Comment of the week: Nulty on use and misuse of mathematics
Timothy Nulty posted this comment on Comment of the week: Radford on Lawson and Nuno
As a product of Cambridge, I find it not in the least surprising that Lawson is as well….he is a clear throwback to the “Old Cambridge” In the “old days” at Cambridge (I did my doctorate there between 1966 and ’72) exactly the kind of ontological rigor was not only emphasized but required by all who were members of what was (then if not any more) a genuine intellectual community in the Economics Dept. The kind of flaccid sloppiness that underpins so much of what appears rigourous in the “mainstream” of modern economics was simply not tolerated. An anecdote by way of example: Kenneth Arrow came for a period as a visiting scholar at one point during my time there. As was normal, he presented several papers that he was working on to the “community” for discussion and feedback. As was usual, all members of the “community” attended faithfully and seriously–from the most famous to the lowliest grad student. Arrow launched into his lecture on this occasion and, also as was usual, covered the blackboard with maths. Well into the performance one member of the “Old Cambridge” school interrupted and questioned a key point in his mathematical reasoning. There followed a short argument at the end of which Arrow agreed with the criticism and acknowledged that he was mistaken on that point–but that “the rest of the argument was correct”. To which the cantabridgean replied: “yes, but it isn’t interesting–because it no longer applies to much of anything in the real world”.
That, I submit, is a nutshell summary of the problem with most of mainstream economics. Its rigor is admirable. But, if one is rigorous about the assumptions, it only applies to a small set of problems. The rigour of its internal methods are not matched by the rigor applied to matching its assumptions with the situations to which it is routinely applied.
That said, I also strongly agree with the criticism of heterodoxy as being just as in-grown and given to talking only with one another! Tiresome in the extreme!!
Ref Math: Mathematics is simply a language. Different languages are better at conveying certain relationships and concepts than others. Anyone who has become fluent in non-indo European languages (as I have) will confirm the large differences in the efficiency, richness and precision between the capacity of different languages to convey different types of intellectual content. Math is one more language: with a vocabulary and grammar that is extremely well suited to expressing and analysing certain types of concepts and relationships–but very poor at expressing–or analysing–others. Ditto for many computer languages (which are generally–but not entirely-derivatives of the language of mathematics but frequently involve richer components geared to specific situations and problems).
As with all tools: it is simple, useful and wise to use those the fit the problem and not to pretend that you can use, for example, a screwdriver as a catalysy in a desired chemical reaction. It is equally foolish not to use a screwdriver on a screw because of ideological dislike for screwdrivers or because screwdrivers won’t solve all problems.
regards
Timothy Nulty
Jericho, Vermont
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Real-World Economics Review Blog 
There is a risk that when one is carrying a screwdriver, everything looks like a screw.
There is a risk also that when one only carries a screwdriver, one only knows how to screw.
Arrow may have had another encounter of this kind, when he was at a Conference of the Santa Fe Institute. The following is a quote from my book Economia http://betternature.wordpress.com/booksanddownloads/economia/ , quoting in turn from Mitchell Waldrop’s Complexity. The quote is from my Chapter 6, Is the Neoclassical Theory Scientific?, which I have posted at the above site (http://betternature.wordpress.com/booksanddownloads/economia/neoclassical-scientific/).
I think economists who aspire to do better can learn a lot from practising scientists.
(By the way, while I agree with Timothy Nulty’s sentiment about the misuse of mathematics, I don’t agree it is simply a language. It is a pre-worked logical structure and set of tools, very useful but not at all like a fluid, metaphorical language.)
The extract:
In 1987 a conference at the Santa Fe Institute brought together a select group of prominent physicists and economists to discuss the implications of new theories of complexity and to cross-fertilise their disciplines. The physicists were awe-struck by the economists’ mathematical prowess but startled by their lack of reference to the real world.
“They were almost too good,” says one young physicist, who remembers shaking his head in disbelief. “It seemed as though they were dazzling themselves with fancy mathematics, until they really couldn’t see the forest for the trees. So much time was being spent on trying to absorb the mathematics that I thought they often weren’t looking at what the models were for, and what they did, and whether the underlying assumptions were any good. In a lot of cases, what was required was just some common sense. Maybe if they all had lower IQs, they’d have been making some better models.”
The economists were startled in turn by the physicists’ casual attitude towards mathematics. If a rough back-of-the-envelope calculation would enable the physicists to compare their theory with observations, they might not worry about doing a fancier calculation. The goal in physics is not a theoretical structure that is as elaborate as possible, the goal is a theory that represents how the real world works to a useful level of approximation. Waldrop quotes the unconventional economist Brian Arthur
“They kept pushing us and pushing us,” says Arthur. “The physicists were shocked at the assumptions the economists were making – that the test was not a match against reality, but whether the assumptions were the common currency of the field. I can just see [Nobel physicist] Phil Anderson, laid back with a smile on his face, saying, ‘You guys really believe that?’”
Before the Copernican revolution the universe was reportedly believed to composed of spheres interacting in the most complex ways. The world was thought to be comprised of tiny triangles. Observation and calculations made these models irrelevant as new and better ones were formulated. This seems to work well in science.
Economics is a different kettle of fish. A new factor enters the equation: Vested interest. And vested interest groups ensure that economists that reinforce the status-quo with their theories are given all the accolades and have their ideas communicated to the broad mass of people. They are also placed in the top jobs that convey these ideas to the next generation of economists.
It is really no different from what happened in the Soviet Empire where everybody had to study their variant of Marxism. The same is going on in North Korea at this time.
In order to get around this problem, we should resurrect the term “Political Economy” and start afresh.
Breaking the neoclassical brainwashing monopoly and working on a science of economics are not mutually exclusive, they need to be pursued in parallel.
Good science knows its limits. There are many aspects of economies that wait to be understood better than they are now, if we broaden the scope of our enquiries by dumping the neoclassical straightjacket. At the same time, economic phenomena are part of society and influenced by politics, so resurrecting political economy is also very sensible. In fact we desperately need to re-conceive economies as a part of, and subservient to, societies, rather than as separate from and dominant over societies.
The modern science of systems has moved well beyond the old reductionist clockwork conceptions that worked brilliantly for many physical systems. For example, well-conceived models have provided important insights into social phenomena, such as the effect of social interactions on ant foraging or stock market fluctuations. Paul Ormerod’s books, especially Butterfly Economics, provide glimpses. Such models move beyond simple cause-and-effect into a world of feedbacks and multiple states.
The essence of science is the exploratory attitude coupled with careful comparison of hypotheses with observations of the world. We use this approach in everyday life. It can be used more broadly.
With respect to complexity, you raise a vital point. It is quite possible for a system to exhibit properties that are not attributable to its components. Thus breaking the link between micro and macro. This is why the entire effort to connect them was a waste of time, and ultimately fruitless.
In any case I follow David Marr and his three levels of analysis. In his work they are the computational; the representational; and the implementation. In economics I see them as separate transactional; processing; and systemic layers of an economy. We can eliminate the old micro by looking at transactions and their properties. We can incorporate institutions like markets and firms by studying the processes through which transactions are mediated. And we can orient macro analysis towards an examination of the aggregation and outcome of those processes. There are clear linkages between each level of detail, but each has its own properties. Each is a response to endemic uncertainty. None requires perfection or rationality. All connect with the social context within which exchange takes place. Together they are complete. Yet each stands alone.
With respect to political economy: I am not sure we need to make economies “subservient” to societies. I agree they are not separate. I simply think of them as two aspects of the same entity. Neither dominates the other. Both inform the other. They are inseparable.
Finally: I too have read of the response of the physicists at Santa Fe. It remains remarkable that economics can persist in its self regarding irrelevance despite such responses from the outside. The stubborn disregard of intelligent and well meant criticism is unbelievably irksome. It is also testimony to the enormous inertia yet to be overcome.
Peter
You say
“With respect to political economy: I am not sure we need to make economies “subservient” to societies. I agree they are not separate. I simply think of them as two aspects of the same entity. Neither dominates the other. Both inform the other. They are inseparable.”
Yet they have been separated and political economy has been maligned over some decades now by the separatists.
Peter I think you overstate the effect of emergence on limiting the relationship between micro and macro.
Emergent properties are not *possessed by* components, but they *are* *attributable to* components. There are many models in which deterministic interactions among components give rise to emergent phenomena, so emergent (macro) phenomena *are* accessible to fruitful exploration starting from component (micro) behaviour.
On the other hand the emergent behaviour of a complex system may be unpredictable and unreproducible *in detail*, though nevertheless revealing a recognisable general character from one example to another. It is the source of the general character that we can aspire to understand.
Your comments on David Marr’s ideas are interesting – but which David Marr? There’s a well known Aussie journalist by that name who hogs the Google response.
I take your point with respect to emergence. I was trying to focus attention on the way in which complexity weakens the claim of a tight, and inevitable, relationship between micro and macro phenomena made by certain economists. It is certainty, or clarity, of that tight relationship I see as severed. That lower level phenomena enable and influence systemic phenomena I have no doubt.
The David Marr I was referring to was the British neuroscientist who worked at MIT during the late 1970’s and died unfortunately at an young age. He contributed to the field of artificial intelligence and computational neuroscience. I was drawing on his notion of the levels of analysis needed to understand information processing systems. His only major book was “Vision: A computational investigation into the human representation and processing of visual information” which was published posthumously. I learned about his work via Paul Glimcher’s book: “Decisions, Uncertainty, and the Brain” which is subtitled “The Science of Neuro-economics”. Hopefully that puts him on the map for you!