Complex Numbers (Book)

Blog Calendar

◄ April ►
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
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 5 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 7 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.

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.

3 Like • Comment • View 2 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.