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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.
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First, a plug for the June round of
Just do eight entries (chosen from 16 prompts) in a month.
I'll be participating, myself... but not today.
Today, we try to talk sense about senses.
I've noted in the past that we really have more than the classical five senses, but I don't think I'd seen this article, which is from 2017. It's talking about different "extra" senses, anyway.
The world we experience is not the real world.
I think several philosophers would agree. Several other philosophers would vehemently disagree. As for me, first you'd have to define "real," and good luck with that.
It’s a mental construction, filtered through our physical senses.
Yesterday, I banged my shin on a mental construction.
How would our world change if we had new and different senses? Could they expand our universe?
We already have new and different senses, courtesy of technology. They translate input into output discernible by one of the Five. A Geiger counter, for example, detects ionizing radiation (which we have no sense for) and converts it to auditory (the clicking sound) and visual (a gauge), which our brains can interpret. The article also treats writing as sense-substitution, trading the auditory (language) for the visual (writing on a page).
More recently, researchers in the emerging field of “sensory enhancement” have begun developing tools to give people additional senses—ones that imitate those of other animals, or that add capabilities nature never imagined. Here’s how such devices could work, and how they might change what it means to be human.
Some animals can detect electrical fields. I can't imagine what that would feel (or look, smell, sound, or taste) like.
Which gives me an opportunity to once again trot out my great epiphany about the Classic Five: They are all, at base, touch. Even vision, which relies on the impact of photons on our retinas.
Researchers are working on other technologies that could restore sight or touch to those who lack it. For the blind, cameras could trigger electrodes on the retina, on the optic nerve, or in the brain. For the paralyzed or people with prosthetic limbs, pressure pads on real or robotic hands could send touch feedback to the brain or to nerves in the arm.
All of which sounds pretty cool, and used to be relegated to science fiction. Well, yesterday's science fiction often becomes science.
Autistic people might even gain a stronger social sense.
Careful, there. I know several autistic people with strong social sense. They tend to have different perspectives, and those perspectives are often more useful. Don't fix stuff that ain't broke.
Last year, MIT researchers revealed the EQ-Radio, a device that bounces signals off people to detect their heart rate and breathing patterns.
Finally, a device that can tell you if someone's into you.
We can also substitute one sense for another. The brain is surprisingly adept at taking advantage of any pertinent information it receives, and can be trained to, for instance, “hear” images or “feel” sound.
Sounds like induced synesthesia to me.
Scientists are also exploring ways to add senses found elsewhere in the animal kingdom.
The article talks about things like direction sense and echolocation, but echolocation is basically hearing. I've read that some humans, especially blind ones, have learned this trick without technological aid.
In the future, cochlear implants could be tuned to pick up really low frequencies, such as those used by elephants, or really high ones, such as those used by dolphins. Bionic eyes could be built to allow humans to see ultraviolet rays (as butterflies, reindeer, dogs, and other animals can) and infrared light (as certain snakes, fish, and mosquitoes can).
As cool as all that would be, all it would do is extend our existing classical senses.
Some researchers think we may eventually install a port in our brains that would allow us to swap in different sensors when we need them.
Because that always ends well in SF stories.
We might also gain senses that no other animal has. The vibrating vest Eagleman created can be programmed to receive any input, not just sound. He says it could be used to monitor the stock market, or sentiment on Twitter, or the pitch and yaw of a drone, or one’s own vital signs.
Ah, yes, 2017, when Twatter was still marginally relevant.
“You can do whatever you want,” says Neil Harbisson, a “cyborg artist” who’s originally from Spain. “You can design a unique sense that is related to your interests or to your curiosity.”
Well, I know some people who could benefit from a sense of humor implant.
Also... "cyborg artist?" Come on.
Perhaps we’ll even achieve that so-called sixth sense: ESP.
That's not as farfetched as the article implies. It's not much of a stretch to imagine electrodes that pick up signals from one brain and transfer them to the electrodes of another, either through implants or induction. Doubtful that we'd be able to "read" the minds of unwilling subjects anytime soon, though.
But last I heard, we still haven't figured out how to keep the brain from outright rejecting any implanted electrodes. Yeah, yeah, Neuralink (also mentioned in the article; it was new at the time). As with most Muskmelon projects, that's more hype than anything else.
Exactly how all this tinkering will change us remains to be seen.
And this is what science fiction is for. |
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