Complex Numbers (Book)

Blog Calendar

◄ May ► 2022
S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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!

about 11 hours 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

about 13 hours 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.

May 10, 2022 at 4:53am

#1032196

Hell is Empty, and All the Devils Are Here

Occasionally, lifehacker will actually have a useful article.

How to Summon a Demon
Want a hell-spawn of your own? Need someone to play chess with? Try summoning a demon!

If I’ve learned nothing else from heavy metal, horror movies, and Dungeons and Dragons, I’ve learned that demons are awesome. I want to invite as many as possible into my life to do my bidding and compete in fiddle contests.

You have learned the wrong lessons, grasshopper. The only evil thing in Dungeons and Dragons is the DM.

This do-at-home rite is adopted from a handwritten, untitled grimoire written around 1577.

For context, this was just before Shakespeare became a thing. Hm, what if... nah.

A note of caution before you begin your ritual: Many experienced magical practitioners (wizards, warlocks, necromancers, etc.) maintain that even a simple ritual requires a lifetime of dedicated spiritual practice and should not be undertaken lightly, lest great harm befall you.

Yeah, these days we call that "gatekeeping." What's the point of magic if you can't use it to take shortcuts?

With that out of the way, let’s summon something! The original spell is sometimes confusing due to the age of the language and the fact that it’s handwritten, but I did my best.

Ever tried to puzzle out Shakespeare's original handwriting? Well.

Obviously, I'm not going to recopy the spell here; that's what the link is for. Some highlights:

Step three: Recite the oration. Stand over your glass and recite the following Latin aloud. Use a commanding, deep voice (it’s cooler that way): “Omnipotens sempiterne deus adesto magna[e] pietatis tue misteriis, adesto piis Invocationibus nostris ut speculum istud quod in tuo nomine bene dicere facto…”

It goes on like that for a looooong time. You can see the rest in the original text. Make sure you read it all and don’t mispronounce any words, though, or this might not work.

Here's the thing: no one alive knows how Latin was actually pronounced. We have some educated guesses, but things get lost over time. More, the language was so widespread that there were certainly regional dialects, in addition to the foreign accents of people who learned Latin as a Second Language. Some of these dialects became pidgins or creoles, and later evolved into Spanish, French, and so on.

It's kind of like how you can't say "be sure to pronounce English correctly." There is no One Correct Pronunciation, despite what the BBC tries to tell us (in one particular British accent).

After this transcription of the ritual (which, to be absolutely clear, is presented in what seems to be a self-parody of other lifehacker how-to guides), the article goes into some interesting history, which is the actual reason I'm linking this.

Rituals to summon supernatural entities or forces have been (and are) practiced in lots of spiritual traditions, from Shintoism to Santeria. Different rites have different meanings and implications in different traditions, so know that I’m only talking about the Western idea of calling explicitly evil entities into the material plane. Like you see in horror movies.

One thing about the long-running show Supernatural that stuck with me was that the showrunners there actually did their research.

Summoning a demon to do your bidding is central to the Testament of Solomon, a text falsely credited to King Solomon that was written somewhere between the end of the 1st century CE and the high medieval period. In it, an angel gives Solomon a ring inscribed with a pentagram.

This is one of the reasons why the pentagram gets a bad reputation. It shouldn't, really. It's a symbol of unity and harmony and balance, and also has some really cool mathematical properties that I won't go into right now, much to your relief.

(Right now everyone who thinks math is evil is nodding vigorously and itching to make a comment about it.)

Even the whole "inverted" thing is made-up.

Of course, everything we do is made-up, but that part's really made-up.

The Key of Solomon, for instance, does contain spells (like “How to make the holy garters”) but they only work for the most pure, virtuous, pious man.

I know "garters" is a word whose meaning has shifted over time, but this is still amusing.

The idea of summoning demon-y demons for your own gain, as an act of evil, catches on widely with the publication of Malleus Maleficarum (“Hammer of Witches”) in 1478.

This is an important point. Even if we take at face value the idea that one can summon a demon (there are metaphorical interpretations, but, like the author, I'm using the phrase literally), which we don't, this is kind of like some of the things we see even today on the internet.

For example, maybe some kids have started doing something stupid they saw on DikDok or whatever. This is nothing new in society; kids are always doing stupid shit, which is partly how natural selection still works on humanity. But us olds would have never heard about it if someone hadn't hit the Moral Panic Button and started going, "Look at what these idiot kids are doing." This just spreads the ideas more widely, and even some adults who somehow managed to survive childhood with most of their fingers and eyes go, "Hey, that looks like fun. Hold my beer."

That publication caused WAY more evil in the world than the supposed evils it was railing against.

Fake or not, a lot people died for real because of Hammer of Witches. As many as 80,000 people, mostly women, were tortured and murdered during the witch trials that were heavily influenced by Kramer’s book. So if any tome is cursed…

There are none so evil as those who proclaim themselves to be righteous.

No, that's not a quote; that's an original Waltzism.

No, I don't claim to be righteous.

The article goes on to point out that while the idea of summoning demons is "fake" (again, I call it metaphorical), there exists true evil in the world, and usually, that evil is the group that is conjuring up the moral panic in the first place.

After all, if you really want to summon a demon, all you have to do is go on the internet and say things like:

"We should institute socialized medicine."

"Cannabis should be universally legal."

"Living wage for all."

"Musk is an ass."

or

"Chicago pizza isn't pizza."

The metaphor I keep referring to in this post is that demon-summoning is actually about confronting the darker aspects of one's own nature (and we all have darker aspects). But there are people in the world who deliberately do evil, though they insist they're doing good.

At least if literal demon-summoning were real, you'd end up with an entity that knows it's evil. That, you can work with. It's a lot harder to banish those who are certain they're righteous.

5 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.