Complex Numbers (Book)

Blog Calendar

◄ July ►
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:

Brandiwyn🎶

about 22 hours 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

July 12, 2024 at 12:49pm

#1073868

Arsenic and Old Rice

Apologies for the Torygraph link today. If it helps, I'm going to rag on the article. Today in "You're doing it wrong!":

How we are all cooking rice incorrectly - and could be endangering our health

Millions of cooks are endangering their health by cooking their rice incorrectly, scientists believe.

Which scientists? The link provided with that lede goes to another Torygraph article scaremongering about lung cancer risk from high glycemic index carbohydrates, which violates at least two principles: 1) make your link relevant to the argument; 2) don't freakin' cite your own prior article as a source.

Putting more water in the pan or even steeping it overnight is the best way to flush out traces of the poison arsenic, they found.

Arsenic is well-known as a poison, but it's part of the natural environment (yet another reason I distrust "natural" claims).

I can't be arse(nic)d to go into much detail here, but it's an element on the periodic table, not some factory-produced compound.

The chemical contaminates rice as a result of industrial toxins and pesticides which can remain in the soil for decades.

It is true, however, that certain processes can concentrate and redistribute the element.

Experts have long debated what level of arsenic is safe, with new limits set by the EU in 2016.

"Safe" is misleading. The only thing I found on limits has to do with American public drinking water, where the limit is 10 parts per billion.

Usually. But that's for inorganic arsenic; organic arsenic (which, as that link points out, has nothing to do with the marketing concept known as "organic") is less toxic. Remember, it's an element, so it shows up in different kinds of molecules.

But experiments suggest that the way rice is cooked is key to reducing exposure to the toxic but naturally occurring chemical.

Or we could, I don't know... stop polluting everything?

Prof Andy Meharg, from Queens University Belfast, tested three ways of cooking rice for the BBC programme Trust Me, I’m a Doctor.

I'm way more inclined to trust the BBC than the Torygraph. Which doesn't mean they're perfect.

In the first, he used a ratio of two parts water to one part rice, where the water is “steamed out” during cooking.

In the second, with five parts water to one part rice, with the excess water washed off, levels of arsenic were almost halved.

And in the third method, where the rice was soaked overnight, levels of the toxin were reduced by 80 per cent.

That first one is the usual method, at least here in the US.

There's just one problem with the alternative methods. Well, perhaps more than one, but the one that jumped out at me was: that's a lot of water wasted. Which I guess isn't much of a problem if you're in the UK, where, I'm assured, it rains all the goddamned time. But in many parts of the world, water is precious (and becoming more so as time goes on).

This isn't usually much of an issue in what we've called "first-world" countries, but they get a different problem: insecure and sometimes questionable water supply. Which, as I've noted above, has a maximum arsenic level greater than 0.

Wells and other sources aren't formally tested at all.

To summarize, rice is a staple for more than half the world; rice has been found to have an unspecified but presumably risky level of arsenic; and using 2-3 times as much water, and possibly even more for rinsing after, might reduce arsenic levels... at the cost of time, water, and effort.

And once again, fixing the problem of industrial pollution falls squarely on our shoulders, rather than those of the companies who did the pollution in the first place.

5 Like • 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.