Complex Numbers (Book)

Blog Calendar

◄ March ► 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:

Brandiwyn🎶

a day 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.

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.

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

1 Like

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.

2 Like

March 3, 2021 at 12:05am

#1005709

Not Now

Sometimes it seems that the entire purpose of mystics and philosophers is to twist logic around until what's real becomes illusion, and what's make-believe becomes real.

The problem of now
The injunction to immerse yourself in the present might be psychologically potent, but is it metaphysically meaningful?

But sometimes, one comes along and puts things back into perspective.

What I will dub the ‘connection thesis’ is a central claim of various spiritual practitioners, authors, lecturers and workshop leaders; it’s the contention that we should focus our full attention on the present moment precisely because of its singularity.

After which the author meticulously dismantles the entire idea, and it is glorious.

The singularity of the now might appear to be a deep and profound insight. It’s the springboard for various more practical strategies for achieving enlightenment and self-enhancement. But the claim that it is always now is so trivial that it can’t support any interesting inference, and there are other ways of justifying these same strategies and practices.

Essentially, it's the temporal equivalent of saying, "Wherever you go... there you are."

The article builds logical structures that I can't do justice to in this blog post; best to actually read it if you're interested in this sort of thing.

I'll just add a few of my own observations about the pervasive "now" idea:

1) By the time you perceive something, it's already in the past (even if only microseconds); there is no "now." Yeah, I know I've said this before but it's relevant.

2) Memory isn't a linear recording like a cassette tape (if you remember those). It's more holographic. When you access a memory, your perception focuses on the memory. It may or may not be a faithful re-creation of the past; most times, it isn't. But the important point is that the memory comes to your attention in something very close to the present moment. In other words, it would be part of the "now" if there were such a thing. And since it's not filtered through our senses, it's even closer to the elusive "now" than anything external that we perceive.

2a) A similar thing applies to thoughts about the future.

3) Failing to plan for the future or consider the consequences of our actions or inactions is objectively a Bad Idea. Living all the time "in the present" is self-defeating.

4) Being able to learn from the past and project those learnings into the future is a big part of what makes us human. To ignore everything except the tiny temporal slice of perceptions that most recently happened... well, that denies a huge part of humanity.

As I've said before (I think), I understand that one can obsess too much over what was and what might be, so it makes sense that sometimes you want to focus on what's here before you. Like if you're with a friend or lover, presumably you don't want to be thinking about a different friend or lover when interacting with them. And you probably want to do some things "now," or in the near future, rather than waiting for some nebulous far future time when you think conditions might be better.

Most importantly, though, I think it's a mistake to swap reality and fiction. There are levels of reality -- ideas are real in a sense, thoughts are real, even fictional characters have a particular kind of reality. But I'm pretty sure that the reality is that anyone who tries to tell you "everything you perceive is an illusion" is blowing smoke up your ass and probably wants some of your money, which has an entirely different kind of reality.

The singularity of the present is emphasised by influential spiritual teachers and it appears, at first, to be a profound truth. It is, however, superficial and not substantive enough to support the inference to immersion in the now. From the perspective of philosophy of language, we can see the impotence of now. From that of philosophy of time, we see that presentism doesn’t, in itself, have any implication for psychology, and eternalism is a non-starter.

And sometimes bullshit seems profound, but upon stepping in it, you find that it is, indeed, bullshit -- which nevertheless has the advantage of making an excellent fertilizer.

4 Like • Comment • View 2 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.