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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 9 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

February 16, 2020 at 12:11am

#975619

Critical

Today, we learn "how to spot a bogus health fad." Sadly, "you see it on the internet" is not a complete answer, nor necessarily a factual one. Sigh. That would make life a lot easier for critical thinkers.

https://www.self.com/story/spot-bogus-health-claim

8 Simple Ways to Spot a Bogus Health Fad
Opinion: The plural of anecdote is not "data."

By Yvette d'Entremont

Hey, that looks French. I think it means "Yvette d'Entremont."

In 2018 the global weight-management market was valued at $212 billion, and the wellness industry was worth a staggering $4.2 trillion in 2017.

I have this vision of enterprising capitalists selling junk food to us with one hand and gym memberships with the other. Good capitalism. Bad ethics. But it might explain why there's a Krispy Kreme right across from my gym.

You may be wondering: In an internet landscape offering cures of suspect origins for all that may be ailing you, is it even possible to sort out what’s real from what will inevitably just become a pile of dust-gathering items in your collection of dubious supplements and accessories?

Surprisingly, yes.

It's called "science." Failing that, not jumping on every promise that some random influencer makes would go a long way.

1. Does it promise too much?

Ever seen a product or a diet that claims it can do everything? It won’t just make you lose a few pounds, but it’s going to clear up your acne, make your nipples perkier, and earn you thousands of dollars a week working from home in your Rainbow Cat Unicorn Underoos.

Now I'm going to buy stock in the company that makes Rainbow Cat Unicorn Underoos. They can't fail.

This crap is age-old. The term "snake oil" comes from the products hucksters would sell from their carriages, all of which promised everything.

2. Does it blame all your health woes on a single thing?

I had a friend who's a chiropractor, and she was absolutely convinced that subluxations were the cause of all disease.

3. Is the evidence confined to anecdotes?

What this section leaves out is the nonequivalence of correlation and causation. Most diseases either a) eventually kill you or b) get better. If the disease was going to do (b) anyway, it doesn't matter how many vitamin pills you took. And if it was going to do (a) anyway, then you're not around to push the "cure." See also: Steve Jobs.

4. Who’s promoting it?

Don’t take this as a hard-and-fast rule that something isn’t reputable if it’s being promoted on Instagram.

Nevertheless, if it's being promoted on any sort of social media, I consider it immediately suspect until proven otherwise.

5. Which scientific or medical boards or bodies have evaluated it?

You know those labels that let you know, give or take, “these claims haven’t been evaluated by real doctors or scientists, may contain up to 30% unicorn dander”?

I'm the first to admit that science doesn't know everything. Hell, that's the entire foundation of science: "we don't know everything, but we'll find out what we can." So not everything has been tested - nor can it legitimately be. It's possible that your grandmother's herbal remedy for whatever actually works. As we all know, aspirin started out as a natural herbal (sort of) remedy. Then it comes down to "if I use this method, am I closing off other avenues of possible relief?"

6. Are you drawn to it for reasons other than its efficacy? Like, say, desperation to find a solution?

I feel for people with no recourse. Having lived through the whole Laetrile debacle (feel free to Google it if you're too young or don't remember), it's clear to me that desperate people will hare around looking for desperate measures. But sometimes, as they say, the cure is worse than the disease - though I'd be hard-pressed to think of anything worse than cancer. I understand that if you're actually dying, you'll grasp at whatever straws life, or snake oil salesmen, throw your way. The problem is that these things often substitute for actual care that could actually work.

7. Is there a way to measure evidence that the product works?

If something is claiming to tinker with your health, assess the study quality (if there even was a study), and don’t let yourself be the lab rat for a product that’s probably just going to be a wallet cleanse.

"Wallet cleanse" is what I'm going to call all claims of "cleanses" from now on.

8. And if it seems like bullshit but you just can’t put your finger on it, ask around.

I like to think I have a pretty good bullshit detector, but I could be deluding myself. We've gotten to where we put equal stock in what some Internet huckster says as we do in what doctors say, or even get swayed more by the former. Yes, doctors are people and people are fallible, but so are "alternative medicine" promoters. Me, I don't always follow a doctor's advice, but that doesn't mean I don't respect it; it just means that I think the doctor doesn't understand my basic philosophy: that there's no point in living longer if you have to give up the things that make life worth living.

So, don't believe everything you hear. More importantly, don't believe everything you think.

2 Like • Comment • View 1 comment

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