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Long, long ago, I was watching an episode of TOS when a character usually or often on the bridge of the Enterprise made a comment about raising the number 1 [sic] to some power.

I don't remember who it was, or what point he was endeavoring to make -- I do remember that the comment was not ironic -- but it sure was a low point in Star Trek for me. That I just groaned and continued to watch says multitudes about the addictive power of Star Trek.

Who said this, and in what context? (Actually, after so many decades, I can't be 100% positive it was in TOS.)

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    SCOTT: Scotty, sir. We have a reading on the power source Mister Spock requested. When we first monitored, it was generating alternating cycles totalling one hundred to the twentieth power Waltham units. - TOS: The Apple – Valorum May 27 at 20:03
39

"Court Martial" (TOS 1x15)

Kirk is facing a court martial. In his defense, the Enterprise crew are trying to find someone hiding aboard the ship.

From the transcript:

KIRK: Gentlemen, this computer has an auditory sensor. It can, in effect, hear sounds. By installing a booster, we can increase that capability on the order of one to the fourth power. The computer should bring us every sound occurring on the ship.

Kirk says the line in this video clip, starting at the 55-second mark:

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    So obviously mathematical language has changed a little since the 20th century. – Harry Johnston May 28 at 1:11
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    I'm surprised by the fuss about this. It's simply 1E04, or 1*(10^4). He's just talking scientific notation in short form. – motoDrizzt May 28 at 5:06
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    I think Behrens' interpretation makes the most sense to me, but these are all plausible; I think I'd say "one to the fourth power" as "x^(1..4)" or "1e4" would be a misspeak if ever said seriously, but it's the sort of mistake a tired or distracted mathematician could really make. – lahwran May 28 at 5:28
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    @motoDrizzt Saying "one to the fourth power" as a shortened form of the number 1E4 would be like saying "eight" as a shortened form of the number 38. (The actual shortened form would be "ten to the fourth", or just "ten thousand".) One can easily retcon why Kirk would have misspoken, but you can't seriously argue that it wasn't a mistake. – Sneftel May 28 at 8:24
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    @Galastel Was it actually in the script? It's possible the script had something similar (like 10 to the fourth) and he happened to misspeak it in the take they used. – IllusiveBrian May 28 at 12:37

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