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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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:

tj-Merry Mischief Maker

about 12 hours ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

about 18 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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This is a private area. Access has been restricted and you may not view it under its current settings. If you feel you should have access, please contact the area's owner and request access.

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2 Like

Annette

about 18 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

a day ago
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

September 8, 2024 at 9:02am

#1076471

Revisited: "Orange You Glad This Wasn't You?"

My first random selection of a past blog entry landed on one I'd already revisited. I knew that could happen, obviously, but I was still mulling over whether to do another revisit, or just skip it and roll again.

I've decided, instead, to point to the previous Revisited, thus: "Revisited: "Best Waste of Time EVER""

But that's all I'm going to say about it.

And then I rolled again, and got this discussion of an article, posted about four years ago: "Orange You Glad This Wasn't You?"

That's the one we'll look at today.

Something a little different today.

Yeah, back then, maybe it was "a little different," but I think now it looks like just another article I could riff on.

The link, to a 2020 bit about Tropicana's orange juice marketing disaster back in 2009, is still there... but when I looked, it said "Member-only story."

That's their right, of course, but nothing from Medium has ever captured my attention enough to become a "member," and to me, there are very few articles on the internet worth reading that aren't also worth sharing. So I don't bother. I pay WaPo for a subscription, because that's the newspaper I grew up with (if indeed I grew up at all), but that's about it.

Therefore, all I can do is talk about my own reactions. Even the specific "rebrand" they're talking about is hidden and forgotten.

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'll ever apply these techniques. But, being entirely altruistic and thinking only of my readers, I perform the public service of informing them.

Okay, no, I just find this stuff fascinating for whatever reason, and I'd rather learn from others' failures than from my own.

But maybe this will help someone else. Or, hey, maybe you just like orange juice.

The reality is a bit of both.

Coke's "New Coke" fiasco personally affected me. I don't drink orange juice, so I never noticed a rebrand.

Yes, almost 40 years later, and I still carry trauma from that horrible year.

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

Not any more, if you're not a member.

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.

Much as I rag on myself for having no artistic talent (I don't) or not understanding marketing (I don't), I do have some background in graphic design and artistic composition. Part of being a photographer. I maintain that I wasn't very good at it, but I understand some of the theory, just like I understand some music theory even though I'm a terrible musician.

Then I quoted the following from the original article:

“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?

On which I commented:

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.

Having had four years to think about it, I'm still unable to articulate what that metaphor is, but I'm still sure there is one, taunting me. I think it's encapsulated in the line, "Give me a clear symbol of it, and I’m good to go." People respond to symbols; that's kind of our thing as humans, to let one thing stand for another, or for an abstract concept.

But I'm reminded of what might have been my first lesson in marketing failures, which, to be fair, could have been an urban legend. The story went something like this: In some less-developed country, it was standard practice to show an image of the contents of the can on the label. If it's beans, for example, the can depicts beans. For carrots, there's a picture of carrots. That way, even those who can't read (a large portion of the population) would know what's supposed to be in the can. Anyway, the fail I heard about was that Gerber tried to enter that market, but couldn't... because their baby food cans had a picture of a baby.

Almost every barbecue joint I've ever seen uses a pig as a mascot. This is not because they're marketing to literal pigs. Metaphorical ones, maybe, but their customers generally don't root for truffles and oink.

In any case, I think I've discussed other marketing mistakes in here since then. That entry's comment section is also good for examples, because I turned it into a Merit Badge contest, which is something I haven't done for a while. Except for last week's free badge giveaway, of course.

But I can't leave this without noting that the header for this blog doesn't exactly depict what's in the can. So I guess I really do fail at marketing.

1 Like • Comment • View 1 comment

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