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.
Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.
Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs
I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.
Thailand versus Montana versus New York versus Costa Rica.
Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.
Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.
Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.
You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.
"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."
This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).
Are you a procrastinator? What do you do when you are procrastinating doing something else? If you’re not prone to procrastination, how do you stay motivated?
As I've noted before -- fairly recently, if I recall correctly -- I put the "pro" in procrastination.
I figure if something's worth doing, it's worth doing at the very last minute. And why do anything today that you can put off until tomorrow -- or later?
Lately, though, I find myself procrastinating less than in earlier times. This is because of age, I suppose, and perhaps a greater unwillingness to deal with the consequences of potentially being late.
There are still upsides to procrastination. For example, the only time I ever get any housework done is when I decide that the annoyance of doing housework is less than the annoyance of doing the thing I'm supposed to be doing. Yes, that's one of the things I do when I'm avoiding other tasks. If the task I'm trying to accomplish is housework, though, I somehow find the time to organize my emails or something.
And there are, in fact, some things I never put off until the last minute. If I'm down to one beer in the fridge, for instance, then I've waited too long to buy more beer. This never happens. On a more serious note, I haven't been late paying a bill in many years, even the ones I can't put on autopay.
There's still a part of me that wants to wait, though. If I had a session with a shrink (which I totally should but I've been putting off finding one), I'd probably assert that it's because I want to give myself time to thoroughly consider something before doing it. I do that with writing, too; I won't start a story until I've thought about it long enough to know what I want the beginning and end to be like. This is a reason why my output is so sporadic.
Likely there's something deeper at play which, ideally, the shrink would fish out. But maybe I don't want to know, hence my procrastination in making appointments.
I could probably find more to add, here, but perhaps that can wait until tomorrow.
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