## Friday, October 31, 2008

### Hyp(otenuse) to be a Square

Pythagoras was one of the earliest of the Greek philosopher/scientist/mathematicians. In fact, he's said to have coined the term philosopher, from the Greek terms meaning "love of knowledge." Partly due to the natural effects of historical perspective, and partly due to the secrecy maintained by the cult of Pythagoreans, not much is known with certainty about him or his works.

He's best known for the theorem about right triangles that bears his name, though he probably didn't originate it. Also up there is his work on producing tones with strings of various lengths and tensions.

So next time you're playing Guitar Hero, think of Pythagoras.

## Wednesday, October 29, 2008

### Pythagoras

Play Audio

You might not think there would be any use
Knowing the square of the hypotenuse
(Which is the sum, Pythagoras confides,
Of the squares of the opposite two sides.)

This theorem which comes from geometry,
Combined with bits of trigonometry,
Is useful when we calculate how far
It is to something distant, like a star.

He traveled much, and probably had learned
This theorem, which he proved when he returned.
He did invent mathematical abstraction,
And useful concepts, like that of the fraction.

But numbers, even fractions, wouldn’t do
For representing the square root of two.
He formed a cult of number-based fanatics
That practically invented mathematics.

Another of Pythagoras’s strengths
Was working out how strings of different lengths
When plucked made different pitches to the ear. He
Could have called this notion his string theory.

## Friday, October 24, 2008

### Spinning my wheels

I'm sitting in my office. The fan is blowing on me. I'm rolling my mouse around. I'm tilting and swiveling and rolling around in my desk chair. In a few minutes, I'll take the elevator, then go get on a train to take me to where my bike is parked, so I can ride home past all the cars.

And I can't think of anything to say about the wheel.

## Wednesday, October 22, 2008

### The Wheel

Audio

When people first moved things around
Across the dirt and rocks and ledges,
They tired of dragging on the ground
And started piling stuff on sledges.

This worked out for quite a while
But they eventually learned
The sledges could be moved with style
By rolling them on logs that turned.

Meanwhile, in making pots and bowls
And other stuff formed out of clay,
A round shape was one of the goals
Met by use of a spinning tray.

So putting these ideas together
Folks could make some simple parts:
Axles held by straps of leather,
holding wheels to move their carts.

Even now, the gear and pulley,
Bike and train, automobile,
Don't mean that people have fully
Made use of this thing, the wheel.

## Monday, October 20, 2008

### Still Here

I know we've fallen way behind lately. Blame it on the Red Sox. There are still thousands of great ideas to cover, and if those run thin, I certainly have plenty of dumb ones to add to the mix.

So stay tuned. We'll be back.

(There's a homophonic clue about the topic of our next post in here, but don't waste too much time on it.)

## Friday, October 10, 2008

### Separation of Powers

The phrase "checks and balances" appears nowhere in the U.S. Constitution. Rather, it's a concept that describes the distribution of various powers and responsibilities among the various branches of government. The concept of separation of powers goes back to ancient times. It's interesting, though, that this is still hotly debated. The current U.S. administration has been accused of ignoring the system of checks and balances, and of grabbing power to institute an imperial presidency.

Of course, if one political party controls all the branches of government, that tends to defeat the system of checks and balances anyway. Perhaps some stronger measures are needed to ensure that diverse viewpoints are represented.

## Wednesday, October 8, 2008

### Checks and Balances

Play Audio

The famous Lord Acton remarked, quite astutely,
Absolute power corrupts absolutely.
Government structures that follow this principle
Make sure that no single branch is invincible.
No one branch gets to have all of its druthers;
Each one must answer to one or more others.
The whole legislature can pass lots of laws
But courts overturn them if they find some flaws.
Some chief executives make their own moves,
But some acts require that the Congress approves.
The most independent branch, the Supreme Court,
Is made up of those whom the others support.
So, by this system, all branches are checked,
And should treat each other branch with some respect.

## Friday, October 3, 2008

### With Liberty and Justice For All

From the sound of that phrase, "with liberty and justice for all," one might almost think the two go hand in hand. But nothing could be farther from the truth. Liberty, or more simply freedom, appears to be about not being a slave, not being subject to a tyrannical government, or not being constrained by a rigid, conformist society. In conservative parlance, though, liberty is also a code word for freedom from taxes and government involvement.

Likewise, justice is not just about being counted innocent until proven guilty, or not having to face cruel and unusual punishments. Justice is also about having an opportunity to strive for the rewards society has to offer. It's about succeeding based on accomplishments, rather than on family background, hereditary wealth or social connections.

Unfortunately, nature is inherently unjust. People, through no fault or virtue of their own, may be born with incredible advantages or horrible disadvantages. We can't correct this. But we can make life a little more equitable but creating a society in which those who are disadvantaged get a little help at the expense of those who have more than their share. It's only fair.

## Thursday, October 2, 2008

### Liberty Vs. Justice

Play Audio

The idea known as liberty
(Or sometimes simply “being free”)
Is often in a rivalry
With what we call equality.
Now liberty means I can do
Most anything I might want to.
But if I’m better off than you,
You may not have that freedom too.
Justice is, you may observe,
The goal folks get what they deserve.
But life can throw us all a curve,
Those who command and those who serve.
For nature isn’t always fair,
And folks don’t get an equal share.
One kid’s born broke, and one’s an heir,
So how could there be justice there?
So though we must indeed be free
To function in society
It’s not enough. There needs to be
Some measure of equality.