Complex Numbers (Book)

Blog Calendar

◄ April ► 2021
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
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:

Write_Mikey_Write!

about 3 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 4 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

April 11, 2021 at 12:01am

#1008209

Brain Trust

Today in You're Doing It Wrong, "Thinking:"

Your Brain Doesn't Work the Way You Think It Does
A conversation with neuroscientist Lisa Feldman Barrett on the counterintuitive ways your mind processes reality—and why understanding that might help you feel a little less anxious.

This is one of those articles that is basically a book promotion, but to reiterate: This is a writing site, and I'm not going to rag on anyone for promoting their book, here or elsewhere. And honestly, this one looks like it might be interesting.

People tend to feel like we’re reacting to what’s actually happening in the world. But what’s really happening is that your brain is drawing on your deep backlog of experience and memory, constructing what it believes to be your reality, cross-referencing it with incoming sense data from your heart, lungs, metabolism, immune system, as well as the surrounding world, and adjusting as needed. In other words, in a process that even Dr. Barrett admits “defies common sense,” you’re almost always acting on the predictions that your brain is making about what’s going to happen next, not reacting to experience as it unfolds.

Or as I like to put it: we think we have free will, but that's an illusion; we don't so much make choices as rationalize our choices after the fact.

“Predictions transform flashes of light into the objects you see. They turn changes in air pressure into recognizable sounds, and traces of chemicals into smells and tastes. Predictions let you read the squiggles on this page and understand them as letters and words and ideas,” Barrett writes. “They’re also the reason why it feels unsatisfying when a sentence is missing its final.”

Oh, she's smart and funny? I think I'm in love.

Anyway, my own brain is (metaphorically) running on fumes right now, so I don't have a lot more to say. The article proceeds in interview Q&A form, and both Qs and As are interesting and insightful. But one quote by Barrett stands out for me:

Your brain is making guesses about what is going to happen next, so it knows how to act next to keep you alive and well. It’s continuously drawing on your past experiences to create your present. The really cool thing about this? It's really hard for people to change their past. However, by changing your present, you are cultivating a different future. By changing what you do and say, and feel, you are seeding your brain to predict differently in the future.

This, of course, has implications for psychology and probably even philosophy. I think I suspected this on some level, because this is why I don't stop trying to learn new things. Thus:

The actions and the experiences that your brain makes today become your brain's predictions for tomorrow. So making an effort to cultivate new experiences and learn new things today is an investment in who you will be tomorrow. Some people have control over many things in their lives, and some people have less control because of their life circumstances, but everyone can control something.

So it's worth a read; the article isn't all that long. And for once, I'm actually tempted to buy the book. Or, to put it another way, I've been conditioned to accept advertisements disguised as journalism, and when said ads spark my confirmation bias, my brain wants me to buy the book so I can learn more.

7 Like • Comment • View 6 comments

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