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Thursday, Nov. 21, 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:

Robert Waltz

about 24 hours ago
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

a day ago
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

a day ago
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

a day ago
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

Brandiwyn🎶

Nov 18, 2024 at 11:19am
In response to "Losing Weight Is Easy"

Has anyone ever told you how annoyingly pedantic you are?

Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless.

3 Like

tj-turkey-jobble-jobble-hard-J

Nov 17, 2024 at 4:04pm
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

October 29, 2024 at 9:35am

#1079108

The Numbers Don't Lie

From Big Think, an article about how the numbers sometimes lie:

The “McNamara fallacy”: When data leads to the worst decision
Don’t make the mistake of blindly following quantitative metrics — whether you’re helping clients or looking for lunch.

Or do they?

In 2014, I took a weekend break to York.

You know what sometimes lies? Anecdotes.

York is a lovely city in the north of the UK, with an ancient cathedral, quaint cobbled roads...

Oh, hell no.

...and an interactive Viking experience.

Is that where you get hung by the ankles and forced to watch your clan murdered and village pillaged while you're upside-down?

The reason for the anecdote is quickly revealed: the author made the mistake of trusting online reviews whilst choosing a restaurant, Skewers, which turned out to have high ratings due to drunks lovingly appreciating their late-night-early-morning fare.

Let's be clear, here: This is not a failure of TripAdvisor. It's not a failure of the food establishment. It's certainly not a failure of the well-meaning drunks. The blame lies entirely on the author. I travel quite a bit, and I prefer to form my own opinions of places I visit, rather than relying on others' (sometimes real, sometimes not) experiences. Sometimes, it sucks, but usually, I'm pleasantly surprised. Either way, I get to write reviews of my own, which may or may not factor into someone else choosing to visit.

The story of Skewers is an example of the McNamara fallacy, and learning about it can help us all (especially the underprepared tourists among us).

In spite of my misgivings about the opening anecdote, I'm willing to read on.

Fortunately, the author again gets quickly to the point, which is how I know I'm reading Big Think and not The New Yorker:

The McNamara fallacy is what occurs when decision-makers rely solely on quantitative metrics while ignoring qualitative factors.

So, like, when you rely only on the studies that claim booze is bad for you, and ignore how good it makes you feel.

The fallacy is named after Robert McNamara, the U.S. Secretary of Defense during the Vietnam War, where his over-reliance on measurable data led to several misguided strategies where considering certain human and contextual elements would have been successful.

I'm no expert on war history, but claiming that different decisions "would have been successful" strikes me as arrogant. I'd weasel out with "might have been successful," instead.

The McNamara fallacy is not saying that using data is bad or that collecting as much information as you can is wasted time.

I'm just leaving this here lest someone be thinking, "What's the point in data, then?"

For example, it’s not uncommon for someone to deeply love a book that has few or no reviews on Goodreads. It’s possible to enjoy a restaurant or a movie in spite of what others say. Data is a great starting point, and a great many idiotic and dangerous things are done when we ignore data, but it doesn’t always make for the best decisions.

I'm very familiar with that assessment, anyway. People are different, and you might love something others hate, or vice-versa. Reviews and the like are aggregations, and blindly following them is roughly the same thing as blindly following the crowd. You can do that if you want, but I don't, because that way, I miss out on the joy of making my own discoveries.

If everyone liked the same things, there'd only be one beer, and that would be a boring world indeed.

I have a much bigger problem with the explicit comparison of "finding a place to eat" and "running a war where people die."

Still, I suspect the basic ideas of the fallacy are sound, and the article goes into other examples and applications thereof, which I don't feel the need to reproduce here.

Fear not, though; it's short, and there are very few actual numbers. So, a solid four stars out of five from me. Your experience may vary.

3 Like • Comment • View 5 comments

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