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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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Today's article is a perfect storm for me. Astronomy, crackpottery, and the rambling postmodern writing style of The New Yorker.
Have We Already Been Visited by Aliens? 
An eminent astrophysicist argues that signs of intelligent extraterrestrial life have appeared in our skies. Whatâs the evidence for his extraordinary claim?
The default answer to any headline that asks a question is always "no."
The article begins, in typical TNY style, with the history of the discovery of âOumuamua -- you know, that weird interstellar object that blew through our solar system a few years ago. The article itself, though, is only a couple of months old.
As astronomers pored over the data, they excluded one theory after another. âOumuamuaâs weird motion couldnât be accounted for by a collision with another object, or by interactions with the solar wind, or by a phenomenon thatâs known, after a nineteenth-century Polish engineer, as the Yarkovsky effect. One group of researchers decided that the best explanation was that 1I/2017 U1 was a âminiature cometâ whose tail had gone undetected because of its âunusual chemical composition.â Another group argued that âOumuamua was composed mostly of frozen hydrogen. This hypothesisâa variation on the mini-comet ideaâhad the advantage of explaining the objectâs peculiar shape. By the time it reached our solar system, it had mostly melted away, like an ice cube on the sidewalk.
Actually, the correct term would probably be "sublimated," like dry ice in the sun.
Now, to me, there's only one thing more wrong than jumping to the conclusion that a strange interstellar object is the product of alien technology, and that is completely discounting that as a possibility. It's important to keep an open mind. That said, the "alien technology" hypothesis would require a much higher level of support, as it it is, indeed, an extraordinary claim.
By far the most spectacular account of 1I/2017 U1 came from Avi Loeb, a Harvard astrophysicist. âOumuamua didnât behave as an interstellar object would be expected to, Loeb argued, because it wasnât one. It was the handiwork of an alien civilization.
While Loeb certainly has credentials, that doesn't mean he's necessarily right.
In an equation-dense paper that appeared in The Astrophysical Journal Letters a year after Werykâs discovery, Loeb and a Harvard postdoc named Shmuel Bialy proposed that âOumuamuaâs ânon-gravitational accelerationâ was most economically explained by assuming that the object was manufactured.
That's not how Occam's Razor actually works.
âNo, âOumuamua is not an alien spaceship, and the authors of the paper insult honest scientific inquiry to even suggest it,â Paul M. Sutter, an astrophysicist at Ohio State University, wrote.
That, too, is a specious argument -- again, while unlikely, I don't think it's wise to rule it out entirely.
âCan we talk about how annoying it is that Avi Loeb promotes speculative theories about alien origins of âOumuamua, forcing [the] rest of us to do the scientific gruntwork of walking back these rumors?â Benjamin Weiner, an astronomer at the University of Arizona, tweeted.
This, though I despise Twitter with the fire of a thousand suns, makes sense.
Loeb has now dispensed with the scientific notation and written âExtraterrestrial: The First Sign of Intelligent Life Beyond Earthâ (Houghton Mifflin Harcourt). In it, he recounts the oft-told story of how Galileo was charged with heresy for asserting that Earth circled the sun.
I will reiterate here that I'm not going to rag on anyone for promoting their book. However, as far as I'm concerned, anyone who invokes Galileo immediately gets thrown into the "crackpot" bin. Galileo had hard proof, and was facing execution from a theocratic establishment. Literally no one is saying that Loeb should be tortured and executed for his beliefs, and few scientists are going to come out and say, unequivocally, "technology-using aliens categorically do not exist." All they're saying is that we need more proof than just "none of our other hypotheses fit."
In âExtraterrestrial,â Loeb lays out his reasoning as follows. The only way to make sense of âOumuamuaâs strange acceleration, without resorting to some sort of undetectable outgassing, is to assume that the object was propelled by solar radiationâessentially, photons bouncing off its surface. And the only way the object could be propelled by solar radiation is if it were extremely thinâno thicker than a millimetreâwith a very low density and a comparatively large surface area. Such an object would function as a sailâone powered by light, rather than by wind. The natural world doesnât produce sails; people do. Thus, Loeb writes, â âOumuamua must have been designed, built, and launched by an extraterrestrial intelligence.â
Sometimes I forget that other people haven't been breathing, drinking and eating science fiction their entire life the way I have. Solar sails are currently speculative, in that we haven't created one yet, but the physics behind them is sound.
Again in typical TNY fashion, the article goes on a side quest to talk about extrasolar planets.
The first planet to be found circling a sunlike star was spotted in 1995 by a pair of Swiss astronomers, Michel Mayor and Didier Queloz. Its host star, 51 Pegasi, was in the constellation Pegasus, and so the planet was formally dubbed 51 Pegasi b. By a different naming convention, it became known as Dimidium.
Can I just take a moment to note just how awesome the name "Dimidium" is? It's really a shame that the moniker got slapped on a planet that it's unlikely we'll ever be able to visit.
No one knows what fraction of potentially habitable planets are, in fact, inhabited, but, even if the proportion is trivial, weâre still talking about millionsâperhaps tens of millionsâof planets in the galaxy that might be teeming with living things. At a public event a few years ago, Ellen Stofan, who at the time was NASAâs chief scientist and is now the director of the National Air and Space Museum, said that she believed âdefinitive evidenceâ of âlife beyond earthâ would be found sometime in the next two decades.
The key word here is "believed." And I'll issue my usual proactive caveat: "Life" is not the same thing as "technologically capable sentients." Life on earth proceeded to evolve quite nicely for over four billion years before one species started launching spaceships, and if that species disappeared, life would continue to evolve quite nicely. Evolution doesn't have an endgame, and those qualities that we call "intelligence" aren't the only survival traits; if you don't believe me, go look at a cockroach.
This article doesn't disagree with me here:
Assuming that there is, in fact, alien life out there, most of it seems likely to be microscopic. âWe are not talking about little green menâ is how Stofan put it when she said we were soon going to find it. âWe are talking about little microbes.â
We are what we are because of a singular event in evolutionary history: the combination of two very different kinds of microbial life, a combination that vastly increased the energy-generating power of a cell. The development of eukaryotic life was what enabled complex organisms, such as cockroaches, birds, fish, and us, to develop.
On Earth, many animals possess what we would broadly refer to as âintelligence.â Kershenbaum argues that, given the advantages that this quality confers, natural selection all across the galaxy will favor its emergence, in which case there should be loads of life-forms out there that are as smart as we are, and some that are a whole lot smarter.
While it's tough to argue against this, and I don't want to even try, I will point out that intelligence doesn't automatically translate to technological sophistication. Few would argue, today, that dolphins aren't intelligent, and yet they show no proclivity, or an appropriate anatomy, to build complex structures and send some of those structures into space.
Sigh. I suppose I have to take a moment to make my usual plea: comments to the effect of "why are we looking for intelligent life out there when there's clearly none down here?" will be met with scorn and ridicule. The fact that we can make such comments immediately negates them. That joke was funny once, when Monty Python did it, and is now about as funny as seventh-planet puns.
This, in his view, opens up quite a can of interstellar worms. Are we going to accord aliens âhuman rightsâ? Will they accord us whatever rights, if any, they grant their little green (or silver or blue) brethren? Such questions, Kershenbaum acknowledges, are difficult to answer in advance, âwithout any evidence of what kind of legal system or system of ethics the aliens themselves might have.â
I have to wonder how a scientist can get so far into science without at least encountering science fiction, which has addressed these questions in myriad ways.
As disconcerting as encountering intelligent aliens would be, the fact that we havenât yet heard from any is, arguably, even more so. Why this is the case is a question thatâs become known as the Fermi paradox.
Look, I've discussed the Fermi paradox and the related Drake equation in here before, and I really don't feel like rehashing all of that. There's a search function for blogs here, and if you're interested in what I've said about them in the past, use "Fermi" or "Drake" to find earlier entries.
Or, hell, I'll save you the trouble:
"Occam's Drake"
"No, It's Not 36."
"Alone"
Hell, this one even mentions 'Oumuamua and Avi Loeb, but from a different source and several years ago: "Inalienable"
I guess I've been harping on this shit for way too long and I'm sure my regular readers are tired of it already. I have a crap memory, so I remembered writing about it but not exactly what I said, so it's not surprising that I've repeated myself.
So I won't belabor this much further, just quoting one more paragraph from the TNY article:
Itâs often said that âextraordinary claims require extraordinary evidence.â The phrase was popularized by the astronomer Carl Sagan, who probably did as much as any scientist has done to promote the search for extraterrestrial life. By whatâs sometimes referred to as the âSagan standard,â Loebâs claim clearly falls short; the best evidence he marshals for his theory that âOumuamua is an alien craft is that the alternative theories are unconvincing. Loeb, though, explicitly rejects the Sagan standardââIt is not obvious to me why extraordinary claims require extraordinary evidence,â he observesâand flips its logic on its head: âExtraordinary conservatism keeps us extraordinarily ignorant.â So long as thereâs a chance that 1I/2017 U1 is an alien probe, weâd be fools not to pursue the idea. âIf we acknowledge that âOumuamua is plausibly of extraterrestrial-technology origin,â he writes, âwhole new vistas of exploration for evidence and discovery open before us.â
And I'm not saying we shouldn't speculate, or pursue the possibility of finding alien life or technology. It would be cool as shit if we did find some (even if they do end up wiping us out because we're a bunch of assholes). Just remember, for now, it's all in the realm of speculation.
As always, I appreciated all of the comments from yesterday.
KĂĽre ŕšŕ¸Ľŕ¸ľŕ¸˘ŕ¸Ą Enga  , that's interesting about the number 7. I was aware of the Chinese superstition surrounding the number four, and of course our own Western equivalent concerning the number 13. I've stayed in Chinese-owned hotels without a fourth floor, and I've been in American-owned buildings without a 13th.
ForeverDreamer  , I had an uncle who was in WW2 and was diagnosed with, at the time, shell-shock. He was never quite right in the head, and he unfortunately died in 1992, having never really gotten the treatment he needed.
Grin 'n Bear It!  , welcome!
Elisa, Stik of Clubs  , I haven't seen the Bean either, except in pictures, but the artist who created it really, really hates it when people call it the Bean (it's official name is Cloud Gate and it was created by professional asshole Anish Kapoor, and anything that pisses off Kapoor is okay in my book).
And out of those four, the die rolled a 1, so the MB goes to KĂĽre ŕšŕ¸Ľŕ¸ľŕ¸˘ŕ¸Ą Enga this time!
Like I said, I'll do this again soon. Thanks again for the comments, everyone! |
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At my job, we only sold a cheap house wine for white zin, and when people ordered it I had to try to restrain my facial muscles from giving stank face. 
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