Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ February ►
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
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Friday, Feb. 7, 2025

5:18am EST

Members: 651

Guests: 1,617

Total Online: 2,268

Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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:

tj wanderlust-words-in-motion

about 14 hours ago
In response to "So Much Energy"

I always thought electroweak{i/} was a bad choice of terminology. It sounds like the batteries in you flashlight are almost dead! They should have used a term like "electronuke" which sounds like some super-hero stuff. There's no need to fear, Electronuke is here!"

Also, when crossing Higg's field, beware of Higg's boson (cross between a boar and a bison) or you may get killed; unless of course, Electonuke shows up and saves your ass.

Alright, maybe I should be writing a story instead of leaving a comment...

1 Like

Graham B.

about 17 hours ago
In response to "So Much Energy"

The only energy-carrying particle that concerns me is the Joeson, as in "I need my morning cup of Joeson to get me up." It's responsible for the strong nootropic force (for me, anyway).

3 Like

Lazy Writer est 4/24/2008

about 18 hours ago
In response to "So Much Energy"

I need to find some of that energy..because mine is worn out!

2 Like

tj wanderlust-words-in-motion

a day ago
In response to "That Healthy Glow"

Yes, they do still make black lights, most are LED. We have one above my wife's plants, it helps them survive through the winter with our lack of sunlight. They seem to be more purple than the black lights from days gone by. Interestingly, they make our Australian Shepard glow purple (her black areas) and they make our Husky's blue eyes glow, but not the black on his fur.

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "The Fault in Our Stars"

I knew you (or someone) was going to write this; it was in my horrorscope.

2 Like

🌖 HuntersMoon

a day ago
In response to "The Fault in Our Stars"

I don't care what this article says... My psychic told me that Astrology is 100% accurate!

1 Like

tj wanderlust-words-in-motion

Feb 3, 2025 at 4:32pm
In response to "Look! Up In the Sky!"

Beware anyone wearing a black suit waving a pen looking device in front of you. Actually, they likely dress as regular people, and the device is hidden in an actual pen. Maybe they've even put the device in the pens we use! Clearly, that's because there's a government agency tasked with removing our memories of certain encounters.{i/}

2 Like

🌖 HuntersMoon

Feb 3, 2025 at 9:22am
In response to "Look! Up In the Sky!"

2 Like

Lazy Writer est 4/24/2008

Feb 2, 2025 at 10:54pm
In response to "Revisited: "Friend""

Christ is coming back...no one knows when...Only God himself...we are told to be ready...by that, the Bible means giving your heart and soul to Christ. It is a free gift. He does not force you to believe. I am not a member of any end of the world group but I do believe my Bible.

tj wanderlust-words-in-motion

Feb 2, 2025 at 11:10am
In response to "Revisited: "Friend""

I had an employee that requested some time off the week leading up to December 21, 2012 to be with his family. They had prepped and prepared for over a year and wanted to be together, in shelter, for the end of the world. On December 22 he came into work looking like he had not slept all night, head hung low, and not a word to say about the rest of us still hanging around. In March, he and his family all moved to Florida, probably to start prepping for the next end of the world.

2 Like

February 6, 2025 at 11:29am

#1083418

So Much Energy

I'm made of energy? Then why is it so hard to wake up in the morning? From Big Think:

You’re made of energy: The strange truth about where mass comes from
“A person’s mass is made not of ‘stuff’ in the way we normally think about it, but rather our mass is made of energy.”

"Mass is made of energy" shouldn't be such a new concept for anyone with passing knowledge of science. The equation, from Einstein. describing the relationship between mass and energy isn't exactly obscure or complicated.

But it does get a bit weird and, of course, common-sense-defying, because common sense is usually wrong.

If I asked you where your mass comes from, your answer might involve an extra muffin or two.

Oh, I'm way beyond that point.

However, if I ask a science enthusiast the same question, I would expect to hear that the real origin of mass is from a physical phenomenon called the Higgs field.

Which opens the question of where the Higgs field comes from, but okay, yes, I've heard that.

While that claim is often seen in popular science stories, it turns out not to be true at all. Indeed, the Higgs field contributes very little to the mass of the Universe. The reality is far more interesting.

Reality usually is. Except when it's not.

The Higgs field was a theory devised in the 1960s as a kind of Band-Aid to save another theory that was popular at the time. Physicists had devised a theory that two of the known quantum forces – electromagnetism and the weak nuclear force – were actually two manifestations of a single underlying force: the electroweak force. (Electromagnetism is responsible for electricity, magnetism, light, and much of chemistry, while the weak nuclear force is responsible for certain forms of radiation.)

And there it is again: punting the description of the weak nuclear force. I know I've said before that I've looked into it more closely, and it's way above my pay grade.

There was a problem with this new and unified force — it predicted that all subatomic particles have zero mass.

Which would, in turn, mean that nothing has mass, because everything is made up of subatomic particles (by "thing" here, I mean something made of matter).

This is obviously and demonstrably false, much like Zeno's paradox can be refuted by walking out of the room.

This Higgs field theory predicted the existence of a particle called the Higgs boson – often called “The God Particle” by some science reporters.

Yeah, and they ought to have known better.

If you add up all of the mass of all the quarks in our 200-pound person, you find that the quarks weigh about 4 pounds.

I'm going to give this article a pass on conflating "mass" with "weight." This time. I think it conveys the right general idea.

It turns out that inside each proton and neutron, the quarks are moving at very high speeds; indeed, these speeds can approach the speed of light.

Kind of mind-blowing, yes?

Protons and neutrons are very tiny balls, about a quadrillionth of a meter across.

I'll give the "balls" thing a pass, too.

If protons are composed of outrageously fast quarks held inside that tiny volume, there must be equally outrageously strong forces holding them together. Strong forces can also mean high energy...

As I understand things (and I probably really don't), a "force" is carried by a massless particle, making this also counterintuitive.

In fact, all matter is made of energy. In a (very loosely true) way, the pseudoscientific woo-woo crowd is right: We are all energy.

Yeah, in a sense, they may be right about this one thing. Even a blind squirrel finds the occasional nut, as they say.

Obviously, there's a lot more at the link, and you're not going to get the full gist of it by reading my few quotes. It's not very long, though. But what does it mean? Hell if I know. Meaning is the job of philosophers.

6 Like • Comment • View 3 comments

© Copyright 2025 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://shop.writing.com/main/profile/blog/cathartes02/day/2-6-2025