Your accurate understanding of the first paragraph of my hastily knocked-out post, shows the importance of "theory-of-mind" in enabling human communication. But this depended entirely on your
ability to accurately model my
state of mind when writing it.
However you are mistaken when imagining that my (inept) use of textual montage was in response to the sequence you referenced from 2001, which, by the way, is not really an example of montage, but arguably the most famous example of a match cut
in cinema history — 2 million years of technological advancement summed up in an instant — although not nearly as well matched (in angle and screen location) as it might have been.
I agree that a semicolon would have improved my paragraph immensely, although since WinCompose, I've taken to using thin-space em-dash thin-space instead. This can be obtained by typing ⎄␣- (compose space hyphen).
While walking, I mentally tried various ways to consistentise the whole power/base/exponent/log terminology debacle. The two major categories of such attempts involve power = constant exponent (similar to coefficient = constant multiplier) versus power = baseexponent
My best attempt to retain "power = constant exponent" goes like this:
"Power function" could be considered a shortening of "poweral
function", as opposed to "exponential
function". A "poweral" function must have a constant
exponent, so the argument must become the base. An "exponential" function can
have a variable exponent, and if it is to be different from a poweral function, then it must
have a variable exponent, so the argument must become the exponent and the base must be a constant.
The operations could be called "poweration" versus exponentiation, although by analogy with "exponentiation" it would make more sense if causing the argument to become the base was called "basiation" and a power function was instead called a "basal" function (as contrasted with an exponential function).
But then what do we call the binary function xy
when both are variable?
And why isn't there a word for a constant base if there is one for a constant exponent. Ah, but a "base" is
a constant. Consider the case of a logarithm base or a number-system base. So we actually need a word for a variable
base. It turns out we already have one. It's called a "root". The 4th root of 34
is 3. So why don't we say that the base-3 exponent of 34
is 4. Instead we say the base-3 logarithm of 34
is 4. But the logarithmic is considered the inverse
of the exponential, not a synonym for it! And my head explodes.
Going the other way works much better, i.e. power = baseexponent
or even power = rootlog
. One only has to invoke a historically recent slip of the tongue in going from 34
being "the 4th power of 3" to the still-acceptable "3 to the 4th power" to the mistaken "3 to the power 4". The mistake is in dropping the "th".
Actually, no, the mistake is in keeping the word "power" while dropping the ordinal "th". Calling it simply "3 to the 4" is fine.