the number 1 raised to any power equals 1
...But apparently the argument was that Kirk might not be talking about "the number 1". Instead, he might be using "one" in the sense of "this one", "the item of interest".
That is, whatever the numerical value of heartbeat intensity, it would be raised to the fourth power.
"Jettison" implies " get rid of." Were it a probe, they would say "launch" or "release" wouldn't they?
Certain types of payload today are "launched" from aircraft or naval vessels, others are "dropped" or "released", yet others are "deployed"; there are nuances to this all.
"Launch" might be reserved for payloads moving away on their own power, while "jettison" would mean abandoning an immobile buoy (say, a storm sensor) to the given location.
Has anyone brought up again the computer getting Spock's service rank wrong?
It would not be difficult to assume that Spock got a field promotion after the chain-of-command-rearranging losses of the pilot episode, and never got that officially confirmed at a starbase until the events of this episode. Essentially, he was "frocked" in the outer fringes of space, spent the first half a dozen episodes (in stardate order at least) far away from civilization and bureaucracy, and continued to receive mere LtCmdr pay until "Court Martial".
This doesn't explain why he would continue to be a Lieutenant Commander after the events of the episode, though.
We might of course postulate that McCoy is a LtCmdr (junior grade, 1.5 stripes) and Spock is a LtCmdr (senior grade, 2 stripes) while Kirk is a Commander (2.5 stripes) and a full Captain would have the three full stripes that best match the scenario where Starfleet braid = Royal Navy braid minus one. Or something complicated like that.