Complex Numbers (Book)

Blog Calendar

◄ June ► 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	29	30
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 8 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 10 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.

June 3, 2021 at 12:02am

#1011209

Paper or Plastic?

Normally, I cheerfully ignore articles that claim "If you're doing x to help the environment instead of doing y, you're actually making things worse." I tend to assume they're coming from people who are trying to sell/promote y.

Your cotton tote is pretty much the worst replacement for a plastic bag

Not so sure about this one, though.

And look, I get it. We got conned into low-flow toilets that use 1/3 less water, but you have to flush 3 times as often. And water-reducing shower heads that cut water use by 50% but you end up doubling the length of your shower.

As far as I can tell, though, LED bulbs are actually a good thing. But enough about that. Let's get back to shopping bags.

If you’re trying to contribute as little as possible to the two global calamities of climate change and the swirling gyres of forever-materials slowly filling our oceans, there’s a useful formula to keep in mind: Use fewer things, many times, and don’t buy new ones.

Also don't have kids, but for some reason no one ever mentions that.

But are plastic bags better or worse than paper? And what about a cotton tote? Let’s rip this bandaid off right away: There’s no easy answer.

Oh, good, the possibility of nuance. None of this "Wind farms kill birds and contribute to noise pollution so let's go back to coal, everyone!" "Signed, The Coal Industry."

The article goes on to lay out the pros and cons of our shopping bag choices.

The table below, using data from the Denmark study, compares the environmental performance of LDPE bags to other bags, assuming that the LDPE bags are reused once as a trash bin liner before being incinerated (incineration is the best possible disposal for these bags, according to the report).

Of course, you're going to have to go to the link to see the actual table. I have no idea how solid the information is, but let's take it at face value for now.

On a personal note, I get groceries delivered. Sometimes they show up in plastic bags. Some of said bags end up as trash bags. Most get dumped into the purposed recycling bin at the grocery store on the rare occasion that I can be arsed to go to the grocery store. What happens to them after that is Not My Problem.

Other times, the groceries come in paper bags, which end up in general paper recycling, and as far as I know, they actually get recycled.

The important numbers are at the bottom of that table I mentioned. To "have same cumulative environmental impact (water use, energy use, etc.) as a classic plastic bag," an organic cotton bag would need to be reused 20,000 times.

As a point of reference for that, 20,000 days is over half a century.

Cotton fabric can last a long time, but rarely that long if it sees frequent use. And that's assuming you use the tote every day, which is not a good assumption.

The report also assumed the cotton could not be recycled, since very little infrastructure exists for textile recycling.

Maybe it can be used as a cleaning rag when it becomes holey?

Plus, knowing how many resources it takes to make a piece of cotton, treat fabric items in your home like infinitely reusable resources worth their carbon-mitigating weight in gold. Find new uses for old clothes, use textiles until they wear out, and when you want something new, buy vintage.

Ahem.

Bite me.

Also, no. Don't put all this shit on us. All that does is shift responsibility. Individually, we're a bunch of dumb-asses, me included. Collectively, well, we're still a bunch of dumb-asses and, as the past year or so has taught us, there are significant numbers of people who will simply never go along with a program for the common good..That just puts an extra burden on the people who do. But when small groups of people get together with a financial incentive to do so, we can be quite clever. So take your it's-all-your-fault mentality and shove it; find a way to fix the problem at the source, not at the destination.

6 Like • Comment • View 3 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.