MGTutoring.com. A Rational Perspective on Education.

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.

Poetry of Parmenides

Filed under: History,Logic,Philosophy — Administrator @ 7:53 am

The Stanford Encyclopedia of Philosophy has some fragments of the (philosophic) poetry of Parmenides, with philosophic commentary. They say about Parmenides:

Parmenides of Elea, active in the earlier part of the 5th c. BCE., authored a difficult metaphysical poem that has earned him a reputation as early Greek philosophy’s most profound and challenging thinker. His philosophical stance has typically been understood as at once extremely paradoxical and yet crucial for the broader development of Greek natural philosophy and metaphysics. He has been seen as a metaphysical monist (of one stripe or another) who so challenged the naïve cosmological theories of his predecessors that his major successors among the Presocratics were all driven to develop more sophisticated physical theories in response to his arguments.

Copyright © 2008 by John Palmer

© Metaphysics Research Lab, CSLI, Stanford University

Here are some lines of his poetry:

And the goddess received me kindly, and in her hand she took/ my right hand, and she spoke and addressed me thus:/ “O young man, accompanied by immortal charioteers/ [25] and mares who bear you as you arrive at our abode,/ welcome, since a fate by no means ill sent you ahead to travel/ this way (for surely it is far from the track of humans),/ but Right and Justice did.” (Fr. 1.1-28a)

You must needs learn all things,/ both the unshaken heart of well-rounded reality/ [30] and the notions of mortals, in which there is no genuine conviction./ Nonetheless these things too will you learn, how what they resolved/ had actually to be, all through all pervading. (Fr. 1.28b-32)

Come now, I shall tell—and convey home the tale once you have heard—/just which ways of inquiry alone there are for thinking:/ the one, that [it] is and that [it] is not not to be,/ is the path of conviction, for it attends upon true reality,/ [5] but the other, that [it] is not and that [it] must not be,/ this, I tell you, is a path wholly without report:/ for neither could you apprehend what is not, for it is not to be accomplished,/ nor could you indicate it. (Fr. 2)

It is necessary to say and to think that What Is is; for it is to be,/ but nothing it is not. These things I bid you ponder./ For I shall begin for you from this first way of inquiry,/ then yet again from that along which mortals who know nothing/ [5] wander two-headed: for haplessness in their/ breasts directs wandering thought. They are borne along/ deaf and blind at once, bedazzled, undiscriminating hordes,/ who have supposed that it is and is not the same/ and not the same; but the path of all these turns back on itself. (Fr. 6, supplementing the lacuna at the end of fr. 6.3 with arxô and taking s’ earlier in the line as an elision of soi, as per Nehamas 1981, 103-5; cf. the similar proposal at Cordero 1984, ch. 3, expanding parts of Cordero 1979.)

(more…)

September 29, 2009

Happy National Coffee Day!!

Filed under: Holidays & Greetings — Administrator @ 1:56 pm

In “National Coffee Day Deals” (My Fox National, Tuesday, 29 Sep 2009, 10:36 AM EDT), Mike Brody writes:

Rejoice, it’s National Coffee Day. No one really knows how the event got started, but those who enjoy a hot Cup of Joe don’t really care — they just want their java fix.

See Coffee Universe for info on coffee; all you want to know and more.

HT: Grace DC.

Laziness and a Lack of Logic

Filed under: Culture,Education — Administrator @ 10:23 am

In “Low Graduation Rates and the Total Lack of Student Effort“  (Phi Beta Cons Blog, 09/25 01:52 PM), David French writes:

A week ago I was on a Southwest flight from Dallas sitting next to a very pleasant middle-aged woman who was busily grading papers. As I finished watching one of America’s greatest cinematic masterpieces on my (brand-new) MacBook Pro, I glanced over at some of the work. It looked identical to the work I see from my ten-year-old daughter and her classmates: Mostly simple sentences, a few dreadful spelling mistakes, and virtually no complex analysis. Unlike my daughter’s classmates, however, this teacher’s students skipped entire sections of their tests — failing to answer half the questions.

I was just about to open my mouth and say, “Fifth grade?” when I caught myself.  Instead, I said “What grade?”

“Junior English.”

“High school?

“Yes. In suburban Chicago.”

I almost choked on my peanuts.

I thought of this exchange as I read Richard Vedder’s Minding the Campus essay on low graduation rates. Out of every 100 American students who enter high school, only 20 get an undergraduate degree. This is a remarkable failure rate, especially given two factors that Richard mentions: (1) grade inflation (no one flunks anymore) and (2) soaring amounts of financial aid.

Why so many failures? I think the heart of the problem is — to use Richard’s phrase — the “willingness to work.” Simply put, American college students are lazy on a scale that boggles the mind. It’s a laziness that starts early and develops year by year as “breathe-in, breathe-out” promotions (just stay alive and you’ll get through) allow students to not only progress from kindergarden to twelfth grade, but do so with a solid “B” average. It’s a laziness reinforced by the extraordinarily low academic demands of even elite universities. I studied half as hard in law school as I worked my first year in the “real world.”

September 28, 2009

Leucine

Filed under: Exercise, Health & Nutrition — Administrator @ 10:05 pm

There are some good amino acids (click on “More Details” under “Proteins & Amino Acids”) in eggs, but you’d have to eat about 11 eggs to get the Leucine I get (1.6 g) in 4 tablets of NOW Sports’ BCAs.

DietaryFiberFood.com has a chart showing the grams of leucine per 100 grams of various foods. It’d be easier to eat meat to get enough leucine.

I don’t know if the two sources are consistent; I have not checked out their figures yet.

U.S. Wellness Meats is a place where you can buy some good-quality meat to get your essential amino acids.

Update (9-29-09, 10:15 AM): You can get meat, butter, and cheese also from Slanker’s Grass-Fed Meats, aka Texas Grass Fed Beef. I had forgotten about them; someone was nice enough to remind me.

Ape Intelligence

Filed under: Animals,Biology,Science — Administrator @ 7:58 am

NOVA and National Geographic made a fascinating documentary entitled “Ape Genius,” in which they showed how apes learn and how they function mentally. In one segment of the show, they compared how chimpanzees and human children learn and function; someone posted videos on YouTube in two parts: child vs chimpanzee, part 1 and child vs chimpanzee, part 2. There are also some fascinating, interesting segments on problem solving in apes and learning by imitation. You can watch the whole show (one hour, divided into six parts) on NOVA’s Website. They give you the option of watching it in Quicktime or Windows Media.

On a related note, National Geographic has an article (which I have not read) entitled “Almost Human,” by Mary Roach. They also have some interesting video clips on ape intelligence.

Another good segment, from National Geographic’s “Human Ape,” is about self-recognition.

Arrive: An Etymology

Filed under: Words — Administrator @ 7:24 am

Dictionary.com says of the word “arrive:”

1205, from O.Fr. ariver “to come to land,” from V.L. *arripare “to touch the shore,” from L. ad ripam “to the shore,” from ad “to” + ripa “shore,” with an original meaning of coming ashore after a long voyage. Sense of “to come to a position or state of mind” is from 1393.

Arrive. Dictionary.com. Online Etymology Dictionary. (c) Douglas Harper, Historian. http://dictionary.reference.com/browse/Arrive (accessed: September 27, 2009).

I love etymology…

September 26, 2009

Some Opera

Filed under: Art — Administrator @ 10:18 am

The Flower Duet “Viens, Mallika, les lianes en fleurs” from the opera Lakmé (by Leo Delibes (see also Wikipedia)), performed by Erika Miklosa (as Lakmé) and Bernadett Wiedemann (as Mallika) in the Bela Bartok National Concert Hall, Budapest, 2006.

Maureen Thompson: Painter

Filed under: Art — Administrator @ 10:04 am

Maureen Thompson has done some good work, worth taking a look at. It’s what I like: Romantic Realism. She does Classical Realism, actually.

Some Ballet

Filed under: Art — Administrator @ 9:54 am

Polina Semionova doing some ballet (3 min, 3 sec).  There are more videos of Polina performing ballet on Facebook, and a short bio on Wikipedia.

HT: Sascha S.

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