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Tuesday, May. 21, 2024

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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:

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

October 13, 2020 at 12:01am

#995761

The Answer to the Ultimate Question

Meaning? Purpose? A Jedi craves not these things.

https://theconversation.com/lifes-purpose-rests-in-our-minds-spectacular-drive-t...

Life’s purpose rests in our mind’s spectacular drive to extract meaning from the world

What is the purpose of life?

Life needs no purpose. What's the purpose of a rock? Its destiny is to be ground down into dust, but that doesn't make it the rock's purpose. We can give it another purpose - a paperweight, say, or a weapon - but that doesn't mean it was destined for that.

Whatever you may think is the answer, you might, from time to time at least, find your own definition unsatisfactory.

Every definition is unsatisfactory.

Humanity’s purpose rests in the spectacular drive of our minds to extract meaning from the world around us.

That's not a purpose, either. That's a result. You're basically talking about what we talked about in here a while back: apophenia, the seeing of purpose or meaning when there isn't one.

For many scientists, this drive to find sense guides every step they take, it defines everything that they do or say.

Which is not to say that curiosity isn't a good thing.

Take words, for instance, those mesmerising language units that package meaning with phenomenal density. When you show a word to someone who can read it, they not only retrieve the meaning of it, but all the meanings that this person has ever seen associated with it. They also rely on the meaning of words that resemble that word, and even the meaning of nonsensical words that sound or look like it.

I've actually been thinking along these lines for a while now. It came from beginning to study another language. Not only must one know what a word means, there's all kinds of metadata associated with it: what it applies to, how other people have used it in sentences, perhaps where you first encountered it, and (in the case of pronouns and words in certain other languages) its gender... just to name a few. And for people like me, the "meaning of words that resemble that word" is how I make puns. Like the one I've been suppressing since I started writing this, about having to go swimming to find one's porpoise in life.

There, I feel better now that I've gotten that out of my brain.

And yes, you do it too, even if you don't realize it. For example, I'm willing to bet that if you've encountered The Hitch-Hikers Guide to the Galaxy, you're poised to include the number 42 in a comment below, especially if you read this entry's title.

Recently, we have been able to show that even an abstract picture – one that cannot easily be taken as a depiction of a particular concept – connects to words in the mind in a way that can be predicted. It does not seem to matter how seemingly void of meaning an image, a sound, or a smell may be, the human brain will project meaning onto it.

Just like we project meaning onto life, even when it's not there.

In other words, the goal of our existence ultimately seems to be achieving a full understanding of this same existence, a kind of kaleidoscopic infinity loop in which our mind is trapped, from the emergence of proto-consciousness in the womb, all the way to our deathbed.

As was eloquently pointed out in Babylon 5, "we are what the universe has created so that it can figure itself out."

I don't believe that either, but as guiding principles go, it is rather appealing.

The proposal is compatible with theoretical standpoints in quantum physics and astrophysics...

I'm glad they didn't lead with that, because it would have made me stop reading the entire article. Hijacking quantum physics to support your pet philosophy is cheating, like ending a story with "...but it turned out it was all a dream."

Perhaps it does not matter if you find this proposal satisfying, because getting the answer to what the purpose of life is would equate to making your life purposeless. And who would want that?

*raises hand*

I'm comfortable with the lack of meaning or purpose. At least, I am today. I wasn't always. And as usual, ask me again tomorrow and I'll probably say the purpose of life is to enjoy beer. Right now, I have too much of a headache from doing that earlier. And sometimes I think that the sole purpose of life is to increase overall entropy (which all life does), thus hastening the eventual heat death of the universe.

But look, I'm not dismissing the article entirely. If I did that, I wouldn't have linked it. I find it interesting, but that doesn't mean I agree with it. It's perfectly reasonable for an individual to create their own meaning, or purpose, and live for it. I only object to the idea that there's one answer for everyone.

Even if that answer is 42.

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