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Saturday, Nov. 2, 2024

2:21pm EDT

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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:

🌕 HuntersMoon

about 4 hours ago
In response to "She Said Spatchcock"

In my experience, exposing the breast doesn't make it dryer. Just saying'

1 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "Cave In"

I think it was one of the gateways, but after the riots, the denizens of Hell closed that portal for fear of what might get in.

Wordsmitty ✍️

a day ago
In response to "Cave In"

Makes you wonder what might be under your city - or house.

2 Like

Elisa: Stik or Treat

a day ago
In response to "Cave In"

"Well, clearly, that's because Minneapolis is actually a gateway to Hell."

Easy there, J.D. Vance.

In all seriousness, my guess is to actual recycle this heat they'd probably build pipelines to direct the heat energy to the nearest power plant (maybe Hennepin Island?) to spin turbines. This would involve converting buildings to run on heat pumps first (maybe with natural gas backups because subzero days do still happen). Regardless, whatever recycling involved would be an indirect process. Putting that heat and also hated fumes directly into buildings would be wildly unpopular. It's bad enough when southern winds bring the manure scent into the metro in the late autumn. This would make that scent a bit more permanent than we'd like.

2 Like

Write_Mikey_Write!

a day ago
In response to "Cave In"

Seeing as how I'm reasonably certain you keep up with each other's blogs, I can't help but wonder what a certain well-informed, Stik-like Minneapolitan will have to say about this.

2 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "Phases"

Perhaps, if the full moon drives one to madness, the half moon will only make one half-crazy.

1 Like

Brandiwyn🎶

Oct 29, 2024 at 12:18pm
In response to "The Numbers Don't Lie"

I hear ya. I like to think I'm discerning enough to detect fakes, but that might just be my ego talking. When it comes to local businesses, I also go to social media and request recommendations. With both reviews from strangers and recommendations from friends, I give more credence when more (anecdotal, heh) details are provided. It's more an art than science, but liars either have such flawless details that their story sounds fabricated, or they get embarrassed when they trip themselves up. Truthtellers make errors, because memories are fallible, but they get more confused than embarrassed. Ultimately, the only way to really know is to try the product/service yourself. Which is why you'll hear about my Cancun vacation next month, but you don't have to believe me.

1 Like

Robert Waltz

Oct 29, 2024 at 11:07am
In response to "The Numbers Don't Lie"

Brandiwyn🎶

- I, too, look at the 1-star reviews, though again, reviews aren't my sole criteria. But sometimes it's blatant fake reviewing from the competition: "Don't stay here! It has rats, bedbugs, and roaches! Stay at this other place instead!" where "this other place" is clearly owned by the reviewer.

On the other paw, five-star reviews are often salted by the establishment in question.

Used to be, you could look at the four- and two- star reviews to get more honest, nuanced opinions, but the establishments, and their competition, have figured out that trick.

Which is one reason why reviews aren't my sole criteria.

(None of this applies to WDC reviews, or to the artificially inflated Uber rating system)

Brandiwyn🎶

Oct 29, 2024 at 11:00am
In response to "The Numbers Don't Lie"

And I was going to conclude by saying, when evaluating Caribbean vacation destinations, even if 5,000 people gave it a 4.8 rating, if the one star reviews were from seven people who encountered rats in their rooms, I'm very likely to not choose this destination.

2 Like

Brandiwyn🎶

Oct 29, 2024 at 10:58am
In response to "The Numbers Don't Lie"

Well, that was annoying. I was still in the process of editing, so please excuse the multitude of errors. I also intended to italicize the quotes from your post. Stupid f****** Parkinson's.

1 Like

November 2, 2024 at 9:58am

#1079387

She Said Spatchcock

I guess sometimes Lifehacker is good for a laugh. Laughacker? I don't know.

Spatchcocking Your Chicken Is Worth the Effort
Those thighs aren't going to crisp tucked way under there.

Settle down, Beavis.

Roast chicken is an everyday pleasure—a good fit for both special occasions and midnight snacks.

Which is why my grocery store sells rotisserie chicks.

While you might be familiar with the classic roasting style, with trussed legs and tucked wings, this method can lead to overcooked breasts and soggy thighs, two phrases I want nowhere near my chicken.

Heh heh heh huh huh

There’s a better way to roast your chicken for more even cooking: spatchcocking.

Bwaaaaahahahaha

You can spatchcock, or butterfly, any bird.

That bit might only be funny if you're familiar with British slang.

Traditional roasting puts the driest cut of meat (the breast of the chicken) at the top, often closest to the heating element—before you've even turned up the heat, it’s a recipe for overcooking. The parts that are juiciest (i.e. the thighs) are lower, if not completely under the rest of the body, and shielded from direct heat.

Somehow I'm hungry for wings, now, and I hate wings.

Illustrated instructions follow. I'd suggest not going to the link if you're vegan or vegetarian, or, like me, are allergic to hard work.

1 Like • Comment • View 1 comment

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