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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:

Aiva Raine

about 10 hours ago
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

a day ago
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

a day ago
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

a day ago
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

Aennaytte: Free & Wild in GoT

a day ago
In response to "Going to the Dogs"

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

March 31, 2021 at 12:02am

#1007361

The Cure

Going back to Scientific American for this one.

The Power of Psychedelics
They worked for my depression. Could they be the future of psychiatry?

Just to be clear, here, I haven't used psychedelics. Some people I know have. What I have had is depression, and meds that never worked for it.

In 2012, I had my first psychedelic experiences, as a subject in a clinical trial at Johns Hopkins University School of Medicine’s Behavioral Pharmacology Research Unit.

Pretty sure you don't have to go to Johns Hopkins to find shrooms in Baltimore.

Prior to their 1971 prohibition, psilocybin and LSD were administered to approximately 40,000 patients, among them people with terminal cancer, alcoholics and those suffering from depression and obsessive-compulsive disorder. The results of the early clinical studies were promising, and more recent research has been as well.

Some drugs are legitimately dangerous. Some are only dangerous in context; I wouldn't want to encounter a tripper (or a drunk) driving on the road. Many are considered dangerous but probably have medicinal benefits; I've always seen shrooms as one of those. The main reason for prohibition in their case is we can't have people thinking for themselves, making their own decisions, or exploring alternative mental states; if people did all that, where would capitalism find its wage slaves?

Eight years after my sessions, researchers continue to prove the same point again and again in an ongoing effort to turn psychedelic drug therapy into FDA-sanctioned medical treatment.

To be fair, "prove" is a bad word here. Research supports (or doesn't); it can disprove, but it can't "prove."

Psychedelic drug therapy subverts the timeworn patriarchal hierarchy by creating an atmosphere of cooperation and trust rather than competition and domination.

Gender-Studies-like-typing detected. Doesn't mean it's wrong, though.

MDMA (3,4-methylenedioxymethamphetamine) is rapidly proving effective in treating PTSD.

Chemical names can sound scary (if, that is, one can pronounce them at all). They shouldn't. As I've harped on too many times already, everything we ingest is made up of chemicals, and I guarantee you a lot of them have long names. Granted, this one includes "methamphetamine," but it's important to note that MDMA (aka Ecstasy or Molly) is not meth.

The success of the cancer studies has led to investigational treatment for patients suffering from intractable depression, early-stage Alzheimer’s, anorexia nervosa and smoking addiction.

On the other foot, there's a long history of Puritanical pearl-clutching in the US, and any medicine that alters one's mental state is frowned upon (including alcohol, which in fairness is probably way more dangerous than cannabis or psychedelics). This alone is probably what's been stalling approval of effective therapies. There's also this persistent idea that we should be self-sufficient, and not turn to altered states of consciousness to relieve the pain of everyday life. That's pernicious.

Clearly, abuse of any drug (or any substance in general) has its dangers, but personally, I'd like to see a follow-up on these studies of psychedelics. I still have little desire to use them recreationally, but this is one thing science is for: to get closer and closer to the truth. Some say psychedelics help with that on a personal level; why not combine the two?

Anyway, check out the article, if you can get past the gender-studies lingo involved.

3 Like • Comment • View 5 comments

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