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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.
April 18, 2023 at 10:09am April 18, 2023 at 10:09am
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Ah, a rare example of the wild Cracked article that I have Issues with.
I can only expect so much from a dick joke site, though.
Science, at least the way it’s taught to us at an elementary and high-school level, feels like it’s all about proof.
That much, I can agree with. The proof thing is wrong, but the statement is fairly accurate.
In reality, there’s a huge amount of science that, even after tests and studies, remains at best a heavily supported theory.
*record scratch*
Couldn't even finish the first paragraph before I found the first Issue.
I know I've written this before, but in science, a "theory" doesn't mean the same thing as when you or I use the word. I can't be arsed to go into detail right now, but "a heavily supported theory" is what used to be known as a "law" in science, as in "Newton's Second Law." It's based on observation and/or experiment (it's hard to do experiments on, say, a planetary nebula) and makes predictions. When lots of those predictions are confirmed, as is the case with the theories of relativity, gravity, quantum mechanics, and evolution—to name a few—it's basically settled science.
Which doesn't mean it can't be refined, or even overturned. And some have a higher confidence level than others. But science is all about theory (in the scientific sense).
And hey, keep in mind that this is likely going to be a fairly surface level exploration from a verified Bachelor of Fine Arts holder. Scientists, I personally invite you to absolutely go off in the comments.
I'm not a scientist, and I'm not commenting there. Instead, I'm ranting here.
4. Planet Nine/Planet X
Planet Nine is the name given to a theoretical, massive planet deep out in the reaches of our solar system, and a name that truly salts Pluto’s fresh wounds of being kicked out of the club.
Again with the Pluto thing. I've ranted about that before, too. But this is an example of something that's neither right nor wrong. It's not "theory" (in either sense) that demoted Pluto to dwarf planet status. It's us humans needing to characterize and organize things.
The reason scientists think it exists comes from that classic moment that sparks so many discoveries: a scientist going, “Well, that’s weird.”
Or if they're being less flippant about it, "This observation does not conform with previous observations."
Long ago, scientists looked at the orbit of Mercury and said, "Well, that's weird." So they proposed several solutions, one of which was an as-yet-undiscovered inner planet, which they named Vulcan. I'm going to pause here so you can think of Spock jokes.
Ready?
Okay. Turns out the weirdness was because their theory of gravity was incomplete. Once Einstein figured out the whole "relativity" thing, the oddnesses of Mercury's orbit became perfectly (or nearly so) explained, and Vulcan disappeared. Not that it was ever there. The idea disappeared.
All of which is to say that there's some evidence that's leading some scientists to believe the theory of gravity needs another tweak. Would this account for Planet Nine? Hell if I know.
3. Dark Matter
Decent SF show from Netflix. Oh, wait, they mean actual dark matter.
For a pretty complicated scientific theory, it’s surprising how commonly known of a term “dark matter” is. This can most likely be attributed to it sounding absolutely bad-ass, more like something the Avengers have to steal from a space prison than something based on high-level mathematics.
That's a pretty common issue with the unknown: it allows writers to speculate, after which readers/viewers might think the speculation is actual fact. I've seen shows where "dark matter" is used to produce all kinds of plot motivations, such as superpowers.
Again, some peculiarities in gravity are what tipped off science to the idea of this unobserved type of material.
While this isn't the whole story of dark matter, it's not a bad brief summary.
This, incidentally, is why I said above that some scientists believe the theory of gravity needs another tweak. Maybe dark matter isn't matter at all, but some other effect.
This is analogous, I think, to the old idea of the luminiferous ether. Basically, back when the ascendant idea was that light was a wave, they were stuck on the idea that it needed material to wave through, like a sound wave needs matter to propagate, or an ocean wave needs water. The ether, then, had to have certain properties, not the least of which was being entirely, or almost entirely, intangible to matter, or else the planets' orbits would decay rather quickly.
Again, though, Einstein saved the day, and destroyed ether theory with the observation, in this case, that light had properties of both wave and particle, and didn't need matter to propagate through.
Now, I might have fallen into the same trap as this Cracked article, because I'm not an expert. But even if I got the details wrong, my point stands: dark matter might not be matter at all; the observations could fit another theory entirely. One which hasn't been discovered.
Which is a good thing. I'd hate to reach the limits of discovery.
2. Unknown Elements
Another staple of science fiction.
You'll have to read the article on this one, I'm afraid, but it always bugs me when SF shows throw out "new element" as if you can slot something between a n-proton atom and an n+1-proton atom.
Which doesn't mean that there can't be exotic matter, elements made of something other than protons, neutrons, and electrons. But that's mostly speculation, too.
1. Pathogenic Fungus Capable of Infecting Humans
This one was quite popular recently. There was a whole show about it, the most impressive thing about which was it was apparently a good show based on a video game, which is rarer than unobtainium (see what I did there?)
If you were hoping this was nothing more than a spooky story, I have bad news: It’s very possible.
In the broadest sense of "possible."
Of course, our body temperatures would have to lower first, or fungi would have to evolve to live at higher temperatures. Well, why not both?
Sure, there's nothing in principle that would prevent either of these things.
Climate change has been forcing fungi to adapt to naturally higher temperatures, and human body temperatures have been dropping, with humans today having a body temperature of approximately 1 degree Fahrenheit lower than in the early 1800s.
And this is my last Issue (promise). The drop in human body temperature can be explained by improvements in medical care over the last 200+ years. A "human body temperature" is necessarily an average of a sample, and back in the early 19th century, that sample would be more likely to include individuals with low-grade infections that cause fever.
That's the flip side of there being things we don't understand: we can use them to scare the living shit out of each other. |
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