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Sunday, Nov. 17, 2024

10:44am EST

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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

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

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

June 26, 2024 at 10:04am

#1073197

The Oz Hypothesis

Couple of things to warn everyone about concerning today's link. First, and most importantly, it's from Metro (a UK tabloid), so it's not exactly reputable. Second, though most relevant, the page contains images that you probably don't want your boss or coworkers to see you looking at (in other words, NSFW). These include poorly-rendered nude sketches. It is not, however, pornographic.

In short, view at your own risk.

Disclaimers out of the way, here it is:

Secret medieval manuscript could actually be a very old sex guide

Yes, they mean the Voynich Manuscript.

Which I'll call the VM from now on because I'm lazy.

The Voynich manuscript has fascinated both scientists and the public for more than a century since it was rediscovered by a rare books dealer in 1912.

Many "rediscovered" books turn out to be more modern hoaxes. If the VM is a hoax, it's a very, very good one. So good that it's still worth figuring out the purpose of it.

Now however, two historians from Macquarie University in Sydney, Australia, think they may have found the meaning behind it – sex.

Lots of people have made guesses, educated and otherwise, about what it's for. These range from aliens having a laugh at our expense to, well, this, which I'll call the Oz Hypothesis.

Claiming it's about sex is a sure way to get people to notice, much as my cat refuses to pay attention to me until I say, "Treat!"

But while we don’t know who the first owner was, it’s fair to say they lived during a rather prudish time.

...says the article, immediately following the sentence with two illustrations from the VM featuring nekked wimmin.

Writing for The Conversation, study co-author Dr Keagan Brewer said: ‘One section contains illustrations of naked women holding objects adjacent to, or oriented towards, their genitalia. These wouldn’t belong in a solely herbal or astronomical manuscript. To make sense of these images, we investigated the culture of late-medieval gynaecology and sexology – which physicians at the time often referred to as “women’s secrets”.’

I probably would have been better off just linking that Conversation article, but then I wouldn't have had the opportunity to snark on the hilarious juxtaposition of "lived during a rather prudish time" and illustrations of women apparently bathing.

This suggests to avoid censorship, the author used a mix of the cipher and illustrations to share their message.

The problem with the Oz Hypothesis is that ciphers only work for communication when they can be, well, deciphered. The VM has been analyzed more thoroughly than a postmodern stream-of-consciousness novel, by some of the most accomplished cryptographers in the world, and no one has been able to crack the code.

This is also a problem for pretty much every other guess about the VM, with the possible exception of "space aliens playing a hoax."

Anyway, the article touches on some of the evidence for the Oz Hypothesis. Which, to me, is no more or less compelling as evidence than several other hypotheses (well, more compelling than "aliens," maybe).

But the sex angle is practically guaranteed to generate clicks.

2 Like • Comment • View 1 comment

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