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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 10 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 5, 2020 at 12:02am

#974890

Maths and Polymaths

Ever feel inadequate?

Well, today's link isn't going to help.

https://www.bbc.com/worklife/article/20191118-what-shapes-a-polymath---and-do-we...

Why some people are impossibly talented
Polymaths excel in multiple fields. But what makes a polymath – and can their cross-discipline expertise help tackle some of society’s most pressing challenges?

If it weren’t for an actress and a pianist, GPS and WiFi might not exist.

In the late 1930s and early 40s, Hedy Lamarr was already the toast of Hollywood, famed for her portrayals of femme fatales. Few of her contemporaries knew that her other great passion was inventing.

Even today, most people don't know how awesome Hedy Lamarr was.

Besides helping to outline the specific traits that allow some people to juggle different fields of expertise so successfully, new research shows that there are many benefits of pursuing multiple interests, including increased life satisfaction, work productivity and creativity.

Despite having once served as an "expert witness," I don't consider myself an expert at anything. I do have a lot of interests, I think, but I can't say I score high in life satisfaction; I don't care about work productivity; and I'm about as creative as a paramecium.

There are, of course, some good reasons why we might be hesitant to pursue multiple interests. One is the fear that we might spread ourselves too thinly if we devote ourselves to more than one avocation. With a divided attention, we would fail to achieve success in any domain – the idea that the “Jack of all trades is the master of none”.

Yep, that's me. Hardly "all" trades, though.

In reality, there is some evidence that developing diverse disciplines can fuel creativity and productivity. So while the pursuit of a second or third interest may seem like a distraction, it can actually boost your success in your primary field.

Now we get to why I bothered to read and link this article. Presumably, the people reading this are writers, and what have we writers always heard? "Write what you know." I've said before that this advice should probably be turned around to "Know what you write," but either way, a lot of writers can benefit greatly from cross-discipline study. Some of the things I learned about personal finance, for example, can be applied to weight loss; both involve budgeting and tracking.

And when we write, we draw from all kinds of different sources. Sometimes it's sufficient to look something up when you need it, but better still if you have some background in the subject in question. While I'd wager none of us have experience in microgravity -- few people do -- some basic knowledge of orbital mechanics and Newtonian physics can help one write more compelling science fiction.

Some people figure they just go to school for some number of years and train in their chosen field. That's one way to get through life. Me? I'll stop learning when my brain turns to mush, through disease, injury, or death. I can't be afraid or unwilling to learn new things, because I never know when some obscure fact will pop up in my writing.

Problem is, the universe of human knowledge is expanding exponentially. I doubt that it's possible for any one person to know everything, as much as some people like to act as if they do. So we all have to be selective. But you can't know ahead of time what will be useful and what won't, so for me, I just assume that all knowledge is potentially useful.

There's no such thing as useless trivia, and yes, all of this will be on the quiz.

2 Like • Comment • View 3 comments

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