Science is all about making proposals that can be tested (especially after Karl Popper’s formulation of the Falsifiability Criterion), and then undergoing the experience of having that proposal rejected. This is the essence of any successful process — not that it eliminates errors altogether, but rather that it is able to make corrections despite these errors so that the target need never shift.
Professor Alain Connes recently gave his opinion of Xin-Jing Li’s proof for the Riemann Hypothesis — a proof which relies in part on Professor Connes’ work – in a blog comment to his own blog (by way of Slashdot):
I dont like to be too negative in my comments. Li’s paper is an attempt to prove a variant of the global trace formula of my paper in Selecta. The "proof" is that of Theorem 7.3 page 29 in Li’s paper, but I stopped reading it when I saw that he is extending the test function h from ideles to adeles by 0 outside ideles and then using Fourier transform (see page 31). This cannot work and ideles form a set of measure 0 inside adeles (unlike what happens when one only deals with finitely many places).
Self-correcting extends to other professions, as well. Scott Hanselman recently posted to correct an opinion he discovered here which he felt required some testing. Through his own tests, he discovered that nesting a using directive inside a namespace declaration provides no apparent performance benefit over placing it outside the namespace.
This leads him to draw these important lesson:
- Don’t believe everything you read, even on a Microsoft Blog.
- Don’t believe this blog, either!
- Decide for yourself with experiments if you need a tiebreaker!
The sentiment recalls Ralph Waldo Emerson’s memorable words:
There is a time in every man’s education when he arrives at the conviction that envy is ignorance; that imitation is suicide; that he must take himself for better, for worse, as his portion; that though the wide universe is full of good, no kernel of nourishing corn can come to him but through his toil bestowed on that plot of ground which is given to him to till. The power which resides in him is new in nature, and none but he knows what that is which he can do, nor does he know until he has tried.
Trust thyself: every heart vibrates to that iron string. Accept the place the divine providence has found for you, the society of your contemporaries, the connection of events.
A similar sentiment is expressed in Hobbes’ Leviathan, though with a wicked edge:
And as to the faculties of the mind, setting aside the arts grounded upon words, and especially that skill of proceeding upon general and infallible rules, called science, which very few have and but in few things, as being not a native faculty born with us, nor attained, as prudence, while we look after somewhat else, I find yet a greater equality amongst men than that of strength. For prudence is but experience, which equal time equally bestows on all men in those things they equally apply themselves unto. That which may perhaps make such equality incredible is but a vain conceit of one’s own wisdom, which almost all men think they have in a greater degree than the vulgar; that is, than all men but themselves, and a few others, whom by fame, or for concurring with themselves, they approve. For such is the nature of men that howsoever they may acknowledge many others to be more witty, or more eloquent or more learned, yet they will hardly believe there be many so wise as themselves; for they see their own wit at hand, and other men’s at a distance. But this proveth rather that men are in that point equal, than unequal. For there is not ordinarily a greater sign of the equal distribution of anything than that every man is contented with his share. [emphasis mine]
We find it again expressed in Descartes’ Discours de la mÃ©thode. Descartes, it might be remembered, occasionally exchanged letters with Hobbes:
Le bon sens est la chose du monde la mieux partagée; car chacun pense en être si bien pourvu, que ceux même qui sont les plus difficiles à contenter en toute autre chose n’ont point coutume d’en désirer plus qu’ils en ont.
Both Hobbes and Descartes formulate their defense of common sense somewhat ironically. In a recent post, Steve Yegge takes out the irony (or perhaps takes out the kernel of truth and leaves nothing but the irony) in his argument against Joel Spolsky’s widely aknowledged criteria for a desirable employee: "smart, and gets things done."
According to Yegge, the crux of the problem is this:
Unfortunately, smart is a generic enough concept that pretty much everyone in the world thinks [he’s] smart.
So looking for Smart is a bit problematic, since we aren’t smart enough to distinguish it from B.S. The best we can do is find people who we think are smart because they’re a bit like us.
So, like, what kind of people is this Smart, and Gets Things Done adage actually hiring?
And yet the self-correcting process continues, on the principle that we are all smart enough, collectively, to solve our problems in the aggregate, even if we can’t solve them as individuals.
Presidential candidate Barack Obama recently held a news conference to correct a misunderstanding he had made a few hours earlier about his stance on the Iraq War. According to CNN:
Obama on Thursday denied that he’s shying away from his proposed 16-month phased withdrawal of all combat troops from Iraq, calling it "pure speculation" and adding that his "position has not changed."
However, he told reporters questioning his stance that he will "continue to refine" his policies as warranted.
His comments prompted the Republican National Committee to put out an e-mail saying the presumed Democratic nominee was backing away from his position on withdrawal.
Obama called a second news conference later Thursday to reiterate that he is not changing his position.
This is, of course, merely a blip in the history of self-correction. A more significant one can be found in Bakhtin’s attempt to interpret the works of Rabelais, and to demonstrate (convincingly) that everyone before him misunderstood the father of Gargantua.
Bakhtin’s analysis of Rabelais in turn brought to light one of the great discoveries of his career: The Carnival — though a colleague once found an earlier reference to the concept in one of Ernst Cassirer’s works. Against the notion of a careful and steady self-correcting mechanism in history, Bakhtin introduced the metaphor of the Medieval Carnival:
The essential principle of grotesque realism is degradation, that is, the lowering of all that is high, spiritual, ideal, abstract; it is a transfer to the material level, to the sphere of earth and body in their indissoluble unity.
Degradation and debasement of the higher do not have a formal and relative character in grotesque realism. "Upward" and "downward" have here an absolute and strictly topographical meaning….Earth is an element that devours, swallows up (the grave, the womb) and at the same time an element of birth, of renascence (the maternal breasts)….Degradation digs a bodily grave for a new birth….To degrade an object does not imply merely hurling it into the void of nonexistence, into absolute destruction, but to hurl it down to the reproductive lower stratum, the zone in which conception and a new birth take place.
The Carnival serves to correct inequalities and resentments in society and its subcultures not by setting it upon a surer footing, but rather by affording us an opportunity to air our grievances publicly in a controlled ceremony which allows society and its hierarchical institutions to continue as they are. It is a release, rather than an adjustment. A pot party at a rock festival rather than a general strike.
As for the Internet, it is sometimes hard to say what is actually occurring in the back-and-forth that occurs between various blogs. Have we actually harnessed the wisdom of crowds and created a self-correcting process that responds more rapidly to intellectual propositions, nudging them over a very short time to the correct solution, or have we in fact recreated the Medieval Carnival, a massive gathering of people in one location which breaks down the normal distinctions between wisdom and folly, knowledge and error, competence and foolhardiness?