Complex Numbers (Book)

Blog Calendar

◄ March ► 2021
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

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

© 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.