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Saturday, Nov. 16, 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:

Write_Mikey_Write!

a day ago
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

a day ago
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

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

December 23, 2021 at 12:02am

#1023564

Something New Under the Sun

Warning: today's link is a slideshow. I tried some usual tricks for unsliding it, but I think they're on to my attempts to deprive them of precious clicks, and I can't be arsed to figure out any new method tonight.

10 Scientific Advances That Will Actually Make You Hopeful for the Future

As such, I normally wouldn't share something like this, but in this case, the combination of "hope" and "future" made me laugh, so here are some excerpts along with my snark.

mRNA Vaccines and the end of disease

If there’s a silver lining to the global pandemic, it’s the speed of the vaccine roll-out. Spurred by massive amounts of public cash and backed by decades of research, Pfizer’s COVID-19 vaccine was the first “Messenger RNA” medicine to be fully approved by the FDA. It’s unlikely to be the last.

...and half the population won't trust them.

Self-driving cars

Widespread adoption of self-driving cars is taking longer than was initially predicted, but once the technology is locked down and the public is comfortable with robot-driving, everything will change for the better.

Hahahaha.

Oh wait, you're serious.

HAHAHAHAHAHA.

Look, I'm a big proponent of autonomous vehicles. As far as I'm concerned, they can't roll out fast enough (and this is coming from someone who loves to drive). Mainly so I can get home from bars, but also, incidentally, because they will be safer.

Yes. They will. Stop laughing; that's my job. Oh, sure, you've heard the stories of test vehicles crashing or hitting people. Those only stand out because it's new technology. Every year in the US, something like 40,000 people die as a result of meat-driven vehicles. Imagine if every single one of them were reported on the way a single AV mishap is.

Would AVs reduce fatalities to zero? No. Nothing can make it perfectly safe. But as far as I'm concerned, if the fatality rate (and, in general, injury rate) could be reduced by a standard deviation or two, it's worth adopting. But no, people focus on the "it kills people!" part without considering that the current system kills people and we just accept it as the cost of doing business. What we need to focus on is "it will kill fewer people."

Also remember that there are a lot of individuals and groups that make money from the current system. Not just car companies, who could probably retool, and not just professional drivers, but municipalities who get their revenue from speeding tickets. That revenue would dry right up like the Mojave after a drizzle. They have a vested interest in promoting the "It's not safe!" propaganda.

Point, and the reason I laughed above, is that because of these and a myriad other factors (including loss of the illusion of being in control), "the public" won't ever be comfortable around robot drivers. Half the holdouts will be afraid of handing decisions over to an AI, and the other half will be afraid the AI will take over the world and enslave humanity. So no, I'll have to plan on staggering home from bars until the day I die (probably from being hit by a drunk driver).

Just so you know, I had a lot more written in this section, but I deleted it. I have a lot to say about it, which is one sign that I need to shut up about it. So this is me shutting up now.

De-extinction

Living robots

Advances in genetic engineering are getting us ever closer to saving endangered animal species from extinction and even bringing extinct species back to life.

Scientists at Tufts university have created living robots.

Science fiction and horror movies and books ought to be required reading/viewing for anyone going into science, especially bioscience and robotics.

Full body haptic suits

The idea of a full body suit that allows users to experience the feeling of a virtual or augmented space along with its sights and sounds is a little creepy. It’s like the background material in a dystopian science fiction movie or something.

So is everything else on this list.

In any case, of all the ones I'm highlighting, this is the one that I could see becoming reality. Because sex.

Carbon vodka and garbage sunglasses

The Air Company markets a Vodka they say they is made from carbon dioxide, so you can get drunk and eliminate carbon from the atmosphere at the same time.

How about some advances in editing technology while we're at it? "they say they is made," indeed. Feh.

Regardless, all vodka is made from carbon dioxide. Because it's made from plants. And plants sequester carbon. They turn the carbon into starches and/or sugars, which yeast then turns into magic fluid.

I can't be arsed to find out if this company's process is somehow more efficient or environmentally friendlier.

Anyway, I don't mean to be negative about scientific advances. Of course I'm excited about real progress. Let's just remember that almost no invention comes without a cost of some sort, sometimes one that only becomes obvious after the fact. The only question is whether the benefits outweigh the costs. So no, none of these make me hopeful about the future. That would require us having done something about climate change 30 years ago, not now that it's too late.

4 Like • Comment • View 3 comments

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