In The Tholian Web, when the Tholians show up to bully the Enterprise away, Spock says that they are on a rescue mission and need to wait exactly "one hour and fifty-three minutes" for the Defiant to reappear. Once that very specific time is up and nothing happens, the Tholians open fire.

Why did Spock give such an exact time? Sure that's what he normally does. But he's aware of "The renowned Tholian punctuality", and he's already given the order to not move an inch in case this makes the necessary time fluctuate. He should know that enough though his calculations are correct, it's a very sensitive situation that could easily go wrong in many unpredictable ways. Why not instead claim that he needs "two hours" (about a 5% margin of error), so that if Kirk is even five minutes late everything's still fine? Or really hedge his bets and go for "two hours and fifteen minutes"?

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You need to look at this one like a Vulcan. Spock didn't give himself any margin for error because if they don't transport the Captain at the next interval he'll suffocate before they can try again.

While a puny human would want to give enough time to recover his body (and build in some margin in case their calculations were wrong) Spock decides that, logically speaking, since his calculations are perfect, there's no sense causing a diplomatic incident over someone who's going to die anyway. Either they get him or they don't.

SPOCK: Approximately two hours before the attempt can be made.

MCCOY: Spock, are you sure that Jim is still alive?

SPOCK: The Captain was caught in our transporter beam when the Defiant phased out. It is possible he was spared the shock of transition and survived. However, if we are to recover him, we must catch him at the precise moment during the next interphase, or he will die. And there can be no margin for error. His environmental unit can provide breathable air for no more than three point six two hours.

In hindsight it would have been beneficial to build in some "wiggle room" as he'd failed to take into account that the arrival of the Tholian ship had de-stabilised the rift, but that was something that couldn't have been foreseen based on the evidence at hand.

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