Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ March ►
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

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Monday, Mar. 3, 2025

5:41am EST

Members: 621

Guests: 2,852

Total Online: 3,473

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:

Annette

about 15 hours ago
In response to "Revisited: "Real Men of Genius""

My second son was born at almost the exact same time as one of my uncles died. When second son was a baby, we looked out for signs whether there was some reincarnation going on.

If there was, then he is a great example of nurture versus nature. Where my uncle was creative, sensitive, and mentally destroyed by the time he was a teen, my son's creative side is thriving, he has turned his sensitive nature into a passion for anthropology, and he knows he is loved unconditionally.

Maybe reincarnation is simply one generation deciding to put a stopper on past generations' bad habits.

1 Like

🌖 HuntersMoon

about 17 hours ago
In response to "Revisited: "Real Men of Genius""

Elisa, Stik of Clubs - It's what makes you unique and so darn loveable!

The same can be said for Robert Waltz if "irascible" is considered weird.

1 Like

Elisa, Stik of Clubs

about 19 hours ago
In response to "Revisited: "Real Men of Genius""

I'm pretty sure some of your beliefs, habits, or activities, and mine, would get pegged as weirdness if we were famous.

I am not famous, but plenty of my habits and activities are pegged as weird, anyway. Thanks, autism!

2 Like

Amethyst Angel 🍀

a day ago
In response to "Opti-Miss"

I struggle with feelings of nihilism, tbh. It's very easy for me to become numb and paralyzed, so I have the desire to cling to optimistic worldviews even though my dualistic tendencies tell me there's no reason to believe in them... Sigh. This is a depressing subject.

1 Like

BIG BAD WOLF is Merry

a day ago
In response to "Opti-Miss"

One might wonder.

Robert Waltz

a day ago
In response to "Opti-Miss"

Elisa, Stik of Clubs

- my comment about etymology was just me kicking myself for never seeing the linguistic connection between optimal and optimist. Seems obvious in hindsight. I've railed many times against arguments from the dictionary, and noted that dictionaries are descriptive, not prescriptive.

And I agree; I was too binary in the optimism/pessimism divide. As with almost everything else, there is middle ground.

tj wanderlust-words-in-motion

a day ago
In response to "Opti-Miss"

difference between an optimist and a pessimist:

1 Like

Elisa, Stik of Clubs

a day ago
In response to "Opti-Miss"

I have thoughts. Let's get going in breaking them down.

Optimism is, after all, by its nature delusional; ‘realism’ or outright pessimism might seem more justifiable given the troubles of the present and the uncertainties of the future.

"Seem?" No. It absolutely is.

That's a pretty bold claim being made there. In my opinion, bold claims require evidence to back them up. It might make sense to those of us with the right combo of priors (as mentioned in a previous entry) to reach this conclusion about the nature of optimism. For those who do not have those priors, we gotta consider their perspective when backing up claims like this.

or someone with such strong opinions about optimism, and such a keen interest in etymology...Leibniz’s view, put forward in his book Theodicy (1710), did not win instant acclaim.

Etymology can be fun, and knowing the origins/definitions of words can certainly help guide arguments. At what point though, do we (including Leibniz) fall into the trap of the dictionary definition fallacy?

The problem is, lots of people seem to accept it as scientific fact—which it is not.

This is news to me. I've always seen it more as a fun creative exercise among those I've seen discuss it.

In other words: ask yourself, "Can God be surprised?" An all-knowing entity couldn't possibly be surprised, any more than it could create a rock so heavy even that entity couldn't lift it.

I think the difference can be split here. I have heard that there are two ways a story can go for a reader/viewer: that it's a complete surprise how the story ends or the story's ending is predictable but how that ending is reached is surprising. I feel like god could not be surprised by the end result but could be surprised by the methods used to achieve that result.

I think things can change for the better, but, absent well-meaning and well-thought-out human intervention, probably will not.

Here's probably where I have the biggest bone to pick. How often are people willing to work to at least try some sort of intervention? This is where I think a lot of frustration on the optimism/pessimism debate actually lies. It's less a matter of where on the spectrum you fall and more a matter of how actively you behave in that capacity. There are certain combinations that I have issues with: pessimists who don't at least due their due diligence to solve a problem before giving up, optimists who are super passive, optimists who build their optimism in ways that lack empathy and take actions that border on antisocial. Likewise, I'm more willing to give a pass to pessimists who make multiple attempts to set things right throughout their lives. They continuously try to do the work and don't just get all their proactive behaviors out of the way in their youth. In this particular framing (framing optimism/pessimism through a combo of mindset and action rather than only mindset) there is a fair amount of gray area, and oddly enough I think accepting this notion would actually make people feel more comfortable. It's no longer just a binary choice. A bit of flexibility may actually give people more incentive to start that intervention.

[Visit the entry for more...]

1 Like

Kåre เลียม Enga

a day ago
In response to "Opti-Miss"

Aspirations rather than beliefs.

My weakness... I'm not good with certain abstractions.

Is belief static? Is aspiration more mutable? *ack*

I believe the "sun is out" and I look out my window and sigh "it is so" but the truth is that the Sun blinked out 5 minutes ago and I'll know this in 3 minutes and 20 seconds. I also believe that in 12 hours it will not be sunny here... but that's based on past experiences and isn't a given. Are beliefs stuck in the Past?

I am a nineteenth generation Lunatic (I live on the Moon). My family legend states that they came here from elsewhere; but, I look into the void and see only distant stars, not the rising and setting of the Teal Sphere of Legend. We moved, they say, to not be reminded of our Exile (an even older Legend). I can't believe it. Follow this map they say... you'll find that all Legends are merely the retelling of a Truth we no longer understand. So I set off taking notes along the way. I jot down places, faces, abandoned artifacts. The world may as well be flat. Each day, the Bright Star comes up, then goes down to reveal the silver dots of the the Night. Last night, there was a glimmer of blue on the horizon though; I set out towards it. [From My Tome: "Aspiration", published in 547 AL]

So maybe I believe what I sense and call it reality, falsely believing that it won't change; but, I have aspirations that it can and I'm ready to "make it so". As I age I still aspire to make anywhere I'm planted a better place before I leave; if not, maybe I'll be the one that is changed.

2 Like

tj wanderlust-words-in-motion

Feb 28, 2025 at 4:51pm
In response to "With Pride"

#away!

1 Like

March 2, 2025 at 10:48am

#1084644

Revisited: "Real Men of Genius"

Just digging back to April of 2021 today, a time that is simultaneously far in the past and only four years ago. I did an entry based on a Cracked article: "Real Men of Genius"

The title, which I didn't explain then, comes from an old (90s-noughties) ad campaign for a product I despise, but whose promotions I found amusing. Yes, ads can be amusing. Maybe once a decade.

The article itself

still exists; Cracked seems to have a pretty good archive, which is good, because I haven't been impressed with their latest output.

Me: It's been said that with genius comes a certain level of insanity.

I didn't clarify this then, but I don't really believe what's "been said" in this case. Humans can be weird; weirdness isn't necessarily insanity; and a famous person's weirdness tends to get amplified. The article doesn't mention mental illness; that was all my take, and I probably shouldn't have done it.

That amplification seems to be the case with the first one, about Nabokov. Lots of people have sleep problems. Would his have been well-known if he hadn't been?

As for the next item: George Patton claimed to be the reincarnation of several past soldiers. What I didn't acknowledge then, and probably should have, is that lots of people hold a belief in reincarnation. It's more common in Eastern cultures, but it's hardly unheard-of in the West. So, whether one believes Patton or not, he was hardly alone in his assertions.

Not really anything else to add or subtract, except that I'm pretty sure some of your beliefs, habits, or activities, and mine, would get pegged as weirdness if we were famous. The title of the original article specified "famous smart people with little-known problems," but it's not like you could build an article around unknown people with little-known problems.

Comment • View 3 comments

© Copyright 2025 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://shop.writing.com/main/profile/blog/cathartes02/day/3-2-2025