Complex Numbers (Book)

Blog Calendar

◄ February ► 2021
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
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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

February 15, 2021 at 12:05am

#1004505

Plastics.

It is not likely that every problem caused by technology has a technological solution. But many do. Here's an example.

Plastic trash can now be recycled into ultra-strong graphene
Plastic decomposition is sped up by the flash Joule heating method

Packaging from the grocery store, lint from our clothing, plastic shopping bags – plastics and microplastics are everywhere, and they’re not going anywhere.

Mr. McGuire: I want to say one word to you. Just one word.
Benjamin: Yes, sir.
Mr. McGuire: Are you listening?
Benjamin: Yes, I am.
Mr. McGuire: Plastics.
Benjamin: Exactly how do you mean?
Mr. McGuire: There's a great future in plastics. Think about it. Will you think about it?

I'm sure this is not what McGuire meant in The Graduate, but yes, indeed there was a great future in plastics. A very, very long one indeed.

In order to speed up this decomposition process, scientists from Rice University are transforming these discarded plastics into non-toxic, naturally occurring materials. They're doing this by using a newly developed technique called “flash Joule heating,” to rapidly heat plastic materials to very high temperatures .

"But where's the energy coming from to-" "Shut up."

Currently, there are a few plastic recycling techniques that are widely used, with differing results.

Now, I've heard -- without a lot of confirmation -- that many plastics don't get recycled at all, even if they're labeled with recycle symbols, sorted carefully into categories, left in a recycling container instead of the trash can (rubbish bin for my Brit friends), and picked up by a green truck with a great big RECYCLE logo on it. This is, I've heard, because plastics are generally difficult to recycle. Aluminum and other metals? Easy; melt it down and you get... aluminum or whatever. Glass? Also easy. Melt it down and you get glass. Melt plastic down and those handy long-chain hydrocarbons break apart and you get methane, carbon dioxide, and all sorts of fun-to-pronounce chemicals.

Even more shockingly, each plastic bag is used for, on average, less than one hour.

Depends on what you mean by "use." and what you mean by "bag." Why, I have plastic bags in my freezer that have been in use since 1996. I suppose one of these days I should remove the 25-year-old meat, but I can't be arsed.

Okay, that's hyperbole. Still, it might be time to go through the freezer.

In contrast, the “flash Joule heating” method turns plastic into graphene, which is highly recyclable and very stable. Graphene itself is incredibly strong and stretchy – 200 times stronger than steel. Graphene is a single layer form of graphite, a naturally occurring carbon-based mineral that is commonly found as pencil lead.

What the hell, MassiveSci? I expect better than this from you. Graphite (as well as graphene) is carbon-based in the same sense that the clear liquid coming out of your faucet is "water-based." That is, it's pure carbon. Like diamond, only generally not mined by 8-year-old slaves.

By directly generating graphene from plastic waste, it is possible to reduce its production cost.

Again, graphene is carbon. Plastics are based on long-chain hydrocarbons. I don't see very much in the article about what happens to all the other little atoms. "Some hydrogen and hydrocarbons." Okay, then what?

Generating graphene directly from plastic could disrupt the graphite supply chain, thereby decreasing mining activity and reducing pollution caused by mining.

Job killer!

In the meantime, you can help fight plastic waste by making one small but significant change in your life: bring your own reusable fabric bag to the store with you.

You know. I'm old enough to remember that groceries used to be packed in brown paper bags exclusively. Paper, of course, is both fairly easy to recycle or, if you can't be arsed to recycle it, biodegradable. Then the grocery stores started stocking those flimsy plastic bags that (con) couldn't carry much more than three tomatoes without breaking but (pro) had handles. Plastic bags were better for the stores because they were cheaper and lighter, and you could store like 1000 of them where you could only store like 100 paper bags (note: those numbers are wild-ass guesses, but the idea is valid). There was a transition period you might recall when shoppers were offered a choice. "Paper or plastic?" became even more ubiquitous for a few years than "Credit or debit?" and "You want fries with that?"

Finally they trained consumers to not want paper bags anymore, and they quit asking, instead just dumping the groceries into plastic bags. This end of the "Paper or plastic?" era somehow coincided with the first scaremongering about OMG MICROPASTICS WTF NONBIODEGRADABLE IT'S EVERYWHERE. Hell, some areas flat-out banned plastic bags, and didn't go back to paper. And bringing my own bags to the grocery store is Not Going To Happen. (I don't go to the store anymore anyway, instead opting for delivery -- which usually comes in plastic bags. I don't give a shit.)

I'm not saying there isn't a problem with microplastics. I'm saying, like, why the fearmongering? Unless it's a massive campaign financed by pissed-off paper bag manufacturers, or the makers of reusable cloth grocery bags. Yeah... that's my working theory. It's like how I've always thought that PETA is actually run by the soybean industry in an effort to sell more tofu.

Anyway. Point is, this is pretty clever technology and I hope it actually becomes a thing.

3 Like • Comment • View 4 comments

© 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.