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Monday, Nov. 18, 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:

tj-turkey-jobble-jobble-hard-J

about 8 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

a day 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

October 7, 2023 at 9:13am

#1056913

Autonomy

It doesn't matter how safe they are; there are those who are scared shitless of them, and no amount of logic or number-talk will change their minds.

Are self-driving cars already safer than human drivers?
I learned a lot by reading dozens of Waymo and Cruise crash reports.

Because I don't have a vested interest in anything, I'll say up front that the answer to the headline question turns out to be "maybe."

There's not a lot I need to quote from the article; it's there if you want to read it. I doubt it'll convince anyone of anything, though.

Neither will I, but I'm going to talk about the subject anyway. I've done it before, in "Putting the Auto in Automobile"

, and others, and I'll try not to repeat myself too much.

Here's the important quote:

Of course self-driving cars are flawed—all technologies are. The important question is whether self-driving cars are safer than human-driven cars.

And that's where data analysis comes in. The issue, and this is touched on in the article, is that AV incidents are scrutinized to a much finer level of detail than all but the worst HV (human-driven vehicle) incidents, and every little bump and ding is subject to this scrutiny. Imagine if you had to fill out incident reports and have questioned every decision you made leading up to the event every time you hit a squirrel in the road, or dinged someone's bumper in a parking lot.

Point is, accurate comparisons are hard. And while traffic fatalities are, in one sense, common (usually on the order of 40,000 deaths per year in the US), in another sense, they're pretty rare: according to the linked article, an average of one per 100 million miles driven.

And this is just me, but I'm not sure if we can take fender-benders as a proxy. That is, you expect x number of serious injuries for y number of minor incidents with human drivers, and the ratio of x over y is probably fairly constant year to year. Human drivers make mistakes. Robots make different mistakes.

On the other hand, we can't just set the robots loose, see how many people they kill, and then make a decision. That would be slightly unethical. No, we have to start somewhere.

"Waltz, we don't 'have to' start anywhere."

Yes, we do. I want my self-driving car so I can go bar-hopping. And I want it NOW. I'll even accept it before my promised flying car, thanks.

Anyway, getting back to serious. Data. Unlike some people, I can be persuaded by logic. If it turns out that reliable data show that AVs are safer, I'll be convinced.

But there will always be technophobes who will insist that it's better to risk being killed by a human driver than take a lower risk of being killed by a robot driver. Because robots are scary. This is akin to being scared shitless of flying, despite all the statistics. (I despise flying, myself, but that's because they've managed to turn it into the world's most uncomfortable travel experience; I feel fairly safe flying, just grumpy.)

And those are the people we need to convince. Not me. Problem is, I don't know how to appeal to emotion. So meanwhile, I'll just continue to drink at home, and in places where Uber can happen.

5 Like • Comment • View 3 comments

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