Complex Numbers (Book)

Blog Calendar

◄ August ► 2023
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

August 19, 2023 at 10:11am

#1054312

In a Vacuum

One thing that often bugs me about science fiction movies and shows is when they get the "science" part wrong.

How long could you survive in space without a spacesuit?
The vacuum of space is unforgiving, and time is not on your side.

It usually doesn't stop me from enjoying the story, unless it's egregious, but how long would it take to make sure you get something right?

Today's topic, though, is one that we don't have much empirical data on. It's not like we can shove people out of airlocks and time how long it takes until they die. Well... not ethically.

And yet, some recent shows don't seem too far off the science on this one.

Many of us have dreamed of going into space.

Preferably inside of something.

But traveling in space brings a whole set of challenges and hostile environments, so it's vital to recreate the conditions on Earth that have allowed life to evolve and flourish.

As I've mentioned before, we can only live in a zone of atmosphere proportionally thinner than an eggshell. Everywhere else in the universe, as far as we know, will kill us in varying amounts of time, from instantly to slightly longer than instantly. Hell, even our evolved environment kills us, but usually over a matter of years, not seconds.

Spacesuits allow astronauts to venture outside their spacecraft for short periods, by providing the air, water, pressure and physical protection needed for a human to survive.

Sucks if you're one of the people who also need companionship to survive. I guess there's the two-way radio for that.

Sci-fi movies and shows, including "2001: A Space Odyssey" and "The Expanse," have portrayed astronauts suffering — and surviving — short exposures to outer space without a spacesuit, while others have depicted a range of grisly deaths.

I thought The Expanse was great, but it didn't always get the science right, either.

"Within a very short time, a matter of 10 to 15 seconds, you will become unconscious because of a lack of oxygen," according to Stefaan de Mey, a senior strategy officer at the European Space Agency (ESA) charged with coordinating the strategy area for human and robotic exploration.

I still don't think that's the worst part.

Bodily fluids, such as saliva and tears, would begin to boil. A human body would also expand, but the skin would be elastic enough to cope with the pressure change, de Mey said, adding that horrific movie portrayals of exploding humans are not accurate.

And it's even worse than that. Fluids don't start to boil because they get hot. They boil because the pressure drops. You know how water boils at a lower temperature in Denver than it does in New York? Well, space is even more empty than Denver air, and the boiling point drops even further.

Depending on where you are, you can boil and freeze at the same time.

Because you'd be unable to alter your dire situation, brain death would follow within minutes, unless you were rescued and brought back to the safety of the pressurized, oxygen-rich environment of a spacecraft and resuscitated.

"Within minutes?" Weasel! Of course, as I said, we have no empirical evidence of this, so uncertainty is understandable. So I'm going to go with the time it took to rescue Star-Lord in Guardians 3.

Spacesuits also protect from various types of radiation. In LEO, there is protection from some forms of radiation. Prolonged or long-term exposure to electromagnetic radiation from the sun would cause health issues, including radiation sickness and an increased risk of cancer. UV light would also burn the skin.

Sure. I just got yeeted out an airlock, and my first (and last) thought is, "Boy, it sucks to be exposed to this much radiation."

Being in space without an EVA suit becomes very deadly — very, very quickly. While someone could survive this grim scenario, they would want to have very little air in their lungs and get back to the safety of a pressurized spacecraft within seconds — or hope to be rescued and resuscitated within minutes.

I think the important takeaway here is that death by airlock isn't instantaneous, not like if you're standing next to the fusion reactor when it explodes. No, you'd have time to think about it, much like those seconds between when you jump off the building and hit the pavement.

In the latter case, though, the last thing that goes through your mind would be concrete.

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.