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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 11 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 10, 2020 at 12:21am

#975188

Well, Actually...

I'm starting to think Cracked has improved again. It was funny, then it kinda sucked, and now I think it's often funny once more. But it's also educational.

https://www.cracked.com/article_26746_5-famous-psychological-studies-that-were-h...

5 Famous Psychological Studies (That Were Hugely Overhyped)

Since this has to do with science and science reporting, I have things to say about it.

We cling to certain psychological studies like they're the only mental life preservers in this great big raging ocean of crazy.

Of course, they are not. There is also booze.

5. Your Answer To The Trolley Problem Has No Relation To What You'd Do In Reality

The infamous Trolley Problem is a popular thought experiment in Intro to Philosophy, as well as a beloved pop culture trope.

It has certainly been mined for Comedy Gold by writers for Cracked and other sites.

The result found almost no correlation to what participants said they would do and what they actually did.

Stop the presses! People say one thing and do another? THIS IS HUGE!

Okay, but seriously, though, there are practical applications to the Trolley Problem, but they don't necessarily involve individuals.

Consider an outbreak of a completely hypothetical contagious virus. This completely hypothetical virus has a fatality rate of 2%, meaning 1 person in 50 who contracts it dies. Further assume that it infects 1/10th of the world population, so it kills one person in 500 overall. These are, of course, all numbers I'm extracting from my nethers, but so are the Trolley Problem numbers.

Now, some scientists invent a vaccine for Hypothetical Contagious Virus, HCV. But owing to genetic differences among individuals, the HCV vaccine is itself deadly to 1 in 50,000 people. Administering this vaccine is, consequently, a Trolley Problem - assuming you could spread it to the entire human population, you're killing 150,000 people with it. But without it, 15 million people could contract HCV and die.

There might be overlap between the two groups, but it's likely that some vaccinated individuals will die who wouldn't have if they'd just contracted the virus. Overall, though, you're saving 14,850,000 lives.

The Trolley Problem is, at least in part, about the ethics of action vs. inaction. The above numbers really are completely hypothetical (and in no way reflective of how pandemics or vaccines actually work), but you can apply a similar calculation to, say, the invention of self-driving cars; if 30,000 people a year die in autonomous vehicle accidents, but 40,000 a year would die in human-driven vehicle accidents, is it not better, overall, to go with robot cars? Or are we just going to focus on the lives lost and the fear of the unknown, rather than the reduction in fatalities?

4. The "Bystander Effect" Isn't The Whole Story About Kitty Genovese

I've known for a long time that the Bystander Effect is completely overblown (although it did create an excellent origin story for Rorschach in the Watchmen graphic novel).

So at this point, "Genovese Syndrome" should be the name for when people parrot old myths to look cynical instead of bothering to check basic facts.

I can be cynical with the actual truth; I don't need myths for that.

3. Power Posing Doesn't Change Anything In Your Body

Your body language says a lot about how you're feeling, which is why you don't give a big presentation while slouched over like you're four hours into a Gears Of War marathon. And supposedly, a "powerful" posture can make you powerful.

Yeah... the only surprise here is that someone took this shit seriously in the first place.

But while the original study found a positive correlation with power posing, later experiments didn't. In 2017 alone, 11 different experiments tried to replicate the original's results, and all of them found that power posing apparently does nothing for your body.

This also speaks to that other cognitive bias we have that I can never remember the name of: we tend to believe the first thing we hear on a subject, and subsequently ignore contradictory information. This is why it's so damn hard to convince people of anything, even though it's one thing the scientific method was designed to overcome.

2. No, Your Ego Doesn't Get "Depleted"

Unfortunately for fans of thinking less, psychologists tried to replicate Baumeister's results and very much could not. A previous meta-analysis was also reviewed, and the results weren't pretty there, either. The theory appears to only apply if you personally have been convinced that your willpower is a finite resource.

Again, a finding that fails upon attempts at replication - and again, one that wasn't nearly as widely publicized as the original hypothesis. This is my problem with science reporting, in a nutshell.

1. Maslow's Hierarchy Of Needs Needed More Real Science

It's the idea that there's a logical order to human need. First you fulfill your physiological needs, like sleep, water, and pizza. Safety, like not being beaten up for your pizza, comes next. Once you're safe, you can look to fulfill your need for social belonging (getting invited to pizza parties), esteem (being lauded for bringing good pizza), and finally self-actualization (building a pizza oven and inviting people over to witness the depth of your pizza skills).

Dammit, Cracked! Now I'm hungry!

When research into Maslow's structure came along, it showed that humans can fulfill their needs in any order, and can feel self-actualized even when their basic needs aren't being met.

Yep. I'll happily eat pizza even when sleep-deprived.

Being connected to others, knowing what the hell you're doing, and feeling like you have some control over your life is the best way to happiness. Well, unless someone tries to replicate the latest data and determines that it's all bunk.

Drinking beer, listening to music, and being snarky on the internet is my best way to happiness.

Your mileage, as always, may vary.

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