Wednesday, January 18, 2017

Oppenheimer on Bohr (1964 UCLA)



I came across this 1964 UCLA talk by Oppenheimer, on his hero Niels Bohr.

Oppenheimer: Mathematics is "an immense enlargement of language, an ability to talk about things which in words would be simply inaccessible."

I find it strange that psychometricians usually define "verbal ability" over a vocabulary set that excludes words from mathematics and other scientific areas. A person's verbal score is enhanced by knowing many (increasingly obscure) words for the same concept, as opposed to knowing words which describe new concepts beyond those which appear in ordinary language.

Is it more valuable to have mastery of these words: esoteric, abstruse, enigmatic, cryptic, recondite, inscrutable, opaque, ... (all describe similar concepts; they are synonyms for not easily understood),

or these: mean, variance, standard deviation, fluctuation, scaling, dimensionality, eigenvector, orthogonal, kernel, null space (these describe distinct but highly useful concepts not found in ordinary language)?

Among the simplest (and most useful) mathematical words/concepts that flummox ordinary people are statistical terms such as mean, variance, standard deviation, etc. One could be familiar with all of these words and concepts, yet obtain a low score on a test of verbal ability due to an insufficiently large grasp of (relatively useless) esoteric synonyms.

See also Thought vectors and the dimensionality of the space of concepts , Toward a Geometry of Thought and High V, Low M

Added from comments:
I'd like to clarify something that was probably confusing in the original post and my subsequent comments. 
One of the things I noticed in the SAT reading comprehension sections my kids were looking at is that one is NOT being asked to making subtle distinctions between nearby concepts/words. One is merely being asked to know that X (esoteric word) is a synonym for Y (common word), without having to know the subtle difference between X and Y. 
So, if my kid didn't know that "Brobdingnagian" is a synonym for "big" they might not be able to answer a multiple-choice question about a paragraph containing the sentence: "But of course the error was of Brobdingnagian proportions." To answer the question doesn't require knowledge of Gulliver's Travels -- I could un-befuddle my kid (allowing him or her to easily answer the question) just by saying "Brobdingnagian means big"! 
So, at least this psychometric exam (the SAT) isn't even testing fine distinctions -- it just tests whether you know that X1, X2, ... , XN are synonyms of a very primitive concept like BIG. What is the value of taking N larger and larger (in this sense; not the fine distinction sense)? Surely there are diminishing returns...

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