Complex Numbers (Book)

Blog Calendar

◄ April ► 2023
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:

Writer_Mike

about 6 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

QPdoll

about 22 hours ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

a day ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

April 9, 2023 at 12:02pm

#1047885

Revisited: "Once More With Feeling"

It's Sunday (some say Easter Sunday), so it's time once again to forget the worries of the present and focus on the disaster of the past.

Apparently, back in 2020 (a pretty bad year from most perspectives), I'd had a few blog entries, most of which I vaguely remember, talking about panpsychism, the persistent belief (for it is a belief, not scientific knowledge) that consciousness arises in complex life because every thing in the universe, including subatomic particles, has a rudimentary form of consciousness. I may not be getting it exactly right, but that's the gist of it.

Naturally (pun intended), I push back—not from any deep-seated need to be special, but because it's not, as far as I've been able to tell, a testable, falsifiable hypothesis. Apparently, I pushed back a few times, based on the title of the entry ("Once More With Feeling"

), and the first line:

This is probably the last bit about panpsychism I'll be linking. For now. Maybe.

And I can't be arsed to scour every day since August 11, 2020 to see if I talked about it again until now.

But let's turn this into a Merit Badge Mini-Contest.

Yeah, I know, I haven't done one of these in a while. Interest seemed to peter out. But maybe I'll start them up again, perhaps once a month. Not today, though.

Anyway, the link (available at the original entry above) is still active, if you're interested in what this publication, and one philosopher, has to say about it.

This entry is about what I have to say about it.

In the link above, I copied the "elevator pitch" for panpsychism:

In our standard view of things, consciousness exists only in the brains of highly evolved organisms, and hence consciousness exists only in a tiny part of the universe and only in very recent history. According to panpsychism, in contrast, consciousness pervades the universe and is a fundamental feature of it.

And today, rereading this, I realized that I didn't address the misconception about evolution: that there are "highly evolved organisms" as opposed, apparently, to less-evolved organisms.

That point of view is dangerously self-centered.

Every living being on Earth shares a common ancestor. Every living thing on Earth has therefore been subject to evolutionary pressure for the same amount of time (3-4 billion years; the exact time is irrelevant to this discussion so I won't bother splitting hairs on it). We have certain adaptations that have made us very good at becoming an invasive species, even to the extent of being able to live in places like Antartica and, for at least a little while, on the moon.

But that doesn't make us "highly evolved," any more than a bacterium is "highly evolved" because it acquired antibiotic resistance from its progenitors.

None of this means that panpsychism is right. I'm just pointing out that the "standard view" noted in the quote is kind of a straw man. I can accept the idea that any living thing has some form of consciousness, but every nonliving thing? I'mma need evidence. "Consciousness pervades the universe" is more in the realm of theology, which requires no evidence.

Anyway, the original entry goes deeper into other arguments, which I won't rehash here. Bottom line is, sure, it's a legitimate philosophy; it's also older than recorded language in humans (in the form of animism). It makes for good creative writing, and excellent (if later forgotten) stoned dorm room conversations.

What it's not, is science.

It may be, someday, when we know more. Which is why we do science.

5 Like • Comment • View 2 comments

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