Complex Numbers (Book)

Blog Calendar

◄ May ► 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:

Write_Mikey_Write!

about 13 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 15 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.

May 16, 2020 at 12:30am

#983678

Who Ya Gonna Call?

I ain't 'fraid'a no ghosts.

PROMPT May 16th

Do you believe in ghosts or other supernatural entities? Have you ever experienced something you could not explain?

No. And yes.

Just to get this out of the way first: the word "supernatural" is a semantically null term. If something exists, it's natural. If it exists and it's human-made, it's still natural because we are natural. If something exists and it's outside our experience, it still exists, and is therefore natural.

But, okay, I can accept that we have the word "supernatural" and it generally refers to concepts outside the realm of everyday experience. Or science. Or however you want to define it; I'm trying to, but it's slippery. "Attributed to some force beyond scientific understanding or the laws of nature" according to one dictionary definition, but I don't really like it because belief in the supernatural preceded scientific understanding and formulation of the laws of nature.

Now, I do believe in Supernatural. It's a fun show, and I'm sad that it's about to end. The concepts -- ghosts, werewolves, vampires, demons, angels -- can make for great fiction. Or not-so-great fiction. I mean, seriously, I do like the show, but objectively it's kinda silly.

An argument can be made that even conceptualizing something makes it real, in a sense, but I'll save that argument for the next time Santa Claus shows up, which, given the state of retail in the US right now, should be, oh, sometime around tomorrow.

"But Waltz, what about all the eyewitness accounts of ghosts and fairies and whatnot? Surely they can't all be hoaxes." Well, I'm not saying they're all hoaxes. Some are, of course, like the footage of Bigfoot and Nessie. But I have no doubt that people have seen things they can't explain, even things that currently defy explanation. That doesn't mean we should jump right to the "it's the spirit of a little girl that was brutally murdered in 1886 and now she seeks vengeance" or whatever.

Consider, for example, infrasound

.

But the main focus here is on the science behind hauntings. Even if you don't admit you believe in ghosts, it turns out there might be explanation for hauntings that any Scully can appreciate: infrasound. Infrasound refers to low-frequency sounds vibrating from 0.1 to 20 Hz, just below the threshold for human hearing. It's used for monitoring earthquakes, in World War I, for locating artillery. But it was engineer Vic Tandy in 1980 who discovered that infrasound could be responsible for perceived "hauntings."

I didn't listen to the attached podcast - I've never listened to a podcast and I'm not going to start now - but a simple Google search can get you more information on the link between infrasound and reported hauntings. In essence, not only does it affect emotion (causing anxiety and fear and so on), but it can also create visual apparitions.

As the above linked article points out, it's not the final word on the subject. There's plenty that hasn't been explained. Hell, that's what I love about science: always something else to try to figure out.

Now, don't get me wrong; I try to keep an open mind about such things. But, like anyone, I'm biased. It's just that in my case, I'm biased on the side of rational explanations. I just assert that the existence of ghosts and whatnot would require solid evidence, and that evidence just isn't here. We live in a time when nearly everyone carries around a high-quality camera / video recorder, and so you'd think that more "supernatural" stuff would be captured. Of course, the flip side of that is that photos and videos are more easily faked than ever.

You may note I haven't said anything about space aliens. That's because, while they're lumped in with "supernatural," if they existed, they wouldn't, by any useful definition of the word, be supernatural. I've argued before that our reports of flying saucers and strange lights in the sky are a product of our scientific, technological age; the same phenomena, 200+ years ago, would have been (and was) attributed to angels or whatever. We make shit up, but we make shit up based on what we do understand. Again, yes, I accept that people have seen stuff in the sky that they couldn't process. Hell, I have. I just didn't make the cognitive leap from "stuff I don't understand" to "we're being visited by little blue cosmonauts from Procyon IV."

Incidentally, many UFO sightings -- and I use the term literally, as in "unidentified flying object" -- can be attributed to atmospheric mirages or rare weather phenomena. And alien abduction stories track with my own experiences with sleep paralysis.

As I've said before, it's a big universe, and I'd be extremely surprised if we were the only spaceship-builders in it. But as to whether they like to barnstorm our little planet, well, I'm not convinced. And yet, we probably know more about space than we do about our own minds; there's still a lot to be discovered there. What we do know is that we humans are really, really good at making shit up -- intentionally or not.

5 Like • Comment • View 7 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.