%%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)       |
| It's not very often that I talk about the plain meaning of this blog's title. I generally let the various puns on it rule here. "Complex" has several meanings, as does "numbers." But today is one of those days. I know a lot of readers don't "get" math, but the video I'm linking today is more about history than it is about equations and such—though there are certainly equations used to illustrate the points. Periodically (pun intended), I go down a YouTube math/science video rabbit hole (though I have enough sense not to link a lot of them here), but I can't remember if this link was the result of one such journey, or if someone brought it to my attention. Since it's a YouTube video, I'm linking it here as usual, but also embedding the video if you can't be arsed to click through. Since it's a video, I can't do my usual quote-mining here, but to paraphrase what I feel are the important takeaways: Mathematics started out as a way to quantify the world. As such, things like negative numbers were anathema for a very long time (you can have three oranges, but you can't have negative three oranges). It was only when mathematicians let numbers be the abstractions that they actually are that math became a powerful tool for science, paradoxically allowing us to gain a much deeper understanding of reality. Such abstractions shouldn't be so difficult to understand. As writers, we work in abstractions too—we call them metaphors, and as with math, they often reflect a deeper reality than the one in front of our noses. This, by the way—the ability to think in metaphor—is, in my estimation, the thing that makes humans different from all other animals on Earth. It's why we're able to send rockets into space, some of them containing powerful space telescopes  that search deep into space and time, giving us an even greater understanding of the universe.(The link in the previous paragraph is to the BBC article talking about the first image released from the Webb telescope, just yesterday. I have some issues with the way the article describes things, but this entry isn't about that, and it's good enough to get a sense of what's going on. Also the picture is really damn awesome.) So it turns out that so-called imaginary numbers and, by extension, complex numbers, really do describe reality at its most fundamental (so far as we've been able to determine) level. A far cry from counting grains of wheat, for sure. But it all comes from the same mindspace. The video quotes Freeman Dyson (yes, the guy who conceptualized the Dyson sphere): "...nature works with complex numbers and not with real numbers." The phrase "real numbers" has a specific definition in mathematics, but the rest of us have a different conception of the meaning of "real." Using the layman's understanding of "real," well, all numbers are real, even the imaginary ones that don't seem, at first glance, to correspond to anything we can see or touch. Or, alternatively, all numbers are metaphors, describing an abstraction of what we can see or touch. Either way, math is just crazy good at describing the world we know of as "real." In many cases, such as the one in the video above, the math existed first, only to later find a use in science. It's all real. Even the stuff we don't understand. Especially the stuff we don't understand. |
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
