Once the Enterprise was traveling at warp, they should have been able to use photon torpedoes without adjusting the shields. Since the probe was following them, the explosions would occur behind them. Traveling at warp, the explosion radiation could never catch up to the ship.
In the scene where Barclay is discussing a problem with Albert Einstein, the board they use for their discussion actually shows just basic formulas from Einstein's "Theory Of General Relativity," nothing a physics student in his third year couldn't comprehend let alone the chief engineer of a spaceship in the 24th century. Their conversation on the other hand is mainly nonsense and not related to the formulas on the board.
Picard: Has Mr. Barclay done anything that could be considered... potentially threatening?
Troi: Well... he did make a pass at me last night. (Riker looks shocked) A good one.
Barclay: The moon, yes, that'll be my home, my... paradise. I shall find there all the souls that I love; Socrates... Galileo... and when I arrive, they will question my worthiness. "What the devil is he doing here among us? Philosopher, scientist, musician, duelist? Here lies Hercules Sauvingnan, de Cyrano de Bergerac!" I would not have you weep any less for that charming, good and handsome Christian. I only ask this... that as the great cold surrounds my bones, you allow a double meaning for your mourning vale. And when you let fall your tears for him, some few will be... for me.
Barclay: Checkmate in nine moves.
Troi: I didn't know you play chess.
Barclay: I don't!
(Riker and Barclay walking after Barclay beefed up the Enterprise's shields in order to destroy the alien probe.)
Riker: Mr. Barclay! Everyone's still trying to figure out exactly how you did it.
Barclay: Well, it - it just occurred to me that I could set up a frequency harmonic between the deflector and the shield grid using the warp field generator as a power flow anti-attenuator and that of course naturally created an amplification of the inherent energy output.
Riker: (looking perplexed) Uh-huh, I see that....
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