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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:

Kåre Enga in Udon Thani

about 21 hours ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

about 21 hours ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

about 22 hours ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

a day 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

Apr 23, 2024 at 6:51pm
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

Apr 23, 2024 at 3:31pm
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

Apr 23, 2024 at 3:14pm
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

Apr 23, 2024 at 3:11pm
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

Apr 23, 2024 at 3:04pm
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

Apr 23, 2024 at 2:58pm
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?

March 21, 2019 at 12:47am

#954673

Depressing

https://aeon.co/essays/the-evidence-in-favour-of-antidepressants-is-terribly-fla...

I've ranted here about certain science issues, though specifically I've noted my problems with nutrtitional studies and the way they're reported. This one, however, is about antidepressants.

Do antidepressants work?
Depression is a very complex disorder and we simply have no good evidence that antidepressants help sufferers to improve

Like many people, including some I consider role models or otherwise greatly admire, I've struggled with depression. I know there are readers here with mental health issues as well. Let me state up front that I've never been suicidal - that's always the first question people ask, so I wanted to get that out of the way.

As always, let's first consider the source. I have no problem with Aeon, but I do wonder about the particular author:

Jacob Stegenga is a lecturer in philosophy of science at the University of Cambridge. He is the author of Medical Nihilism (2018). He lives in Cambridge.

Well, since I ragged on Oxford the other day, it's only fair to consider Cambridge. When I see the words "philosophy of science," my inner skeptic goes on high alert. In fact, anytime I see "philosophy," this happens. I'm not saying philosophy is bad - I think it's important - but it's very easy to draw utterly logical conclusions from bad premises. So one needs to be aware of any lurking biases - ironic, because the article discusses biases in studies. Also, this might be an ad for the guy's book. Not that there's anything wrong with advertising your book.

Your grief and guilt overwhelm you. You are so tired you cannot think straight. Your simple joys are lost in an invisible agony. You have pain in your head and back and stomach, real pain. The swamp of your soul suffocates you with despair. All this is your fault, you are worthless, and you might as well die. This is how depression can feel, though people’s experiences of it, including the severity of symptoms, can vary widely. This terrible disease affects about one person in 10 at some point in life and, to treat it, many millions of people have taken antidepressants. Unfortunately, we now have good reasons to think that antidepressants are not effective.

Okay, gotta be honest here - my own experience has never been that severe. I've been prescribed antidepressants in the past, mostly SSRIs, some SNRIs, and if you've had any experience with this issue yourself, you probably know what those are. Those medications act on the neurological pathways that affect certain neurotransmitters in the brain. It's pretty basic stuff as far as biological psychology goes, but that field is itself not what I'd call "basic."

The meds each did one of three things for me:

1) Nothing.
2) Hallucinations, and not fun ones.
3) Made things worse.

To be fair, (3) might have happened anyway - can't tell with a sample size of one. I'm pretty sure that (2) isn't what was supposed to happen, and (1) happens more often than we'd like. And that's kind of the point of the article.

The vast majority of these studies are funded and controlled by the manufacturers of antidepressants, which is an obvious conflict of interest.

And now we get into some crossover with my problems with nutritional science.

The trials that generate evidence seeming to support antidepressants get published, while trials that generate evidence suggesting that antidepressants are ineffective often remain unpublished (this widespread phenomenon is called ‘publication bias’). To give one prominent example, in 2012 the UK pharmaceutical company GlaxoSmithKline pleaded guilty to criminal charges for promoting the use of its antidepressant Paxil in children (there was no evidence that it was effective in children), and for misreporting trial data.

And Paxil was the shit that made me hallucinate. Look, if you want me to hallucinate, give me LSD. Not that I've ever tried it, but I've heard that microdoses might be effective in treating depression - moreso than antidepressants, anyway.

The placebo effect is when patients improve merely as a result of the medical care they have received rather than as a result of the biochemical properties of their drug. The idea is that the mere expectation that you will get better after receiving medical care can itself contribute to you getting better. Some diseases are more responsive to placebo than others, and depression is one of the most placebo-responsive of all diseases.

This makes sense, though entire articles are out there that go into more detail about the placebo effect. Unfortunately, the response of depression to placebo is one thing that leads some people to believe that it's "all in your head" and you can just think yourself better. There might be some truth to that, but it doesn't mean the disorder isn't "real." I mean, technically, pain is all in your head - well, your nervous system in general - but only assholes think you can think yourself out of pain.

In short, we have plenty of reasons to think that antidepressants have no clinically meaningful benefits for those suffering from depression. Conversely, we know that these drugs cause many harmful side-effects, including weight gain, sexual problems, fatigue and insomnia. Some studies have demonstrated a link between antidepressants and the risk of violence, suicide, childhood and teenage aggression, and psychotic events in women.

Which would fall into my "making things worse" category above.

Conversely, there is another theoretical consideration that seems to speak against antidepressants. Some critics claim that many diagnosed cases of depression are not cases of real disease, but rather involve the ‘medicalisation’ of normal life – normal grief, stress, anxiety or simply suburban sadness being brought into the jurisdiction of medicine.

I've had some experience with this, I think. A doctor prescribed me some SNRI medicine because I just couldn't be arsed to cook my own food (healthy) when it was so easy to order from GrubHub or stop by McDonald's (not quite as healthy). After taking the medicine for a while, I still ate at McDonald's. As I told the doctor when I informed her I'd be tapering myself off of them, "they still haven't come up with a pill to fix moral failings."

How, then, did I get past that? Well, I don't know, but antidepressants didn't do it.

So, bottom line? Apparently, if a course of treatment works for you, then it works. It doesn't mean it would work for me. I keep hearing that a positive attitude can make you healthier and live longer. If so, this might well be my last blog entry, because every time I get a positive attitude, I bury it like the abomination that it is.

2 Like • Comment • View 2 comments

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