Complex Numbers (Book)

Blog Calendar

◄ December ► 2022
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

December 1, 2022 at 12:02am

#1041189

Never Mind

I don't have a lot to say about today's article from The Guardian; I went to the movie theater yesterday (review below) and I'm worn out from all the sitting, drinking, and popcorning.

Is the body key to understanding consciousness?

Most headline questions are answered "no," but this one's not so simple. Besides, the brain is part of the body.

In 2018, billionaire Silicon Valley entrepreneur Sam Altman paid a startup called Nectome $10,000 to preserve his brain after he dies and, when the technology to do so becomes available, to upload his memories and consciousness to the cloud.

Cheaper than most funerals.

This prospect, which was recently popularised in Amazon Prime’s sci-fi comedy series Upload, has long been entertained by transhumanists.

People who actually read science fiction, like me, have been exposed to the concept for far longer than transhumanists, or even Amazon, have been around.

Although theoretically possible, it is rooted in the flawed idea that the brain is separate from the body, and can function without it.

How, exactly, is it "theoretically possible?" I've never heard a compelling reason why it should be.

The idea that the mind and brain are separate from each other is usually attributed to the 17th-century mathematician and philosopher René Descartes, who believed that the body is made of matter, and the mind of some other, non-physical substance.

Remember a couple entries ago I said Descartes was "right about a lot of things, but...still subject to human biases and observational inconsistencies?" This is an example of those things.

Besides, mind/body duality goes back way before Descartes, though as I understand it he codified it somewhat.

Modern brain research rejects the distinction between the physical and the mental. Most neuroscientists agree that what we call “the mind” is made of matter. The mind is hard to define, but the consensus now is that it emerges from the complex networks of cells in the brain.

I don't know about "made of matter," but there's a lot I don't know about this.

But most people still view the mind and brain as being distinct from the body.

It's a useful metaphor to think of mind and body as separate, but that's all it is: a metaphor. Like thinking of atoms as if they were little solar systems.

Being conscious does not just mean having awareness of the outside world. It means being aware of one’s self within one’s surroundings. The way we experience our body is central to how we perceive our self.

If you want to get really philosophical about it, you can go off on how the "outside world" is filtered through our senses and thus an inaccurate representation of the actual "outside world;" it's all really inner experience. As interesting as that may be to contemplate, it's irrelevant.

Phantom limbs are a striking demonstration of the importance of the body for self-consciousness.

The article then goes into how that phenomenon relates to consciousness, and also gets into body dysmorphias, but what I found most relevant to writers is the bit about how people didn't believe in phantom limbs at first, and it took a fictional story to bring it into public awareness. I mean, behold the power of fiction, right?

So I'm skipping over a lot, but in the end:

If self-consciousness is based in bodily awareness, then it is unlikely that a lab-grown “mini-brain” could ever become conscious, as some ethicists have claimed.

I always wondered about that aspect of consciousness "uploads." Of course, you have people thinking we're all uploads, and that the universe is a big computer simulation, but that raises way more questions than it answers.

By the same token, transhumanists’ claim that we will one day gain immortality by uploading our brains to supercomputers will probably always be science fiction.

I'd be very cautious about saying something will "always" be science fiction. We can be quite clever in figuring stuff out and inventing things. But I would bet that it's a very, very long way away.

One-Sentence Movie Review: Black Panther: Wakanda Forever:

I suppose it would have been asking too much for this sequel to be as good as or better than the first one; it certainly didn't suck (and was very respectful to the memory of Boseman), but it's a little incoherent in parts and significantly short on action for a MCU movie.

Rating: 3.5/5

5 Like • Comment • View 1 comment

© Copyright 2024 Waltz en France (UN: cathartes02 at Writing.Com). All rights reserved.
Waltz en France has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.