Complex Numbers (Book)

Blog Calendar

◄ October ► 2023
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:

QPdoll

about 10 hours ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

about 14 hours ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

2 Like

October 14, 2023 at 9:18am

#1057351

Quantum Mind Tricks

The article today, from The Conversation, is about a year old, but that shouldn't matter.

Four common misconceptions about quantum physics

But debates about quantum mechanics – be they on chat forums, in the media or in science fiction – can often get muddled thanks to a number of persistent myths and misconceptions.

Oh, it's way worse than that. I think there are still authors out there promoting books about harnessing the power of the quantum realm with your mind, or some such gobbledygook.

Remember: the bolded and italicized bits below, taken straight from the article, are the misconceptions. So if you skim this entry, please don't walk away thinking I'm endorsing misinformation.

1. A cat can be dead and alive

Erwin Schrödinger could probably never have predicted that his thought experiment, Schrödinger’s cat, would attain internet meme status in the 21st century.

I've met people who knew about Schrödinger's Cat, but weren't aware that it was a thought experiment. They believed Schrödinger had actually stuffed a cat in a box with a quantum choice contraption. I'm not ragging on them, but I think it's important to note that, to the best of my knowledge, no cats were harmed (or not harmed, or a superposition of the two) in the pursuit of knowledge about quantum physics.

Which is way more than other branches of science can say.

It suggests that an unlucky feline stuck in a box with a kill switch triggered by a random quantum event – radioactive decay, for example – could be alive and dead at the same time, as long as we don’t open the box to check.

The obvious issue with this thought experiment is that, if it requires consciousness to collapse a quantum state, a human doesn't need to open the box; a cat possesses consciousness and knows it's alive (or doesn't know anything, if it's dead).

Is it really both alive and dead as long as we don’t open the box? Obviously, a cat is nothing like an individual photon in a controlled lab environment, it is much bigger and more complex.

And that's the non-obvious issue.

In any event, Schrödinger came up with his Rube Goldberg cat-quantumizing machine idea to refute certain ideas about quantum physics, not to demonstrate its truth.

2. Simple analogies can explain entanglement

This one was way more immediately relevant last year, when the article came out, because 2022's Nobel Prize in Physics was all about quantum entanglement (this year's was about attosecond pulses of light, which, well, look it up; it's cool as hell).

There's a lot to absorb here, and I can't really do this section justice with cherry-picked quotes, but the upshot of it is this: There's no suitable macro-world analogy for quantum entanglement.

I'd also add that QE doesn't imply superluminal information transfer, as some people insist it means. It's plenty weird, but it doesn't defy the cosmic speed limit.

3. Nature is unreal and ‘non-local’

Another reminder that the above heading is false. But in this case, I'd add "probably."

Despite Bell’s theorem, nature may well be real and local, if you allowed for breaking some other things we consider common sense, such as time moving forward.

I've banged on in here about time on numerous occasions. Suffice it to say that, in the quantum realm, common sense needs to go right out the window.

I hate the concept, anyway.

Put another way, quantum equations, insofar as I understand them, don't have a time arrow. Time, then, is best viewed as an emergent property of macroscopic matter. Which is fine; lots of perfectly real things, such as temperature or life itself, are emergent phenomena.

However, most options on the table — for example, time flowing backwards, or the absence of free will — are at least as absurd as giving up on the concept of local reality.

This sentence, of course, is one of the main reasons I saved this article. The absence of free will isn't absurd at all; it is, as far as I'm concerned anyway, settled science.

4. Nobody understands quantum mechanics

But I'm not always right. For instance, I've crafted similar sentences to this #4 heading. This is my chance to qualify it; I do believe it's correct in at least one sense.

A classic quote (attributed to physicist Richard Feynman, but in this form also paraphrasing Niels Bohr) surmises: “If you think you understand quantum mechanics, you don’t understand it.”

I believe that quote is correct for people like you, me, and the author of Using Quantum Jedi Mind Tricks to Win the Lottery and Get Laid (or other books to that effect).

Quantum physics is supposedly impossible to understand, including by physicists. But from a 21st-century perspective, quantum physics is neither mathematically nor conceptually particularly difficult for scientists. We understand it extremely well, to a point where we can predict quantum phenomena with high precision, simulate highly complex quantum systems and even start to build quantum computers.

And while this is true—the calculations are, from what I've heard, far more accurate than in any other branch of science—that doesn't mean there aren't still arguments over what it all means. That is, questions of interpretation, like "many-worlds," are still open.

Where the true difficulty lies, perhaps, is in how to reconcile quantum physics with our intuitive reality.

Fair, because they are very different. I certainly don't claim to have it all figured out (unlike some writers), but as with anything else, that's not going to stop me from blogging about it.

3 Like • 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.