Complex Numbers (Book)

Blog Calendar

◄ August ► 2021
S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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:

Write_Mikey_Write!

about 2 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 4 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

August 30, 2021 at 12:02am

#1016354

In Pursuit

This... this is satire, right? This has to be some sort of philosophical parody.

Spare a Thought for the Billions of People Who Will Never Exist
As world population growth slows, the never-conceived are the ultimate forgotten ones.

Now, this source - Bloomberg - is obviously pro-capitalist, and capitalism absolutely relies on population growth. You need wage slaves and consumers, or your company doesn't make as much money, and that would be terrible. And the value of your company depends not on absolute profits, but on profit growth year over year. So it's not surprising that a bastion of capitalism would sound the bells of terror over the very idea that maybe future population will, not necessarily be lower, but not grow as quickly as they'd like.

But I don't know. That's speculation. The article is, at least on the surface, more philosophical.

A couple decides to have one child instead of two, or none instead of one. This happens all over the world. Billions of children are never conceived.

And? What matters are actual lives, not imaginary ones.

How real is the loss of a life that never began?

None. None real.

Is there a right to exist?

For a person who exists, usually yes. For a person who doesn't exist, well, that's like saying "There has not been a Martian born on the Moon, but there should be and therefore they have a right to exist!"

Is there an ideal size of the world population?

I'm sure there is, but ideal for what, and for whom? I wouldn't even attempt to guess at what the ideal size of the world population of humans is; we'd have to take into account arable land, pollution, resource availability, and myriad other factors, not the least of which would be weighing any benefit of a larger human population against the existence of other species.

These related questions become more pressing as population growth slows.

There is population. There is population growth. And then there is change in rate of population growth. These things can be seen as analogous to position, velocity, and acceleration. "As population growth slows" refers to a decrease in acceleration. And I absolutely reject the hypothesis that these questions are "pressing;" they're mere philosophical abstractions.

The late University of Oxford philosopher Derek Parfit wrestled with the question of the world’s ideal population in an influential 1984 book, Reasons and Persons. He didn’t delve into the carrying capacity of the planet, and he stayed away from the issue of abortion, which occurs after conception and thus raises a different set of concerns.

Well, that year doesn't have any dire connotations. Anyway, any meaningful discussion of ideal population size has to take into account "the carrying capacity of the planet," which to be fair is a shifting, chaotic target because so many things - like climate and technology - affect it.

Also, just to be crystal clear, I too am staying away from the issue of abortion. That has nothing whatsoever to do with any discussion here, and I only mention it to dismiss the topic out of hand.

In an abstract, theoretical way, the British thinker presented what he called the “Repugnant Conclusion.” Here’s how he stated it: “For any possible population of at least 10 billion people, all with a very high quality of life, there must be some much larger imaginable population whose existence, if other things are equal, would be better, even though its members have lives that are barely worth living.”

As a "conclusion," that is, on the surface, utter nonsense. But one must delve into how he reached that conclusion in order to consider specific arguments. I haven't read the book, so I have to rely on this author's summary.

Parfit’s utilitarian logic was that if each person on the planet is happier alive than dead—even if just barely—then the total amount of happiness in an extremely large population, let’s say hundreds of billions, would be greater than the total happiness of a smaller population whose average happiness is greater.

That's... that's not logic. First it relies on extremely questionable premises; second, why would the "total" matter?

I guess they're considering "not born" to be the same as "dead?" That's crap. Also, it is impossible to be happy, or feel any other emotion, if you don't exist; most living people would rather stay alive, sure, but dead (or never-existant) people don't have the ability to "rather." And finally, what the declarative fuck does happiness have to do with anything, and how do you define it? It sounds like the author assumes an absolute scale, like the kelvin temperature scale, where "dead" is like "absolute zero" where happiness is concerned, and it can only go up from there. But... depending on how you define happiness... it's more like the Celsius scale, where 0 happiness is some arbitrary point, and it's absolutely possible to be alive and to feel negative happiness.

If you don't believe me, congratulations; obviously, you've never been unhappy. Good for you.

It’s simple arithmetic.

No. No, it is not. How in the hell do you put a numeric value on an abstract concept? Any attempt to do so is necessarily subjective. And before anyone goes "but money is an abstract concept and we put a value on that," yes, but money still has a tangible reality aspect, whereas happiness, like love or pain confidence, can only be self-reported, and only against one's prior experience.

One way to escape the Repugnant Conclusion is to maximize average happiness instead of total happiness.

Another way is to stop worrying about happiness. Surely there are other means of self-evaluation?

Another possible escape from the dilemma is to assert that some irreplaceable things are lost in the transition from a smallish, well-off population to a huge population of people just getting by. As Parfit put it, first Mozart goes away, then Haydn, etc., until all that’s left is “muzak and potatoes,” no amount of which can compensate for the loss of Mozart.

Counterpoint: we also end up with an absolute fewer number of murderers, rapists, cannibals, etc. For every Mozart there's a Dahmer.

Oxford philosopher Hilary Greaves wrote in 2017 in an article titled “Population Axiology” in the online journal Philosophy Compass that there’s no way out of Parfit’s conundrum without surrendering one or another moral intuition, so one’s solution to it “appears to be a choice of which intuition one is least unwilling to give up.”

All due respect to any philosophers involved, but there is definitely a way out: don't use "happiness" as any kind of marker. As I said, it's squishy and undefinable, and there has got to be a more objective measure, like life expectancy or crime rate or how well any individual's objective needs, such as clean air, water, food, and companionship, are being met. Sure, one could say that fulfilling those needs provides "happiness," but I still say that a lot of people living unhappy lives would rather never have been born in the first place.

The question of the ideal world population size may never be resolved by philosophers.

Clearly not. That's going to take actual science.

In conclusion: bullshit.

7 Like • Comment • View 4 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.