MGTutoring.com. A Rational Perspective on Education.

October 28, 2009

Theoretical Statistics Is Practical and Life-Giving

Filed under: Mathematics,Philosophy,Quotes,Science,Statistics — Administrator @ 10:55 am

In “The Median Isn’t the Message,” Stephen Jay Gould (evolutionary biologist who taught at Harvard University) wrote:

My life has recently intersected, in a most personal way, two of Mark Twain’s famous quips. One I shall defer to the end of this essay. The other (sometimes attributed to Disraeli), identifies three species of mendacity, each worse than the one before – lies, damned lies, and statistics.

Many people make an unfortunate and invalid separation between heart and mind, or feeling and intellect. In some contemporary traditions, abetted by attitudes stereotypically centered on Southern California, feelings are exalted as more “real” and the only proper basis for action – if it feels good, do it – while intellect gets short shrift as a hang-up of outmoded elitism. Statistics, in this absurd dichotomy, often become the symbol of the enemy. As Hilaire Belloc wrote, “Statistics are the triumph of the quantitative method, and the quantitative method is the victory of sterility and death.”

This is a personal story of statistics, properly interpreted, as profoundly nurturant and life-giving. It declares holy war on the downgrading of intellect by telling a small story about the utility of dry, academic knowledge about science. Heart and head are focal points of one body, one personality.

Mr. Gould also goes on to discuss how the Platonic view that the type or kind is (most) real is false; what is true is the Aristotelian view that the individual (“variation”) is real. He says:

We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. (Thus we hope to find an unambiguous “beginning of life” or “definition of death,” although nature often comes to us as irreducible continua.) This Platonic heritage, with its emphasis in clear distinctions and separated immutable entities, leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua. In short, we view means and medians as the hard “realities,” and the variation that permits their calculation as a set of transient and imperfect measurements of this hidden essence. If the median is the reality and variation around the median just a device for its calculation, the “I will probably be dead in eight months” may pass as a reasonable interpretation.

But all evolutionary biologists know that variation itself is nature’s only irreducible essence. Variation is the hard reality, not a set of imperfect measures for a central tendency. Means and medians are the abstractions.

Notice how Mr. Gould is talking about kinds of things as being separate from variation, shadings, and continua. I don’t know if he’d say everything was like that, even individuals, but if so, I’d have to disagree: individuals are distinct and separate; this is given clearly (by real, immutable cause-effect relationships) in perception. Kinds of things, conceptual categories, come about only by recognizing things in their reality- and perceptually-given background of variation: tables grasped as related to but contrasted with furniture and other items in a house; trees grasped as related to but contrasted with grass and bushes; people grasped as related to but contrasted with other animals; engineers grasped as related to but contrasted with other human professions.

Concepts are only ways of categorizing individuals based on cause-effect and explanatory relationships. Individuals are most real; types or kinds are real, but have a “secondary, dependent existence” to individuals.

October 20, 2009

Achieving Excellence

Filed under: Quotes — Administrator @ 10:10 am

Someone wrote on the Internet — see a post on the Moomin Light blog and EDUCAUSE’s Edupage of 28 February 1999:

As for Fred Astaire’s dancing, both George Balanchine and Mikhail Baryshnikov called him the greatest, most original dancer of all time. A perfectionist, Astaire was uninterested in the advice of others, and wrote in his autobiography: “I believe that if you have something in mind in the way of creation, you are certain to come up with inaccurate criticism and damaging if you go around asking for opinions. It is the easiest thing in the world to become discouraged by a well-meant suggestions which may throw you off your original train of thought.” The perfectionism paid off. Movie director Rouben Mamoulian said, “Fred Astaire makes it look easy by only taking the greatest of pains. He works harder than any newcomer. He never lets up. You’d think his entire life and future depended on the outcome of each dance. He keeps at the top because he does the impossible — he improves on perfection.”

Read the rest of the post on Moomin Light. Good stuff.

Fred Astaire and Ginger Rogers dance, and Ginger Rogers sings, in a clip from “Roberta”. I love how, at about the 5 minute mark, they talk and fight through dance and their feet, and I love the little slide they do when they are done fighting and they go back into closed hold.

HT: Henry S

October 19, 2009

Rudyard Kipling: A Quote

Filed under: Quotes — Administrator @ 11:22 am

I keep six honest serving-men

(They taught me all I knew);

Their names are What and Why and When

And How and Where and Who.

Quote from a poem in “The Elephant’s Child” by Rudyard Kipling.

October 16, 2009

William Blake: A Quote

Filed under: Quotes — Administrator @ 7:51 am

“A fool sees not the same tree that a wise man sees.”

Quote from Yahoo! Education, which gives the attribution for this quote as: “William Blake (1757–1827), British poet, painter, engraver. The Marriage of Heaven and Hell, plate 7, “Proverbs of Hell,” (c. 1793), repr. In Complete Writings, ed. Geoffrey Keynes (1957).”

I’d add that the same relationship applies between a poor or mediocre teacher and a good teacher — even if the former is not a fool! The wisdom of the latter is well worth the money…

October 15, 2009

Samuel Johnson: A Quote

Filed under: Quotes — Administrator @ 10:00 am

“Man is not weak. … Knowledge is more than equivalent to force. The master of mechanics laughs at strength.”

Quote from Samuel Johnson.com, which gives the attribution for this quote as “Johnson: Rasselas [Imlac] Note: If you haven’t read it yet, please read this note of caution regarding quotes from Rasselas.”

I’d add that mechanics relies on mathematics...

October 9, 2009

Danica McKellar: A Quote

Filed under: Mathematics,Quotes — Administrator @ 5:52 am

In the course of reviewing a math book written by Danica McKellarMath Doesn’t Suck, Denise at Let’s Play Math Blog posted a good quote from Mrs. McKellar:

But now Danica McKellar’s second book is out, and the first one has been released in paperback. A friendly PR lady emailed to offer me a couple of review copies, so I gave Math Doesn’t Suck a second chance.

Danica McKellar knows far more about math than I do. She majored in mathematics at UCLA and graduated summa cum laude in 1998.

As McKellar writes:
Working on math sharpens your brain, actually making you smarter in all areas. Intelligence is real, it’s lasting, and no one can take it away from you. Ever.

And take it from me, nothing can take the place of the confidence that comes from developing your intelligence — not beauty, or fame, or anything else “superficial.”

Math isn’t easy for anyone. It takes time and persistence to understand this stuff, so don’t give up on yourself just because you might feel frustrated. Everyone feels like that sometimes — everyone. It’s what you do about those feelings that makes you who you are.

It’s in those moments when you want to give up but you keep going anyway that you separate yourself from the crowd and build the skills of patience and fortitude that will allow you to excel throughout your entire life — no matter what you choose as a career.

Danica McKellar is an actress (an intelligent one!!). Check out her interview on NPR.

September 30, 2009

Rejecting the Non-Existent

Filed under: Education,Logic,Mathematics,Quotes — Administrator @ 7:54 am

There is a great deal one can learn about logic and objectivity from mathematics. It is a very important subject to study. In Elementary Mathematical Analysis, Colin Clark says:

Suppose we wish to prove: “1 is the largest positive integer.”

Let x denote the largest positive integer. Then x>= 1, so that x^2 >= x. But x^2 is also a positive integer. Therefore x^2 = x. Dividing by x, we obtain x = 1.

What is the error in this “proof”? The moral of this example is that if we refer to nonexistent objects as if they existed, we may be led into foolish errors. Mathematicians seem to have learned this moral; politicians probably never will.

p. 107, Elementary Mathematical Analysis by Colin Clark, Wadsworth Publishers of Canada, Ltd., (c) 1982. ISBN 0-534-98018-X.

As Parmenides said: ‘What is not, neither is nor can be thought.’ A is A; A is Not Non-A.

September 11, 2009

On the Value of Hard Work

Filed under: Quotes — Administrator @ 7:04 am

Maybe It’s My Fault” by Michael Jordan

July 15, 2009

Another False Attribution?

Filed under: Quotes — Administrator @ 5:47 pm

“The capitalists will sell us the rope we use to hang them” is attributed sometimes to Lenin, sometimes to Stalin.

But…in his “On Language” column entitled “Useful Idiots Of the West” (Published: Sunday, April 12, 1987), William Safire says:

Librarian [Grant] Harris [of the Library of Congress] got back to me, however, with a lead to the possible source of both the ”rope” remark and the ”useful idiot” attribution. Former Colgate Prof. Albert Parry writes in The St. Petersburg Times: ”You will not find the rope prophecy in any of the voluminous Lenin works published in the Soviet Union.” Right.

He suggests we look instead in the 1966 book ”People and Portraits: A Tragic Cycle” published in New York by Inter-Language Literary Associates, written by Yuri Annenkov….

Here is what Mr. Annenkov claims he copied from notes in Lenin’s handwriting, italics in the original: ”To speak the truth is a petit-bourgeois habit. To lie, on the contrary, is often justified by the lie’s aim. The whole world’s capitalists and their governments…will give us credits…they will toil to prepare their own suicide.”

Look, I know it’s a little farfetched. …However, this gives us one clue about the source of the ”sell us the rope” attribution, and the ”deaf, dumb and blind” phrase may be one of the phrases that helped start the ”useful idiots,” whether or not originally by Lenin.

A version of this article appeared in print on Sunday, April 12, 1987, on section 6 page 8 of the New York edition.

Copyright 2009 The New York Times Company

June 30, 2009

On Good Writing

Filed under: Education,Quotes,Recommended Books — Administrator @ 9:22 am

“[A] piece of literature may be more appropriately compared with a living organism than with a mechanism. As Plato says in one of his dialogues, ‘You will allow that every discourse ought to be constructed like a living organism, having its own body and head and feet; it must have middle and extremities, drawn in a manner agreeable to one another and to the whole.’ A vital order permeates a good poem, short story, or drama, and to a large extent a piece of expository art intended to be primarily ‘useful’ rather than ‘fine.’ “  (p. 105, Writing and Thinking by Norman Foerster and J.M. Steadman, Jr., Houghton Mifflin Company, (c) 1931 Foerster and Steadman.)

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