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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Elycia Lee ☮

about 7 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

about 20 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

about 23 hours ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

February 25, 2020 at 12:02am

#976273

Hack This

Worth reading if you want a decent takedown of "lifehacks." Or even if you don't. Especially if you don't.

https://medium.com/personal-growth/the-problem-with-hack-culture-b0ddf43784e9

The Problem with ‘Hack’ Culture
Most of it is complete, utter bullshit

I mean, really, it's right there in the subhead.

Venture down the self-help aisle of any bookstore and you’ll see it littered with titles about hacks, quick fixes, burning fat, and accessing mystical sounding theta brainwaves.

Lifehack: Don't browse the self-help aisle. Better yet, if you know there's something you want to improve, go to Amazon, find appropriate books and read the reviews. Yeah, yeah, I know, support your local bookstore and all that. But don't feed their "self-help" beast.

But the internet age has ushered in a whole new era: The maddening proliferation of hope — clouded in broscience.

"Broscience." I'm not sure I like that. But it's apt.

Use polyphasic sleep to hack your energy levels.

That one might work if, like me, you're naturally polyphasic, and can adjust your schedule accordingly. Then again, it might not.

The problem with all of these grand promises? The vast majority of them are bullshit. Complete, utter bullshit wrapped in complex sounding broscience.

Sturgeon's Law again. 90% of all published works are crap.

Now here's the part that addresses us as writers.

But the reality is that the onus shouldn’t be on the consumer of information; it should be on the writer, speaker, or influencer who has the power to make a difference. When you have a platform, you have a responsibility.

The downside of free speech is that everyone can exercise it. Wait, that's the upside. No, the actual downside is that it requires discerning consumers of said speech, which is difficult if you don't even know what to watch out for. I'll mention a few keywords to watch out for, apart from "hack:" cleanse, homeopathic, natural, ancient. I'm sure you can think of more.

For too long now, we’ve focused on the details, the finishing touches, the small things that may or may not work: Why am I concerned with whether or not I put cream or butter in my coffee but OK with binge drinking at the bar a few times a month?

Because I don't drink coffee but I do drink beer? Oh, wait, the author apparently thinks binge drinking is bad. Never mind.

In our diets, we go nuts over whether 80 percent of calories should be carbs or fat, all the while overlooking that a lot of what we eat — both carbs and fat — comes wrapped in plastic and bears little resemblance to anything found in nature.

I keep seeing that the true enemy is "processed" or "overprocessed" foods, but I haven't found a good definition for those, yet. I mean, technically, cooking is a process, and - raw-food-diet bullshit aside - cooking is what makes a lot of food more nutritious and digestible. Potatoes, for example. It's probably what allowed our ancestors to evolve these great big brains that most of us don't use.

We are seeking the silver bullet when the reality is we need to zoom out and nail the basics before we even consider the final 2 percent.

And there it is, folks, the buried lede.

It’s for these reasons that I wrote The Passion Paradox and Peak Performance. Am I a self-help guru? No way! But I do feel qualified to bring the focus back on the concepts that actually make a difference.

Look, dude, I'm not saying you're wrong, or that you're right. But I'm not clicking on those book links. Isn't the major part of the problem that too many people "feel qualified" to do this or that, without being actually qualified? Also, I hate reading this far along a halfway decent article only to find that it's a commercial in disguise. Bah.

So, I'm done here. I feel like he has good points, but those are somewhat muted by the fact that he's doing exactly what he's railing against.

Of course, I "feel qualified" to make these assessments.

1 Like • Comment • View 6 comments

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