Complex Numbers (Book)

Blog Calendar

◄ September ► 2023
S	M	T	W	T	F	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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 14, 2023 at 9:14am

#1055730

How To Lose Money

Having lived through the Great Coke Crisis of 1985, I'm still fascinated by how companies can sometimes shoot themselves in the foot.

Oh, Schlitz: How a Historic Ad Campaign Helped Kill America’s Biggest Beer Brand

Coca-Cola, of course, survived their mistake (or perhaps it was a calculated conspiracy

). But can we really blame marketing for taking the L out of Schlitz?

Throughout the first half of the 20th century, the Milwaukee-based Joseph Schlitz Brewing Company held the gold crown as America’s largest brewer.

Which glosses right over the dark, dreary days of Prohibition, a significant chunk of "the first half of the 20th century." Like other brewers, Schlitz endured through diversification. But that's irrelevant right now.

Then a series of business decisions, including a disastrous ad campaign, dubbed the “Drink Schlitz or I’ll kill you” campaign, precipitated the downfall of America’s biggest beer brand.

That campaign lasted less than three months, coinciding with a tumultuous year for consumerism in general (1977). It's said that "no publicity is bad publicity," but I'm not so sure about that; still, I'm pretty sure other "business decisions" were more proximate. Like how they stopped making beer and started making formulaic adjunct lager like their competition.

By the late 1950s, Schlitz lost its top title to another quintessential American beer brand: Anheuser-Busch.

Calling that "beer" is an insult to beer, much like calling Kraft Singles "cheese" is an insult to cheese.

During the 1970s, in an attempt to cut production costs and keep up with growing demands, Schlitz’s owners decided to shorten the beer’s brewing time by implementing a process called “accelerated batch fermentation.”

This, by itself, should have been enough to kill the brand. But, as with New Coke, Americans will put up with a lot of enshittification.

They also opted to replace its malted barley with a cheaper ingredient, corn syrup, and began experimenting with the use of a silica gel to prevent haze once the beer was chilled.

That first bit, there, was enough to make it not-beer. Not necessarily bad; lots of great beverages start with corn syrup. But not beer.

And nowadays, of course, lots of people love hazy beers.

Sales dropped as Schlitz’s customers grew frustrated with the brand and started returning cases of beer.

As tasteless as many Americans are, you mess with their favorites at your own peril. (The silica gel thing resulted in a recall, incidentally, never a great thing for any business).

In an effort to stem its declining sales and improve its spiraling reputation, the company hired an ad agency, Leo Burnett & Co., to launch four television spots.

Now, here's the thing: that could have worked. Marketing, done right, can sell anything, including pet rocks and bottled water. You can have the shittiest product in existence, and if you have the right marketing, it'll sell anyway. And truly great products, without marketing, can fade into oblivion.

But by the time Schlitz did those ads, it had already become a terrible product.

Schlitz closed its Milwaukee brewery in 1981.

For context, home brewing became legalized in October of 1978, yet more proof that Jimmy Carter was a severely underrated President. That paved the way for smaller breweries to get some market niches. And Sierra Nevada opened in 1981, still producing craft beer today (I'm not a fan, but I can't argue that it's not real beer).

Today, of course, is a wonderful time to be a beer snob. I'd call it a "Golden Age," but Golden is associated with Coors, and they suck too.

But there are still beer marketing controversies, as I'm sure you remember from earlier this year.

I mention these things sometimes, because even if you're not trying to market anything (a book, perhaps), we're all affected by marketing every day, and a little cynicism can't hurt. And maybe this will help keep you from getting stranded up Schlitz creek without a paddle.

6 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.