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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

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Show Recent Comments

10 Most Recent Blog Comments:

GeminiGem of House Lannister

a day ago
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

November 6, 2018 at 1:45am

#945003

All A-Clone

One important thing about science fiction - and here, I'm talking about real science fiction, not space opera, though that can be fun - is that it gives us a chance to explore the ramifications of certain technologies before those technologies get a chance to be realized in our lives.

A common theme in SF when I was young was the topic of cloning. The idea had already been around for a long time, and had in fact been used to great success in plants. Every banana you eat, for example, is genetically identical. But of course, that led philosophers and science fiction writers (the distinction is sometimes murky) to speculate on cloning animals, including humans.

And boy, did a lot of them get it wrong. I don't mean wrong in the sense that the writers who predicted flying cars were wrong, but wrong on a basic, fundamental level. Stories abounded of exact duplicates of a human being, down to the last hair and quirky mannerism. Now, I'm not saying that sort of thing will never happen - I wrote a story set in the far future that features this sort of thing - but it's not happening anytime soon.

With exact duplicates of that sort, all sorts of ethical and existential questions get raised, not the least of which is the attempt to define the word "I." It's a simple word, just one letter, and in our normal frames of reference the pronoun has a simple, singular referent. Analogy: You have two thumb drives. You copy your budgeting spreadsheet from one drive to the other, and make changes to one of them. Then your SO goes looking for it to check if you have hookers and blow as line items somewhere. Which one was the original, and which the copy? They both exist, in the sense that binary information can be said to exist.

Well, animals are a great deal more complex than a budgeting spreadsheet, and we simply aren't anywhere near the level of technology required to treat them as such. No, in the real world, cloning is essentially asexual reproduction - you don't end up with a fully-formed Minerva, but with a zygote, then an embryo, then a fetus, then a baby, with all of the life-support requirements that these stages have. It's no different from having a standard baby, except that it got all of its genes from you, and not from you and your hookers-and-blow-budgeting SO.

(Okay, there are differences involving telomeres and possibly environmental changes to genes, but I'm not a biologist so we'll ignore them for this discussion.)

The result is, basically, your identical twin - only several years younger.

But wait, there's more. Check this

out.

Nearly a decade ago, on December 22, 2001, scientists at Texas A&M University announced the birth of CC, the world’s first cloned cat. CC, as in Copy Cat, has the same DNA blueprint as her genetic mother, Rainbow. So, like identical twins they share the same genetic code. That means everything’s the same—their looks, their mannerisms, their…. But wait.

Okay, they named the clone Copy Cat and I have some faith in humanity restored because of that.

A closer view in color reveals they don’t actually look identical. In fact, technically they’re not even the same color. Rainbow, with her spackling of orange mixed in with patches of black accentuated by a white belly and legs is calico while CC, who has no orange coloring at all, is a tiger-tabby.

The article goes on to explain that no, they don't have the same mannerisms, either. An animal clone, then, is clearly a completely separate entity. There is no fuzzy boundary on the pronouns; the two cats are distinctly different.

That article is obviously old now, which means the cats involved are almost certainly ex-cats and that the technology has advanced since then - but I've heard absolutely nothing to convince me that "cloning," as we know it, is anything other than a type of asexual reproduction.

The important takeaway here is that, even if the technology is there to do that with humans, if you were to go out and get yourself cloned tomorrow, there'd be a new entity born about nine months later (probably to a surrogate mother), and the only question would be whether that entity is your sibling or your offspring, or both - and even that is hardly a new conundrum if you live in, say, Alabama. Point is, it's not "you," and you have no say over it beyond, possibly, parental rights and obligations. We already know what to do with a new life; we've been doing it since long before you could call us "human."

(I'm not a lawyer, either, but this is the ethical argument, not the legal one.)

Now, there's a somewhat related question, one that's also been done to death in science fiction - that of artificially grown organs or limbs that could potentially be used as replacement parts. I think I've already established that we can't use clones for that because they are individuals, at least not without their consent (and if you think such consent would be invalid, consider how many people have donated a kidney or part of a liver to a compatible recipient).

Short answer: This is not an ethical question.

Long answer: We're not talking about a separate, conscious, living entity here, but a collection of cells grown in a vat (or whatever medium they use these days). No central nervous system, no thoughts, nothing to have thoughts with, and not even the potential to become an independent organism.

I will add one more thing, as food for thought (pun absolutely intended). But it's a little squicky, so if you're squeamish, stop reading here.

...

Still here?

Fine. You were warned.

There's a persistent cultural taboo in most societies against cannibalism. There are good reasons for that, it's not just a matter of "eating people is icky," but I won't go into them now. Still, in extreme situations, people have been known to violate this taboo: The Donner party, for example, or that soccer team or whatever that crashed in the Andes. You do what you have to in order to survive. So here's the ethical conundrum, if you can look at it without the weight of cultural baggage: what's the actual difference between consuming human flesh to survive, and accepting a donor organ to prolong your life? I mean besides the method by which you get the meat into your body, which to me is a distinction without a difference.

As I see it, the cloning thing is settled ethics. The organ donor thing also seems to be settled by everyone else, but I don't really understand why people get weird about cloning and not about organ donation.

Feel free to discuss.

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