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 = base
exponent.
My best attempt to retain "power = constant exponent" goes like this:
"Power function" could be considered a shortening of "power
al function", as opposed to "exponent
ial 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 x
y 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 3
4 is 3. So why don't we say that the base-3 exponent of 3
4 is 4. Instead we say the base-3 logarithm of 3
4 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 = base
exponent or even power = root
log. One only has to invoke a historically recent slip of the tongue in going from 3
4 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.