Complex Numbers (Book)

Blog Calendar

◄ October ► 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

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

October 26, 2022 at 12:03am

#1039728

Quantum Horseshit

This one's from Slate, so I'm going to have to wash my hands after posting.

How Quantum Theories Took Over TikTok

They are NOT THEORIES.

At best, they are hypotheses. At worst, they're misinterpretations.

With that out of the way...

At first glance, the video seems like an ordinary news recap. “So today the Nobel Prize in Physics was awarded to scientists,” says TikTok creator Sami Moog.

Well... duh. It's not like the Nobel Prize in Physics was going to get awarded to a line cooks. I'm not disparaging line cooks here; I like to eat at restaurants and I appreciate them. But unless the line cook is also a physicist (hey, the economy's tough, and it can happen), she's not going to get the Nobel.

Then things get really trippy. “Your imagination literally makes up your own personal quantum field and it constructs every single thing around you,” he says.

No.

By the end, he’s discussed vibrationally matching your desires and manifesting changes to reality.

Ugh. I need some Advil. Where's the Advil? Or an anvil would do.

Look, I'm not going to get into the long explanation of why that's complete horseshit. But it's complete horseshit.

Moog’s video is a classic example of quantum mysticism, which is the association of a set of metaphysical beliefs and spiritual worldviews with the science of quantum mechanics.

This has been going on for a long, long time, since well before DikDok. As an attempt to reconcile science with spirituality and/or religion, I understand the need for some people to delve into it. But the mysticism makes claims not supported by science. One could, of course, argue that science doesn't know everything. That's fair. It's true. But you don't get to fill in the blanks with wishful thinking, as with the "God of the Gaps."

Over the years, professional physicists have decried what they view as the misapplication of quantum physics principles to unrelated self-help topics—what Caltech Nobel laureate Murray Gell-Mann famously described as “quantum flapdoodle.”

Quantum physics is weird (meaning counterintuitive) enough without making up extra shit. Gell-Mann, incidentally, is the guy who coined the term "quark" for those subatomic particles. He didn't do physics any favors by a) naming them after a line from Joyce and b) calling his early attempt at codifying what's now the Standard Model "the Eightfold Way," which just begs Buddhists to jump right on it.

Hundreds of these “quantum” science videos claim that quantum cosmology allows humans to literally teleport between different realities or communicate telepathically with their past and future selves.

We're not even sure "different realities" exist. Sure, the concept of the multiverse squeezes itself out of at least one interpretation of quantum physics, but it's not testable, not verifiable, and, most importantly, not falsifiable. And there are other interpretations that don't require the universe to split every time a quantum event occurs.

More to the point, even granting for the moment the multiverse hypothesis, there's no way, even theoretically, to communicate between those universes ("Not yet." "Sure, but you still don't get to assert that it happens without evidence.")

As a TikTok user, it isn’t easy to avoid this mystical element.

It's easy for me to avoid it: I stay the hell away from TokTik.

If you watch a video of a trained scientist explaining quantum mechanics, fringe quantum takes are likely to start appearing in your content stream. That’s because TikTok’s algorithm groups the videos within the same “quantum” umbrella. And the recent announcement of the Nobel Prize for Physics has only made this worse.

On the other hand, this happens with YouTube also. I'm always seeing recommendations for videos that are obviously pseudoscientific bullshit. I can usually tell the difference. Your average line cook probably cannot. Again, this doesn't mean the line cook is any less an individual worthy of respect.

On Oct. 4, the Royal Swedish Academy of Sciences announced that Alain Aspect, John Clauser, and Anton Zeilinger had won for “groundbreaking experiments using quantum states, where two particles behave like a single unit even when they are separated.” The academy noted that these experiments, which built upon the 1960s research of John Stewart Bell, cleared the way for new technology such as quantum computers.

Yes. That's what it did. That's huge. It's exactly the sort of thing the science Nobel Prizes are for. It has nothing to do with creating your own reality, though.

By this point, TikTok creators had begun publishing their bite-sized recaps. Hank Green, the popular vlogger and bestselling author, released his own video on the topic. “I’m going to try to explain it [quantum entanglement] to you, without lying to you.”

"Lying" implies that you know one thing but state another. It's more like he's propagating a misunderstanding.

In just under three minutes, Green described how scientists entangled two electrons, each of which has a property called spin. When one such particle is measured, it begins to spin in one direction. The other instantly spins in the opposite direction, even if the two particles are light years apart. As Green says in the video, these experiments proved that Einstein was wrong and that information can pass between quantum particles faster than the speed of light.

No.

There is no known way to transfer information faster than the speed of light (which should properly be called the limit to the speed of information transfer).

Basically, yes, entanglement appears to be real. But there's no way to use it to, say, create an FTL communications device.

To be clear, I haven't seen the particular video in question (for that, I'd have to use KitKot), so that particular summary might be an artifact of the Slate author not communicating well.

A seven-second video released Oct. 7 that features a young woman reacting with the words “The 2022 Nobel prize in physics just got announced and it literally proves that we are all connected”

First of all, no. That's a stretch.

Second of all, stop fucking using the word "literally." It's lost its meaning.

And third, yes, I do believe we're all connected, but that has more to do with well-known interactions.

Another video claims that quantum physics proves that an ordinary human voice can affect a star molecule on the edge of the universe. Um … what?

That's a far more mild response than I would make.

However.

So, which is it: pseudoscience or philosophy? When I discussed with O’Keefe—the Australian science communicator and Ph.D. student—she seemed uncomfortable with a strict binary approach. “I think it’s dangerous to lean too far into scientism, which is when you see the world exclusively through the lens of whether something is backed by science,” O’Keefe said. “Science started as a branch of philosophy, and the scientific method wouldn’t be as formidable as it is today if we didn’t put theories to the test by asking the right questions.” O’Keefe told me that quantum mystics definitely take their unfounded claims too far, but that does not mean that scientists should be discourteous toward people who are more spiritually minded.

Science, at its core, is about observation, hypothesis, and testing. It is not about proving something right; in fact, most of science is about trying to do the exact opposite: prove it wrong.

All ideas have to start somewhere. A lot of science, especially quantum theory, is so completely counterintuitive that one has to wonder what made them think of these things to begin with (hint: it's usually math). Maybe some of these woo-meisters will be supported by a future discovery.

If so, however, it would be coincidental.

What matters is that users apply the tools of information literacy to gauge authority—and that means remembering what TikTok is for.

Destroying Western civilization?

Obviously, TikTok is no Wikipedia; it’s not the place to find a reliable summary of quantum mechanics the way scientists understand it.

Neither is Wikipedia. Apart from the possibility of error, which is real (but far less than the possibility of error on a social media platform), every time I try to get answers to the cutting-edge questions of science, Wiki articles are just too damn advanced.

And even YouTube videos have their limitations. People try to explain quantum physics using analogy, but there are no macro-scale analogies to quantum physics. In everyday life, for example, you can know your car's position and velocity (relative to the road) to a very high degree of certainty. But on the subatomic scale, you can know one, or the other, but never both. Analogies are useful; the danger, however, is taking the analogy to be an exact model of the reality, and drawing conclusions based on that.

The mind is strange enough without us using it to make shit up. Quantum physics is also weird from the perspective of everyday life. And it's entirely possible that at least some of our consciousness can only be explained by quantum effects.

But I'd need to see the science on that. Until then, they're just indulging in wish-fulfilling speculation.

I'm not going to embed the video, but if you're interested, here's someone

on YouTube trying to explain it using analogies.

2 Like • Comment

© 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.