Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ July ►
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	31
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Wednesday, Jul. 31, 2024

4:39pm EDT

Members: 1,006

Guests: 1,422

Total Online: 2,428

Complex Numbers

by Robert Waltz

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.

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:

Averren

about 3 hours ago
In response to "Forgotten Food"

Cultural appropriation? Of foods? Hogwash.

Elisa: Middle Aged Stik

about 4 hours ago
In response to "Forgotten Food"

The issue of people appropriating Black and Indigenous foodways is one of the few areas where I tend to have the most conflicts with the pro-GMO crowd. Some members of that cohort feel that there is plenty of experimentation/crop development to be gleaned from Indigenous heirloom crops. While I think there's likely truth to that, I worry that they are not considering the agency of Indigenous peoples and perhaps working with them to work out an agreement of some sorts. There are fewer crop-related issues when it comes to Black foodways (for now), but the pro-GMO crowd sometimes comes across as perpetuating racist stereotypes about scientific knowledge in the Black community, which in turn has created an opening for the pro-organic crowd (something I'm very unhappy about since it's setting unrealistic expectations from a personal finance point of view).

1 Like

Aiva Raine

a day ago
In response to "The Habits of Nones"

I'm not sure their consensus that higher income equates to a greater disbelief in a higher power is correct. I suspect that having a greater income insulates you from many things- not just the need to believe in a god or gods. You are probably correct in that money does allow more freedom from things people fear- and religion is all about fear.

But I know plenty of people from all income brackets and it seems more and more are slowly trending towards an REM song.

Regardless of the breakdown/income levels- whether the 30% mentioned in the article is atheist, agnostic, couldn't be arsed to care, or used to go to church, but now don't- I'm glad it's that high now. It means things will start to change soon since we have a large enough group of people to effect social change and said group doesn't make decisions based out of fear of imaginary beings torturing them for infinity.

2 Like

Elisa: Middle Aged Stik

a day ago
In response to "The Habits of Nones"

"Unfortunately, by strict application of that definition, monotheists would also be covered, as they do not believe in "gods" but in one "God."

So you see where some of this confusion might be coming from?"

I think that's not much strict as pedantic, myself, partly because at least in writing the lowercase "gods" is clearly being used as an all encompassing term for higher power figures across all belief systems. Would deities have been clearer? Maybe, but it's a word that not everyone involved in such a discussion might recognize. Sometimes the tradeoff in diction creates loopholes like this, but those loopholes may end up being a nonfiction in the long run.

1 Like

🌕 HuntersMoon

a day ago
In response to "The Habits of Nones"

I'm a dyslexic believer... I believe in DOG!

2 Like

Brandiwyn🎶

a day ago
In response to "Unbelievable?"

Re #3 - As a PWP ("Person With Parkinson's"), I can say that no amount of thinking hard about a muscle will help you control that muscle if you don't have adequate dopamine to send that message through your nervous system.

1 Like

Brandiwyn🎶

a day ago
In response to "Unpredictable"

"But I do wonder how one would design a random point generator where every point on the surface of a sphere is equally likely." This sounds like a differential equations problem, but hell if I remember anything from that class.

1 Like

Elisa: Middle Aged Stik

Jul 28, 2024 at 11:18am
In response to "Revisited: "The Truth is Out There""

Sometimes, I make an effort to avoid reusing a title, but much of the time, I can't be arsed.

I may "repeat" titles for multiparters, but somehow I've been able to avoid reusing titles over, um, over 3400 entries.

I still have mixed feelings about PZ Myers. He still bothers me less than the turd nugget who spawned my whole Atheist vs. Atheist series, though.

1 Like

tj ~ HiLo Silver - Away!

Jul 27, 2024 at 3:44pm
In response to "Unbelievable?"

Muscles Grow More When You Concentrate on the Mind-Muscle Connection, I wonder if this also applies to balls?

2 Like

Adherennium Dr of Phoolishness

Jul 27, 2024 at 2:21pm
In response to "Still Planning"

Much underrated in searches is the useful - sign. 'Paris -Olympics' might help.

3 Like

July 11, 2024 at 11:41am

#1073824

We'll Always Have Paris

An entry for "Journalistic Intentions"

[18+] that is somewhat relevant to my current situation...

Paris 1924

Even the math-challenged might recognize that 1924 was exactly 100 years ago; and, given the hype surrounding the Olympics, to which even I, who avoids all sports-related news like I avoid the not-so-great outdoors, was subjected, by now you probably know that this year's Summer Olympics will be hosted by Paris. Again.

If nothing else, I'm pretty sure I've mentioned it here a few times in the context of "I want to visit France, but absolutely not during the Olympics."

Well, I'll provide a travel plan update on Saturday, hopefully, but right now we're looking at early autumn—comfortably after the crowd nonsense.

Meanwhile, though, the hype is in Seine.

(Again, no, I will not get tired of making that pun.)

Specifically, there's been a good bit of buzz surrounding the suitability, or lack thereof, of the River Seine for hosting the swimming events.

Paris is a big, old city, a statement that somehow sounds better in French: Paris est une grande vieille ville. Thus, Paris is full of shit (that probably sounds better in French, too).

This is not to single them out; all big, old cities are full of shit. That's not the cities' fault. Cities are full of people, pretty much by definition, and people are remarkably good at producing shit.

The removal of waste products (as well as the distribution of water) has a long history. Some credit the Romans for having the civil engineering acumen to create aqueducts and sewers. They even dug a massive tunnel under the city for people to shit into; this was called the Cloaca Maxima, and, reportedly, it even had its own goddess, Cloacina. I don't know if they were really the first; much of the history we learn here is Eurocentric. Doesn't much matter for my point here. Before then, and even later in smaller cities and towns, the waste would just run off down the street and hopefully get washed out with the next rain.

But even the Cloaca Maxima had to discharge somewhere; goddess or not, it wasn't magically transported to some faraway Land of Shit (Secaucus, perhaps). In that case, it flowed into the Tiber and thence out to sea.

Other cities followed suit, hiding waste flows underground and directing it into the river. For Paris, that was the Seine.

People eventually figured out that this wasn't a great practice, and designed sewer systems to be separate from storm drainage, but retrofitting older cities like that is a civil engineer's nightmare (and job security).

On top of that, the Industrial Revolution came along and started discharging stuff even worse than shit into the rivers.

All of this was an issue (pun absolutely intended) in 1924. One source,

though it's a British one, says swimming has been banned in the river from 1923, which you might recognize as the year before those Olympic games.

From what I can find, the swimming events that year were held at an indoor pool, Piscine des Tourelles,

which apparently still exists (albeit with a name change).

But what's really interesting is that that France and/or Paris (I'm a bit unclear on who's responsible) has been making Herculean efforts to clean up the Seine. That's a good thing. Or at least, from an outsider's perspective, it's a good thing. But according to that Guardian article I linked above, "The €1.4bn (£1.2bn) state-backed plan has entailed several years of work on wastewater management, treatment plants, filtering stations and storm basins to lower the river’s bacterial contamination from faecal waste."

Converting euros and/or pounds to US dollars or whatever your pitiful local currency is, I'll leave up to you. Call it a billion and a half bucks; close enough.

On the plus side, like I said: job security for civil engineers.

French persons will protest anything, though, including massive expenditures for river cleanup, especially when said expenditures aren't necessarily having the advertised effect.

For whatever reasons (some humans are simply inexplicable), some Parisians have been protesting by shitting directly into the Seine, thus bypassing any attempts to redirect human waste into treatment plants, or whatever it is they've decided to build. Last I heard, the Mayor of Paris

volunteered to go for a swim in the river herself to "prove" that it's clean. This resulted in the protesters producing a map of exactly where to shit upstream and at what time so that it would all hit her at the same time.

If she dies from e-coli, I wonder if anyone will get arrested for merde-er.

(Why yes, this entire entry has been the buildup to that multilingual pun, and I'm exceedingly proud of myself for it.)

7 Like • Comment

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

Printed from https://shop.writing.com/main/profile/blog/cathartes02/day/7-11-2024