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Thursday, Nov. 14, 2024

1:26am EST

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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:

Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 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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