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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 29, 2020 at 12:01am

#976594

D'accord!

Etymology is something of an interest of mine, combining history and language studies... and maybe a bit of mob psychology in the mix.

https://www.mentalfloss.com/article/50042/whats-real-origin-ok

What's the Real Origin of "OK"?

Yes, this is from 2013. So what? It's not like language is going out of style anytime soon.

By Arika Okrent

Oh, I see what you did there, OK-Rent.

"OK" is the all-purpose American expression that became an all-purpose English expression that became an all-purpose expression in dozens of other languages.

Still not as versatile as "fuck," but, OK.

There may be more stories about the origin of "OK" than there are uses for it

Just as intriguing for me as etymology is folk etymology; that is, the stories we tell ourselves about the origins of words or expressions. Some of these are just blatantly wrong, such as the idea that the monosyllabic vulgarity I mentioned above originally came from the acronym "For Unlawful Carnal Knowledge" (now immortalized as the title of a Van Halen album) or "Fornicating Under Consent of the King," each of which expressions contains entirely too much Latin for to be taken seriously - but people still believe one or the other.

Or, one time, I used the phrase "rule of thumb" around an angry woman, who proceeded to chide me for using an expression that "came from an ancient rule about only being able to beat one's wife with a stick no bigger than your thumb." Which is patent nonsense, but OK. No point in arguing with people like that; they're not going to change their minds.

Point is, even the false etymologies tell us something about human nature and what we're inclined to believe.

The truth about OK, as Allan Metcalf, the author of OK: The Improbable Story of America's Greatest Word, puts it, is that it was "born as a lame joke perpetrated by a newspaper editor in 1839."

Lest anyone still be laboring under the misapprehension that comedy isn't meaningful.

It wasn't as strange as it might seem for the author to coin OK as an abbreviation for "all correct." There was a fashion then for playful abbreviations like i.s.b.d (it shall be done), r.t.b.s (remains to be seen), and s.p. (small potatoes). They were the early ancestors of OMG, LOL, and tl;dr.

And we thought the military went overboard with its acronyms.

OK got lucky by hitting the contentious presidential election jackpot. During the 1840 election the "oll korrect" OK merged with Martin van Buren's nickname, Old Kinderhook, when some van Buren supporters formed the O.K. Club.

This process, of a thought taking on a life of its own, is the sort of thing that Dawkins meant when he coined the word "meme," not captioned cat photos. Ironically, such a shift in definition is itself the hallmark of a meme.

Now, you might ask yourself, "How do we know this is true and not the other origin stories?" But that strays perilously close to "How do we know anything at all?" I find epistemology to be a fine, upstanding word, but not something I'd like to argue about.

But, as Metcalf says, its ultimate success may have depended on "the almost universal amnesia about the true origins of OK that took place early in the twentieth century.

And that's the fascinating part to me - to trace how these things develop over time. Sometimes we don't know and have to guess, but even the guesses can shed light on meaning. I'm OK with that.

4 Like • Comment • View 2 comments

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