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Sunday, Nov. 17, 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:

Turkey DrumStik

about 23 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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

May 22, 2024 at 9:26am

#1071517

Jumping Through Loopholes

I'm usually a law-abiding citizen. Or, well, I try to be; sometimes it seems laws are designed so that if They want to get you for something, They can find a reason.

But some laws are fundamentally unjust, and need to be broken. Cracked provides some examples in:

6 Loopholes People Used to Break the Law and Get Drunk
Technically, if you’re on a train, everything is legal

6. Pay to See the Blind Pig

During Prohibition, a bar could not legally operate and sell alcohol. No one could legally sell alcohol (without receiving special exemptions, such as for medicinal use), or manufacture alcohol, or transport alcohol. The law didn’t ban drinking alcohol, however, or handing the stuff to someone else without charging them any money.

It could, of course, be argued that it's hard to drink alcohol if one is prohibited from buying, making, or moving it. But, at least here in the US, lawyers thrive on technicalities.

But suppose an establishment were to hand out a drink for free and charge customers for something else? Say, they charge a customer for some entertainment — for instance, the chance to look at a marvelous animal. As for the drink the barman serves the customer, well, no one’s purchasing that.

Not mentioned: how the pig got blind. Look, I'm all for eating the tasty critters, but mutilating them doesn't fly. This was nearly a hundred years ago, though, and people didn't generally think that way.

This idea is why one alternate name for a speakeasy is a “blind pig.” And if you’re wondering why the police would ever be fooled by this, know that plenty of police didn’t really care about Prohibition laws and were possibly drinking right along with everyone else.

Which may explain why some cops love do do drug busts: it provides them with free product.

5. Instructions on How to Absolutely Not Make Wine

They had this sort of thing for beer, too.

Individual families were still allowed to make a limited amount of wine, but if you were to sell people the raw materials for making wine, along with instructions, you might find yourself in trouble.

This would be like selling fertilizer with instructions on how to ensure it never becomes a bomb. Except there's good reason to keep people from making bombs.

“After dissolving the brick in a gallon of water, do not place the liquid in a jug away in the cupboard for twenty days, because then it would turn to wine.”

These days, of course, the surest way to get a certain group of people to do something is to tell them not to do it.

4. Stick Everyone on a Train

Even when alcohol is legal in the country, you need a license to sell it. One British gin maker, Tapling & Meegan Distilling, dutifully applied for this license, but it was taking too long to get approved. So they did the only reasonable thing and turned to steampunk.

Now, there's a story idea.

Within all the country’s many alcohol regulations is a line of law saying the usual license requirements do not apply to trains in motion.

The downside of this is obvious: motion sickness exacerbated by drunkenness.

3. Let’s Call Beer Something Else

Complex regulations define exactly what beverages are, which is why you generally cannot put lemonade in a bottle and sell it as tomato juice. In Texas, they had a rule about beer: It could not contain more than 4 percent alcohol by volume.

Ah, yes, the old "name a thing something else to get around regulations" trick. No wonder fermented beverage categories can be misleading.

A lager that appears to be beer by most conventional definitions would be labeled, in fine print, “In Texas, malt liquor.”

I'm pretty sure some states still have ABV maximums for beer. As the article notes, Texas isn't one of them. But it's not a good look for a state that prides itself on limiting government interference in peoples' lives. Which, incidentally, they clearly don't do.

2. Turning Nightclubs into Pop-up Restaurants

This next law lasted from 1935 to 2000, in Ireland, a place not entirely unfamiliar with alcohol.

Now that's a cheap shot. Pun intended.

Establishments were not allowed to serve alcohol at night unless they also served a meal.

This sort of thing has been the law here in the US, off and on, depending on where you are. Hell, even my state has a version of the rule, which is why you'll technically never find a bar in Virginia; only restaurants that happen to serve booze.

The dish of choice at these clubs? Curry.

Yeah, that couldn't have ended well.

1. The Inedible Sandwich

That Irish policy hearkens to an older and famous law from New York. Way back in 1896, the same time that they made the controversial decision to raise the drinking age from 16 to 18, the state passed a law saying bars couldn’t serve alcohol on Sundays.

Like I said.

Bars, which served no actual food, qualified for the exemption by offering a sandwich. Not sandwiches, but a singular sandwich that a bar would pass from customer to customer without anyone eating it. This was named the “Raines sandwich,” after John Raines, the senator who wrote the law.

I'd heard about this loophole before, of course. It still amuses me.

The takeaway here is that, if you're clever, you can find a way around unjust laws without flagrantly breaking them. And I approve.

3 Like • Comment

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