Complex Numbers (Book)

Blog Calendar

◄ April ► 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
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 3 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.

April 29, 2021 at 12:03am

#1009331

Hammer Time

One of the stupidest things about this timeline is how much weight people put on what celebrities say.

Science and philosophy can, and should, coexist
MC Hammer's recent tweet has sparked a conversation about the complementary nature of these two fields

Another stupid thing about this timeline is Twitter.

Nevertheless, I can't find any real fault in what MC Hammer said here.

MC Hammer recently brought the hammer down on those who see science and philosophy as fundamentally opposed disciplines. He first tweeted a link to this paper, showing that STEM fields account for 21.3% of citations of philosophy of science journals. Some tweeters responded with unflattering, and inaccurate, characterizations of philosophy that put it at odds with science. In response, MC Hammer had some words of advice praised by scientists and philosophers alike: "It's not science vs Philosophy ... It's Science + Philosophy. Elevate your Thinking and Consciousness. When you measure include the measurer."

As both science and philosophy are interests of mine, I do see that sometimes they're at odds. And they have completely different ways of approaching ideas. I see this as a good thing.

MC Hammer's insistence on the complementary nature of science and philosophy is in line with this 2019 opinion paper, published in PNAS. The authors described a continuum of science and philosophy, as the two fields share "the tools of logic, conceptual analysis, and rigorous argumentation.”

The big difference, as I see it at least, is that philosophy doesn't have to cleave to objective truth. One can draw perfectly logical conclusions from false (or at least unverifiable) premises, leading to faulty conclusions even with rigorous logic, but that's not what science is supposed to be about.

Tweets by MC Hammer promoting these views will hopefully also help to break down harmful stereotypes of the disciplines that might prevent scientists and philosophers from working together for the good of society.

I still think entertainers, no matter how talented or intelligent, have entirely too much sway over popular opinion. It's like... I'm a Springsteen fan because I like his music, but anything he says about anything other than music carries no more weight with me than when anyone else says such things.

In any case, it's always been clear to me that, deliberately or not, philosophy guides science, and science can inform philosophy. Examples? Well, consider animal testing in the biological sciences. For a while, it was generally accepted, but as attitudes changed and we found out more (partly through animal testing), such things were curtailed and subject to ethical review. There's no purely scientific rationale for not doing tests on animals (including human animals), but there's plenty of philosophical reasons not to.

After all, sometimes I wonder if the phrase "curiosity killed the cat" is more about a human's curiosity than the poor cat's.

On a personal note, for anyone who's tired of seeing these things pop up in here, I've signed up for the 30DBC again for next month. It's not like I don't have dozens more articles in the queue; it's just time for something different again.

Speaking of something different, today (Thursday) is the day I officially reach full vaccine protection, two weeks after my second shot. While it's not a good idea to start running around licking doorknobs or bathing in people's sneezes, I intend to celebrate by going to *gasp* a movie theater.

Godzilla vs. Kong looks good. If by "good" I mean "thin plot, mediocre acting, but kaiju battles with budget-breaking CGI." Which in fact I do.

6 Like • Comment • View 3 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.