◄     September     ► S M T W T F S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Archive RSS
Creative fun in
the palm of your hand.

# Complex Numbers

Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
 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. .
Previous ... -1- 2 3 4 5 6 7 8 9 10 ... Next
September 16, 2021 at 12:03am
September 16, 2021 at 12:03am
#1017490
September 15, 2021 at 12:03am
September 15, 2021 at 12:03am
#1017439
September 14, 2021 at 12:02am
September 14, 2021 at 12:02am
#1017367
September 13, 2021 at 12:01am
September 13, 2021 at 12:01am
#1017312
September 12, 2021 at 12:06am
September 12, 2021 at 12:06am
#1017268
September 11, 2021 at 12:02am
September 11, 2021 at 12:02am
#1017222
September 10, 2021 at 12:05am
September 10, 2021 at 12:05am
#1017159
September 9, 2021 at 12:03am
September 9, 2021 at 12:03am
#1017070
 Fight The Power Here's an article from 2017, but one that seems more relevant now than in the Before Time. The Five Universal Laws of Human Stupidity   We underestimate the stupid, and we do so at our own peril. Normally, I'd link to the original source, but it's paywalled. This is a reprint. Stupid people, Carlo M. Cipolla explained, share several identifying traits: they are abundant, they are irrational, and they cause problems for others without apparent benefit to themselves, thereby lowering society’s total well-being. I would be remiss if I didn't note that intelligence isn't the last word on human worth. Half the world's human population possesses below-average intelligence (more or less), and it's possible to be stupid and nice, just as it's possible to be smart and an asshole. A university professor like Cipolla might have had some bias in the matter, though. The only way a society can avoid being crushed by the burden of its idiots is if the non-stupid work even harder to offset the losses of their stupid brethren. Wait, you want me to be smart and work hard? Let's not go too far, okay? Of course, everyone does stupid things from time to time. I think it's a matter of proportion. Let’s take a look at Cipolla’s five basic laws of human stupidity: Oh, good. Having "The Five Universal Laws" in the headline and not stating them in the body would be... well... stupid. Law 1: Always and inevitably everyone underestimates the number of stupid individuals in circulation. No matter how many idiots you suspect yourself surrounded by, Cipolla wrote, you are invariably lowballing the total. Yeah, best to assume everyone's an idiot until they show otherwise, and then still be prepared to revise one's opinion of them upon further observation. But like I said... it's about half the population (depending on what's meant by "average"). Law 2: The probability that a certain person be stupid is independent of any other characteristic of that person. Cipolla posits stupidity is a variable that remains constant across all populations. Every category one can imagine—gender, race, nationality, education level, income—possesses a fixed percentage of stupid people. This may seem counterintuitive. Okay, it does seem counterintuitive. But the whole purpose of reasoning, and of science, is to check our intuition, which is usually less reliable than logic. Law 3. A stupid person is a person who causes losses to another person or to a group of persons while himself deriving no gain and even possibly incurring losses. Cipolla called this one the Golden Law of stupidity. A stupid person, according to the economist, is one who causes problems for others without any clear benefit to himself. I'm just going to come right out and say it: anyone who trusts horse dewormer over a proven (yes, proven) preventative vaccine is, beyond any shadow of a doubt, in this group. But to me, the important thing to know is the spectrum this economics professor proposed to map humanity: This law also introduces three other phenotypes that Cipolla says co-exist alongside stupidity. First there is the intelligent person, whose actions benefit both himself and others. Then there is the bandit, who benefits himself at others’ expense. And lastly there is the helpless person, whose actions enrich others at his own expense. You'll have to click on the link to see the graphic. Law 4: Non-stupid people always underestimate the damaging power of stupid individuals. In particular non-stupid people constantly forget that at all times and places and under any circumstances to deal and/or associate with stupid people always turns out to be a costly mistake. We underestimate the stupid, and we do so at our own peril. There's a quote attributed to Robert A. Heinlein that's relevant and I've kept it in mind for lo these many years: "Never underestimate the power of human stupidity." Law 5: A stupid person is the most dangerous type of person. If "stupid" is defined as above, then yeah, I can believe that. Declining societies have the same percentage of stupid people as successful ones. But they also have high percentages of helpless people and, Cipolla writes, “an alarming proliferation of the bandits with overtones of stupidity.” “Such change in the composition of the non-stupid population inevitably strengthens the destructive power of the [stupid] fraction and makes decline a certainty,” Cipolla concludes. “And the country goes to Hell.” So, based on this, the only way to keep the stupid in check is to actively increase one's position on the article's graph, up and to the right. Can it be done? I don't know. I'm too lazy to try, which I guess puts me in the "stupid" quadrant. I think it takes an economics professor to think of things in this way. I have to wonder what his thoughts on Rational Market Theory   were, considering the percentage of people who act irrationally. It was in vogue around the time he wrote the above. But I can't be arsed to look it up.
September 8, 2021 at 12:02am
September 8, 2021 at 12:02am
#1017010
September 7, 2021 at 12:03am
September 7, 2021 at 12:03am
#1016946
September 6, 2021 at 12:02am
September 6, 2021 at 12:02am
#1016860
September 5, 2021 at 12:04am
September 5, 2021 at 12:04am
#1016794
 Real News In a world where headlines are clickbait and ledes are buried deeper than COVID-19 mass casualties, it can be refreshing to come across a story, however bizarre, that actually qualifies as news. Suspect arrested after allegedly biting Vancouver Police dog   That's right. You read it here, folks: an actual Man Bites Dog   story! A 32-year-old man is facing charges after allegedly biting a Vancouver Police dog on Thursday morning. Now see? That's how you write a lede. It covers the basics: who, what, when, where, and why, with the "how" notably absent but able to be inferred ("with his teeth.") Also, the rest of the article covers that bit. “The suspect allegedly resisted arrest and bit Police Service Dog Mando, which was assisting in the arrest,” VPD said. Mando? Mando? Does he have a companion named Grogu? Perhaps with an insatiable hunger for frog eggs? The suspect was bitten by the police dog during the arrest and treated at hospital. Police Service Dog Mando has minor injuries, VPD said. Oh, you were doing so well until BOOM passive voice. Still, "minor injuries" is encouraging. Police said they are recommending “multiple charges” against the suspect. Might want to test him for rabies while you're at it. Hopefully, after this sad tail, the dog will recover fully and get a new leash on life. He can harness the paw-er of this experience for future encounters. As for the suspect, well... looks like he's boned.
September 4, 2021 at 12:01am
September 4, 2021 at 12:01am
#1016728
September 3, 2021 at 12:02am
September 3, 2021 at 12:02am
#1016645
September 2, 2021 at 12:02am
September 2, 2021 at 12:02am
#1016564
September 1, 2021 at 12:02am
September 1, 2021 at 12:02am
#1016461
August 31, 2021 at 12:04am
August 31, 2021 at 12:04am
#1016405
August 30, 2021 at 12:02am
August 30, 2021 at 12:02am
#1016354
August 29, 2021 at 12:02am
August 29, 2021 at 12:02am
#1016296