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Monday, Nov. 18, 2024

12:37am 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:

tj-turkey-jobble-jobble-hard-J

about 9 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

October 26, 2023 at 10:06am

#1058097

The Dark Side

I put up with reading articles like this one only so I can rag on them.

If You Want To Be Truly Free And Happy, You Must Banish These 4 Thoughts
Nothing good will happen to you if you're negative all the time.

And already I'm negative about it.

Are you clinging to something that is not serving you?

My cats, for some reason, refuse to serve me; they insist that the other way around is the natural order of things.

Do you feel doubt? Failure? Depressed?

Are you about to tell me that I can think my way out of clinical depression?

It’s time to let go of negativity and pain and accept life as it is.

Ha, ha, very funny.

...oh, wait. You're serious.

We encounter numerous toxic people every day who deliver subtle negative messages and instill negative ideas constantly.

And so we come to the root of why they want us to banish the negative and plaster smiles on our faces and pretend everything's sunshine and peaches: being a grump inconveniences other people.

However, in order to cultivate a positive mindset, you need to develop a strong mentality and separate yourself from the general crowd.

Once you do those things, you won't need to cultivate a positive mindset. Life will automatically be less stressful.

By giving more power to negativity, you will send out negative thoughts to the universe and end up attracting and manifesting negative things only.

Ah, yes, the power of magical thinking. Kind of the opposite of "develop a strong mentality" here.

If you let negativity creep into your mind, it will steal all your peace and happiness and put you in a dark pit of suffering.

Follow Master Yoda you must. Heed his words you should. "Fear is the path to the dark side. Fear leads to anger. Anger leads to hate. Hate leads to suffering."

To be clear here, I work to live my life without fear, anger, or hate. If those are the "negative" things they want banished, well, you're never going to banish them entirely, not without giving up everything that's worthwhile in the process. But that doesn't mean you have to let these things control you.

Shift your focus to the positive aspects of life, as there is always a silver lining in even the darkest situations.

Conversely, there's always a dark cloud in even the brightest situations.

Your reality is not based on what others think or say about you.

Neither does it depend on your negative thoughts or self-doubt.

... but you just said that it did, that negative thoughts manifest themselves through the universe's karmic channels or whatever. Which is it? (Answer: neither. Reality includes your thoughts, but is independent of your thoughts. Perception, sure. But not reality.)

So start by letting go of negative perspectives, grudges, jealousy, fear, pain, self-doubt, and toxic relationships that might hold you back.

I could take these one by one, but I have a dentist appointment later this morning, so I have limited time. While I tentatively agree that a lot of those things stunt one's personal growth, a healthy dose of self-doubt is important to keep a person from being too arrogant. And don't get me started on "pain." Assuming that means mental anguish and not physical pain, first, it's not so easy to get past trauma, and second, sometimes you have to wallow in it for a while before you get better.

When you let go of negativity from your past, you will be more mindful and bring your awareness to the present moment and stop worrying about what you cannot control.

I'm all for not worrying about what you can't control, but screw this "present moment" and "mindfulness" bullshit. We're nothing without our pasts, and if we don't concern ourselves with the future, it'll smack us in the faces.

Here are a few proven ways to help you release negativity from your life.

"Proven?" [citation needed]

I won't go into the "few ways." The article is there if you want to draw your own conclusions.

I'm not even saying everything in the article is wrong. As I said above, I'm not a fan of letting anger control me, and I don't live my life in fear. But there's also a hefty dose of airy nonsense and denial of reality, or at least a lack of acknowledgement thereof. Banish anger completely, and there goes one motivation to make positive changes. Banish fear, and you might think it's okay to take that shortcut through Mugger Alley.

Perhaps getting stuck in Pollyanna world is preferable to getting stuck in Eeyore world. But I'd rather not get stuck anywhere.

6 Like • Comment • View 2 comments

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