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Friday, Nov. 1, 2024

12:42am EDT

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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

January 3, 2020 at 12:54am

#972528

Beer for Breakfast

PROMPT January 3rd

Make a list of 20 random things (nouns). Try as hard as you can to make each item on your list as unrelated to the other items as possible. If your muse moves you, you’re welcome to add whatever commentary you like.

psychology
volume
county
appearance
permission
initiative
combination
estate
reception
drama
philosophy
length
procedure
attention
honey
debt
presentation
platform
song
population

I cheated. I literally selected the nouns at random

rather than coming up with them out of my head, which, let's be real here, wouldn't have been random.

It's just part of my natural psychology to be drawn to random numbers. More than anything else, the sheer volume of dice rolls is what attracted me to playing D&D, even from 'way back when I was living out in the back end of a rural county with few people around. When I'm not doing this blogging challenge, randomness makes an appearance through my selection from a list of articles I found interesting in some way.

Once I decide to do something at random, I rarely give myself permission to stray from the results. If I wanted to do something on my own initiative, I wouldn't have randomized the situation. For example, yesterday I somehow found myself at a brewery, staring at a tap list of 22 different beers from which I could select a combination of four for a tasting flight. Well... I could have bought more than one tasting flight, but doing so could negatively affect my estate. So the selection process can be dicey (pun intended, of course) - as much as I like beer, I give some styles a better reception than others.

Without going into too much drama, when it comes to beer, in general, I'm a contrarian - what I like, such as Belgian styles, few others do; what I don't like - sours for example - seem to be popular. I'm comfortable with this philosophy, though, and I'll go to any length to defend my own point of view. Thing is, I'll try almost anything, and when faced with a limit of four out of 22 possible beers, I have a certain procedure for these situations: roll the virtual dice, or in this case, use an app on my phone that is specifically for generating x numbers out of y possibilities, with or without attention paid to whether or not repeated numbers are valid (in this case, not).

I've been pleasantly surprised by this method; I've found beers tasting of lemon, of honey, of blackberry; but mostly they taste like beer - delicious, refreshing beer. I don't do it too often because I'd end up going into debt, but I do enjoy the presentation of a flight of different-colored beers all in a row or a ring on a platform specifically designed to highlight their variation and their luster. The right combination of beers - chosen carefully, or selected at random as I described - is as gorgeous as a song, even if the vast majority of the population would never agree with me.

Well, there. I did it. 20 truly random words, all shoehorned into a praise of beer. I did end up getting more than one flight, and then a couple of pints of different brews, and then a tasting of the style I specifically went to the brewery for. I should have mentioned that this is an exceptionally good brewery.

Then I Ubered home and passed out. Yes, I'm still drunk, but I did this entry anyway.

For anyone who doesn't know what I mean by a "flight" of beer, here's a representative picture from the internet.

8 Like • Comment • View 8 comments

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