Complex Numbers (Book)

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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/

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Write_Mikey_Write!

about an hour 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 3 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').

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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.

May 23, 2023 at 10:06am

#1049998

Authenticity

I've ragged on this sort of thing before, but it's been a while.

Why Authenticity Doesn’t Exist When It Comes To Food
Plus Ronnie Woo Shares a Recipe for Caramelized Hong-Kong Inspired Egg Tart

In my opinion, forcing "authenticity" on food leads to stagnation. It's a lot more interesting to mix things up a bit.

The debate over authenticity in food really comes down to how you define the word “authentic.” The word is often used to describe something that’s either fake or genuine, such as a brand name handbag or a pair of shoes, but in the case of food it doesn’t really apply (unless it’s plastic).

Most things come down to a matter of definition. As I said recently, I consider a hot dog to be a kind of taco. That depends on how you define (and serve) the hot dog, or a taco.

If every time we saw the words “authentic food” and replaced it with the word “traditional,” the sentence itself would probably be much less controversial. But even thinking of “traditional food” doesn’t maintain the intended meaning. I can guarantee that every time a recipe has been passed down to the next generation, changes were made.

Some of that is a search for novelty, but sometimes the changes are because of shifting availability of ingredients or cooking/prep methods.

Authenticity is simply a buzzword that some people have adopted as a way to declare that they are the real food-lovers and are somehow better than you based on what they perceive to be “real.”

And that's my main problem with it, I think: it's another form of gatekeeping.

Now, I know that, in the past, I've declared New York style pizza to be the One True Pizza, and American adjunct light beer to be not-beer. That's inconsistent with what I just said. It happens. I'm almost as loaded with contradictions as I am with pizza and beer. I am large; I contain multitudes.

But here's the important part, a rare instance of me completely agreeing with an article author:

I could care less if something is authentic, or even traditional for that matter – I just care that it’s delicious.

Well. Except that it should have been "I couldn't care less." Do English right! (In fairness, I don't know if English is Woo's first language or not, and here I am gatekeeping again.)

The beauty of having the privilege of eating food for pleasure is that we all are, and should be, allowed to mix and match whatever we want with reckless abandon. To me, the kitchen has no rules.

Yeah, no. The kitchen has plenty of rules. "Don't touch a hot stove." "Keep your knives sharp." "Always preheat the oven."

But now I'm being needlessly pedantic. I know what the author actually means: if you want to create a lo mein burrito, go for it.

Funny enough, there are numerous times where I actually like my interpretation of a traditional recipe more simply because I got to make it my own. Take my spicy almond pesto udon recipe, where I make a spicy version of a traditional Italian sauce and pair it with thick chewy noodles that are typically found in Japanese cuisine. Is this dish traditional? Absolutely not, but it sure is authentic to me (and, I should mention, absolutely delectable).

Many people associate pasta with "authentic" Italian cuisine. And tomatoes. But pasta is the Italian take on an Eastern innovation (noodles), and they wouldn't have tomatoes at all if not for the whole "invasion of the Americas" thing. Just because they added those ingredients long before we were born doesn't mean they're authentic or inauthentic.

While the line that differentiates appropriation and inspiration is not always crystal clear, it is important to not to erase the history or people from which a dish originated from.

This is an important point, though. And it's one that I'm not getting into, except to relate (possibly not for the first time) a personal anecdote:

I was sitting in my local bagel restaurant ("authentic" New York bagels in Virginia) many years ago, enjoying my carbohydrate toroid, when I overheard someone at the next table complain about cultural appropriation. I glanced over and noticed that she was eating a bacon, egg, and cheese bagel.

Why is this irony? Because bagels are indisputably Jewish food (it's a cultural thing, not religious). But bacon is indisputably not. Nor is the concept of eating any kind of meat alongside any kind of dairy product.

Don't get me wrong; I enjoy bacon, egg and cheese bagels, myself. But I also don't complain about food as cultural appropriation.

The meaty (pun intended) part of the article ends with:

At best, authenticity in food is subjective because no single individual or society can define what it is. If everyone stopped viewing cuisine and culture from a stagnant perspective, paid more attention to the deeply rich experiences of cooks (and people) of color, and appreciated all culinary interpretations simply for what they are, the experience of eating could just be fun and delicious. And that’s exactly what I think it should be.

And I like that viewpoint.

The rest of the article is the promised Hong Kong-inspired egg tart, but I'll leave that for people who aren't as lazy as I am to peruse. I'll just add one more short anecdote about authenticity:

Driving through the wildscape of the Olympic Peninsula in the state of Washington, one day many years ago, I started to get hungry. So I pulled off into a strip mall. Said strip mall had not one, but two, restaurants billed as Mexican.

One of them had bright neon in the window, and ads for Corona and Bud Light and, if I recall correctly, even a dancing neon margarita glass. I may not remember the details very accurately, but hopefully I'm at least conveying the feel of the place.

The other one was a simple storefront with big glass windows and some signs in Spanish.

I entered the latter, where the TV was set to a Spanish language station, on mute but subtitled in Spanish, and had Mexican music playing. The food was excellent.

But I like to think that maybe the same people owned both storefronts (there was a Latin food shop in between them), and just ran the Bud Light one as a gringo trap.

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