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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 17, 2020 at 12:05am

#975687

World Enough And Time

Since I'm finally getting around to learning a new language - however badly at this point - language articles get noticed more and thus stuck in my Blog Fodder List.

This is one of them.

https://theconversation.com/language-alters-our-experience-of-time-76761

Language alters our experience of time

Getting this bit out of the way first: no, time is not an illusion. But just like different people might estimate a mile differently (which is why we have measuring sticks), different people perceive the passage of time differently. Or the same person perceives it differently at different times.

And, to make another analogy, I've heard Europeans complain that Americans give distances in time. Like, the nearest city might be a half hour away, or a drive across the country takes three days. So at the very minimum, I'm prepared to accept that there are cultural differences in our perception of time.

My new study – which I worked on with linguist Emanuel Bylund – shows that bilinguals do indeed think about time differently, depending on the language context in which they are estimating the duration of events.

Again, no real surprise. Language gives us a particular way of looking at the world, and switching languages is like switching filters on a lens.

The logic in Aymara appears to be this: we can’t look into the future just like we can’t see behind us. The past is already known to us, we can see it just like anything else that appears in our field of vision, in front of us.

Which is the part I find really fascinating - the perception of time there is completely turned around from what we're used to. Like living in a mirror, where left is right and right is left.

A similar thing that I haven't seen too much written about is the direction of written language. Most Western scripts read from left to right, like we're doing right now. Hence we tend to order things in that direction: door number 1 is on the left, door number 2 in the middle, door number 3 on the right. To number them backwards seems at least weird, like you're about to launch a rocket via countdown.

But other languages, like Hebrew, read from right to left, so I imagine they'd order things the second way naturally.

There are interesting historical reasons for the differences in direction, and I suspect they both have to do with the predominance of right-handed people. If you're writing with ink on parchment, you want the wet ink to be in the clear, and not smudged by your hand as you go along - so you'd be inclined to pull your right hand to the right. Whereas if you're chiseling words on stone, and you're right-handed, you want to hold the hammer in your right hand and chisel in your left. Smudging isn't an issue, but angle might be. So, basically, left-handed people got the short end of the stick - sometimes literally.

None of which explains vertical scripts very well, and I don't have much knowledge about them. Anyway, to get back to what the article is saying, I think there are a lot of unconscious biases that we have, and our perception of time might very well be entangled with our perception of language.

It seems that by learning a new language, you suddenly become attuned to perceptual dimensions that you weren’t aware of before.

Again, if true (I don't know enough about any other language to have personal experience with this), that's really interesting.

But it also shows that bilinguals are more flexible thinkers and there is evidence to suggest that mentally going back and forth between different languages on a daily basis confers advantages on the ability to learn and multi-task, and even long term benefits for mental well-being.

Which relates back to one of my reasons for deciding to learn other languages at my advanced age. I mean, I almost never do anything for just one reason, and the primary reason has to do with booze (naturally), but why not make up for the brain cells lost to said booze by making my mind more flexible?

3 Like • Comment • View 4 comments

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