They should visit a number of different types of asteroids and nuke them to see the effect.
Its really important knowing what will and won't work in protecting the planet from an asteroid impact.
We have zero experience in how effective nuclear weapons are in deflecting or distinguishing asteroids.
I don't think we want to be doing this when threatened by a large asteroid collision.
I think Fermi can be summed up with the comments near the bottom of the Crysis Warhead benchmark in the review done by AnandTech.
"The GTX 400 series completely tramples the 5000 series when it comes to minimum framerates, far more than we would have expected. "
Fermi is a mac truck that ploughs though the tougher scenes.
There is nothing worst than having smoke, explosions, and water falls etc causing graphics spikes.
If you want to find a needle in a haystack you need a needle finder (metal detector).
Almost all of the existing radio telescopes have too narrow a field of view and/or too long a integration time.
What we need is "An L-Band All-Sky Astronomical Surveillance System" as per the Ohio Argus (http://argus.naapo.org/).
5(?) of them would cover the whole sky. Each sees ~100 degree's of sky.
They would need to be located in space to cut down the large amount ground thermal noise and perhaps use superconducting antennas..
e.g. http://www.esa.int/esaLP/ESAQGA2VMOC_LPsmos_0.html but pointing out into space (it is at this very moment as apart of its calibration).
It needs to be able to spot 10 millisecond transients and have a real-time bandwidth of ~20 MHz (i.e. a real time 20 MHz of spectrum display with 0.1 hz of resolution for each image pixel in the sky).
It initially would have a low sensitivity and would be upgraded over time with more antennas and more advanced digital processing (needed to cross correlate all the antennas for all angles)
The technology to attempt this type of device has only recently come available (40nm and under FPGAs/GPUs).
What if "Argus sees a brief, narrowband pulse at 1420.8807 MHz near NGC 752" (http://argus.naapo.org/~rchilders/) was actually coming from the sky. The chances of any radio telescope being pointed at exactly the right spot an being able to see 1400Jy). What if that pulse is only sent once every 5 months? What if there where other pulses outside of the Argus's 60khz bandwidth?
I believe that any SETI beacon ("look here with a bigger telescope") would be a large phased array cycling though a large target list and sending a short burst of pulses on a number of special frequencies.
What if someone had reached a critical mass of enriched uranium before we knew it would start a fission reaction... And did so in a lab within a major city...
I do think LHC is safe. But who knows. Yes the earth has been bombarded by higher energies than those in the LHC.
But are they doing so under the same conditions as those inside the LHC.
What if there is something we don't know that happens with say high energy collisions in a high very magnetic field (which probably doesn't happen naturally).
>fundamental building blocks of those pieces
Just be aware that its false to believe that because X and Y flew out that X and Y where inside the particles before it collided.
That is a macroscopic concept of reality.
Human = pattern recognition and classification (compression) engine with the goal of surviving and reproducing.
Logic, cause and effect etc are just some of the patterns that we have observed and utilized to meet our goals.
A machine that is just logic and cause and effect is vastly inferior to us.
Where a problem is unsolvable or to complex (many are) we can match to the nearest pattern that gives a desirable outcome, regardless of the logic of that match.
We are also error prone (matching patterns in logically unrelated areas) and this allows us to by pass Godel's Theorem where as a machine of pure logic would be stuck.