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Sunday, Apr. 28, 2024

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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:

Lazy Writer est 4/24/2008

10 minutes ago
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

about 4 hours ago
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

a day ago
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

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

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