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.
What was cool when you were young but isn’t cool now? Is there anything that has become cool in recent years that wasn’t cool in your youth?
What was cool when you were young but isn’t cool now?
Mammoth hunts.
Come on, you knew I was going to make that joke.
I gotta say, though, I don't know what's cool and I never did. The entire idea of fashion and popularity eludes me. I suppose the word "cool" itself might qualify. I'm pretty sure that this meaning of the word came about as part of whatever counterculture was prominent at the time, and it's been switching from cool to cold and back again ever since.
One of the idiosyncrasies of English is how some words can mean their exact opposite also, as with "cleave." Such contronyms must be nothing but confusing for those poor sods who have to learn our language. Another is that words for opposite concepts can come to mean similar things, as with "cool" and "hot." And meanings can change over time; I'm told that the original meaning of "nice" was closer to how we use the word in sarcasm today.
I do remember that one thing we did a lot of back when "groovy" was a thing was for kids to ride in the back of pickup trucks, or in cars without seatbelts. Do that now, and you get your kids taken away.
Honestly, I'm not sure how any of us managed to survive.
Some changes have been for the worse, sure, but I don't ever want to be one of those old guys who bemoans the loss of some bullshit "good old days." We have a lot more respect for nerds today than there once was, for instance. Learning science and math has become cool. There's tobacco, which has gone from cool to not-cool, and cannabis, which has gone from not-cool to cool. At least in mainstream culture; in La Résistance, it's always been cool.
The only certainty in life is change, and it's best to try to stay cool about it. And yet some things endure; sunglasses, for example, have always been, are, and always will be, the Platonic ideal of cool.
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