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Monday, Sep. 16, 2024

9:37pm EDT

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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:

Writer_Mike

Sep 14, 2024 at 5:06pm
In response to "One Thing In Common"

I've no doubt you'll be fine with your knowledge of French, however limited you think it may be. After all, you've been working on it since face masks were de rigueur. When I was stationed in Germany, a small group of us ventured across the Rhine into France - Strasbourg, to be exact. One of our number claimed a working knowledge of the local lingo, so we wandered into a small restaurant. Suffice it to say we didn't starve, but her so-called language ability was the stuff of hyperbole.

You'll do better - much better.

1 Like

Wordsmitty ✍️

Sep 14, 2024 at 1:11pm
In response to "One Thing In Common"

Pictures! We'll need to have pictures. No, not of you, not of buildings or countryside. Hevans NO. Don't take pictures of people. Need the important stuff - of the Beer. It'll also be a good record when you get back and are missing a few days here and there.

2 Like

Robert Waltz

Sep 14, 2024 at 10:40am
In response to "One Thing In Common"

WakeUpAndLive️~Happiness

- from that article, Travel expert Samantha Brown added that, sometimes, hotels will provide only one small towel. She thinks there’s a case to be made for bringing a small sports towel on your travels, just in case.

As everyone who's familiar with The Hitchhiker's Guide to the Galaxy knows, one should always carry a towel.

1 Like

WakeUpAndLive️~Happiness

Sep 14, 2024 at 10:31am
In response to "One Thing In Common"

https://www.washingtonpost.com/travel/tips/europe-travel-etiquette-tipping-ameri...

1 Like

WakeUpAndLive️~Happiness

Sep 14, 2024 at 10:19am
In response to "One Thing In Common"

No worries, English will do in Europe in most countries. How exciting it's near your travel date. Still, more than 5x24 hours to go. Take it easy. It should all be fun.

1 Like

Robert Waltz

Sep 13, 2024 at 5:57pm
In response to "Journey Man"

You two are both exceptional individuals, it's true.

1 Like

Annette in Paris

Sep 13, 2024 at 4:29pm
In response to "Journey Man"

As long as there's beer, it's possible to have fun with you for a whole week.

Ken, get your head out of the gutter. I'm talking about visiting micro breweries.

1 Like

Sum1's In San Francisco

Sep 13, 2024 at 4:19pm
In response to "Journey Man"

From your post. Since it's a documented fact that no one can put up with me for more than two hours at a time, I tend to do road trips alone. Hey, I 'put up' with you for a whole day! Or was it the other way around?

1 Like

Aiva Raine

Sep 11, 2024 at 3:36pm
In response to "Drop and Gimme Twenty"

Happy 20th. We're glad you joined and doubly glad you've stayed this long. I look forward to reading your daily blog as part of my own daily ritual.

1 Like

Wordsmitty ✍️

Sep 11, 2024 at 1:02pm
In response to "Drop and Gimme Twenty"

Wow. That sounds mature for twenty. Next year you can get some booze to celebrate.

I'm sure we're all glad you did sign up. Enjoy the day.

1 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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