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Saturday, Jan. 4, 2025

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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:

tj in a winter wonderland

about 13 hours ago
In response to "The Year in the Sky"

It all sounds very interesting and hopefully I will be able to keep an eye on the sky and see some of these. It seems more often than not, it's overcast, or has been for past celestial events. I did, however, get a chance to view the Northern Lights around four this morning. The sky cleared sometime during the night and Max, my Husky woke me up to go out and we enjoyed a few minutes of a spectacular light show.

3 Like

Robert Waltz

about 17 hours ago
In response to "The Year in the Sky"

🌖 HuntersMoon

, depends on definition. Astronomically, it's a moon. Astrologically, it (along with the Sun) is a planet. Anyway, I read that to be "planetary parade plus Moon," but we can chalk it up to Lifehacker being misleading again.

2 Like

🌖 HuntersMoon

about 17 hours ago
In response to "The Year in the Sky"

Regarding the "planetary parade." The moon isn't a planet. It's a moon.

2 Like

Elisa: Snowman Stik

about 17 hours ago
In response to "Marguments"

Oddly enough, this entry rolled out the day the squid and I visited Kennedy Space Center. There was actually a Nars rover model we saw with an interesting note on the information plaque: Not funded by taxpayers dollars.

Ultimately, I feel like while the issue of science communication has seen some improvement, a new problem is emerging. Many communicators have not shown an inclination to have public dialogues with groups who question why we're doing things like going back to the moon. There's been no validation of these concerns by science communicators, which is in my opinion not a good look. And lest you think it's a certain demographic with these objections, well, that's a bias that deserves a re-examination thanks to this piece: https://www.cnn.com/2024/01/05/world/peregrine-moon-mission-navajo-nation-object... remains-scn/index.html .

1 Like

tj in a winter wonderland

a day ago
In response to "Neutral Zone"

I don't tend to think of myself as optimistic or pessimistic, although I do share some of both qualities; I'm realistic.

1 Like

tj in a winter wonderland

a day ago
In response to "Allo, Ow Arya?"

heightened and delighted attention—Hedention

1 Like

tj in a winter wonderland

Jan 1, 2025 at 1:50pm
In response to "Retraction"

Another interesting entry, thank you. As for the Committee for Bug-Free Food, I have also read some of the information on insects in canned foods. I always wonder how that compares to insects in frozen food, vacuum sealed foods, and irradiated foods. I grew up eating fruits and berries right off the tree/shrub/vine and likely consumed a fair number of insects without even knowing it.

2 Like

Jayne

Jan 1, 2025 at 12:52pm
In response to "Retraction"

Wow, 8 retractions in a month + 60 concerns this year. They should get a new journal tagline:

Chemosphere, the vanity publisher for "science".

"Awesome science journal" - Reddit User RandomDude02342

3 Like

tj in a winter wonderland

Dec 31, 2024 at 4:48pm
In response to "The End of December"

I'll drink to that.

2 Like

Elisa: Snowman Stik

Dec 31, 2024 at 11:07am
In response to "The End of December"

The story behind Dry January (which actually started in the UK) is part typical insufferable but also part fascinating, as it serves as a bit of reckoning with the drinking culture over there. It may be a bandwagon thing, but given how alcohol has legitimately killed people I can see how it's caught on.

3 Like

January 1, 2025 at 9:55am

#1081789

Retraction

Well, now that that's over, let's get back to it. What better way is there to start a new calendar year than by pointing out a mistake made in the previous calendar year? A bit from Ars Technica:

Journal that published faulty black plastic study removed from science index
Chemosphere cut from Web of Science, which calculates impact factors.

Some people might not have noticed the black plastic crisis. I didn't see anything about it until the retraction, myself, so I was less prone to primacy bias.

This article goes beyond one single retraction, but I'll point this out anyway: usually, people hear about the study, usually through some breathlessly urgent reporting by someone trying to be first out of the gate, and then the retraction happens... and radio silence ensues, leaving people believing the first report. Worse, some people (exhibiting the aforementioned primacy bias) do hear about the retraction, but the falsified original stays in their brain.

Rarer is the case where an entire journal faces consequences for publishing shoddy studies.

The publisher of a high-profile, now-corrected study on black plastics has been removed from a critical index of academic journals after failing to meet quality criteria, according to a report by Retraction Watch.

If you've been lucky enough to avoid the whole made-up controversy, this article does a fair job explaining the events timeline. It's there if you want to read it.

However, it gets worse.

It appears that the people responsible for the original, retracted study on black plastic kitchenware did make a math error. This is bad enough, as it contributes to primacy bias, though anyone can make math errors or other mistakes (which is one reason you have peer review in science). But the worst part is, it looks like the authors of the original study had an Agenda:

The statement says that, regardless of the math error, the study still found unnecessary flame retardants in some products and that the compounds can "significantly contaminate" those products.

That is not science. That is opinion contaminating science. It's like if the Committee for Bug-Free Food found that 1% of the contents of canned tomatoes was bugs (there is, as I understand it, a maximum allowable bug level in food, as attempting to remove all insect parts reaches a point of diminishing returns, but I can't be arsed to research what it is), but then said they misplaced a decimal and it's actually 0.01%—and then still insisted that there's still bugs in the food and so canned food should be avoided at all costs.

Usually, the next thing you find out is that the Committee for Bug-Free Food is in the employ of someone with a vested interest in selling their own line of (more expensive) bug-free food.

Now, I'm not weighing in on whether you "should" use these plastic utensils or not. It's not an issue of grand global importance, the way the Wakefield disaster was, and still is. I just think any such decision should at least take the science into account. The actual science, not the one with math errors and strongly-held opinions.

7 Like • Comment • View 2 comments

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