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Wednesday, Dec. 18, 2024

1:37am EST

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Complex Numbers

by Waltz Invictus

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:

Aiva Raine

about 6 hours ago
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

about 7 hours ago
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

about 16 hours ago
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

Ichabod Crane-- Mince Pie

about 17 hours ago
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

tj-Merry Mischief Maker

a day ago
In response to "Fork You Too"

Now that I know forks are the center of dining controversy, I'll have to apply this at all family gatherings where demon dining utensils are in use.

1 Like

tj-Merry Mischief Maker

Dec 15, 2024 at 1:06pm
In response to "Revisited: "Those Naughty Brits""

I don't think there's such a thing as kinky sex anymore. Why? Based on the general definition, kinky sex refers to sexual activities and preferences that fall outside standard sexual practices. Nowadays it seems anything goes and there are no norms or standards.

Oh, another thing; do you remember if the link had pictures? Asking for a friend.

1 Like

Wordsmitty ✍️

Dec 15, 2024 at 12:45pm
In response to "Revisited: "Those Naughty Brits""

Waltz Invictus - As they say, you're a more proper man than I. I may even check out the other links with those key words.

2 Like

Waltz Invictus

Dec 15, 2024 at 12:32pm
In response to "Revisited: "Those Naughty Brits""

Thanks for that, Wordsmitty ✍️

. Sometimes I make the effort to find an article from a dead link. This time, I did not.

1 Like

Wordsmitty ✍️

Dec 15, 2024 at 12:29pm
In response to "Revisited: "Those Naughty Brits""

I think we're all glad that society has advanced so far in a decade and a half. Which way is up to you.

For those interested, there's a "Search" option in the Times main page. Page 6 of the results comes up with this link: https://www.thetimes.com/article/4d5f3e63-22c9-45c0-837b-c3ad9d236ae8

2 Like

Elisa: Snowman Stik

Dec 15, 2024 at 9:35am
In response to "Revisited: "Those Naughty Brits""

Damn, another entry that has me wanting to jump in and offer tons of commentary! Let's have at it.

2008 Me: Journalism may not be dead yet, but it's starting to wander and stink.

Dead now. Mostly.

Clearly I need to highlight more non-profit outlets in my link rundowns. I'm finding lots of good reporting on that front. Perhaps I also need to add more examples of this to "Watch This Space!"

[18+]. Even 60 Minutes is still able to provide some good in the weeds reporting. Point is, journalism is struggling, but good reporting is still out there. I'm doing my damnedest to shine a light on the solid examples. I could use a bit more help in the process.

2008 Me: What happened to investigative journalism? Hell, what happened to comprehensive news stories?

Gods, 2008 Me was so young and naïve.

They still exist. Strangely, I have found that at least in my area the local stations actually put some of their most comprehensive stories online. Also, at least the NBC affiliate has a post-local news show that does more comprehensive reporting. Some pieces are fluffy, but others are not. They are more locally focused, but that's probably a good thing these days. Local news has struggled the most, and we're paying the price for that.

2008 Me: Why is this in the "women" section? Men don't want to read about kinky sex? Please.

I'm guessing men are less likely to consider it kinky, outrageous, or naughty. But what the fuck do I know (pun intended)?

Strangely, this seems almost prudish by British standards, especially in light of the fact that Time magazine reported on BDSM in one of its print issues four years prior. And as we know, Time magazine isn't exactly known for sectioning off its content by gender. The Time coverage did include a photo taken in a BDSM dungeon that wasn't too explicit but really captured the D/s component really well. Honestly, I'd expect a UK publication to do that before a US one, not the other way around.

That said, I suspect the articles may have been written for slightly different audiences. If the audience is primarily women, there is likely to be more implicit shame in the picture, as women have been historically more likely to be primed to be ashamed about their sexuality in any capacity. Don't get me wrong. I know men are also subjected to this shaming. However, it tends to be less persistent and less pervasive in terms of different facets being shamed. In a general audience, the shame element can be downplayed. In a women-focused audience, you have to address the shame angle in some capacity, reassuring them that this isn't such a bad thing. This isn't something I'm directly involved in, but given the lack of women on WDC willing to write about this sort of thing these days, I might have to take one exploring this concept in depth. Ladies, if you're thinking about writing something (journal entry, static item, whatever) about this topic, this is your sign to go ahead and do it!

These days, I have preconceived ideas about headline questions: First, if it's a yes/no question, the answer is probably "no."

Snopes is ready to challenge that assumption.

2 Like

December 12, 2024 at 9:23am

#1081071

Life Is

Another day, another book ad. But an interesting book ad, this one from Big Think. I promise something different tomorrow.

A bold challenge to the orthodox definition of life
In “Life As No One Knows It,” Sara Imari Walker explains why the key distinction between life and other kinds of “things” is how life uses information.

I'm not going to weigh in on whether she's right or wrong, or somewhere in between. That's above my pay grade (not that that's ever stopped me before). I do think it's an interesting approach that adds to the conversation of science, even if it's ultimately a categorization issue, like the planetary status of Pluto or the sea status of the Great Lakes.

Sara Imari Walker is not messing around. From the first lines of the physicist’s new book, Life As No One Knows It, she calls out some big-name public intellectuals for missing the boat on the ancient, fundamental question, “What Is Life?”

I'm not sure how ancient, or fundamental, that question really is. With regards to humans and other animals, our distant ancestors could pretty much figure out the difference between life and not-life. With plants, it may have been a bit trickier, as they tend to not move even when they're alive. But I think Jo Cavewoman would scoff at the question. Dog: life. Rock: not life. (Yes, I'm aware that belief in animism might counter what I just said, but I'm talking in generalities here.)

It probably took until we started looking through microscopes that we began to question the boundaries. Is a spermatozoon "life?" How about a virus?

Since then, it's my understanding that people have proposed several different definitions for life, all necessarily based on conditions on Earth, and scientists and philosophers have been arguing ever since, as scientists and philosophers love to do.

Subtitled The Physics of Life’s Emergence, one of the book’s major themes is a critique of the orthodox view in the physical sciences that life is an “epiphenomenon.”

"Epiphenomenon" is another word with a kind of slippery definition. I don't like to quote dictionaries as sources, because they're descriptive and not prescriptive, but the definition I found was "a secondary effect or byproduct that arises from but does not causally influence a process." Which, well, thanks? That doesn't help.

The Wikipedia article

on it is similarly confusing, at least to me, with the added bonus of also coming from a source people don't like to cite.

What's worse, in my view, is when people conflate "epiphenomenon" with "illusion:"

This is the argument, often heard in mainstream popular science, that life is a kind of illusion. It’s nothing special and fully explainable by way of atoms and their motions.

To address the latter assertion first: "nothing special" is a value judgement, and "fully explainable" is laughable hubris.

As for the "illusion" thing, well, I've banged on in here on several occasions against the "time is an illusion" declaration. But that can be generalized to anyone airily calling anything an "illusion." To me, an illusion is something that, upon further study, goes away: a stage magician's trick, or those seemingly moving lines in a popular optical illusion picture. But no matter how much we study, for instance, time, it doesn't go away. I think a better word description would be "emergent phenomenon," meaning that it's not fundamental, but rather a bulk property. Like temperature. One atom doesn't have a temperature; it only has a vibration or speed or... whatever. Get a bunch of atoms together, though, and the group has an average speed, which we read as temperature.

Or, to use everyone's favorite example, the chair you're sitting in. "It's an illusion," some philosophers claim (generally after taking a few bong hits). "It's not real." Well, look, any philosophy that doesn't start with "the chair is real" is a failure, in my view. Your ass isn't sinking through it; therefore, it's real. Sure, it's made of smaller pieces. On the macro scale, it's got a seat, probably a back (sometimes in one continuous piece), maybe arms, legs and/or casters, maybe a cushion for said ass. This doesn't make the chair any less real; it just means there's a deeper level to consider.

Similarly, the cushion, for example, is usually a fabric stretched over some stuffing. The fabric itself can be further broken down into individual fibers. The fibers, in turn, are made of molecules, some of which have a particular affinity for one another, giving the fiber some integrity. The molecules are made of atoms. The atoms contain electrons, protons, and neutrons. Those latter two, at least, can be further broken down until you're left with, basically, energy. And maybe there's something even more fundamental than that.

None of that makes the chair any less real. It just shows that our understanding can go deeper than surface reality. But surface reality is still reality.

And so it is with life. I know I'm alive, for now, and that's reality. I'm pretty sure my cats are, too, and the white deer I saw munching on leaves in my backyard yesterday. Not so sure about the leaves, it being December and all, but I am as certain as I can be of anything that they are a product of life.

Whew. Okay. Point is, I'd like to see these macro-level phenomena labeled something other than "illusion." It's misleading.

In the standard physics perspective on life, living systems are fully reducible to the atoms from which they are constructed.

Yeah, well, physics gonna physic. Just as with your chair, things can be studied at different scales. Biology is usually the science concerned with life. But biology is basically chemistry, and chemistry is basically physics. This doesn't make biology an illusion, either.

Still, they will argue, nothing fundamentally new is needed to explain life. If you had God’s computer you could, in principle, predict everything about life via those atoms and their laws.

I'm gonna deliberately misquote James T. Kirk here: "What does God need with a computer?"

Walker is not having any of this. For her, the key distinction between life and other kinds of “things” is the role of information.

Well, that's amusing. Not because it's not true—like I said, I'm not weighing in on that—but because from everything I've read, physics is moving toward the view that everything is, at base, information. Yes, that might be what energy can be broken down into. Or maybe not. I don't know. But "information theory" is a big deal in physics.

Whether there's something even more fundamental than information, I haven't heard.

Life needs information. It senses it, stores it, copies it, transmits it, and processes it. This insight is, for Walker, the way to understand those strange aspects of life like its ability to set its own goals and be a “self-creating and self-maintaining” agent.

Okay. Great. Let's see some science about it.

As usual, there's more at the link, if you're interested. Might want to sit down for it, though. You know. On that chair which is definitely real and hopefully not alive.

3 Like • Comment • View 3 comments

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