Phys (on quantum computing if i recall) defined a hamiltonian for a turing machine, and actually a quantum hamiltonian (since that is more realistic in terms of physics).
(My own work deals with second quantized hamiltonians for bimetric relational octonionic superturing machines for Cocktrell communist tenured professor societies, since these are more hip).
With the hamiltonian, all you have to do is find the eigenvalues.
H?=E?.
Fortunately these are being found by Rubin, at Brookings, via the Hamiltonan project, which is recap Turing the hamiltonian values.
It can be mentioned that my 'reeview' of K's ideas are similar to my view of people like Vellupai (sic); at a glance I could not really see anything particular new there, which was not already at least implicit in Albin's barriers and bounds. (The only difference i could see is use of 'computational" rather than linguistic kinds of classifications, but these are equivalent.)
media,
Welcome back, long time no read.
Regarding Hamiltonians, their use is quite precise, but that precision applies to lots of things and areas. So, that Feynman used it as you note is not a big deal.
Cockshott and Cottrill have a book forthcoming somewhere or other that pushes a lot of these quite far entitled, _Classical Econophysics_.
Regarding Velupillai and Albin, I would say that while Albin was the first in economics to deal with the questions arising from Godel and deep uncomputability, Velupillai has gone quite a bit further in his more recent papers and books, really pushing the subject quite far, along with such coworkers as Stefano Zambelli, Kislaya Prasad, and Francisco Doria.
BTW, it was this last individual, a Brazilian mathematician, who was quoted by Horgan in his original Sci Am article of 1995 as being the originator of that great wisecrack about "complexity leading to perplexity."
Barkley
regarding hamiltonians, then what do you think of K's claims regarding his? (that is rhetorical, but at a glance at least half of what he has written appears fairly standard in physics). My view is these are 'physicist's hamiltonians' so they get you what you want (euler-lagrange equations) but if you ask a mathematician they will say show me the money (find the symplectic structure). Also, people like McCauley (and Mirowski) would hate them because the hamiltonian (energy) is not standard or intuitive (something you can sell on wall street as an objective function) nor are the e-l equations. Ok, its not E, but GDP or oil. (This also reminds me of McCauley's claim that there is no such thing as a 'nonlinear fokker-planck equation'----presumably all those published papers about them are actually ghosts. or aliens? people who read or write them get sent to siberia for treatment.) but in 1900 they might have said a fractal is useless too (or roundoff error or meaningless).
(i did see an old (50's) economics paper which simulated and graphed something and threw out the 'erratic' solutions as unphysical. 'oh no, dawg'.)
i do like that vellupai discusses Post in a recent paper, since thaT paper (and the other one in that classic collectiion by Turing on 'oracles', seemingly popular recently) i do think set the stage for some open problems. I don't think or can't tell if these are really much further along ('priority methods' or O(n**3)), and also that simply introducing these problems to economics is a major advance (and i do think Albin's work on chomsky grammar classification of economies is isomorphic----but i'd have to compare closely recursion theory and the classification of grammars, which i don't plan to do any time soon----personally I stopped reading about 'grammars' (and albin) once i found out they were turing equivalent. I got the point. No hablar chomsky).
this 'computational' economics is looking like more and more like postmodern general equilibrium theory (so its funny that some in the 'post autistic' movement see it as a cure for the irrelevant mathematicization of Arrow and Hahn. Godel slays the fixed point; transfinite ordinals will cure poverty and the environment.)
I thought it funny that Cotrell (sic) apparently is now fighting the Hayek-Lerner battle over planned economies, by disputing the idea that Godel
proves lerner/Marx wrong. The battle has moved to the transfinite. I see this as an empirical problem; a consumer survey would first determine whether there are in fact an infinite number of goods, and then make sure the rational representative CIA (consumer intertemporal allocation) agent in fact computes the utility of all 2**infinity bundles of goods, and makes a rational choice. If there are an infinity then Cockshott loses, and Hayek is right (I personally think Hayek's 'evolutionary' insights are way overrated, though possibly he arrived at them independently) unless humans are superturing capable. (Ask R penrose).
Does Obama have a position on whether humans are (christian) turing machines? If so, can they prove everything turing machines can, such as containing unprovavable statements? (Following emile 'borel' (of cosmology) post-durkheim (a power couple), the newest approaches to complexity classifications of algorithms is by religion. There is the fastest (or best) religion, etc. With an oracle one can always decide what religion a Turing machine is by choosing the correct input, assuming not not = is (if/f not is not). )
its weird kirman is anti-GET. i saw him as exemplar. i agree with s bowles and gintis. everything is GET (though you may need to add a few interaCTIOn terms, assuming the external universe exists, a la shrodinger's cat) . its like saying prigogine is 'nonBoltzmannian'.
media,
Hmmm, stirring deep waters again, I see, :-).
Hamiltonians in physics imply certain conditions, which is one of the reasons I find K's claims of universality for his definition so odd. There are plenty of systems even in physics for which they are not appropriate. Otherwise, well heck, equations are equations and can be used for whatever as long as the conditions are right. Again, however, there are plenty of areas or processes or phenomena where people use the term "complex" for which Hamiltonians just are not the best or most appropriate tool.
McCauley is very strict on what should be used where and when. He is also the one who says that we should no longer teach principles of economics, replacing it with physics and statistics. He is a hardliner on the idea that science is only about invariance laws.
Mirowski was at the conference and was pushing his markomata view of evolving algorithmic market systems. His markomata paper was published in JEBO in June, 2007, with special comments. He uses the Chomsky grammar, and there was a fuss about this from some of Velupillai's allies, notably Stefano Zambelli. The equation between Turing machines and Chomsky grammars only holds at the highest level. The real problem here is the huge gap between the lower levels of the Chomsky grammar.
Regarding Kirman, he has evolved, as has Duncan Foley. Both were big general equilibrium theorists, although more have forgotten about Foley's position. Both have bought into heteregeneous agents and various forms of complexity. They have moved on, and both were at the conference. Interestingly, Foley's presentation put his current entropic approach to equilibrium into an Edgeworth box, which was heuristically neat, a return to his old GET identity, although with a completely different approach. In this statistical physics approach, equilibrium is a distribution of prices for each good, not a single price for each good.
Barkley
we probably will have to disagree on hamiltonians. as you note, in general it is 'innapropriate' to use a hamiltonian formalism---why bother? however, as a curiosity or from a maTH viewpoint, sometimes converting it into a hamiltonian form may be useful.
i am kind of 'strict' on this, like McCauley. to me there ARE conservation laws and symmetries; whether they have any relevance outside math is an open question. (most systems have not been analyzed this way). (McCauley's writings on the history and limitations of conservation laws in econ, etc. actually I find pretty good, if you forget his definitions of things like a 'nonlinear foker-planck equation' and his use of very restrictive old fashioned ideas about what a hamiltonian is (energy=T+V). Like mirowski, he is good at shwoing what has been wrong, up to a point. But his solutions are lacking (as you have discussed).
i do recall chomsky has basically 4 grammars, where 'theory of algorithms' has many complexity classes, which i barely understand (the 'priority methods' used to follow up on Post's ideas via Kleene's program are one example, and i have no undersrtanding of what if any use these are in real problems; they look like transfinite numbers). so mirowski is narrow here.
but again, one has the fundamental issue---markomata are supposed to be algorithmic alternatives to dynamical systems using differential equations (i.e.
hamiltonians, to me). Whereas I, like others, see algorithms as essentially (discrete approximations of )solutions of differential equations. (This reminds me of discussions comparing the logistic equation with its discrete form---be careful of what approximation you use. ) The distinction is overblown, unless one takes a strict view (maybe like Nelson) that there are only integers, and real numbers are a fiction.
As an alternative to Mirowski, have you seen the PhD thesis on the web called 'quantum feminism'? Perhaps quantized feminist markomata.
Also, while i've never read Follmer's early paper, in retrospect I find at hard to believe that Foley's 1994 paper really contains any more than that. Also, it sounds like Foley's current view maybe is the one i hold---its a variant of GET (albeit without uniqueness or stability). the 94 paper was thought provoking.
of course the 'entropy' approach is as messy as GET when you get past say 2 goods so its hard to know what use it is.
i don't see the 'computational' stuff as 'heterodox', or antiGET, any more than the ising model is heterodox because its not an ideal gas.
Anyone who wishes to denouce the "scientificness" of economics for its lack of invariance laws, be my guest. I just remind that lots of physical/natural sciences also lack such laws, except maybe at very high levels, think ecology and climatology.
Markomata are ultimately markets themselves manifesting themselves as evolving algorithms. Where that leads to, whether analyzed by Chomsky grammars, Turing machines, or whatever, is very much open for debate and discussion.
I don't know about Nelson, but the real hardliner on numbers was Kronecker, who I believe was the one who declared that "God made the natural numbers [the postive integers], and Man made all the rest." Certainly there was resistance by the Church in the late Middle Ages to the introduction of the Indo-Arabic numerals with their zero, fractions, and negative numbers (although the Pythagoreans had allowed for positive rational numbers, easily derivable from the God-created natural numbers). It was their greater usability for computing and accounting in the emerging financial industry of northern Italy that finally allowed Fibonacci and others to push through their formal acceptance over the clunky Roman numerals.
Follmer's paper is much narrower than Foley's, but contains the basic idea. Brock and Blume and others were working on similar ideas in the early 90s as well, an idea burbling around at the Santa Fe Institute.
What is "heterodox" is another matter up for debate.
Barkley
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