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Friday, Nov. 1, 2024

2:33am 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 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

January 10, 2020 at 12:04am

#973073

A Day in the Life

PROMPT January 10th

What are some of the routines you follow in your daily life? Do you typically stick to your routine, or do you prefer more spontaneity?

Bit of both.

I've said before that there's nothing I do on a daily basis. For example, while I try to write in here every day, there's a glaring hole in my December records that represents my trip to California and recovery therefrom.

The closest I get to a daily routine is about as basic as stuff gets: eating and sleeping. My current meal plan involves six small meals per day - but I skip occasionally, again due to travel. More, smaller meals works for me for weight loss; it keeps me from getting too hungry. If I manage to hit my goal weight, and I'm under no illusion that I can be any more successful at that than I am at anything, that will probably change. And while, like most people, I tend to sleep every day, it's not on a fixed schedule; I have the luxury of going to bed when I feel like it, again with a few exceptions.

One thing I have managed to do on a daily basis is language lessons on Duolingo. In an attempt to keep up a streak, I've managed to at least do a few lessons every day since late August. Until I've been at that for a year, though, I can't say I do it every day.

And then there's exercise. I try to hit the gym every day, but some days, especially when traveling, I just walk for half an hour or more. Rarely, I just don't have opportunity for any dedicated exercise. But I'm determined to not make excuses, so probably 99% of the time, some sort of exercise gets done. Someday, I will fail. Today is not that day.

As for spontaneity, I find that difficult on a daily basis now, but it manages to crop up sometimes. The problem is that most "spontaneous" things I want to do involve calories (e.g. food or beer), so I've forced myself into a schedule to help me stay on track. But when I travel, I often pick things to do and see at random.

Contrary to popular belief (one that I, admittedly, foster), I don't drink every day. Well, water, yes. And Crack Zero, certainly too much. But alcohol consumption is maybe once a week at most.

So, when I'm home, and there's nothing particular scheduled, it goes something like: Wake up whenever; shower; breakfast; cat feeding; language lessons; second breakfast (thanks, J.R.R.); exercise; lunch; other obligations; nap; cat feeding; snack; entertainment; blog; light dinner; reading; late-night snack; sleep. Repeat as necessary. Somewhere in there, I find the time to hang out here and keep up with other things on the internet.

You'll note there's no "work" involved; being retired has its benefits, and besides, work was interfering with my video game time. When I was working, I barely had time to get anything else done. You think it takes 8 hours, but it always ended up being way more than that, especially when I was running the show.

And yet, I never seem to have time to do everything I want to do, or "should" do. I find this frustrating. But I guess that's what life is: compromise.

Woke up, fell out of bed
Dragged a comb across my head
Found my way downstairs and drank a cup
And looking up I noticed I was late
Found my coat and grabbed my hat
Made the bus in seconds flat
Made my way upstairs and had a smoke
And everybody spoke and I went into a dream

8 Like • Comment • View 10 comments

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