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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 31, 2019 at 12:15am

#972288

Tribe

Well, here we are at the end of December, the end of 2019, and (in popular imagination anyway) the end of a decade.

If I'm being pedantic, the decade ends a year and a day from now (2020 is a leap year). But let's not be pedantic.

No one seems to know what to call this past decade. I came up with a name for the first decade of the 21st century: the noughties. It didn't catch on, though I did see the BBC use it once. It is, after all, rather British. I don't have a similarly awesome name for 2010-2019.

Next month, I'm once again participating in "30-Day Blogging Challenge ON HIATUS"

[13+], so I'll switch back to that format tomorrow. But for today, I have an older article from 2013. I selected it at random, but it's appropriate enough.

http://nautil.us/blog/we-are-all-princes-paupers-and-part-of-the-human-family

We Are All Princes, Paupers, and Part of the Human Family

Chances are, if you have a famous ancestor far enough back that finding out about them is a surprise, you share them with a small city of other people. And the farther back you go, the truer that is.

Chances are, you have a famous ancestor, period. Ghengis Khan if no one else. Or at least a significant one.

This line of thought led to the revelation that everyone of European heritage alive today is a descendant of Charlemagne, who ruled over much of Europe as the first Holy Roman Emperor.

That gives me an excuse to post one of my favorite songs.

It doesn’t get any less weird when you look at it from the other angle: While you more than likely have four distinct grandparents and eight distinct great-grandparents, past a certain number of generations back, your number of ancestors stops growing exponentially, because they start being the same people.

A good point.

Stretch this back a few thousand years and you can see how you wind up being related to every other member of your species.

Stretch this back a lot farther than that and you can see how you wind up being related to your cat.

Geneticist Luke Jostins did a nice mathematical analysis and estimated that you have only about a 12 percent chance of being genetically related to an ancestor 10 generations ago; by the time you get to a 14-generation ancestor, the probability is nearly zero.

And that's why having kids just to pass along your genes doesn't make any sense. Never bought that argument for it, and I have plenty of other reasons not to have reproduced, but people keep talking about it. Yeah, biological drive and all that, but we also evolved to understand these things and have the persistent illusion of choice. (There are, of course, plenty of other reasons to have kids, and for most people, these seem to overwhelm the reasons not to. That's okay. I'm just talking about my own choices here.)

And the illustrious folks we might like to lay claim to have so many descendants that being descended from them is kind of a moot point.

I have a friend whose brother traced their family line back to Pocahontas. I don't know how accurate the genealogy was, but it was a point of pride for him. While this is cool, if true, I didn't tell him he's probably not one in a million, but one of a million.

The article ends with:

We’re all part of this enormous human fabric, full of fascinating tendencies and bizarre biochemistry. And research is revealing more and more about humanity as a whole and our incredibly beautiful, incredibly unlikely perch in the universe. That’s a tradition to be proud of.

There is no "us" and "them." If I had one wish for the twenties, it would be that we continue to work toward ending tribalism, or at least its more negative effects.

It's not going to happen, but the end of the year is traditionally the time for hopes, right?

4 Like • Comment • View 3 comments

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