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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 21, 2019 at 12:10am

#971798

Asleep Under the Sun

https://www.vox.com/2016/3/18/11255942/morning-people-evening-chronotypes-sleepi...

If you’re just not a morning person, science says you may never be

Sure, I'm a morning person. I'm at my best between about midnight and 4am. That's morning. And then I get my best sleep between 4am and noon. That, too, is morning.

Afternoons can be dreary.

Morning people and night owls are born that way. It's time we accepted that.

Yeah, right. People who think there's some moral superiority in waking up while it's still dark aren't going to change their minds. They have to feel superior about something, I suppose.

If Cassidy Sokolis ever needs to wake up before 11 am, she scatters three alarm clocks throughout her bedroom. Even then, she still often sleeps through the clamor.

Sounds familiar.

We all have a preferred, inborn time for sleeping. Science has validated the idea that there are "morning people," "evening people," and those in between. These are called chronotypes. And just like it’s rare for a person to be 7 feet tall, it’s rare for Sokolis to not be able to sleep until 3 am. We all have a chronotype, just like we all have a height.

Okay, but we can see your height.

And what's more, if we try to live out of sync with these clocks, our health likely suffers. The mismatch between internal time and real-world time has been linked to heart disease, obesity, and depression.

Oh, good; I can blame my biggest health issues on being forced to keep an 8-5 work schedule throughout my career. Score!

"Our clocks don’t run on exactly a 24-hour cycle," Gehrman says. They're closer to 24.3 hours. So every day our body clocks need to wind backward by just a little bit to stay on schedule.

I've heard variations of this in the past. As I recall, they studied this by keeping people in windowless rooms for extended periods of time, with no reference to timekeeping devices, and looked at what rhythm they fell into.

If that sounds like hell to you, believe me, I think so, too. After all, there's a clock on the computer. Going for days without a computer? The horror!

I have, on occasion, wondered what's up with the extra .3 hours (I've also heard .5 hours, but whatever). You'd think, maybe, "evolutionary holdover," but if anything, the Earth's rotation was faster in the distant past.

The second treatment is chronotherapy. Here, instead of pushing the body's clock backward it's wound forward. For a few weeks, a patient will go to bed two hours later every night until she reaches her desired sleep time. "It can work very well, but very few people have the absolute, total control of their schedule for the two weeks that it takes to do that," Gehrman says. Very few of his patients choose this option.

Pretty sure I've mentioned this sort of thing in this blog before, but I can't be arsed to look it up. I did do a sanity check to ensure I haven't linked this particular article before, and I don't think I have. In any case, I'm just quoting the bit above because of my confirmation bias.

I have also wondered what happens to someone, say, who lives on the east coast of the US and is a night owl, if they move to the west coast. With a three-hour time difference, can they keep an earlier sleep/wake schedule, or does the rhythm of daylight gradually reset them to night-owl-hood?

Simply put: Society favors early risers. Think no further than phrases like, "The early bird catches the worm."

My favorite rebuttal to that has always been, "The second mouse gets the cheese."

In any case, I know I've been on this subject before, because as a night owl, it's bugged me for a while. Not being a night owl - I love being up at night and sleeping through the boring parts of the day - but the general Puritanical scowling at anyone who doesn't rise with the accursed daystar.

I'm privileged, I know - I'm in a position where I can (usually) sleep when I want and get up when I want. Does it make me healthier? I don't know; I think the exercise does more for that. But it's just possible that I've been able to keep up with daily exercise for a whole year (an absolute record for me) because I'm not fighting an unnatural, for me, sleep schedule.

2 Like • Comment • View 2 comments

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