Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ September ► 2022
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

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Tuesday, May. 28, 2024

3:58pm EDT

Members: 1,002

Guests: 1,061

Total Online: 2,063

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:

Elisa the Bunny Stik

about 2 hours ago
In response to "Long in the Tooth"

I feel I was too busy as a teen to screw around in convenience stores. On the rare occasion I wasn't at school or working, I tended to hang out by myself. If I hung out with friends, it was usually at someone's house (rarely mine).

Elisa the Bunny Stik

a day ago
In response to "Olive It And More"

Every once in a while, someone will misread the order slip and give me green peppers, which are an abomination, instead of green olives.

They truly are an abomination. If you're going to put peppers on a pizza, make sure it's anything but those little soggy cardboard slice things. Hell, even poblanos would be a major upgrade.

1 Like

Elisa the Bunny Stik

a day ago
In response to "Coming Up the Pike"

Man, people on Fandom Secrets would be aghast at how much you like Strange New Worlds. Personally, I haven't seen much of it. However, I did watch an episode at the gym once and found it enjoyable. It gave me that fascinated feeling I had when watching The Next Generation as a kid.

1 Like

Elisa the Bunny Stik

a day ago
In response to "Burgundy"

I will admit that I'm not much of a wine drinker. I've had reds and whites but tend to prefer reds. Then again, when it comes to booze, I tend to prefer things that are more intense in flavor. White wines...tend not to be that way for me.

2 Like

Elisa the Bunny Stik

a day ago
In response to "Distrust the Process"

That being said, I do think that people going out of their way to demonize ultra-processed foods are causing just as many issues as lobbyists are. These folks' actions exacerbate eating disorders and nervous thinking around food insecurity in equal measure. I wish the conversation around this set of actions was louder.

3 Like

Elycia Lee ☮

a day ago
In response to "Distrust the Process"

To me, as long food is 100% natural, then it is healthy. Pretty much like fruits, veggies and rice. I know people have thoughts about whether rice is good or not, but it is natural food so... I shall go with that.

2 Like

Kåre Enga in Montana

May 25, 2024 at 3:13pm
In response to "Plan Solo"

I'm more introverted than extroverted, but my only apprehension involves language and cultural barriers.

I'm bi- or ambi- but... always annoying. I waver between wanting to be left alone and not wanting to be alone.

I make my adjustments as necessary.

But LANGUAGE and CULTURE: true barriers that can cause problems for some and angst for me. I love strangers but find it frustrating when I can't connect.

For Belgium: make those plans soon. Today's connectivity means booking lodging in advance. In the old days it was show-up-and-ask-if-they-have-a-room. Still possible but not recommended unless cost is not an issue.

I prefer staying in hostels but rarely join in 'events'. I have gone out with fellow travelers however.

Kåre Enga in Montana

May 25, 2024 at 2:58pm
In response to "Banned Camp"

I remember when the movie "Brokeback Mountain" received "F"s from folks who basically commented that they would never NEVER watch such filth. Even those who liked or enjoyed it missed the main theme of poverty (financial, cultural, individual...). Personally, I preferred the short story to the movie. Both made a point that America didn't/doesn't want to face: choice and lack of choice.

That said, if someone were to ban my poetry I could probably live off of the notoriety.

Burning at the stake though seems a more likely outcome.

2 Like

🌕 HuntersMoon

May 25, 2024 at 11:32am
In response to "Banned Camp"

"Any book worth banning is a book worth reading." Isaac Asimov

2 Like

Aiva Raine

May 21, 2024 at 11:34pm
In response to "More Science"

Giggles. Thank you for the laugh- especially this phrase, "I always picture Doc Brown's workshop in Back to the Future. Yes, of course I know it's wrong, but I'd rather be amused than right."

1 Like

September 30, 2022 at 12:07am

#1038358

Cosmological Comedy

My main sources for scientific discussions are YouTube (I must have broken their algorithm because everything I see on the sidebar is comedy, booze, science, philosophy, music, math, or some combination thereof) and, of course, Cracked.

You can go down your own YouTube rabbit hole; today I'm linking the latter.

Cracked Goes Galaxy Brain: 5 Madcap Ideas About The Universe And Reality

Science is generally self-correcting. Theories are discarded or adjusted when new experimental data comes in, or is interpreted differently. But one thing that remains constant, apart from the speed of light, is that no matter how weird we think the Universe is... it always turns out to be weirder.

After all, we’re only here because of a giant explosion that occurred everywhere yet also nowhere, and for no reason, during a time before time. It may have happened infinite times to create an infinite multiverse. It may be happening “now,” though “now” is relative and doesn’t really mean anything worth jack.

Yeah, it's not really an explosion because there was nothing for it to explode into. If it actually happened. There's still some pushback to the Horrendous Space Kablooie theory.

5. Do We Have Another Planet? It May Be A 13.8-Billion-Year-Old Primordial Grapefruit 10 Times Heavier Than Earth

To quote Douglas Adams, "“Space [...] is big. Really big. You just won't believe how vastly hugely mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.” Well, compared to the vast distant reaches of space, even the outer reaches of our solar system might as well be a trip to the chemist (that's pharmacy for us Americans). And, as this section indicates, we don't even know how many things orbit our sun.

One thing that probably will be solved in our lifetime, cyborg or not, is among the most mouth-watering space mysteries: the existence and identity of Planet Nine. Is our solar menagerie hiding at least one more big planet? Or just another derelict Kmart? The unequivocal answer is maybe.

Your lifetime, maybe; probably not mine.

If a hidden planet exists, it’s 400-800 times farther away from the Sun than Earth. So it would trace an elongated 20,000-year orbit. Humans were still wiping themselves with their hands last time it swung around our star.

To be clear, we still do; there's just usually paper in said hand. Unless you're fancy and own a bidet.

Being so far away, scientists can’t see P9, but infer it’s there because nearby objects seem to be pulled by the gravity of something hefty.

On the one hand, that's a totally legitimate way to determine if there's another planet involved; it worked to discover Neptune, as I recall. On the other hand, discrepancies in Mercury's orbit compared to prediction led to the hypothesis that there was another planet orbiting even closer to the sun. They even named the planet: Vulcan. Plot twist: Vulcan doesn't exist; the perturbations turned out to be due to relativistic effects.

Point being, maybe there's another planet; maybe our theory of gravity needs to be tweaked again; or maybe it's Maybelline.

If they do find that planet, please lobby for it to be named Maybelline.

Let’s not entertain such dismal, unexciting possibilities. A much more excellent idea is that P9 isn’t a planet but a black hole. A primordial black hole, dating to the first second of creation. As in, the first second ever.

No.

But it's not as farfetched as you might think. After a certain radius, black holes act just like any other mass. If our sun were to be suddenly replaced by a black hole of the same mass, all the planets would continue orbiting sedately just as they do now, not get sucked directly in like pulp SF would have you believe. Which we'd notice just before we froze to death.

4. We Can Theoretically Wee Actual, Individual Aliens By Making A Solar System-Sized “Virtual Telescope”

Please don't wee aliens. They might get pissed off.

Scientists just achieved the most amazing visual feat ever: capturing an image of Sagittarius A*, the bulldog of a black hole at the center of our Milky Way.

This article came out about the same time as JWST started producing real images, and some of them are pretty amazing. Still, imaging something that far away is pretty amazing, sure.

It has the mass of 4 million Suns, packed into an infinitely tiny point.

That's a bit misleading. The dimensions of a black hole are undefined because dimension implies space, and the whole point (see what I did there) of a black hole is that it warps space so completely that the concept of "distance" or "radius" or "diameter" is meaningless. And the event horizon, whose diameter can be inferred, isn't infinitely tiny. Whatever. I'm quibbling about language written on a dick joke site that can't even edit out obvious typos in headers.

Anyway, the image is helpfully included in the article, but it hardly matters; you've seen it. It's become iconic. Even Star Trek started riffing off of it. The real point is HOW they did it, which involves turning widely-spaced Earthbound telescopes into a giant virtual telescope, which is indeed cool. Now imagine putting a bunch of space telescopes in orbit around the sun, say between Earth and Mars, and turning them into a virtual telescope. That's what they mean when they claim we could "wee" aliens. If aliens existed.

3. Sadly, No Telescope Can See An Anti-Universe With Backward Time Which Could Explain Dark Matter. But Math Can

I mean, okay. This is speculation. Math is very, very good at describing the universe (and even perhaps a multiverse), but it doesn't follow that just because math shows something, it must have a physical interpretation.

To be clear, no one yet knows exactly what dark matter is. If it's even matter. That's cool; it means there's more to discover.

2. Neutrinos Will Blow Your Ass Out Of Its Mind

In addition to the Big Bang and other energetic origins, neutrinos come from nuclear reactions in stars

Neutrinos are another thing we don't fully understand. As with anything else we don't understand, speculation runs rampant. Like in this section. Still, as long as we know it's speculation, it's interesting to read about.

1. An Infinite Universe Guarantees The Occurrence Of Things That Are So Unlikely It’s Literally Impossible To imagine, Comprehend, or Perceive

I mean, sure. Infinity itself is impossible to imagine, comprehend, or perceive. It also might not really exist, being perhaps one of those mathematical concepts that doesn't have a real-universe counterpart.

Infinity means that any non-zero event will occur.

I think they mean "any non-zero probability event."

Infinitely.

Not necessarily.

The simplest conception of infinity is "the set of all positive integers." We have notation that can render any arbitrary integer, like 2, or 42, or 10¹⁰⁰ — which is just as far away from infinity as 2 is. But each of those numbers is unique. Sure, our notation uses some combination of ten arbitrarily-assigned digits, so two numbers may seem to have something in common, like 543 and 1345, but just because you label something "infinite" doesn't mean, as is sometimes popularly reported, that there's an exact copy of you running around on some exact copy of Earth somewhere else in the universe.

And since the universe appears to be infinite, this forces us to ask if infinity exists, or is just a human failing to comprehend the true nature of the cosmos.

Or, you know, I could be wrong about that. It's not like I'm any better at comprehending the nature of the cosmos, or infinity, than any other ape.

And to be strict about it, there are different kinds of infinity.

Hope that clears everything up.

3 Like • Comment • View 1 comment

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

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/9-30-2022