Complex Numbers (Book)

Blog Calendar

◄ August ► 2020
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 6 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 8 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.

August 31, 2020 at 12:01am

#991928

Another Month in the Past

Well, tomorrow I plan on going back to the 30DBC for September. We'll see how that goes.

So today's article is short on philosophy and long on speculation, but I thought it was interesting enough to share since this affects many people.

Also, since it's the end of the month, I'll do a Merit Badge Mini-Contest! Details below.

Why the world is becoming more allergic to food

The rise in allergies in recent decades has been particularly noticeable in the West. Food allergy now affects about 7% of children in the UK and 9% of those in Australia, for example. Across Europe, 2% of adults have food allergies.

Obviously the BBC is a Brit-focused site, so they didn't give stats for the US. I suspect it's about the same... at least in reality. When you lump in all the children whose parents just want them to be special, it's probably closer to 40%.

Naw, I just pulled that number out of thin air. I can't be arsed to look it up. But seriously, all the ones who are faking it (as with gluten intolerance, or getting some doctor to sign something that your vicious little yip-yip mutt is actually an emotional support animal) just make things worse for those with serious issues. I suppose as far as Munchausen's-By-Proxy goes, though, things could be worse.

While we can't say for sure why allergy rates are increasing, researchers around the world are working hard to find ways to combat this phenomenon.

Article is from last year, obviously. I'm betting the pace of the work has slowed somewhat.

The increase in allergies is not simply the effect of society becoming more aware of them and better at diagnosing them.

It is thought that allergies and increased sensitivity to foods are probably environmental, and related to Western lifestyles.

Well, then, we're boned.

There is no single explanation for why the world is becoming more allergic to food, but science has some theories.

Insufficient data to know if she's using "theories" in the scientific or colloquial sense. Given her credentials, I certainly hope it's the former.

One is that improved hygiene is to blame, as children are not getting as many infections.

Sounds like a bit of a trade-off to me, but what do I know?

Another idea is that vitamin D can help our immune system develop a healthy response, making us less susceptible to allergies. Most populations around the world do not get enough vitamin D for several reasons, including spending less time in the sun.

Not much you can do about that in the UK. But really, you tell people to slather on SPF60 sunscreen and then wonder why they have VitD deficiencies?

A newer, "dual allergen exposure" theory, suggests food allergy development is down to the balance between the timing, dose and form of exposure.

Well, that tracks with it being an immune response thing, but the article doesn't do enough, in my opinion, to explain why rates are increasing if that's the case.

I went over half a century without allergies. Sometimes I feel like I'm the only one. When I spent some time in the hospital, I got asked about it all the time. The orderly: "Are you allergic to any medications?" Me: "No." Nurse: "Any allergies?" Me: "No." Doctor comes in. "Do you have any allergies?" "I'm allergic to repeating myself." They wheel me down the hall in a gurney. Janitor stops what he's doing: "Are you allergic to anything?" Me: *sigh*

I mean, this is a hospital that, one time, switched a couple of people's babies, and apparently people thought that was a Big Deal (having been adopted, I fail to see the problem), so I can understand them being thoroughly cautious, but fucking stamp it on my forehead or something, will ya? I'm having a heart attack over here; I got worse things to worry about than allergies.

So anyway, some years later, I tried a new brand of protein bar with something called "moringa" in it, and goddamn if I didn't break out in hives. I could feel my blood pressure plummet to something like 40/20. Okay, I don't know what my actual BP was, but the point is, it felt awful.

I can no longer say that I'm not allergic to anything, but unless they put moringa in my flu vaccine, I'm probably safe.

Merit Badge Mini-Contest!

Normally I relate these things to the topic, but I'm allergic to allergy talk. So, since it's the end of the month, I'll just ask:

This year has been utter shit. What are you hoping and/or fearing for September?

As usual, you have until midnight, when the calendar flips over to the new month. Just comment below. There's a Merit Badge going to whoever posts the comment I like best. Could be funny, serious, something in-between; I won't know what I like best until I see it.

Here's some inspiration. Or not. Up to you:

4 Like • Comment • View 5 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.