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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 13 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

September 3, 2023 at 6:09am

#1055066

Revisited: "Cold Hands, Cold Heart"

Dialing back to the ass end of January, 2019, which where I live represents the coldest days of the entire year (on average), the Random Number Gods served up this then-seasonally-appropriate entry: "Cold Hands, Cold Heart"

It was apparently part of an early attempt for me at the 30DBC, falling just a few months after I ended my blogging hiatus. The prompt is in the entry, but I'll repeat it here:

Allow me to share this quote regarding my local weather this week: ”Dangerous wind chills of -45 degrees F (-43 C) to -65 degrees F (-54 C) are expected for most of the period from Tuesday night through Thursday morning. This is a life-threatening situation...” etcetera, etcetera... stay inside... frostbite... etcetera.

One fun math exercise is to work out where the F and C scales cross. It's very simple algebra to do so, but to calm the heart palpitations you just started experiencing upon reading that, the answer is -40. That is, -40F is the same level of nope as -40C.

That weather report (I have no record of which user wrote that prompt) is colder than that.

So, I say again, nope. As I put it in that 2019 entry:

You know there are places on Mars warmer than that, right? You know that, right???

While the average global temperature on Mars is probably around -63C, at the equator, at high Martian noon, it can get up to about 20C (roughly 70F)—very Earthlike temperatures, really, if you discount how short-lived it would be. Almost as short-lived as an unprotected person there. But at least you'd die from decompression and insufficient oxygen, not frostbite.

My attitudes about temperature haven't changed in the last five years:

Look, I spent my childhood next to an estuary of the Chesapeake, just about at sea level. Pretty close to DC, and you might be aware how crappy the weather can be there. Before I even ventured out of Virginia, I experienced extreme weather: bitter cold, muggy humid heat. And I'm here to tell you that - bugs notwithstanding - give me the heat any day of the week.

I dread the coming cooler temperatures.

On the other hand, no amount of clothing - no number of layers, no well-made coats or woolen gloves or thermal socks, nothing - will stop my hands and feet from freezing the moment the effective temperature drops below about 52F. And once those freeze, I'm shit-swimming miserable. So you can keep your freakish Michigan lake effect hellish winters (yes, there is a Hell, and it is in Michigan). You can keep your brisk Alaska arctic circle bullshit. You can keep Chicago.

When I was in college, I got through some of the toughest winter cold by using the proto-internet to look up the current temperature in Nome, Alaska, just south of the Arctic Circle. It always made me feel better to see -20C there when it was 0C here, or whatever. This worked until, one day, some freakish twist of weather made it warmer there than here.

If it weren't for the awesome breweries, wineries, cideries, distilleries, and bars around here, I'd move out in a heartbeat just so as not to deal with another Virginia winter. I've been freezing my ass off most every day since December, and we've only had a few nights of subfreezing lows, this year (last year was relentlessly cold). And I still have February to endure. I don't know how I'll be able to do that.

Obviously, I managed.

This past winter was far warmer than usual around here (no, this is not an excuse to start an argument or bitch about the environment; it's just an observation). Hell, it didn't even snow, but for a few flurries, which still managed to wipe the store shelves clean of bread and milk and cause drivers to slow down to 15MPH. Parts of last winter were almost pleasant; I recall a few 60F+ days. "Pleasant" for me starts at around 72F, and doesn't end until maybe 100F, depending on the humidity. Hell, I keep my summer A/C at 78, and that's more than sufficient for me.

Now, look, I'm not ragging on people who like colder temperatures. Everyone has their comfortable zone; otherwise, we humans wouldn't be living at all sorts of latitudes and elevations. But I like it hot. I keep thinking how nice it would be to live on a tropical island, until I remember that hurricanes are a thing.

I might just throw my hands up into the frigid air and hop a flight to Maui again.

Because that's where my ideal weather lives.

Boy, the end of that entry didn't age very well.

2 Like • Comment • View 2 comments

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