Complex Numbers (Book)

Blog Calendar

◄ July ► 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	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:

Write_Mikey_Write!

about 6 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 8 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.

July 31, 2021 at 12:01am

#1014780

Evolving Door

We'll end July with an article that's mostly for clarification, not for me to rag on. Now, the author has some bias, as always, but it happens to be a bias that I share -- only in her case, it's backed up by facts and education.

Evolution doesn't work the way you think it does
An evolutionary biologist explains all the things you might get into an argument over

Last month in book club we were talking about an adorable newborn baby we had just met over Zoom.

Normally, I'd Stop Reading Right There because everything about that sentence is just plain wrong. But I was able to move past the anecdote and get to the important stuff.

Someone commented that the baby looks like their father. Another person piped up with an evolutionary explanation they had heard before — newborn babies look more like their fathers so that the father will know they’re his and will help raise and protect them.

You know, assuming I were the type of person to do book club meetings over Zoom (meetings that are interrupted by people bragging that they successfully fucked), which I'm not, I wouldn't make uninformed statements about evolutionary effects, however plausible they might sound, in front of an evolutionary biologist. That's just begging for a smackdown.

Some of us started wondering how something like that would even work. We agreed that this kind of “paternal effect” was possible and moved on. Later I looked it up only to learn that this popular hypothesis had been debunked nearly ten years ago.

Just in case you were thinking that this sounds reasonable.

Here's the important part; the rest is commentary:

Any discussion of a scientific hypothesis to explain a pattern should ask first, "is the pattern real?" and second, "could anything else lead to the same pattern?" There is a fine line between “it’s possible” and “it’s probable” and the consequences of mistaking a possibility for the truth can be far-reaching.

Evolution is often treated as synonymous with natural selection, and natural selection is often boiled down to a single phrase: survival of the fittest. This oversimplification is easy to apply to everyday life — but should we? If we don’t carefully manage our assumptions and biases, we are in danger of the same sort of thinking that leads to Social Darwinism, in which Darwin's theory of natural selection is applied to justify social inequities between different groups of people. To prevent that, let’s tease apart the concepts of evolution, natural selection, and fitness.

The article goes on to do so, and I obviously won't be quoting all of it. But I felt it was important to emphasize this thesis.

Some evolution is random, but not all.

It can be important to choose one's words carefully. One of the persistent refrains from the anti-evolution crowd is something like "human beings didn't appear at random!" Thing is, no, we didn't, and neither did cockroaches or oak trees. Random mutations, as the article notes, can be detrimental, neutral, or beneficial to survival and reproduction. It's like if you keep rolling a pair of ordinary six-sided dice, but you only keep the results of 10, 11, or 12. Random shit happens, but the higher number are selected for (in that case, through human decision, so it's an imperfect analogy).

In evolutionary biology, the word "fitness" is the capacity of an organism to survive and reproduce in a given environment.

Another thing that some people misunderstand: we're not "more evolved" than mice, for example. Mice are just as suited for their natural environment (which is not mazes and laboratories) as we are for ours (which might include mazes and laboratories).

Also, evolution doesn't have a "goal." It's a result of mutations and environmental factors, and has no way of looking ahead and going, "There's going to be climate change soon, so we need to adapt to that eventuality."

In social species like humans, this contribution can be indirect — for example, helping to raise your sibling's kids increases your own fitness.

This is another important point to note. People (ironically some of the same people who don't "believe" in evolution) have used the idea that certain people don't reproduce to argue that, for example, being gay is "unnatural." That is arrant nonsense.

Armchair evolutionary psychologists love to reinforce gender stereotypes, touting that men are built for fighting and hunting and not caregiving, or women are less promiscuous and more inclined to prefer monogamy than men.

And I've been railing against that kind of bullshit for years.

Confirmation bias kicks in: people who want these statements to be true will believe them to be true without looking for good evidence. And of course, this danger goes beyond gender stereotypes to racial and ethnic stereotypes.

You know what's worse, in my estimation, than someone going "it's this way because God made it this way?" Its misusing science to marginalize individuals or entire groups.

Moving past evolutionary biology background facts, the author finishes with opinion (one based on said facts), but like I said, it's one that I share:

The existence of natural selection in nature does not justify its application to social policy. The synergy of intelligence, compassion, and social structure in humans has created a unique opportunity to prioritize equity and even the fitness playing field within our species. Some of our greatest achievements as a species have increased access to resources and raised each other’s capacity to survive and reproduce. These innovations are cultural adaptations rather than genetic adaptations — they are passed down through culture rather than DNA.

Some people have internalized the idea that competition is the driving force in evolution. It's certainly a factor. But among humans, cooperation, not competition, is the defining attribute.

4 Like • Comment • View 4 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.