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Friday, Nov. 1, 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:

tj: Tenebrous Jekyll

about 7 hours 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

Battywyn🎶

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"

Battywyn🎶

- 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)

Battywyn🎶

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

Battywyn🎶

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

Battywyn🎶

Oct 29, 2024 at 10:56am
In response to "The Numbers Don't Lie"

You know what sometimes lies? Anecdotes.

Also, dogs, I've heard.

Oh, hell no.

🤣 I love a good inside joke, but my marketing guru would tell you to cross link here

The fallacy is named after Robert McNamara, the U.S. Secretary of Defense during the Vietnam War, where his over-reliance on measurable data led to several misguided strategies

Bet he's proud of his claim to fame.

What's the point in data, then?

The point in data is a decimal separator, unless here in non-english speaking countries, in which case it's more likely a thousands separator.

So, whenever I'm evaluating online reviews for pretty much anything, and for the record I check them for almost everything - I always consider three things: 1. The average rating (eg, number of stars); 2. The The number of contributors to the rating; and three. What the one star ratings say.

1 Like

Annette

Oct 28, 2024 at 2:47pm
In response to "Waste Not"

In Southern California, every single family residence has a green bin. Every trash day, three different trucks make the rounds.

1 for composting
1 for recycling
1 for garbage

Trader Joe's sells almost exclusively packaged foods, even perishables. They have contracts with college food pantries. In many colleges, there are now pantries that are open to the students 4 or 5 days a week plus 1 day when people from the community can drive up and receive a bag with a mix of fresh fruits and vegetables along with non-perishable foods and donated sundries.

Churches are huge food redistribution centers also.

The "too hard to set up" systems have created good jobs here. Instead of seeing food donations as a liability, they have created a supervised and refrigerated second market.

The cost for employees is small because, of course, many of the positions are volunteers. But the supervisors and some of the staff are full time employees with benefits.

The article has thrown up obstacles that are easy to overcome.

3 Like

AnotherDreamer

Oct 28, 2024 at 11:33am
In response to "Waste Not"

https://cdn.prod.website-files.com/6156cebc4c605e281289a232/6156cebc4c605eb8bc89... e%20for%20beginners%2024%2009%2018.pdf

1 Like

Robert Waltz

Oct 28, 2024 at 11:33am
In response to "Waste Not"

AnotherDreamer

- Hey, it's a replicator from Star Trek!

Now let's invent the holodeck.

2 Like

AnotherDreamer

Oct 28, 2024 at 11:27am
In response to "Waste Not"

We the people of the world could use those products before they are compost as free sources for 3D printed foods that could be used for emergency food, or if tasty enough, re sold.https://builtin.com/articles/3d-printed-food

2 Like

December 18, 2019 at 12:02am

#971632

Red Queen's Race

While we're on the subject of weight loss...

https://www.vox.com/2016/4/28/11518804/weight-loss-exercise-myth-burn-calories

Why you shouldn't exercise to lose weight, explained with 60+ studies

Oh look, another "You're Doing It Wrong" article! - or is it?

"I'm going to make you work hard," a blonde and perfectly muscled fitness instructor screamed at me in a recent spinning class, "so you can have that second drink at happy hour!"

Remember yesterday when I said I wouldn't be caught dead in a spin(ning) class? This reinforces that.

Anyway, the article dives into some science, much of which could stand to be replicated or at least extended. When it comes to nutrition (or, in this case, exercise) science, I approach it with a healthy (pun intended, as always) dose of skepticism.

And I'm not going to quote a lot from it. Instead, I'm just going to summarize:

Exercise is good (and necessary), but it probably isn't enough, on its own, for losing weight.

This tracks with my own experience, but of course my own experience is a data point of one and when it comes to fitness, I always find out later I've been lying to myself. So I don't trust my own experience, either.

Still, it was true for me that diet alone, without additional exercise (that is, more than what it takes to walk from the couch to the bathroom and back again a few times a day) doesn't work. It requires both.

So what's the point of exercise? I ask myself that every time I get on the elliptical trainer, and I have to remind myself that it makes me feel less dumb and helps fend off depression. That alone is usually reason enough to keep going; any weight loss benefits are icing on the donut. Mmmmm... donut... *drool*

Ahem. Anyway. That works for me until it doesn't, and then I get back into the funk of "I'm depressed." "I should exercise." "I don't feel like it." "But it'll make you feel better." "I don't want to feel better." "But I hate being like this." "So? Shut up and have another bottle of tequila."

Yes, I talk to myself like that when I'm depressed. Does it help? No.

This article, to get back to the point, still doesn't address the question I had yesterday: So what happens if I reach my goal weight?

I mean, this can't be a fully linear process, can it? Like, say you're losing a pound a week. Just as an example. Somehow, you manage to do this regularly and consistently. But there's got to be a limit, right? Else you waste away to nothing (which, now I think of it, would make an excellent story- shit, Stephen King already did it). You keep eating less and less and exercising more and more, in order to keep that pound-a-week thing going, and at some point, it turns into the Red Queen's Race - it takes all your energy just to stand still.

That's what worries me, if I'm being honest. That there's no end to this self-deprivation; that I'm consigned to a lifetime of gray purgatory. They say success requires a lifestyle change, and while I'm perfectly okay with some lifestyle changes, especially if I know that I can relax at some point... some things just aren't worth the rewards.

It's frustrating, really.

3 Like • Comment

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