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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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Oh, look. Another "time is an illusion" article.
Time feels real to people. But it doesn’t even exist, according to quantum physics. “There is no time variable in the fundamental equations that describe the world,” theoretical physicist Carlo Rovelli tells Quartz.
Okay, well, I readily admit that this guy has studied the subject more than I have. Even so, we immediately run into definition problems. One of these is that while, yes, time disappears at the quantum level, well, so does solid matter; everything at that scale is an energy vibration in a field. It's only in aggregate that we get sand and people and planets and whatnot. Similarly, aggregate a bunch of quantum vibrations together and you get things that are affected by time.
Nevertheless, I think it's a good thing to look at this point of view.
Rovelli’s book, The Order of Time, published in April 2018, is about our experience of time’s passage as humans, and the fact of its absence at minuscule and vast scales.
I'm going to have to put a [citation needed] on the "vast scales" thing. We can see interactions of galaxies far, far away, occurring in some time frame, and even the cosmic microwave background is what it is because of the time elapsed since the Big Bang.
I can't be arsed to order that book, though, so I'll just leave that quote.
Time, Rovelli contends, is merely a perspective, rather than a universal truth. It’s a point of view that humans share as a result of our biology and evolution, our place on Earth, and the planet’s place in the universe.
Right, because obviously, there was no time before we were around to measure it. Then humans came along and, poof, suddenly time starts to pass.
In fact, Rovelli explains, there are actually no things at all. Instead, the universe is made up of countless events. Even what might seem like a thing—a stone, say—is really an event taking place at a rate we can’t register. The stone is in a continual state of transformation, and on a long enough timeline, even it is fleeting, destined to take on some other form.
"On a long enough timeline." We can't even talk about whether time exists without invoking time language. To me, this is all the proof I need that time -- and rocks -- exist.
This seems to be another version of the argument that goes something like "if it's ephemeral, it doesn't really exist." I've rejected that argument out of hand, and while I'm open to counterarguments, my own perspective is that it's only that which is fleeting that can be called "real."
By "fleeting" I mean anything from picoseconds for certain phenomena, to billions of years for things like stars. If you're going to claim that stars don't exist, well, I can't even find common ground with you.
Rovelli argues that time only seems to pass in an ordered fashion because we happen to be on Earth, which has a certain, unique entropic relationship to the rest of the universe. Essentially, the way our planet moves creates a sensation of order for us that’s not necessarily the case everywhere in the universe.
I am not aware of any evidence that time doesn't exist elsewhere in the universe. Sure, as we saw here a few days ago, there may be inaccessible areas of the universe where the rules are different, but in the observable universe, both space and time are things.
But that paragraph does hint at my understanding of the nature of time; it's tied to entropy. The "past" is a time of lower entropy and the "future" is a time of greater entropy. To be simplistic about it. How the universe began in a state of minimum entropy is, admittedly, an open question (as far as I've seen).
If all this sounds terribly abstract, that’s because it is. But there’s some relatively simple proof to support the notion time is a fluid, human concept—an experience, rather than inherent to the universe.
Right, because other animals don't experience time. Which is why my cat starts begging for food right as the accursed daystar begins to approach the western horizon. That, by the way, is another artifact of perception. I know that the planet's rotation moves my location into the side facing away from the sun. And yet, from my limited point of view, it looks exactly like the sun is setting. There's no difference in reality; just in how I describe it. This is analogous to looking at time from a different point of view.
My limited perspective also makes it look like the earth is flat. It is not, and simple tests can reveal that. If you believe it is, boy are you in the wrong place right now.
Also, the arguments that follow aren't "proof."
Imagine, for example, that you are on Earth, viewing a far-off planet, called Proxima b, through a telescope. Rovelli explains that “now” doesn’t describe the same present on Earth and that planet.
Fair enough, which is exactly my argument for why there is no such thing as "the present." There's only the past and, potentially, the future.
This might sound strange, until you consider something as mundane as making an international call. You’re in New York, talking to friends in London. When their words reach your ears, milliseconds have passed, and “now” is no longer the same “now” as it was when the person on the line replied, “I can hear you now.”
Same argument. There's no new information here. All this does is reiterate that information cannot travel faster than the speed of light. And when you talk about "speed," you're talking about distance traveled in some period of time. Again, using time in an argument for the nonexistence of time is inherently contradictory.
The best I can make of that is that time doesn't work the way our intuition says it does, which is a trivial argument. At quantum scales, nothing works the way our intuition says it does. We've known this for a century.
Consider, too, that we don’t share the same time in different places. Someone in London is always experiencing a different point in their day than someone in New York. Your New York morning is their afternoon. Your evening is their midnight. You only share the same time with people in a limited place, and even that is a relatively new invention.
Oh for fuck's sake, now they're conflating the concept of "time" with the ways we measure it, and also noting that we live on a rotating sphere which is only half-illuminated. Rotation implies time. Yes, clocks are arbitrary and standardized, and time zones exist for our convenience. So what? That says nothing about the physical concept of time.
Time even passes at different rates from place to place, Rovelli notes. On a mountaintop, time passes faster than at sea level. Similarly, the hands of a clock on the floor will move slightly slower than the hands of a clock on a tabletop.
A restatement of part of Einstein's theory of general relativity. Also, by "slightly," they're talking about minuscule fractions of a second. Yes, your head is older than your feet because you spend most of the day with your head above your feet. This is an effect that it takes incredibly precise instruments to measure.
But you know what? We have those incredibly precise instruments. What do they measure? They measure time. If you can measure something, it is not nonexistent.
Likewise, time will seem to pass slower or faster depending on what you’re doing. The minutes in a quantum physics class might crawl by, seeming interminable, while the hours of a party fly.
Oh, good gods, that old canard. Yes, our perception of the passage of time varies depending on circumstance. That's a biological effect. Perhaps it has to do with differing rates of the chemical reactions going on in our brains, or maybe there's another explanation, but it doesn't disprove "time." Like, I took a nap today. I felt like five or ten minutes went by, mostly in dreams. When I woke up, though, the clock said it was two hours later. Contradiction! Obviously, therefore, time must not exist!
Meanwhile, cesium clocks continue to tick at the same rate regardless of our perception (assuming you don't move one up or down; see above). The decay of radioactive isotopes is itself a measure of time.
“Time is a multilayered, complex concept with multiple, distinct properties deriving from various different approximations,” Rovelli writes. “The temporal structure of the world is different from the naïve image that we have of it.” The simple sense of time that we share works, more or less, in our lives. But it just isn’t accurate when describing the universe “in its minute folds or its vastness.”
And yet, after all that snark, I can't really find fault with this conclusion. There's still a lot we have to learn.
Rovelli argues that what we experience as time’s passage is a mental process happening in the space between memory and anticipation. “Time is the form in which we beings whose brains are made up essentially of memory and foresight interact with our world: it is the source of our identity,” he writes.
Okay, I promised myself I wasn't going to rag on panpsychism for a while in here, but this argument touches on that concept. Time passes for a rock whether a human observes it or not. Grass grows whether we watch it or not. It did so long before humans arrived on the scene. Well, okay, maybe not that long, because grass is a relatively recent evolutionary development of plants. But the point is, time passes for the grass. It's a seed, it sprouts, it grows, it gets eaten by a bull, it turns into manure, the manure promotes the growth of new grass. It's not like this happens all at once. Does that mean the grass is conscious, too? The manure? No. It means time has elapsed, even if we're not standing there with a stopwatch observing it.
Without a record—or memory—and expectations of continuation, we would not experience time’s passage or even know who we are, Rovelli contends. Time, then, is an emotional and psychological experience.
And without senses, we wouldn't experience input from the outside world; therefore, the universe must not actually exist! (This is an argument that mystics and acid-trippers like to latch onto. It's best to liken that argument to the bovine manure in my last paragraph.) |
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