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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 29, 2019 at 12:02am

#972174

Too Much Like Work

https://www.theguardian.com/news/2019/jan/03/why-exercise-alone-wont-save-us

Article's a year old now, but it refers to New Years resolutions, so it's cycled back again.

Why exercise alone won’t save us

Our relationship with exercise is complicated. Reports from the UK and the US show it is something we persistently struggle with. As the new year rolls around, we anticipate having the drive to behave differently and become regular exercisers, even in the knowledge that we will probably fail to do so. Why do we want to exercise? What do we expect it to do for us? We all know we are supposed to be exercising, but hundreds of millions of us can’t face actually doing it. It is just possible the problem lies at the heart of the idea of exercise itself.

Well, duh. It's a pain in the ass and always takes longer than you think, what with having to change clothes twice, probably shower, and maybe get to the gym or back. Like, I always think, "30 minutes on the treadmill and then some weight-pumping" and I end up being gone for nearly 2 hours.

Evidence about bone strength and density gleaned from fossils of early humans suggests that, for hundreds of thousands of years, normal levels of movement were much higher than ours today.

You know how I'm always bitching about evolutionary arguments? Specifically, there, I'm bitching about wild speculation about how psychological, not physical, traits evolved. The former is guesswork; the latter is revealed by some physical evidence. Whether they're interpreting the evidence reasonably is another issue.

After two centuries of trying, we should accept that exercise is not working as a global fitness strategy while it remains an addition to the working day. In the long view, it is starting to look a lot like a fad. Government guidelines in the UK and other countries that encourage sport and exercise are failing. These strategies struggle because we are trying to get people to give up what little leisure time they have to pursue activities that require substantial additional effort.

I have a different take on it.

First of all, technology got us to this point because it kept inventing things to make our lives easier, as the article points out. Consequently, the obvious solution is technology that keeps our bodies from falling apart if we don't exercise. I think I've posted stuff before decrying the common idea that failing to keep oneself fit is considered a moral failure, a failure of will, whatever - basically, YOUR FAULT. Instead, if we really cared about this sort of thing, we could put all of our efforts to developing a Leisure Pill - something that allows us to sit around all day with no ill effects. You may dismiss this idea as the "easy way out," but the "easy way out" is apparently what got us here; it works for us, and we're really, really good at it, so why not extend the concept?

Second, maybe we're looking at all of this the wrong way. The hidden assumption underlying all of these health articles is that the goal is to live longer. Of course, few people want to die, but after seeing two parents live into their 80s and beyond, both dying of mental degeneration, I'm not sure that a longer life is necessarily better.

There's something to be said for living life the way you want to. Sure, you could stay active, eat no more than 1100 calories a day, don't drink, don't smoke, breathe filtered air, never climb a mountain, avoid driving, etc., and science says you could live a lot longer. And hey, if that's how you want to live your life, great. But if it's not, if you're more of a hedonist like me, does it really make sense to give up the pleasures that make life worth living, for the possibility - not the guarantee, but the possibility - of a few more years of elderly frailty?

4 Like • Comment • View 4 comments

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