Complex Numbers (Book)

Blog Calendar

◄ February ► 2023
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
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Writer_Mike

about 11 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

1 Like

QPdoll

a day ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

a day ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

Sep 21, 2024 at 7:34am
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:46am
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

February 11, 2023 at 12:01am

#1044590

Carp-al Tunnel

Time for another entry in "Journalistic Intentions"

[18+].

This one, selected at random as usual, features koi: Feeding Frenzy

.

Ever notice that koi look like kaiju goldfish? There's a good reason for that, apart from most fish having a similar body plan adapted to swimming: they're both carp.

Apparently, though, they come from different subspecies. While goldfish were bred in China over a thousand years ago,

selective breeding of koi is a more recent Japanese development. For the benefit of my fellow Americans with a limited sense of historical time, by "recent," I mean about 200 years ago.

And goldfish aren't really gold. By which I mean, no, of course they're not made of the chemical element Au, but their coloration always struck me as being more orange than yellow, though it can vary. Not everyone calls them goldfish, either; in French, the name is poisson rouge, which it doesn't take three and a half years of French lessons to know means "red fish."

They're not red, either, but different cultures have different conceptions of color.

No well-known metals are red or orange, so "goldfish" it is.

Koi obviously aren't limited to the orange color, but the point here is that none of these fish are the product of natural selection, unless you take my philosophical stance that we're part of nature, and so anything we accomplish, from air pollution to plastic to miniaturized orange carp, is also natural. "Artificial selection" or "selective breeding" are perfectly good terms for the process, though.

This strikes me as similar to dog or cat coloration. I don't mean different dog breeds, but, like, how a collie can be sable and white or black, sable and white. Or the different patterns of spots on dalmatians. While some koi resemble calico cats in coloration, the calico trait apparently doesn't breed true in cats, being instead a genetic thing associated with the feline X chromosome.

I have heard, but can't confirm, that before we nearly extincted tigers, some of them could also display the calico trait. Which I'd pay to see. As tigers are largely Asian in range, well, that brings us back to the origins of goldfish and koi.

All carp, incidentally, are food. I mean, everything is edible once, but carp has been a staple in many cultures, despite difficulties in its preparation (it's bony as fuck). In Eastern Europe, it can become gefilte fish, which, well, some of my people consider that to be food, whereas I do not.

As pretty as they are in koi ponds, the Asian carp is considered an invasive species in the US. I wrote about an attempt to contain them on the Mississippi River in a blog entry a while back: "Dam It"

. In that entry, I said:

That lock was closed a few years ago, but the structure remains. The reason for the closure was to stop the spread of Asian carp, an invasive species, upriver. So when I was touring the lock, looking into the waters upriver, what do you think I saw? Go ahead, guess.

That's right. An Asian carp.

On the plus side, I guess I caught my first Pokemon.

3 Like • Comment • View 2 comments

© Copyright 2024 Waltz en France (UN: cathartes02 at Writing.Com). All rights reserved.
Waltz en France has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.