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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 25, 2020 at 12:19am April 25, 2020 at 12:19am
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I'm just going to leave this here for your amusement.
https://www.inverse.com/article/34186-stoned-ape-hypothesis
The 'Stoned Ape' Theory Might Explain Our Extraordinary Evolution
A scientist resurfaces a psychedelic retelling of human evolution.
"Might?" It "might" also be utter twaddle.
In 1992, ethnobotanist and psychedelics advocate Terence McKenna argued in the book Food of the Gods that what enabled Homo erectus to evolve into Homo sapiens was its encounter with magic mushrooms and psilocybin, the psychedelic compound within them, on that evolutionary journey.
Hell of a trip, man.
He called this the Stoned Ape Hypothesis.
Because of course he did.
As early humans, he said we “ate our way to higher consciousness” by consuming these mushrooms, which, he hypothesized, grew out of animal manure. Psilocybin, he said, brought us “out of the animal mind and into the world of articulated speech and imagination.”
Granted, I'm no expert on biology, but that sounds awfully Lamarckian to me - heritability of acquired traits, which has even less support than the Stoned Ape Hypothesis itself.
And, because psilocybin mushrooms commonly grow in cow droppings, “the human-mushroom interspecies codependency was enhanced and deepened. It was at this time that religious ritual, calendar making, and natural magic came into their own.”
Take enough drugs and you, too, can confuse correlation with causation.
“What is really important for you to understand is that there was a sudden doubling of the human brain 200,000 years ago. From an evolutionary point of view, that’s an extraordinary expansion. And there is no explanation for this sudden increase in the human brain.”
So we're going to make one up that supports our confirmation bias.
“I suggest to you that Dennis and Terence were right on,” Stamets announced while acknowledging that the hypothesis was perhaps still unprovable. “I want you or anyone listening, or seeing this, to suspend your disbelief … I think this is a very, very plausible hypothesis for the sudden evolution of Homo sapiens from our primate relatives.”
And hey, science is full of hypotheses that started out ridiculous and ended up being... well, mostly true. Really, this one's no weirder than quantum theory. The difference is, quantum theory has experimental support, and makes predictions that can be, and have been, tested. Find a way to do that, and I'll have a nice steaming dish of crow.
McKenna’s theory chalks up the entirety of this complicated phenomenon to a single spark; to him, psilocybin mushrooms were the “evolutionary catalyst” that sparked consciousness by prompting early humans to engage in experiences like sex, community bonding, and spirituality.
Sex has been around since at least the beginnings of eukaryotic life. Community bonding is practiced in many different species. Our nearest cousins, the bonobos, are really, really good at these two things. As for spirituality, there are other explanations.
And yet, they’re equally stumped when asked to answer the question at the root of the debate over the Stoned Ape hypothesis and consciousness research in general: How did consciousness evolve? If it wasn’t psychedelic mushrooms that started the process, then what did?
That's a fair question, and it's good to have competing hypotheses for an answer. But, again... evidence.
If the science behind McKenna’s hypothesis is unstable, what worth does it have in the search for the origin of human consciousness?
I think they're asking the wrong question here. Look, I'm not coming down against the use of mind-altering drugs; that would be hypocritical (even though the ones discussed here are not my cup of mushroom soup). There's plenty of evidence that psychedelics, used carefully, can be beneficial. Maybe they can even expand an individual's consciousness, like the hype promotes. Let's not confuse personal growth with species evolution, though.
And maybe - just maybe - I can see psychedelics being an engine for social evolution. That is, some stoner decides something like, "Hey, we're all ONE, man," and passes that along to his or her fellow apes, who nod in agreement and then proceed to beat each other up over the last roll of toilet paper. But at least they feel sorry about that afterwards.
But in terms of species evolution? It's like the idea that if both of a child's parents had each lost their left pinky fingers in an accident, the kid would pop out with nine fingers. Lamarckian.
However, McKenna deserves credit for sparking an idea in the 1990s that scientists have only recently been able to prove: Psilocybin does alter consciousness and can trigger physical changes in the brain.
Not arguing against that.
The Stoned Ape hypothesis may now be lost to the annals of fringe science, but some remnant of its legacy remains. Now that scientists better understand the way psilocybin physically affects the brain, they can seriously investigate its potential to treat disorders like substance abuse, anxiety, and depression. If that happens — and it looks like it will — psilocybin will become a part of mainstream culture as an agent of positive change. And isn’t that ultimately what McKenna was advocating for?
So the article ends up in the same place I did. This sounds like beneficial research, but it shouldn't be sullied by association with ideas that, at best, are unprovable, and at worst, are made of the same stuff fom which magic mushrooms grow. |
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