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Saturday, Nov. 30, 2024

4:30pm EST

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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:

tj-Merry Mischief Maker

about 24 hours ago
In response to "Shroom with a View"

The use of psychedelics leads to a higher{i/} life form? Sorry, I couldn't resist the pun.

Elisa: Snowman Stik

a day ago
In response to "Shroom with a View"

Originally proposed by ethnobotanist Terence McKenna in his 1992 book Food of the Gods, this provocative idea has recently resurged in popular discourse, thanks in large part to its discussion on Joe Rogan’s widely followed podcast.

Well, now I'm even less inclined to believe it.

Side note: I think we need to more publicly discuss the unintended consequences of Joe Rogan's podcast. It's played a huge (and not always ideal) role in the development of men. I worry that ignoring Rogan's impacts has made them worse.

1 Like

tj-Merry Mischief Maker

Nov 28, 2024 at 12:40pm
In response to "Trolley Pop"

Doing this type of test using mice instead of people is not going to yield the same results. I base this statement on my experience shopping for a few things yesterday and would have loved to be able to "throw the switch" on many of the rude, crude, and socially unacceptable people in the store. But to harm those cute, furry, and innocent mice? I think not.

Sure, mice can be a problem, and we do have to deal with them from time to time, but even in this scenario, I use a live trap and transport the little critters safely to the residence of the above mentioned morons... (in truth I transport them to abandoned buildings)

3 Like

Wordsmitty ✍️

Nov 28, 2024 at 12:27pm
In response to "Trolley Pop"

Are these the same mice that were turned white in that other experiment a few entries back? I would think they may have suffered enough. Or maybe waiting to see if they get shocked would be how they were stressed to turn white. A two-for-one experiment! Would it make a difference if the mice were white or gray? Are there mice in the trolley? , , ,

3 Like

Kåre เลียม Enga

Nov 28, 2024 at 11:05am
In response to "Trolley Pop"

What comes to mind? Any kōan. They aren't necessarily "solvable" either.

2 Like

tj-Merry Mischief Maker

Nov 27, 2024 at 6:28pm
In response to "Inevitable Two"

What about death by Taco Bell?

49-year-old Diane Durre was killed by a falling Taco Bell sign that was knocked over by strong winds. He husband was also injured but survived.

1 Like

tj-Merry Mischief Maker

Nov 27, 2024 at 6:04pm
In response to "Son of an Itch"

The worst itch I've ever suffered was in my left leg between the ankle and the knee. I was bitten by a non-poisonous snake about mid-calf and ended up with a nasty infection in the panniculus tissue under the skin. Yes, the itching was under the skin so there was no relief until after the infection cleared up with medication.

1 Like

Cubby

Nov 27, 2024 at 9:32am
In response to "Son of an Itch"

My worst experience with itching was when I had almost 60 bed bug bites on my arms and face after staying in a Best Western in Gila Bend, AZ last January. Two weeks of itching! Even with Benadryl, I woke up in the middle of the night in our camper itching like crazy. The bites looked very similar to chicken pox. What a way to start a vacation.

2 Like

🐕GeminiGem🎁

Nov 26, 2024 at 1:58pm
In response to "A Touch of Gray"

I know that hair loss is believed to be linked to stress (no idea if there are scientific studies about this, though), so why not graying of the hair?

NaNoNette

Nov 26, 2024 at 1:12pm
In response to "Inevitable Two"

Poe was probably experiencing withdrawal symptoms from some drugs and lots of alcohol.

2 Like

November 30, 2024 at 8:50am

#1080660

Tongue-Tied

Something interesting I found at BBC Future:

The weird way language affects our sense of time and space

It's also a book ad:

In our new book, we explore the many internal and external factors that influence and manipulate the way we think – from genetics to digital technology and advertising. And it appears that language can have a fascinating effect on the way we think about time and space.

And I'll do my usual pointing out that this isn't settled science.

But a growing number of experts believe language can influence how we think just as our thoughts and culture can shape how language develops.

Honestly, I'd kind of figured that was the case. I think in words, myself. Usually English ones. But I've asked other people, and some say they don't.

I imagine kids these days think in emoji.

For example, we know that people remember things they pay more attention to. And different languages force us to pay attention to an array of different things, be it gender, movement or colour.

I'm still just focused on getting French pronunciation close to correct.

Linguists, neuroscientists, psychologists and others have spent decades trying to uncover the ways in which language influences our thoughts, often focusing on abstract concepts such as space and time which are open to interpretation.

I hope they took into account my anecdotal evidence about not everyone thinking in words.

There follows a good bit of examples of the science people did to investigate this. I could probably nitpick some of the methods, but I don't feel like it today.

This is the part that most interested me, as someone trying to be bilingual:

Things start to get really strange, however, when looking at what happens in the minds of people who speak more than one language fluently. "With bilinguals, you are literally looking at two different languages in the same mind," explains Panos Athanasopoulos, a linguist at Lancaster University in the UK. "This means that you can establish a causal role of language on cognition, if you find that the same individual changes their behaviour when the language context changes."

While it is true that I complained about how bad this year's Beaujolais Nouveau was (it was really bad), and joked about how that means I'm turning French, that doesn't mean I'm turning French. When you learn a new language at my advanced age, things go a lot slower.

We aren't necessarily prisoners to thinking a certain way, though. Intriguingly, Casasanto has shown that you can quickly reverse people's mental time representation by training them to read mirror-reversed text, which goes in the opposite direction to what they're used to.

This refers to a part I didn't quote, which stated that people generally conceive of time moving in the same direction as their language writing. In contrast to language learning, I taught myself how to read mirror-reversed text (and upside-down, and upside-down mirror-reversed) when I was a kid, and I still conceive of time's arrow as moving left to right.

Maybe that's a case of just because I can do it doesn't mean I've internalized the connection to conception of time.

There's a whole lot more to the article, but I'll skip to near the end:

As this body of research grows, it is becoming increasingly clear that language is influencing how we think about the world around us and our passage through it.

Again, though, I wouldn't take it as settled science but more of a working hypothesis.

And while being multilingual won't necessarily make you a genius, we all can gain a fresh perspective and a more flexible understanding of the world by learning a new language.

A reasonable assertion, I think. One reason to actually learn a language rather than relying entirely on smartphone apps for translation.

1 Like • Comment

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