Complex Numbers (Book)

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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/

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Brandiwyn🎶

about 23 hours ago
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.

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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.

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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.

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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').

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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.

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Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

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November 11, 2024 at 9:17am

#1079805

What Is the Meaning of This?

Still not quite sure what to make of this Quartz article. It's from 2018, but new to me, though I don't know if the book it's promoting is still available or not.

The secret to a meaningful life is simpler than you think

I don't know; a while back, I arrived at a pretty simple meaning of life: it has no meaning except for what we impose upon it. Impose a complicated meaning, and of course your life is going to be complicated.

Some people seem to spend their whole lives dissatisfied, in search of a purpose.

Or at least in search of that One Perfect Product that will finally live up to its advertising and fix everything wrong with your life.

But philosopher Iddo Landau suggests that all of us have everything we need for a meaningful existence.

The first thing you need for a meaningful existence is an existence.

Philosophers’ answers to this question are numerous and varied, and practical to different degrees. The 19th-century philosopher Friedrich Nietzsche, for example, said the question itself was meaningless because in the midst of living, we’re in no position to discern whether our lives matter, and stepping outside of the process of existence to answer is impossible.

I'm not sure Nietzsche is the best example to feature, but okay, whatever.

Those who do think meaning can be discerned, however, fall into four groups, according to Thaddeus Metz, writing in the Stanford Dictionary of Philosophy. Some are god-centered and believe only a deity can provide purpose. Others ascribe to a soul-centered view, thinking something of us must continue beyond our lives, an essence after physical existence, which gives life meaning. Then there are two camps of “naturalists” seeking meaning in a purely physical world as known by science, who fall into “subjectivist” and “objectivist” categories.

I'm not well-read enough to pick sides there, but the only context in which I know the word "objectivist" has to do with philosophers like Ayn Rand, who can go fuck off.

Landau argues that meaning is essentially a sense of worth which we may all derive in a different way—from relationships, creativity, accomplishment in a given field, or generosity, among other possibilities.

It seems self-evident that we each value different things, so what's meaningful to one person won't do much for another. For instance, lots of people seem to get a sense of accomplishment from working. I, on the other hand, feel accomplished if I can avoid work.

For those who feel purposeless, Landau suggests a reframing is in order. He writes, “A meaningful life is one in which there is a sufficient number of aspects of sufficient value, and a meaningless life is one in which there is not a sufficient number of aspects of sufficient value.”

I don't claim to be an expert on logic or philosophy, but that statement strikes me as both circular and weaselly.

Landau argues that anyone who believes life can be meaningless also assumes the importance of value. In other words, if you think life can be meaningless, then you believe that there is such a thing as value.

I'm not sure I agree with that. If you believe life is meaningless and that's okay, I think you're acknowledging the existence of value, but not necessarily its importance.

In Philosophy Now, Tim Bale, a professor of politics at Queen Mary University of London in the UK, provides an extremely simple answer: “The meaning of life is not being dead.”

See? This sort of thing is why I picked engineering over philosophy.

There are a few other examples of simple answers to the question of life's meaning, and I'm really quite proud of myself for making it this far without quoting "42" as the answer, which, honestly, I'm only doing to forestall the inevitable comment about it.

I'm not sure I buy any of the arguments, though. Perhaps I find meaning in skepticism.

4 Like • Comment

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