Taniyama was not a very careful person as a mathematician. He made a lot of mistakes. But he made mistakes in good direction, so eventually he got to right answers. I tried to imitate him, but I found out that it is very difficult to make good mistakes.

- Goro Shimura on Yutaka Taniyama in Fermat’s Last Theorem

It is an understanding of the incentivized behavior of human beings that allows us to understand and predict invisible-hand outcomes.
Yet, the complexity problem remains. Can we be certain, as a logical matter, that if certain conditions obtain, certain definite types of outcomes will result from the free market process? It is on this type of thinking that the more sophisticated Keynesians might base their arguments for benevolent and effective intervention in the face of economic crisis.

Both the invisible-hand and the mainstream Keynesian argument implicitly take legibility, predictability and stability to be desirable characteristics of economic outcomes. The Keynesian argument sees the illegibility and uncertainty as justification to put in place a system of control whereas the invisible-hand argument claims that the system is legible and at “equilibrium”. The latter operates in a fantasy land and the former through the very act of stabilisation renders stability all the more elusive.

After Poirot has picked up whatever clues he deems relevant, he likes to retire to an armchair or maybe to a table, where he may steady his nerves by building a house of cards: there and then, voila! He uses what he calls his “little grey cells” to order reality and penetrate the truth lying behind the appearance of things. Conan Doyle’s famous detective Sherlock Holmes, on the other hand, proceeds from start to finish looking for visible clues that ultimately will lead him to the truth. Holmes’ close observation of things is symbolized by the magnifying glass, and he will elicit from a person’s garment, perhaps a hat, a complete picture of that person’s age, socio-economic background, present financial status, psychological predispositions, etc. In contrast to Poirot’s ratiocinative brilliance, Holmes’ genius keeps always in direct observational touch with what the world offers him. Poirot is the French rationalist par excellence whereas Holmes is the English empiricist pure and simple.

The concept of mathematics found outside the Graeco-European praxis was very different. The aim was not to build an imposing edifice on a few self-evident axioms but to validate a result by any suitable method. Some of the most impressive work in Indian and Chinese mathematics examined in later chapters, such as the summations of mathematical series, or the use of Pascal’s triangle in solving higher-order numerical equations, or the derivations of infinite series, or “proofs” of the so-called Pythagorean theorem, involve computations and visual demonstrations that were not formulated with reference to any formal deductive system. The view that mathematics is a system of axiomatic/deductive truths inherited from the Greeks, and enthroned by Descartes, has traditionally been accompanied by the following cluster of values that reflect the social context in which it originated:

1. An idealist rejection of any practical, material(ist) basis for mathematics: hence the tendency to view mathematics as value-free and detached from social and political concerns
2. An elitist perspective that sees mathematical work as the exclusive preserve of a high-minded and almost priestly caste, removed from mundane preoccupations and operating in a superior intellectual sphere

Mathematical traditions outside Europe did not generally conform to this cluster of values and have therefore been dismissed on the grounds that they were dictated by utilitarian concerns with little notion of rigor, especially relating to proof.

A Conservationist’s Lament

The world is finite, resources are scarce,
Things are bad and will be worse.
Coal is burned and gas exploded,
Forests cut and soils eroded.
Wells are dry and air’s polluted,
Dust is blowing, trees uprooted,
Oil is going, ores depleted,
Drains receive what is excreted.
Land is sinking, seas are rising,
Man is far too enterprising.
Fire will rage with Man to fan it,
Soon we’ll have a plundered planet.
People breed like fertile rabbits,
People have disgusting habits.

Moral:
The evolutionary plan
Went astray by evolving Man.

The Technologist’s Reply

Man’s potential is quite terrific,
You can’t go back to the Neolithic.
The cream is there for us to skim it,
Knowledge is power, and the sky’s the limit.
Every mouth has hands to feed it,
Food is found when people need it.
All we need is found in granite
Once we have the men to plan it.
Yeast and algae give us meat,
Soil is almost obsolete.
Men can grow to pastures greener
Till all the earth is Pasadena.

Moral:
Man’s a nuisance, Man’s a crackpot.
But only Man can hit the jackpot.

Source

When at long last will the day come that will bring home the realisation to all of us that weapons to cope with the vast mass of facts must first be forged, each by itself? – that this vast mass possesses countless different aspects, demanding countless different approaches? When at long last shall we have learned our scientific craft to the point where we can grasp what our neighbour is doing and calmly till our own field rather than attack him?

He would be saddened to realise that such a day has clearly not yet arrived.

In his excellent biography of Schumpeter, Thomas McCraw notes:

One of Schumpeter’s greatest admirers was Paul Sweezy, a young Marxist economist who served as his assistant in the course on economic theory. Sweezy found it exceptional that in all of Schumpeter’s teaching, he completely omitted any reference to his own work. “I tried to convince him that students often came to Harvard to study under him and that he owed it to them to give an exposition and elaboration of his own theories. He listened sympathetically but never did anything about it.” When people argued that Schumpeter did not try to establish a Schumpeterian school analogous to the German Historical School or the Austrian School, Samuelson responded that “he did leave behind him the only kind of school appropriate to a scientific discipline – a generation of economic theorists who caught fire from his teaching.”

Schumpeter had that “rarest of all qualities in a teacher,” Sweezy wrote. “He never showed the slightest inclination to judge students or colleagues by the extent to which they agreed with him. Keynesians (regularly in a substantial majority after 1936) and Marxists (often in a minority of one as long as I was in Cambridge) were equally welcome in his circle. He didn’t care what we thought as long as we did think.” On the other hand, for those who did not think, Schumpeter could be derisive – often ridiculing the intellectual flabbiness of his fellow conservatives. “When I see those who espouse my cause, I begin to wonder about the validity of my position.”

On a similar note, Michael Lewis touches upon the remarkable humility of Daniel Kahneman:

Twenty minutes into meeting the world’s most distinguished living psychologist I found myself in the strange position of trying to buck up his spirits. But there was no point: his spirits did not want bucking up. Having spent maybe 15 minutes discussing just how bad his book was going to be, we moved on to a more depressing subject. He was working, equally unhappily, on a paper about human intuition—when people should trust their gut and when they should not—with a fellow scholar of human decision-making named Gary Klein. Klein, as it happened, was the leader of a school of thought that stressed the power of human intuition, and disagreed with the work of Kahneman and Tversky. Kahneman said that he did this as often as he could: seek out people who had attacked or criticized him and persuade them to collaborate with him. He not only tortured himself, in other words, but invited his enemies to help him to do it. “Most people after they win the Nobel Prize just want to go play golf,” said Eldar Shafir, a professor of psychology at Princeton and a disciple of Amos Tversky’s. “Danny’s busy trying to disprove his own theories that led to the prize. It’s beautiful, really.”

He called a young psychologist he knew well and asked him to find four experts in the field of judgment and decision-making, and offer them $2,000 each to read his book and tell him if he should quit writing it. “I wanted to know, basically, whether it would destroy my reputation,” he says. He wanted his reviewers to remain anonymous, so they might trash his book without fear of retribution. The endlessly self-questioning author was now paying people to write nasty reviews of his work.

The result of Kahneman’s collaboration with Gary Klein was a fascinating paper that explored the common ground between their hitherto diametrically opposed perspectives.

My memory, sir, is like a garbage heap.

— Funes the Memorious, Jorge Luis Borges

One popular conception of how systems such as Watson can aid human beings is by acting as a kind of extension of the database of the human brain and giving us better and speedier algorithms. So a doctor could instantaneously access all the information and data that he cannot possibly analyse on his own. Implicit in this conception is as assumption that we are better off if we can process and store more information and that our own limited, forgetful memory is not up to the task of dealing with complex domains such as medical diagnosis. And a robotic aid is surely so much better than memory-enhancing hormones or training to become a memory athlete. However, the assumption that more memory is better is unwarranted. As Gerd Gigerenzer notes “the philosophical world in which perfect memory would flourish is a completely predictable world, with no uncertainty” whereas human cognition is adapted to an unpredictable and uncertain environment.

The importance of limited memory in learning was highlighted in a study by cognitive scientist Jeffrey Elman. Elman demonstrated that under certain conditions, initial restrictions on the memory of an artificial neural network may improve its ability to comprehend the complex grammatical relationships that are key to learning a language. In Elman’s words:

one might have predicted that the more powerful the network, the greater its ability to learn a complex domain. However, this appears not always to be the case. If the domain is of sufficient complexity, and if there are abundant false solutions, then the opportunities for failure are great. What is required is some way to artificially constrain the solution space to just that region which contains the true solution. The initial memory limitations fill this role; they act as a filter on the input, and focus learning on just that subset of facts which lay the foundation for future success.

 It is in this context that the limited memory capacity of infants has a positive impact by acting “like a protective veil, shielding the infant from stimuli which may either be irrelevant or require prior learning to be interpreted.”

The most striking example of how perfect memory can malform human intelligence is the case of the Russian journalist and mnemonist Shereshevsky. While studying him, the neuropsychologist Alexander Luria found that Shereshevsky possessed a memory of almost unlimited capacity and durability. Luria tested Shereshevsky’s memory by asking him to repeat arbitrary series of numbers, words and syllables that Luria provided him with, a task that Shereshevsky completed without error no matter how long the series and how long back the series had been given to him. Indeed, he possessed a flawless recollection of series’ that Luria had given him as long as 15 years ago. In many respects, Shereshevsky’s mind resembles that of a computer. Luria notes that when asked to reproduce a particular word in the series, Shereshevsky “would pause for a minute, as though searching for the word, but immediately after would be able to answer my questions and generally made no mistakes” as if he were searching through a vast database with an incredibly accurate and efficient algorithm. Perfect memory however carried a high cost. Shereshevsky struggled to understand the meaning of simple passages of text (especially poetry or metaphors), “a struggle against images that kept rising to the surface of his mind.” He found it almost impossible to extract any true meaning from them or to be truly aware of anything at an abstract level. In this respect, Shereshevsky resembles Jorge Luis Borge’s famous character ‘Funes the Memorious’ whose prodigious memory meant that he was “incapable of ideas of a general, Platonic sort”.

(Winter has given them gold for silver

To stain their water and bladed green for brown to line their banks)

From different throats intone one language.

So I believe if we were strong enough to listen without

Divisions of desire and terror

To the storm of the sick nations, the rage of the hunger-smitten cities,

Those voices also would be found

Clean as a child’s; or like some girl’s breathing who dances alone

By the ocean-shore, dreaming of lovers.

Source

Rough Transcript (emphasis mine):

we spend so much time, resources and money trying to see the future. Really we’re spending money trying to delude ourselves. You’ve no chance of seeing the future. It’s better to recognise that.…..the worst thing that happened to western civilisation was the US government’s program in the 1970s to try and reduce fatalities from road accidents and it led to the creation of the airbag and it cost billions to achieve. If they’d asked me, I would have invented a sharp object like a dagger and I’d have had it in the steering wheel and you would eliminate fatalities because by god you’d drive carefully now…..(a hedge fund manager) was running a statistical merger arbitrage fund…I was reading, being deeply impressed by the intellectual rigour that he was applying to his ideas. He then goes on to record his experience in Dallas,Texas with an oil rig business…the degree of knowledge that he brought to bear on his subject matter. In fact, before he took the position on, he took an engineering course at university to get insight. And all he was doing was building this superior airbag. And in 2008, both of their funds disappeared. They were actually driving their cars too fast. So in some respects, I don’t want to know. I had an analyst who left us last year. And he had some fantastic insights on this pharmaceutical business, he started telling me and I started getting excited to think I could see the future and suddenly rather than having a 50 basis point holding in my fund I had a 250 basis point holding. And of course it had a profit warning and fell forty percent. Again we had deluded ourselves, this notion that we have seen the future. So in some respects, I go around and I don’t wanna know. I don’t wanna do stock research. I want to have that itch, that trepidation that says I don’t know the complete picture here. And therefore I watch things like a hawk and if the chart breaks down I trade, I sell. So ‘plasticine man’ is someone who, you can pull it apart very quickly and then put it back together. I used to say…I was the centipede. I had a hundred legs – hundred legs, I could let go of one or two, I ain’t gonna procrastinate. Procrastination kills you in a business which is determined by risk.

Having less information is often better in an uncertain environment because it acts as a defense against overconfidence. If only the paranoid survive, then not having the complete picture is one way to stay paranoid. Once we feel like we have all the information, then we often struggle to cope with our overconfidence. As Daniel Kahneman puts it:

We’re blind to our blindness. We have very little idea of how little we know. We’re not designed to know how little we know. Most of the time, [trying to judge the validity of our own judgements] is not worth doing.

No one questions that government is by nature authoritarian; if an alternative is seen to rule by legitimate force it is the abolition or minimisation of government, leaving people to organise their affairs by custom. There are theoretical anarchists in ancient China, but no democrats.