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Old May 25 2013, 04:41 AM   #82
Cookies and Cake
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Location: North America
Re: Updating FJ's technical manual?

aridas sofia wrote: View Post
For example, if he is saying "one to the fourth" and you read it as "one to the 1/4" you end up with factors of 1,-1,i, -i. That is more interesting than just one - particularly the imaginary numbers.

http://forums.xkcd.com/viewtopic.php?f=17&t=86266
No, that would still be wrong.

By the convention of principle values, whereby one branch of a multi-valued function is selected to avoid ambiguities, exponentiation is a single-valued function.

Under that convention, one raised to any power, fractional or otherwise, is still one.

On the other hand, negative one, when raised to a fractional power, is complex and can be purely imaginary. For example, negative one raised to the one-half power is the imaginary unit, but positive one raised to the one-half power is still just plain old one.

(Note that (-i)^2=-1 also, but the selection of principle square root means that (-1)^(1/2)=+i unambiguously.)

Besides, he (and, it was Kirk/Shatner) still said one to the fourth and not one to the one-fourth. But even if he had said one to the one-fourth, the value would still be one (by the convention of principle values).

Interesting idea, actually, but there's just no (reasonable) way to make lemonade out of these particular lemons. It's really just Treknobabbly gobbledygook in this case, I believe.

GSchnitzer wrote: View Post
Constitution
Ah, yeah, that would make perfect sense. Yeah, making the blueprints out to be plans of the Constitution was a perfect loophole.
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