Look, but don't worry about them...
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One of my colleagues was mentioning a book he'd read in which the author claimed that the most important thing we should be doing was figuring out a way to deflect "killer asteroids" (I assume or meteorites) intent upon destroying the Earth. The author was apparently saying our greatest need as a society was to prepare our giant flyswatter and have it standing at-the-ready because we might only have a few weeks of warning. He was apparently claiming that the failure to redeploy the world's resources into this grand task was a sign of lack of vision and outright irresponsibility on the part of the world's leaders.
We don't have a lot of big meteorites smacking into the Earth. Locally devastating ones in the last 1000 years can likely be counted on a single hand (Tunguska... anything else, estimates are around 1/300yrs but I can't think of any others that hit over land). Globally devastating asteroid impacts are way back in time (dinosaurs or so). So the odds that we'll have a small, locally devastating meteorite, say one that wipes out a 200km wide area, in the next 500 years or so are reasonable, but not certain. They may hit in a populated area, or way off in a corner somewhere. Even worst-case scenario we might lose 40-100 million lives. Yes, that would be a tragedy, but the world would continue, the human race would not be extinguished. For the globally-devastating asteroids, the chances that a one-in-multiple-million-year event will happen in the next 500 years seems low, but it's probably worth looking out for them just in case.
"We can't see them in time, so let's create a technology that can swat an asteroid away with just a few weeks notice." There's a silly assumption in there, that we can only see what we can currently see. Heck, we've already got projects under way to map the Near Earth Objects (NEO) and see whether there's anything likely to strike us any time soon. We've found a few "scary" rocks (initial estimates giving possible collisions), but nothing which on further analysis turned out to be particularly likely to strike. If we continue the surveys, focussing the efforts of a few thousand scientists on making them more accurate, more comprehensive, etceteras, we can likely be reasonably sure that there's nothing *in the neighborhood* on a collision course for the next 500 years.
How about the flyswatter itself? As I'm sure most of you are aware, in space slow-and-steady with lots of "leverage" can produce a lot more total force than fast-and-hot. There are lots of groups working on drive technologies that, if planted on an asteroid ten or twenty years before a predicted crash, could readily deflect the stone. These may require nuclear reactors and a robot-manned trip to get them to the asteroid, but they're relatively cheap and straightforward. Anything that's talking about diverting a devastatingly-large rock that's already within a few weeks of hitting the Earth, by comparison is going to have to be an extremely large, powerful device (or force)... you're likely looking at a nuclear density again, but likely as an explosion.
So why not worry about it? Let's say we complete the NEO survey and can say that there is a vanishingly small chance of anything hitting us from the local neighborhood in the next 500 years. Maybe we do another study and track to see if there's anything extra-solar-system at some point too. That gives us approximately 500 years of technological advance (assuming society continues) to come up with better technologies with which to construct a flyswatter. It seems extremely unlikely that over the next 500 years we will fail to create a working fusion power plant, for instance. Such a thing would make a flyswatter far easier to build. There are so many other issues that are far more likely to lead to the collapse of civilization in the near term that it seems ridiculous to think we should put "all our resources" into solving this "problem".
Anyway, was supposed to be at the client site before I even started writing this, so I suppose I should head out.
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