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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.
February 20, 2023 at 8:50am February 20, 2023 at 8:50am
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I don't remember when I saved this article, but it's from January, so it couldn't have been that long ago.
What? I can't even remember what I had for breakfast this morning, and it's 8:30 am as I write this.
The brain is an extraordinary organ, with many wonderful qualities, including the ability to forget — which may actually be a good thing. “If we remembered everything that we experienced, our brains would be hoarders, clogged with all sorts of useless crap that gets in the way of what we really need,” says Charan Ranganath, a professor of psychology and the director of the Dynamic Memory Lab at the University of California Davis.
Yeah, except my brain decides that I really need jokes, song lyrics, and something embarrassing I said when I was 9, rather than where I left that damn screwdriver or someone's name five seconds after they tell me.
In today’s constantly plugged-in, always-on world, people are faced with a barrage of information — emails, news, pointless meetings, traffic updates, chitchat from family members — far more than anyone can process, Ranganath explains.
I don't know about you, but I'm sick and tired of people blaming tech for everything.
These issues with remembering often rear their heads at the least convenient times: when you’re in a rush and can’t find your keys, when you enter a room and don’t know what you came for, when you’re talking with an acquaintance whose name escapes you, when a friend refers to a nice moment you shared and you have no recollection.
The room-entering thing at least has a plausible explanation: you're in, say, the living room, and you notice that a panel of your awesome vintage 70s wood paneling is loose. So you decide to get a hammer and some finishing nails from the garage. You step out of the gloriously golden light of the wood-paneled room into the harsh LED glare of the shop, completely different surroundings. And your memory is tied to the visuals from the living room. You shake your head, go to the kitchen, make a sandwich, return to the living room... where you suddenly remember, oh, yeah, hammer and nails.
Another method to help you pay closer attention to the tasks at hand is what Braun calls the PLR technique: pause, link, and rehearse. This can help you both remember someone’s name and recall the reason you walked into a room. If you’re hiding a birthday present for your kid but fear you won’t remember where you put it, take five seconds to pause and focus on where you’re putting the gift, as “opposed to just putting it down and looking away and doing something else,” Braun says. Then look at the surroundings — this is the “link” step — and contextualize where you hid the present with its environment: in your closet, next to a bin of shoes.
That supports my surroundings hypothesis.
Use technology to your advantage, Ranganath and Schacter agree: Put meetings in your phone’s calendar (be detailed about who you’re meeting, where, and why) and make sure alerts are turned on, set reminders, and take photos of events to refer to later.
See? Tech is also a solution. No, I don't always remember who played the weird cousin in that obscure buddy movie from somewhere in the 70s or 80s, but Google does. I refer to it as my auxiliary memory.
Events that occur during heightened emotional states — fear, joy, anxiety, excitement, sadness — are more memorable. It’s why you remember your wedding day and perhaps not your 10th date. In order to remember more mundane things — where you’re storing dress shoes you wear once a year, a name, an item you need to pick up at the store — make these things extraordinary, says five-time USA Memory Champion and memory coach Nelson Dellis.
So, hire someone to scare the living shit out of you when you have something you'd like to remember. Got it.
Dellis recommends spending five minutes before bed recalling what happened that day. Did you see a beautiful sunset? Did your kid have a funny retort to a simple question? Did you eat something delicious? Replay small but lovely occurrences you’d like to savor.
That sounds nice in theory, but in practice, you're going to spend those five minutes berating yourself for neglecting to tip the delivery driver, or coming up—finally—with the perfect retort for that zinger your friend shot your way at lunch.
Okay, look, I'm not saying this article doesn't have some value. On the contrary. I just like to make snark. But as someone with a memory like a steel sieve, I'll probably forget to implement any of its suggestions. |
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