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Saturday, Apr. 27, 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:

Elisa the Bunny Stik

about 8 hours ago
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

August 24, 2020 at 12:04am

#991450

Orange You Glad This Wasn't You?

Something a little different today.

Also, Merit Badge Mini-Contest below!

https://medium.com/better-marketing/the-worst-rebrand-in-the-history-of-orange-j...

The Worst Rebrand in the History of Orange Juice
They paid $35 million to then lose $20m in sales

So why am I linking something about orange juice? Because it's a product, and some marketing techniques apply to a broad range of products... like, for instance, your writing.

Not that I know jack squat about any of this. Which is why I read them -- to confirm that not only do I not understand, but I will quite probably never understand. But maybe this will help someone else. Or, hey, maybe you just like orange juice.

In hindsight, it’s easy to see why Tropicana’s 2009 rebrand failed.

No. No, it really isn't. Not to me. And even the author explains, later, that it shouldn't have taken hindsight.

Less than 30 days after launch, they pulled the new design off the shelves and went back to the old one.

Which probably explains why this is the first I'm hearing about this. Coke's "New Coke" fiasco personally affected me. I don't drink orange juice, so I never noticed a rebrand.

The article helpfully includes "before" and "after" pics.

Without even getting into the subjective topics of visual appeal and recognizability, some design flaws practically stare you in the face.

But do they, really?

After the rebrand, the font was thinner, the same color as the remaining text, pushed to the side, and, worst of all, vertical. No matter how great your juice is, if it can’t heal neck pain, don’t force me to tilt my head sideways to read your name.

I have the ability to read text upside down, sideways, backwards, mirror image, upside down mirror image... the latter takes me a bit longer, to be sure. I can also write in all those directions. The sideways text wouldn't even impinge itself upon my consciousness. But hey, not everyone can be a super-genius, I suppose, and you have to market to morons.

What’s more, white font on a yellow background is a weaker contrast than dark green on a white background — especially considering they stuffed it inside the juice glass.

Okay, on that part, I can see their point.

Beautiful design is important, but if it’s not functional, it won’t matter.

Function is more important than form. Well... for me. Engineer, remember? But I can admit that when it comes to trying to sell shit, part of the function is to catch a viewer's eye (or ear in the case of radio). That requires form.

“Historically, we always show the outside of the orange. What was fascinating was that we had never shown the product called the juice.” Really? I mean, it’s juice. Give me a clear symbol of it, and I’m good to go. And what could be clearer than the actual fruit the juice is from?

Somewhere in there, I think, is probably a metaphor for promoting one's writing. I'm not quite sure what it is, but I'm pretty sure it's in there.

The one thing I’ll give them credit for is the cap of the new carton. It had the haptic structure of an actual orange. “We engineered this little squeeze cap so that the notion of squeezing the orange was implied ergonomically.”

Look, I know what "haptic" means, but a few paragraphs ago this author was complaining about jargon (I didn't copy that part, but it's there). Also, making your orange juice cap look like an orange is a surefire way to get me to purchase a competitor's brand. If, that is, I were inclined to buy orange juice.

But then, I freely admit I'm not a typical consumer.

So, anyway, like I said, maybe someone else can make more sense out of this. And hell, why don't we make it a mini-contest?

Merit Badge Mini-Contest!

Know any good (by which I mean bad) marketing failures? Comment below. The one I like best will earn its author a Merit Badge. Two restrictions today: 1) Don't talk about New Coke. I know about New Coke. I suffered through the Great Coke Crisis of 1985, and I have no wish to relive those horrid months. 2) Don't use this blog as an example of a marketing failure (I'm including this because I'm the sort of asshole who would do something like that, and besides, I'm not trying to sell anything here. Quite the opposite.)

If you can't think of one, it's not cheating to use Google. Mostly I just want to understand this marketing thing better, and, just like they kept showing us the newsreel footage of the Tacoma Narrows Bridge collapse

as a warning in engineering school, I think we can learn from failures as much as from successes. It's best if it's not our own failure.

6 Like • Comment • View 9 comments

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