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Wednesday, Apr. 24, 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:

Aiva Raine

about 4 hours ago
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

a day ago
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

a day ago
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

a day ago
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

Aennaytte: Free & Wild in GoT

a day ago
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

Aennaytte: Free & Wild in GoT

a day ago
In response to "Going to the Dogs"

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

March 7, 2021 at 12:02am

#1005950

Praise Cheeses!

Today, in Adventures in Nutrition Science, another about-face:

Great News, America: Cheese Isn’t Bad for You
Don’t feel sheepish reaching for that manchego. Cheese doesn’t deserve its unhealthy reputation.

Well, at least the headline isn't in the form of a question.

Cheese is among the ultimate guilty pleasures. It’s gooey. It’s fatty. It’s delicious. It just has to be bad for you, right?

I mean, sure, cheese is good, but guilty pleasure? I hate that phrase anyway. Either enjoy something and wallow in it, or don't. No need to be coy about it.

Wrong. A large body of research suggests that cheese’s reputation as a fattening, heart-imperiling food is undeserved.

And this is why people have a distrust of science in general. Personally, I gave up on that field long ago, when they couldn't make up their cursed minds about eggs.

Just to be clear, nutrition science is wishy-washy like this because there are lots of hidden variables, variations among populations, suspect methodology, publication without peer review, incentives to find one result or another (that "chocolate is good for you" study was funded by chocolate companies, e.g.) and, most of all, a lot of really bad, breathless reporting about it all.

In the end, people extend their distrust of nutrition science to science in general, because your average person wants The One True Answer, which science can't give, but in other disciplines it's at least easier to approach. This is how you get shit like vaccine scares or climate change deniers.

“There’s almost no evidence that cheese causes weight gain—and in fact, there’s evidence that it’s neutral at worst,” says Dariush Mozaffarian, the lead author of the 2011 paper and dean of the Tufts Friedman School of Nutrition Science and Policy. “There’s no evidence that cheese is linked to cardiovascular disease, and in some studies, it’s even a little bit associated with lower risk. And then, for diabetes, again, it’s at worst neutral, and maybe protective.”

And so people end up back to believing whatever the hell they want to believe, and cherry-picking whatever study results back up their pre-existing beliefs. This particular quote I just pasted backs up my pre-existing belief, so I choose to believe it. Besides, even if someone posted "cheese will kill you dead," it wouldn't stop me from eating that delicious goodness. Because what's the point of living if you can't do the things that make life worth living, including eating cheese?

So just to recap so far: The evidence tends to show that cheese does not make you gain weight. Why hasn’t this amazing news spread more widely?

Probably because no one has bothered to put it into commercials or fund PR campaigns, the way they do with studies about booze or chocolate.

In the case of cheese, there could be several reasons for the surprising lack of impact on weight, though more research is needed. Cheese is fermented, meaning it has live bacterial cultures. That could have a positive effect on the gut microbiome, which appears to play a role in weight regulation. The fermentation process also creates vitamin K2, or menaquinone, which experimental studies have linked to improved insulin function. Insulin regulates blood sugar levels, hunger, calorie expenditure, and fat storage. (One upshot is that hard, aged cheeses, which are more fermented, probably provide more benefit than soft, less fermented ones.) There’s also some promising research about the benefits of a compound called the milk-fat globule membrane, which is intact in cheese but not in milk or butter.

All of these things are speculations requiring further research.

Other high-fat foods, like avocados, have lately enjoyed a reputational rehabilitation. Cheese, not so much. One reason may be the fact that cheese contains not just a lot of fat but a lot of saturated fat, a major dietary scofflaw linked to higher blood cholesterol and rates of cardiovascular disease. But here, too, the science says cheese doesn’t deserve its stigma. While cheese does have high saturated fat, that doesn’t appear to correlate with higher risk of heart disease.

I should probably make the point here (I didn't see it in the article) that they're talking about cheese. You know... real cheese? Not Cheez-Whiz or Chee-Tos and definitely not the plastic abomination labeled "Pasteurized Process Cheese Food," like a certain well-known brand of "singles."

Anyway, it's worth reading the linked article, if only to see for yourself some of the lines of research that support the conclusion. I still cringe at the writing style, but hey, not everyone can be me.

And while I'm on the subject of cheese, I thought I'd share my favorite dessert. No, it's not cheesecake (which is delicious, but it would take a lot to convince me that it's in any way "good for you"). This particular combination of flavors synergizes well, and, most of all, it's dead easy to prepare.

All it takes is:
Pears
Walnuts
Stilton cheese
Port wine, preferably tawny port.

I indulged in this deliciousness yesterday, in fact. And now with the article I linked above, I can't even claim it's just me enjoying something I shouldn't, as all of those things are now... Good For You.

6 Like • Comment • View 8 comments

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