Complex Numbers (Book)

Blog Calendar

◄ June ►
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:

Wordsmitty ✍️

about an hour ago
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

1 Like

🌖 HuntersMoon

about 5 hours ago
In response to "Gray Matters"

I've always believed "better gray than gone away..."

1 Like

tj-Merry Mischief Maker

about 24 hours ago
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

tj-Merry Mischief Maker

Dec 23, 2024 at 4:55pm
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

Dec 23, 2024 at 12:56pm
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

Dec 20, 2024 at 6:06pm
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

June 14, 2024 at 9:44am

#1072638

And Time Again

There are lots of subjects we don't fully understand. This is a good thing and it makes life interesting.

We Still Don’t Fully Understand Time

Interesting, but also amusing, because here's an article about time from Time. Or is that from Time to time?

In our everyday lives, time is a precious commodity. We can gain or lose it. We can save, spend or waste it. If our crimes are revealed, we risk having to do time.

Notice the phrasing in that last sentence: "If our crimes are revealed..." Not "If you do crime and get caught," no, straight to "You know what you did even if the authorities don't, yet."

To scientists, time is something we can measure. Clocks have, over the centuries, been the high tech artifacts of their era—the water clock, the pendulum clock, Harrison’s chronometer, and so forth up to the incredible precision of atomic clocks—marvels of modern technology, albeit without the evident aesthetic quality of more traditional timepieces.

You know, it occurred to me the other day that the first computers were clocks. When you think about it, they have the ability to compute the current time based on an input value (the time you set it at). I got this insight when I saw an astrolabe—a device that computes the movement of sun, moon, and planets—described as an early computer. But what's a clock besides a simpler astrolabe, one that only focuses on the sun with respect to the earth?

I guess it's a categorization thing, like with hot dogs or Pluto.

The article spends a few paragraphs going into the history of our conception of time, delving into philosophical, religious, and scientific matters, but not telling me anything new.

Then:

The traditional view, even among those who accept Darwinian evolution, is that we humans are necessarily the culmination of the evolutionary tree.

Yeah, that may be the "traditional" view, but there's no evidence for this egocentric idea. Not that there's any compelling evidence against it, besides pedantically wondering what "culmination" means, when we could be wiped out while other species (cockroaches being the most popular example) continue to exist.

But even in the immensely concertinered timescape that modern cosmology reveals, extending billions of years into the future as well as the past, this century is special. It’s the first in the 45 million centuries of Earth’s history when one species, ours, can determine the entire planet’s fate. We’ve entered what’s sometimes termed the ‘anthropocene.’

Actual scientists have denied the idea of the anthropocene,

but the name's stuck in public consciousness now, and good luck digging that tick out.

Perhaps our remote descendents will have a much-enhanced lifespan; they might even become near-immortal.

Or perhaps they'll lose capacity for cognitive function. We're already seeing that happen. Assuming, of course, that the collective "we" will have descendants. That "traditional view" up there assumes that evolution is about gaining functions such as what we call intelligence, but really, it's about genetic survival (that's simplistic, of course, but close enough for my argument). When "intelligence" stops being a survival trait, evolution starts to select against it.

So this is more of a philosophical essay on the state of humanity than anything meaningful about time. That's okay, though. I'd comment on more of it, but it seems I'm out of time.

3 Like • Comment • View 2 comments

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