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March 3, 2008

A Deep Sense of Miserable Ignorance

Posted by David Corfield

On p. 171 of Peirce’s lectures, Reasoning and the logic of Things, having favourably compared the universities of Europe to those of America, he explains what is wrong with the latter’s pedagogy:

In order that a man’s whole heart may be in teaching he must be thoroughly imbued with the vital importance and absolute truth of what he has to teach; while in order that he may have any measure of success in learning he must be penetrated with a sense of the unsatisfactoriness of his present condition of knowledge. The two attitudes are almost irreconcilable. But just as it is not the self-righteous man who brings multitudes to a sense of sin, but the man who is most deeply conscious that he is himself a sinner, and it is only by a sense of sin that men can escape its thraldom; so it is not the man who thinks he knows it all, that can bring other men to feel their need of learning, and it is only a deep sense that one is miserably ignorant that can spur one on in the toilsome path of learning. That is why, to my very humble apprehension, it cannot but seem that those admirable pedagogical methods for which the American teacher is distinguished are of little more consequence than the cut of his coat, that they surely are as nothing compared with that fever for learning that must consume the soul of the man who is to infect others with the same apparent malady.

Does this explain the success of This Week’s Finds?

Posted at March 3, 2008 3:38 PM UTC

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Re: A Deep Sense of Miserable Ignorance

Here a nice collection of Christian Siebeneicher on how arithmetics was teached long ago. If subconscious attidudes influence teaching, here an article on how to detect such attitudes.

Posted by: Thomas Riepe on March 4, 2008 1:25 PM | Permalink | Reply to this

heart of the wise; Re: A Deep Sense of Miserable Ignorance

John Baez has given us the classic Taoist tale of ignorance (monks, brige, fish). A Christian nugget is:

“The heart of the wise inclines to the right, but the heart of the fool to the left.”
[Ecclesiastes 10:2]

See also the special 125th anniversary issue of Nature:

Nature 372, November 2002

As a result of that issue, I taught several hundred senior citizens a course entitled “The Frontiers of Ignorance.”

In teaching Astronomy, Biology, Computer Science, Mathematics, and many other subjects I am again and again startled by penetrating questions from students that clarify for me that something which I thought I understood, I didn’t understand well enough.

Cf. Thomas Kuhn’s “Structure of Scientific Revolution” – which, agree or disagee, changed the dialogue on the subject. David Corfield knows this better than I.

For that matter, attention to the most deeply buried footnotes in science journals make it clear that good scientists admit that their work is on the frontiers of ignorance. Much of what was in textbooks when I was a boy is sinply untrue today. And tomorrow…?

Posted by: Jonathan Vos Post on March 4, 2008 4:40 PM | Permalink | Reply to this

Re: heart of the wise; Re: A Deep Sense of Miserable Ignorance

“Much of what was in textbooks when I was a boy is sinply untrue today.”

Much of what was in textbooks when I was a boy was also untrue then. I was taught by physics teachers at primary school that water flowed down the plug hole counter-clockwise in one hemisphere and clockwise in the other. Yet when I ran home eagerly to check the direction of flow in my own hemisphere (the southern one), I found that this was not true for any bathtub or sink in my family’s house. The water flowed in every which way, and often changed direction mid-flow. My fellow students observed the same. When we asked the teacher about this discrepancy, he accused us of lying.

Only years later did I learn that local factors, such as the exact position of the tap relative to the hole, the shape of the bathtub or sink, and the degree of pressure of the water emitted from the tap, could overwhelm any effects caused by the earth’s rotation. I now know that science proceeds by making abstractions and generalizations with claims to universality which happen to be contradicted by the facts on the ground in every specific instance. It makes no sense to speak of such claims being “true” or “false”, since being abstractions, they don’t apply anywhere.

Posted by: Peter on March 4, 2008 5:27 PM | Permalink | Reply to this

Everything You Know Is Wrong; Re: heart of the wise; Re: A Deep Sense of Miserable Ignorance

I mostly agree. However, I consider the matter to be more subtle.

Abstraction, generalizations, and claims to universality…

I may have mentioned before, and don’t want to repeat, my meta-claim that there are 5 non-overlapping magesteria, each of which has a paradigm of “truth” and a paradigm of “proof.”

The two at issue here (leaving aside for now Legal-political; aesthetic; and revealed/religious) are Axiomatic Truth and Empirical Truth.

Mathematics does make claims to absolute truth, in the Axiomatic magesterium.

Science (including Physics) does not. Science (properly) makes limited, temporary, partial, conditional claims, contingent on experiment design, experiment execution, instrumentation, noise, error, data analysis, interpretation, and the feedback mechanisms of The Scientific method.

When I was a boy, the Noble Gases could not form compounds; Pluto was a planet (and the most distant); the role of DNA in heredity was mere hypothesis; there had only ever been once species of humans; Mars had always been cold and dry; nobody considered building machines nor computers at the nanometer scale; computers were classical (nobody thought of making them quantum); spaceflight was the domain of Science Fiction, despite those troublesome Tsiolkovski, Goddard, von Braun, and Clarke fellows; extraterrestrial intelligence was purely the domain of science fiction (and woe to the scientist who discussed it in public); the cosmos was smoothly expanding; and venereal disease could be easily avoided or treated.

Ahhh, the Good Old Days.

Firesign Theatre released in October of 1974, on Columbia Records, a comedy album entitled: “Everything You Know Is Wrong.”

As wikipedia reminds me, after it was recorded, a movie version was made, with the group lip-syncing to the album. The cinematographer for this was Allen Daviau, who later filmed E.T. the Extra-Terrestrial. The film was released on a VHS format videotape in 1993 by The Firesign Theatre. (UPC barcode 735885 100131. Currently available from the Lodestone Catalog / SKU# MSUG001.)

Two of the characters introduced on this album, Ray Hamburger (pronounced Ham-ber-jer’) and Harold Hiphugger, reappear on the group’s later album “Give Me Immortality or Give Me Death.”

The “Official stolen government training film of the secret plan to deal with an alien uprising” is a parody of, among other things: General Curtis LeMay’s statement that the Communists of North Vietnam should be “bombed back to the stone age”. LeMay is also noteworthy for having furiously informed Barry Goldwater that he was not permitted to access rumored secret UFO information supposedly being kept at Wright Patterson Air Force Base, leading UFO-philes to suspect that LeMay knew of the existence of alien spacecraft and was hiding information related to First Contact. The album’s title was appropriated by Russ Kick for a collection of writings for his Disinfo series.

The more that I read, study, research, and teach, the more I suspect that, indeed, “Everything I Know Is Wrong.”

Posted by: Jonathan Vos Post on March 4, 2008 8:50 PM | Permalink | Reply to this

Re: Everything You Know Is Wrong; Re: heart of the wise; Re: A Deep Sense of Miserable Ignorance

“Everything I Know Is Wrong.”
I’d prefer Cusanus more differentiated motto. More on medieval philosophy and logic here.

Posted by: Thomas Riepe on March 5, 2008 1:41 PM | Permalink | Reply to this

De Sousa on “Darwin’s Doubt” and Plantinga; mRe: A Deep Sense of Miserable Ignorance

The question of how ignorant we are is coupled to the question of whether Mathematics is a social contruct. Recent debate on this harks back to Darwin’s comments.

Darwin on My Mind

Literary Review of Canada
Volume 16, Number 2
March 2008
Pages 20-21
Darwin on My Mind

Evolutionary theory best explains how—and why—we reason.

by Michael Ruse

Why Think? Evolution and the Rational Mind
Ronald de Sousa
Oxford University Press
194 pages, hardcover
ISBN 9780195189858

Everything we believe about evolution could be false. And this is obviously to reduce Darwinian epistemology to a reductio ad absurdum. If our theory of knowledge embraces indifferently the true and the false, so long as it is expedient, we are in deep trouble. Plantinga calls this “Darwin’s Doubt,” because it was even expressed by a worried Darwin himself, in correspondence written toward the end of his life: “With me the horrid doubt always arises whether the convictions of man’s mind, which has been developed from the mind of the lower animals, are of any value or are at all trustworthy. Would anyone trust in the convictions of a monkey’s mind, if there are any convictions in such a mind?” (As a matter of fact, Darwin immediately excused himself as a reliable authority on such philosophical questions, but Plantinga leaves this somewhat awkward point unmentioned.)

De Sousa has a two-part response to this criticism. First, he argues that our mathematical abilities cannot be the result of natural selection. “On the evolutionary scale, mathematics is part of our present rather than of our evolutionary past. It is therefore out of the question for mathematical talent as such to have been a factor in evolution by natural selection.” Then he goes on to say:

“Once mathematics had emerged into the light of day, there was still nothing to guarantee that it could prove useful outside the domains in which our practical skills had already been operating for millennia. And yet, pure mathematics notoriously finds all kinds of startling applications in the solution of technological and scientific problems that our ancestors could not possibly have conceived of, and it does so by generating theories that would have remained wholly unintelligible to them. That strongly supports the idea that mathematics can uncover aspects of the universe of which neither the usefulness nor even the existence could possibly have been manifested in the environment of our evolutionary adaptations (EEA) in which the basic functions of the brain were being shaped by natural selection. As [Eugene] Wigner has argued, this constitutes at least prima facie evidence for the conclusion that the truths of mathematics do not merely reflect projective constructions of our brains, but probably correspond to an objective reality.”

I am not sure about either of these steps. It is true that an ability for calculus was not needed in the jungle or the move out onto the plains—students of human evolution think that the key break from the chimps occurred about five million years ago when our ancestors came down from the trees and out into the open—but this is not to say that the components of reasoning abilities were not produced by selection. There are good biological reasons why humans have innate abilities at counting, working with sets, geometrical understanding, and so forth. It is true that these rather modest talents then need to be put together, but that is what education is all about.

In any case, I agree that the power of mathematics is pretty impressive. Let me correct that—incredibly impressive. And I agree it is hard to see how it works so well if it is not true. But I am not sure that this will meet Plantinga’s criticism. He argues that even if we discount the known ways that selection misleads us (I guess if he had heard of it, he would put the Wason experiment in here), it could be that selection is systematically misleading us all of the way. In a sense, his argument is a version of that used by Descartes in the Meditations—we think we are on safe ground against skepticism when we turn to mathematics, but an evil demon could be misleading us systematically about even that. You, silly person, think that 2+2=4 and that Stephen Harper has your best interests at heart, but—who knows?—a malevolent god could be deceiving you….”

Posted by: Jonathan Vos Post on April 12, 2008 9:10 PM | Permalink | Reply to this

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