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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.
August 27, 2020 at 12:12am August 27, 2020 at 12:12am
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Oh, Guardian. And you were doing so well.
Scientists say most likely number of contactable alien civilisations is 36
New calculations come up with estimate for worlds capable of communicating with others
In case you're not aware, The Guardian is a British rag; hence the British spelling. Now, on with the show:
They may not be little green men. They may not arrive in a vast spaceship. But according to new calculations there could be more than 30 intelligent civilisations in our galaxy today capable of communicating with others.
And there "could be" a magical griffon roosting in a tree in my backyard. I can't prove there isn't. After all, it's magical and might be invisible.
Experts say the work not only offers insights into the chances of life beyond Earth but could shed light on our own future and place in the cosmos.
I'm all for shedding light on our own future and so on, but the fact remains that the only spacefaring, communicating civilization [just because they spell it with an s doesn't mean I'm going to] that we know of is us.
Usual disclaimer to ward off the inevitable jokes and human-haters: if I use the word "intelligent" in this post, read it to mean "technologically equipped with the ability to send signals across, and visit, space." Also, "they haven't shown their little green faces because we're terrible," or words to that effect, is utter tripe, and I don't have the time or patience to go into why right now. Perhaps a future entry.
“I think it is extremely important and exciting because for the first time we really have an estimate for this number of active intelligent, communicating civilisations that we potentially could contact and find out there is other life in the universe – something that has been a question for thousands of years and is still not answered,” said Christopher Conselice, a professor of astrophysics at the University of Nottingham and a co-author of the research.
1. Not the first time.
2. It's a guess, not an estimate.
3. The timescale of any communication with someone else in this galaxy is potentially, on average, on the order of 50,000 years, round trip.
4. "Other life in the universe" doesn't necessarily mean intelligent life. I've covered this before.
In 1961 the astronomer Frank Drake proposed what became known as the Drake equation  ...
Which is not an equation as such, but more like a way to think about these things. Nothing wrong with thinking about them. To be fair, the article points this out:
But few of the factors are measurable. “Drake equation estimates have ranged from zero to a few billion [civilisations] – it is more like a tool for thinking about questions rather than something that has actually been solved,” said Conselice.
And yet, guesswork remains guesswork.
“Basically, we made the assumption that intelligent life would form on other [Earth-like] planets like it has on Earth, so within a few billion years life would automatically form as a natural part of evolution,” said Conselice.
And the basis for that assumption is...? Just because intelligent life can appear doesn't mean that it must appear. Again, I know I've said this before, but evolution does not require that an intelligent species develop. Nor does it proceed toward any sort of ultimate goal. Life on Earth existed for something like four billion years, most of that time underwater, before we showed up. Those qualities that led us to eventually travel into space are not necessary for species survival. Just ask the millions of other species that infest this orb. Oh, wait, you can't because we can't communicate concepts with them, and yet most of them thrive just fine, and even more would, too, if we weren't actively, if inadvertently, trying to eliminate them. Yes, some are quite clever, but they aren't using radios or building spaceships, which is what we're talking about here.
The assumption, known as the Astrobiological Copernican Principle, is fair as everything from chemical reactions to star formation is known to occur if the conditions are right, he said.
I think it probably is fair to assume that, given the right conditions (whatever they may be), life will arise in semi-stable environments. Whether that life develops radio and whatnot is another question, entirely unrelated.
He added that, while it is a speculative theory, he believes alien life would have similarities in appearance to life on Earth. “We wouldn’t be super shocked by seeing them,” he said.
It's not even a theory. And I think "similarities" is entirely too broad a term. If we found life and there were no similarities, how would we know it was life?
The team add that our civilisation would need to survive at least another 6,120 years for two-way communication. “They would be quite far away … 17,000 light years is our calculation for the closest one,” said Conselice.
This differs from my number above because he's using "probable closest one" and I was using an average. Either way, it's a long damn time. Now, sure, maybe we get lucky and we find that birdlike creatures on a planet orbiting Alpha Centauri are starting to send out bird porn broadcasts that we pick up, but even there, we're talking a 9-year round trip communication.
Dr Oliver Shorttle, an expert in extrasolar planets at the University of Cambridge who was not involved in the research, said several as yet poorly understood factors needed to be unpicked to make such estimates, including how life on Earth began and how many Earth-like planets considered habitable could truly support life.
I'm not going to argue with experts, but "how life on Earth began" is irrelevant to this discussion as, obviously, it did. Oh, sure, you can have your pet hypothesis that it originated elsewhere (say, Mars) and migrated here as microbes on asteroids, but all that does is kick the can down the road on the question of "how life began." And I will grant that since it started here, it probably started elsewhere, though not necessarily through the same processes. What I will not grant is that it necessarily evolves what we're calling intelligence.
Dr Patricia Sanchez-Baracaldo, an expert on how Earth became habitable, from the University of Bristol, was more upbeat, despite emphasising that many developments were needed on Earth for conditions for complex life to exist, including photosynthesis. “But, yes if we evolved in this planet, it is possible that intelligent life evolved in another part of the universe,” she said.
Oh, now we've gone from galaxy to universe. I would not be in the least surprised to find that around one of the 200 billion stars in each of the 200 billion galaxies in our observable universe (wild-ass guess here, but that order of magnitude), someone else didn't trek into space. Whether it happened more than once in this galaxy, which is the only one where we can reasonably expect some sort of communication, well... sure, maybe. But maybe not. We simply do not have enough information to state with any kind of certainty that "intelligence" happened elsewhere than on Earth.
“[The new estimate] is an interesting result, but one which it will be impossible to test using current techniques,” he said. “In the meantime, research on whether we are alone in the universe will include visiting likely objects within our own solar system, for example with our Rosalind Franklin Exomars 2022 rover to Mars, and future missions to Europa, Enceladus and Titan [moons of Jupiter and Saturn]. It’s a fascinating time in the search for life elsewhere.”
And I'll say this once more for emphasis: the search for extraterrestrial life in our own solar system is looking for microbes (or whatever equivalent). It would be a big fucking deal if they found some and were able to demonstrate to a high level of certainty that it wasn't seeded from Earth. I'd say there's a fair chance, and I hope they succeed.
But sorry, guys... no Martians, no Vulcans, and, sadly, no Orion slave girls.
Or, hell, maybe I'm completely wrong. I kind of hope I am. But the evidence doesn't make it seem likely. |
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