%%USERNAME%%    %%ACCWORDS%% %%ONOFF%% |
 |    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. ![Merit Badge in Quill Award
[Click For More Info]
Congratulations on winning Best Blog in the 2021 edition of [Link To Item #quills] !](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quill_Award-1375927_6.gif) ![Merit Badge in Quill Award 2
[Click For More Info]
2022 Quill Award - Best Blog - [Link To Item #1196512] . Congratulations!!!](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quill_Award_2-1375927_6.gif) ![Merit Badge in 30DBC Winner
[Click For More Info]
Congratulations on winning the Jan. 2019 [Link To Item #30dbc] !!](https://images.Writing.Com/imgs/writing.com/writers/badges/group-30DBC_Winner-2064535_14.gif) ![Merit Badge in Blogging
[Click For More Info]
Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif) ![Merit Badge in Highly Recommended
[Click For More Info]
I highly recommend your blog.](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-Highly_Recommended.gif) ![Merit Badge in Opinion
[Click For More Info]
For diving into the prompts for Journalistic Intentions- thanks for joining the fun!](https://images.Writing.Com/imgs/writing.com/writers/badges/genre-Opinion-1150.gif) ![Merit Badge in High Five
[Click For More Info]
For your inventive entries in [Link To Item #2213121] ! Thanks for the great read!](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-High_Five.gif) ![Merit Badge in Enlightening
[Click For More Info]
For winning 3rd Place in [Link To Item #2213121] . Congratulations!](https://images.Writing.Com/imgs/writing.com/writers/badges/general-Enlightening.gif) ![Merit Badge in Quarks Bar
[Click For More Info]
For your awesome Klingon Bloodwine recipe from [Link to Book Entry #1016079] that deserves to be on the topmost shelf at Quark's.](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quarks_Bar-2046190_12.gif)       |
| This BBC article (whose headline resembles a Cracked headline) is a few years old now, but all that means is they might be missing a few recent ones. In recent history, a few individuals have made decisions that could, in theory, have unleashed killer aliens or set Earth's atmosphere on fire. What can they tell us about attitudes to the existential risks we face today? Already, I have a bad feeling about this. Sounds like an Agenda, which I don't expect from the BBC. In the late 1960s, Nasa faced a decision that could have shaped the fate of our species. Following the Apollo 11 Moon landings, the three astronauts were waiting to be picked up inside their capsule floating in the Pacific Ocean – and they were hot and uncomfortable. Nasa officials decided to make things more pleasant for their three national heroes. The downside? There was a small possibility of unleashing deadly alien microbes on Earth. No. No, there wasn't. They thought there might be such a possibility, so I understand the caution, but in hindsight, there was never any danger from that. A couple of decades beforehand, a group of scientists and military officials stood at a similar turning point. As they waited to watch the first atomic weapon test, they were aware of a potentially catastrophic outcome. There was a chance that their experiments might accidentally ignite the atmosphere and destroy all life on the planet. Again: no, there wasn't. They thought there might be such a possibility, and they went on with the tests anyway, which says more about humans than I care to admit. This sort of writing demonstrates some sort of fallacy that, well, I don't know what it's called, and it's hard to back-search these things. The people in those cases were acting on imperfect knowledge. I mean, we all are, all the time, but not usually with imaginary stakes so high. Let me maybe give you an example. You're walking through the woods one day, and you come across a pedestal with a single, big, red button on it. There's no writing, no pictograms, nothing to indicate what (if anything) pressing the button might do. From cartoons, you know that pressing the Big Red Button is generally a Bad Idea, but those are cartoons, not reality. You're human, and you're faced with a mysterious button in a strange location to find a button. The urge to push it is real, palpable. How can you, curious ape, just... walk past it? You can't. Billions of years of evolution can't be overcome by the moral lessons in cartoons, not easily. Maybe it opens a secret cache with 10 million dollars in nonsequential, unmarked bills. Maybe a genie would come out to grant wishes, and you could wish for more than $10M. Okay, that's unlikely. Maybe nothing will happen. That seems most likely. Maybe a piano will drop onto your head when you press it, killing you. Or maybe it connects to the gigantic planet-exploding device hidden deep in the core. Wow, that's really unlikely. What you're doing, whether you realize it or not, is risk assessment. Each possible event has a probability. Each possible event also has a desirability. Assigning probabilities is tough, and it's even tougher without Bayes' Theorem to help you assess the probability through the lens of prior knowledge. It's also very difficult if you have no way of knowing what every possible outcome is. But the point is, if you can do that, even roughly, and multiply the probability by the desirability, you can more easily rank your choices. Finding a stash of money? Low probability but desirable. Blowing up the planet? Really low probability, but undesirable. In the end, billions of years of evolution win out, and you press the button. Only through hindsight can you really know if you made the right choice or not. Getting back to the examples from the article, yes, of course, I'd heard about them before. Take the astronauts thing. High probability: no deadly space microbes. Result: no disaster. Low probability: deadly microbes. Result: Astronauts die, Earth saved. Or, Result: Everyone dies. That last one would be Bad, so I don't blame them for hedging with the "deadly microbes" scenario. It's kind of like the Trolley Problem, only your action shifts the trolley onto a random track where a random number of people are tied. I don't know if I'm explaining all this very well, but my main point is, the article does a really bad job distinguishing "what we thought the probability was at the time" and "what the probability actually was, in hindsight." The remainder of the article does a much better job explaining risk and our reaction to it, but the way it's described at the beginning stuck in my craw, so I could no more resist posting about it than you could resist pushing that Big Red Button. |
View Portfolio
Visit Notebook
Send Gift Points
Awards
Badges
Send Email
Community Newsfeed
General Discussion
Sponsored Items
Book of Trinkets
Static Items
Books
Groups
Interactive Stories
Audio
Campfire Creatives
Community Notes
Crossword Puzzles
Documents
Folders
Images
In & Outs
Madlibs
Photo Albums
Polls
Product Reviews
Quizzes
Survey Forms
Web Pages
Word Searches
