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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

a day 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

a day 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

a day 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?

August 6, 2020 at 12:03am

#990052

Panpsychoticism

We should all know by now that when a headline asks a question, the answer is almost certainly "no."

https://blogs.scientificamerican.com/observations/could-multiple-personality-dis...

Could Multiple Personality Disorder Explain Life, the Universe and Everything?
A new paper argues the condition now known as “dissociative identity disorder” might help us understand the fundamental nature of reality

I will, however, give them credit for referencing Douglas Adams.

In 2015, doctors in Germany reported the extraordinary case of a woman who suffered from what has traditionally been called “multiple personality disorder” and today is known as “dissociative identity disorder” (DID). The woman exhibited a variety of dissociated personalities (“alters”), some of which claimed to be blind. Using EEGs, the doctors were able to ascertain that the brain activity normally associated with sight wasn’t present while a blind alter was in control of the woman’s body, even though her eyes were open. Remarkably, when a sighted alter assumed control, the usual brain activity returned.

That's actually pretty cool. I don't know much about psychology and even less about psychiatry, but it's still cool.

The article goes into some detail about DID, before getting into the question in the headline.

Now, a newly published paper by one of us posits that dissociation can offer a solution to a critical problem in our current understanding of the nature of reality. This requires some background, so bear with us.

Background? All the paragraphs leading up to this quote (most of which I didn't copy, but they're at the link) were background. But okay -- like I said, I know very little so that was a decent introduction.

According to the mainstream metaphysical view of physicalism, reality is fundamentally constituted by physical stuff outside and independent of mind. Mental states, in turn, should be explainable in terms of the parameters of physical processes in the brain.

Any essay that uses "metaphysical" unironically is suspect.

But there's a brief introduction there to the "hard problem of consciousness," which I'm pretty sure I've mentioned in here before, in connection with panpsychism -- a philosophy I provisionally reject. "Provisionally," because there's no real science behind it, only conjecture. Could be true. Could be false. Can't be tested at this time.

To circumvent this problem, some philosophers have proposed an alternative: that experience is inherent to every fundamental physical entity in nature.

Yep. Panpsychism. But okay, I'll bite.

However, constitutive panpsychism has a critical problem of its own: there is arguably no coherent, non-magical way in which lower-level subjective points of view—such as those of subatomic particles or neurons in the brain, if they have these points of view—could combine to form higher-level subjective points of view, such as yours and ours. This is called the combination problem and it appears just as insoluble as the hard problem of consciousness.

From my purely amateur perspective, it sounds more like the same problem, only stated differently.

The obvious way around the combination problem is to posit that, although consciousness is indeed fundamental in nature, it isn’t fragmented like matter. The idea is to extend consciousness to the entire fabric of spacetime, as opposed to limiting it to the boundaries of individual subatomic particles.

Ever seen a map of the universe? They've made some. Here's one.

I've noted a superficial similarity to a neural network

before. But physical similarity isn't support for this hypothesis; it could be coincidence.

And here is where dissociation comes in.

This view—called “cosmopsychism” in modern philosophy, although our preferred formulation of it boils down to what has classically been called “idealism”—is that there is only one, universal, consciousness.

Pretty sure philosophers have posited something similar since time immemorial. That's also the basis for at least one conception of the Divine. But just because a philosopher (or a scientist for that matter) says something, doesn't mean it's fact.

You don’t need to be a philosopher to realize the obvious problem with this idea: people have private, separate fields of experience.

Basically, if there's only one Universal Consciousness, how come we all appear to live separate existences?

So, for idealism to be tenable, one must explain—at least in principle—how one universal consciousness gives rise to multiple, private but concurrently conscious centers of cognition, each with a distinct personality and sense of identity.

That's not the only thing that "one must explain" to accept this, at least in theory. There's also the small matter of communication across vast distances, communication that can't be attributed to "quantum entanglement." Consciousness requires communication, and the speed of light is a hard limit; this has been supported by evidence as well as mathematics.

And here is where dissociation comes in. We know empirically from DID that consciousness can give rise to many operationally distinct centers of concurrent experience, each with its own personality and sense of identity. Therefore, if something analogous to DID happens at a universal level, the one universal consciousness could, as a result, give rise to many alters with private inner lives like yours and ours. As such, we may all be alters—dissociated personalities—of universal consciousness.

Okay, I have to admit here that although I categorically dismiss the idea, it is attractive to me. The idea of universal oneness, of breaking down barriers; that all is, indeed, One -- well, I think most people have to drop acid to get into that mindset, and I've never dropped acid. But I think a lot of problems would be ameliorated if we stopped thinking of things as separate entities but as parts of a whole.

That doesn't mean I'm going to embrace this stuff, of course. Just that, if it turns out to be the case, it would have beneficial implications. For instance, that there is no "us" and "them," only "us."

Moreover, as we’ve seen earlier, there is something dissociative processes look like in the brain of a patient with DID. So, if some form of universal-level DID happens, the alters of universal consciousness must also have an extrinsic appearance. We posit that this appearance is life itself: metabolizing organisms are simply what universal-level dissociative processes look like.

Whether factual or not, the other thing that appeals to me is its syncretic nature -- to take ideas from several different branches of science and philosophy and put them into a coherent whole. Wait -- that's just another aspect of universal oneness, isn't it? We make distinctions between, say, cosmology, psychology, biology, chemistry, physics... when in reality the boundaries are far more blurry, if they exist at all.

Insofar as dissociation offers a path to explaining how, under idealism, one universal consciousness can become many individual minds, we may now have at our disposal an unprecedentedly coherent and empirically grounded way of making sense of life, the universe and everything.

Insert "42" joke here. You know you want to.

Just remember: the key word in the last sentence I quoted is "may." I find it highly unlikely, personally. Just to be clear, though: I do believe that everything is One Thing; just not necessarily in the manner described here. Like I said, this stuff is appealing -- which is all the more reason to be skeptical about it.

2 Like • Comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
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