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Thursday, May. 2, 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

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

🌕 HuntersMoon

about 7 hours ago
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

1 Like

Elisa the Bunny Stik

a day ago
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
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

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

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

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
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 Montana

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 Montana

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 Montana

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

April 19, 2024 at 10:31am

#1069178

Mind the Menu

I've done entries before about this sort of thing, but it doesn't look like I've addressed this particular article. It's quite ancient by internet standards, but I don't get the impression that much has changed on this subject since 2016.

8 Psychological Tricks of Restaurant Menus

These aren't necessarily bad things, but being aware of them might at least give you a little smug feeling next time you encounter one.

A restaurant’s menu is more than just a random list of dishes.

"Random" doesn't mean what they think it means.

It has likely been strategically tailored at the hands of a menu engineer or consultant to ensure it's on-brand, easy to read, and most importantly, profitable.

Funny, I don't remember menu engineering as an option when I went to engineering school.

As for "profitable," don't say that like it's a bad thing. Sure, focus on profits above all else is greedy, but if a business doesn't turn a profit, it's not a business much longer.

1. THEY LIMIT YOUR OPTIONS.

The best menus account for the psychological theory known as the “paradox of choice,” which says that the more options we have, the more anxiety we feel.

This is also not a bad thing. Your options usually aren't actually limited: you could go to a different restaurant, eat at home, or choose not to eat.

Some big chain restaurants have enormous menus with lots of options. Less "menu" and more "book." Think Applebee's, though I haven't been to one of those in so long that I don't know if it's still the case that their menus are about the length of War and Peace. People keep going back, though, as evidenced by the fact that many of them still exist, having survived the pandemic.

The problem with those encyclopedic menus, for me, isn't the overwhelming number of choices. No, it's the knowledge that the only way I know of to prepare that much of that variety of food is to have frozen pre-packaged portions that get microwaved.

2. THEY ADD PHOTOS.

Including a nice-looking picture alongside a food item increases sales by 30 percent, according to Rapp.

Oh no! The horror! We're being manipulated by being shown images of what we might want to eat!

No, the only problem with this is when the actual served dish is far removed from the idealized photo. Food menu photography is an art of its own. I dabbled in it a bit back in college. The photography part wasn't hard. The hard part was faking the food item in such a way that it looked hyperreal, like the actual food but... more appetizing, even though it wasn't made of real stuff.

Still, it's helpful to the consumer if the image roughly corresponds with the ingredients and serving size you're actually going to get.

3. THEY MANIPULATE PRICES.

One way to encourage you to spend more money is by making price tags as inconspicuous as possible. “We get rid of dollar signs because that’s a pain point,” says Allen. “They remind people they’re spending money.” Instead of $12.00 for that club sandwich, you’re likely to see it listed as 12.00, or even just 12.

Meh, whatever. That's on you.

One thing that has changed since this article originally came out, and it happened very recently, is that Wendy's announced that it would implement "surge pricing" much like Uber does, charging more at peak hours. Easy enough to do now that fast-food menus are mostly digital display screens, I suppose.

The problem is, in my amateur opinion, that they went about it in exactly the wrong way. They said "we'll increase prices at peak times," and people were outraged. How dare they? Whereas if they'd quietly increased prices across the board, people probably would barely notice, especially if they don't eat fast food very often. More, if they'd framed it as "we're going to decrease prices during off-peak hours," my feeling is that the vast ravening herd would have praised them for being so generous, even if it were accompanied by a quiet, general price-hike.

Don't believe me? Consider the popularity of matinee movies and happy hours, which are marketed exactly like that.

I don't care, because I eat at Wendy's maybe once a year, if that. But last I heard, the company's damage control was working full blast on their backpedal.

4. THEY USE EXPENSIVE DECOYS.

On menus, perspective is everything. One trick is to include an incredibly expensive item near the top of the menu, which makes everything else seem reasonably priced. Your server never expects you to actually order that $300 lobster, but it sure makes the $70 steak look positively thrifty, doesn’t it?

I've written about this decoy pricing before, most recently here: "The Real Decoy"

5. THEY PLAY WITH YOUR EYES.

Just like supermarkets put profitable items at eye level, restaurants design their menus to make the most of your gaze.

Again, this isn't necessarily a bad thing.

6. THEY UTILIZE COLORS.

According to Allen, different colors help conjure feelings and “motivate” behavior.

Some of these color associations strike me like astrology, but, I reiterate, so what? Marketers have been using color to catch our eyes for as long as there's been color.

7. THEY USE FANCY LANGUAGE.

Longer, more detailed descriptions sell more food.

Duh. You put a menu item up that says "green beans," and I think of the slop my mother used to make of those stringy bastards. Label it "haricots verts" (French for, literally, "green beans," in case you didn't know) and describe it as "lightly braised in olive oil with crushed roasted almonds and just a hint of garlic," and I'll take a double portion, please.

All food is better in French. That's just a fact.

Related:

“People taste what you tell them they’re tasting,” Rapp says. Consider this: In another study, researchers presented two different groups with the same red wine but with different labels. One label said North Dakota (do they even make wine there?), the other said California. In taste tests, the “California” wine squarely defeated the “North Dakota” wine even though both groups' glasses were filled with “Two-Buck Chuck”.

1) Yes, they make wine in North Dakota. From what I hear, it has a terroir reminiscent of fracking.

2) This is why I hate blind taste-tests. I eat and drink for the whole experience, not just the stimulation of one sense.

3) That "study" involved more psychological manipulation than any of these listed "tricks."

8. THEY MAKE YOU FEEL NOSTALGIC.

We all have that one meal that takes us back to childhood. Restaurants know this tendency, and they use it to their advantage.

Maybe I'm in the minority here, but I assert there's nothing inherently wrong with nostalgia. As long as you identify it for what it is, and understand that not everything "back then" was roses and sunshine.

For instance, when I was a kid, there wasn't a publicly-available internet. Some might think that was better. I do not.

In any case, I think it helps to know these things, even though I don't think any of them are inherently deceitful. At least, not any more than most marketing. But being aware might help you catch when someone really is trying to trick you, usually some university psychologist who's feeding you Two-Buck Chuck.

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