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Complex Numbers
Complex Numbers
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
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This guy looms large around here. Sometimes literally, what with all the statues.
Like many of the Founding Fathers, Thomas Jefferson was a dad.
I mean, it's right there in the group's name.
Article is from Art of Manliness, which is biased toward fatherhood as a prerequisite for "manliness," whatever that is. I'm not defending the site here, or Jefferson's personal life.
And like a lot of dads, he often took the opportunity to dispense unsolicited dad advice to his children.
I like to think he made numerous, cringeworthy puns as well. They're called "dad jokes" now, but I'm living proof that you don't have to be a dad to make them.
In an 1825 letter to John Spear Smith, Jefferson laid out his refined list of adages that he called his “Decalogue of Canons for observation in practical life.”
You might recognize "decalogue" as the Greek name for what we call the Ten Commandments. Jefferson, as should be widely known, was not above editing the Bible.
I'm not going to get much into the explanations of the rules; you can go to the link for that. No, as a fellow Charlottesvillian and graduate of the University he founded, I'm going to note my own version of the Rules, updated for life nearly 200 years later.
1. Never put off till tomorrow what you can do today.
Waltz: Never put off until tomorrow what you can put off until the day after tomorrow. Life's too short to focus on productivity all the time.
2. Never trouble another for what you can do yourself.
Waltz: Never do yourself what you can pay someone else to do for you. (And I can't resist pointing out that this Rule is pretty fucking ironic coming from a slaveholder.)
3. Never spend your money before you have it.
Waltz: Own, don't rent.
4. Never buy what you do not want, because it is cheap; it will be dear to you.
Waltz: Never buy what you do not want. (This Rule took me a while, I guess because language changed in two centuries. I think that last phrase can be translated as "it will be more expensive in the long run.")
5. Pride costs us more than hunger, thirst, and cold.
Waltz: We really need to come up with a different word; there's good pride and bad pride. (Did Jefferson, landed gentry, know hunger or thirst? Cold, I have no doubt of.)
6. We never repent of having eaten too little.
Waltz: Don't go hungry if you can at all avoid it. It's distracting.
7. Nothing is troublesome that we do willingly.
Waltz. Doing nothing is always an option. Unless you're hungry.
8. How much pain have cost us the evils which have never happened!
Waltz: How much pain have cost us the embarrassing things we did that we only remember at 3 a.m.
9. Take things always by their smooth handle.
Waltz: Laziness is productive.
10. When angry, count ten before you speak; if very angry, a hundred.
Waltz: Actions speak louder than words.
Okay, I stole that last one from my mom, who was fond of repeating proverbs (which are things entirely different from pronouns, again illustrating how freakin' weird English is). And obviously, I don't actually believe it, because here I am typing words.
Anyway, I'm sure you'll have your own opinions on these things. Let's not fall into the trap of thinking that because a famous person from history said it, it's any more profound than if a nobody from today says it. |
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