aridas sofia wrote:
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 multivalued function is selected to avoid ambiguities, exponentiation is a
singlevalued 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 onehalf power is the imaginary unit, but positive one raised to the onehalf 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 onefourth. But even if he had said one to the onefourth, 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:
Constitution

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