Saturday, June 01, 2013

Best Source Of SAT Essay Prompts

When it comes to the SAT, nothing is more important than practice in achieving an outstanding essay score. And nothing counts more than the use of quality essay prompts. 

Although a google search for "sat essay prompts" will return nearly 100,000 hits, most of these will not yield a large number of SAT-like essay prompts useful to average students preparing to take the SAT.

By far the best online source of SAT essay prompts I've seen is found here. (Look near the top of the page, under the heading "SAT Essay Prompts.")

This assemblage contains essay prompts taken from actual SAT tests given since March, 2005, and is large enough to give even the most ardent SAT student more than enough essay outlining and writing practice.

As such, this collection is perfectly suited to the needs of those getting ready to take the SAT!

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Wednesday, May 01, 2013

2 = 1

All kinds of falsehoods can be "proven" true if subtle errors in reasoning are allowed to go unnoticed. I get a kick out of debunking these faulty arguments.

See if you can find what's wrong with the well-known "proof" that 2 = 1, outlined below:


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Given.
a = b

Multiply both sides by a.
a² = ab

Add a² on both sides.
a² + a² = a² + ab

Simplify the left side.
2a² = a² + ab

Subtract 2ab from both sides.
2a² - 2ab = a² + ab - 2ab

Simplify right side.
2a² - 2ab = a² - ab

Factor 2 out of each term on left side.
2(a² - ab) = a² - ab

Divide both sides by a² - ab.
2(a² - ab)/(a² - ab) = (a² - ab)/(a² - ab)

Which "proves:"
2 = 1

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Can you find the error?

Come on ... don't look ahead until you at least give it a try!

All right, here's the mistake:

Look at the eighth step. If a = b (given), then a² - ab = 0. Division by zero is impossible, and therefore not allowed. Breaking the "never divide by zero" rule breaks the proof.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Monday, April 01, 2013

Budgeting for Lazy People

Successful budgeting can be summed up in a single key principle:

Live below your means.

One often hears how important it is to live “within one’s means,” but this isn't good enough. Such a level of spending makes saving impossible. In order to save, you must learn to be happy living below your means (i.e. spending less on fun than you are actually able to spend, given your income).

You can’t save if you don’t earn! Until you begin your career, make sure to set your sights on well-paying  employment and/or side hustles that will enable you to live comfortably and happily well below your means.

Until you earn average local income, save at least half of each paycheck after taxes and essential expenses are paid (your “disposable income,”) and spend the rest on whatever you want.

The Rule of Fourths

Once you’re earning above average income, budget roughly one fourth of your gross earnings (total income, before any deductions) into four major categories:

1. Taxes

2. Living Expenses

3. Savings

4. Spending (fun)

The amounts committed to each area probably won’t amount to exactly 25% each, but do your best to approximate that number.

The savings category should be split in roughly equal amounts between tax-advantaged retirements savings (401K, IRA, Roth IRA, etc.) and general investments (those with no particular tax advantages). Be sure to reinvest all earnings from your investments, to take advantage of the power of exponential growth (compounded earnings).

The spending category includes travel, toys, entertainment, and anything and everything else. Have fun spending this money any way you wish. You’ve earned it. Enjoy life and make memories!

Once you earn enough that your monthly expenses comprise roughly half of the budgeted 25% of your gross income (about 15% or less) … congratulations! It’s time to move up and incur higher expenses (e.g. move to a nicer place, buy a better car, get premium cable tv, etc.).

Once your household income is above average, observing the Rule of Fourths is a simple, effective way to sensibly balance four key requirements of a good life: living lawfully, prudently, comfortably, and joyfully.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, March 01, 2013

ADD: Harmful Disorder Or Helpful Variation?

Thom Hartman has extensive experience working with and writing about various aspects of the ADD/ADHD debate.

See Hartman's Web site here and some of his writings about ADD/ADHD here.

Hartman has a lot to say about a number of things, not the least of which is the current state of education in America.

In particular, Hartman formulated the Hunter vs.Farmer Hypothesis to explain the existence of ADHD. In short, Hartman suggests that, far from a harmful disorder, ADHD is simply the chromosomal vestige of mankind's early existence as intuitive, instinctive, impulsive hunter-gatherers, before the agricultural revolution lead (through natural selection) to the birth of an entirely different kind of human being, namely, the logical, careful, patient farmer type.

I strongly endorse his views, and I urge you to visit his site, read his thoughtful and interesting articles, and go on to some of the other links he lists there.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, February 01, 2013

Can Your Computer Read Your Mind?

The first time you visit this site and follow the instructions, you may think your computer has come to life and has found out how to read your thoughts. You might even suppose our machines are ready to take over the world (bringing to mind “Hal,” the infamous on-boight supposeard computer in Stanley Kubrick’s masterpiece film “2001: A Space Odyssey”).

Try it a few times:

http://www.albinoblacksheep.com/flash/mind

You won’t believe it. Seems impossible. Take a minute or two right now and see if this doesn’t make you scratch your head in amazement.

But have no fear ... it’s all just simple algebra!

Here’s how it works:

Any two digit number has a ten's digit called "t" and a unit's digit called "u." The value, v, of any two digit number (and therefore of the original two digit number you pick from the puzzle page) is 10t + u. The sum of the two digits, s, is: t + u. You are instructed to subtract the digit sum from the original number; let's call this result "r."

Therefore:

r = v – s = (10t + u) – (t + u) = 9t.

Since t can only be a whole number from 0 through 9, n = 9t can only be a multiple of 9 less than 90: 0, 9, 18, 27, ... 81. So, no matter which two digit number you initially select, you will end up looking up a multiple of 9 in the chart! The writer of the program on this site has been careful to place the same symbol next to each multiple of nine in each version of the chart shown to viewers, and has instructed the program to expose that symbol in the "crystal ball" when the user clicks on it.

Go back to the puzzle page. No matter how many times you open a new and totally different puzzle page, you will notice that, on each new page, all multiples of 9 less than 90 are always associated with exactly the same symbol (the other numbers will never come up, and so they are assigned random symbols).

Here's an entertaining variation of the game:

First, send someone a number/symbol chart together with a letter the game's instructions. Then, after this person tells you he's received the letter, has calculated his "magic number," and has found and focused on their "magic symbol," you mail him another letter in which you tell him which symbol you "psychically" picked up (of course, this is the symbol associated with each multiple of 9 on the rigged chart you sent).

For even more fun:

After your victim receives the initial letter from you, you might like to place a harmless bet with the victim (say, for lunch at the winner's favorite restaurant), that you will, in fact, be able to "perceive" his magic symbol through your superior psychic powers. When you successfully "intuit" his symbol, you’ll not only get a good laugh out of it, but a free lunch with a good friend as well (unless your friend is unusually adroit with numbers, he will totally miss the pattern underlying this trick).

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.