Complex Numbers (Book)

Blog Calendar

◄ January ► 2020
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

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:

Elycia Lee ☮

about 9 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

about 22 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

a day ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

January 11, 2020 at 12:19am

#973126

Faithless

PROMPT January 11th

Do you tend to be skeptical or trusting when meeting new people? Is your first impression of someone generally accurate, or does their true character surprise you?

Depends on if they open with "Let me tell you about this wonderful business opportunity | charity | religion | diet."

There was once a subdivision project I worked on where the primary road had to cross the main gas pipeline serving my city. I designed the road, taking due care with the gas main crossing, but one problem remained: while I knew how deep the gas main should have been buried, we didn't know how deep it was actually buried, or even if it was where the drawings claimed it was. So I allowed for some leeway in the design.

Prior to construction, the contractor used a backhoe to dig - very carefully - a test pit over where the gas line should be, and behold, it was in the right place horizontally, if slightly deeper than expected vertically. I went out to inspect the site. I saw not one, but two mains, maybe 8 or 12 inches in diameter. As I was watching them take measurements, an old dude - I'm not sure what his affiliation was: city, developer, contractor, landowner, whatever - came up to the pit smoking a cigarette.

One of the most important lessons in civil engineering (and, I'd wager, other disciplines) is risk management. You not only have to take into account the probability of something happening, but the potential result of failure. For example, if you're building a dam and it has maybe a 1% chance of failure in its 100 year+ lifetime, it matters whether there's a town downstream from it or not. If there isn't, then the 1% chance of failure might be acceptable. But if there is, you maybe work to reduce that chance.

In this case, the chance of there being a gas leak in the main was very slight, though nonzero. But the potential result - if a stray spark from the cigarette touched off a natural gas flare - could be catastrophic. Moral: don't smoke around an open pit with gas pipelines at the bottom, you fucking idiot.

The point of all of this, as relates to the prompt, is that I apply the general principles of risk management to people. Most people aren't murderers. Most people aren't thieves. Most people, even if they don't care about you, won't actively do something to harm you. But the chance with someone you don't know is nonzero. You can't go through life simply avoiding everyone - well, maybe some people can, but I don't trust them worth a concrete barrier that blocks a river - so you take some risks.

Unfortunately, a lot of people generalize this to "people suck." But this ignores simple math: the vast majority of people don't have ill intentions. People don't, as a rule, suck. It's like the folks who say "there's no such thing as a bad dog; only bad owners." Well, I can say that about people, too, though "owner" is definitely the wrong word there, and is probably the wrong word for human companions to dogs.

I realize that this flies in the face of common knowledge, but common knowledge is often neither. There are whole religions based on the idea that we're fundamentally bad and have to work hard at being good. All you have to do is to look at the people who say, "people suck." Do the people who say this suck? Mostly, no. They're saying this because someone did something that didn't live up to their standards. They have standards. Therefore, they're not as bad as the person they're complaining about and generalizing from.

So I go into meeting people with the assumption that they're decent human beings. Most of the time, I'm right. Probably they're self-interested, but hear me out here: it's in most of our self-interests to get along with other human beings. It's part of our nature, along with curiosity and going "awwwww" when we see Baby Yoda on The Mandalorian.

Fortunately, I am immune.

But I digress. I knew a kid when I was a kid who went on to do 20+ years for murder. That's one I know about; I probably knew other people who did bad things. Those people are in the minority. I also knew people who became doctors, firefighters, scientists, etc. What was I going to do, not have any friends because a few of them might grow up to be convicted felons?

So yeah, we have to be careful. Trust might not come easily, but people at least deserve the benefit of the doubt. Innocent until proven guilty and all that.

As for "true character," I have some concerns about that phrase. None of us are angels (hell, angels aren't always angels), even if the worst things we've done don't quite measure down to my felonious former friend. Many people, seeing someone get angry or do something bad, assume that's their "true colors," when they might just be having a bad day. That's part of their character, sure, but it's not all of it.

My father, as I'm sure I've mentioned before, was no saint. I wasn't really abused apart from the occasional spanking for misbehavior (which, I will reiterate, wasn't considered abuse at the time), just... well, I'm not going to go into it here; I knew him better than almost anyone, and I saw all sides. But later in life, when he had Alzheimer's, a disease that seems to reveal who people "really" are, one day I went to visit him in the nursing home and it happened to be time to eat. Seeing that I had nothing to eat, he offered me some of his meager meal. Another time - or maybe it was even the same visit; I can't recall - he literally offered me the shirt off his back because I was wearing a t-shirt and he thought I looked cold. And he didn't even know who I was.

Even if you think you know someone, you don't. You have to have a little bit of - this is going to sound strange coming from an atheist - faith. But not faith in something numinous or overarching; I mean faith in humanity. Because as bad as some of us can be, they're outnumbered by people trying to do the right thing.

And because I found out yesterday that Neal Peart, objectively the greatest drummer of all time, passed away this week, today's musical selection is from Rush, and the lyrics (also by Peart) relate to this entry's theme. Thanks, Neal. You will be missed.

I don't have faith in faith
I don't believe in belief
You can call me faithless
You can call me faithless
I still cling to hope
And I believe in love
And that's faith enough for me
And that's faith enough for me

And that's faith enough for me

10 Like • Comment • View 8 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.