I should draw the following distinction:
There are two issues: (1) the proportionality constants
(2) The phenomenon of the existence of these constants
I am not treating the constants as vectors or doing anything with them; am only dealing with the fact that they exist. So I'm adding "perspectives" or dimensions.
I nearly just re-worded the book's dimensional analysis with my "reference length" for "time" to get an answer "1" (1 dimension). But then I thought I should accumulate the knowledge of having used "reference lengths" as well as "lengths" somehow; so I figured it meant adding perspectives.
Sure, the constants possibly till now have always been co-linear because no-body ever treated length and time as variations on the same thing?
(Although they actually do and call it "space-time")
I had to introduce the orthogonal jump to maintain the fence between the constants, a fence that was previously held in place because you always had a separate "length" constant and a separate "time" constant.
The leap to self-reference was not carefully worked out; trying something out there that obviously needs more thought.
Think I've solved Dr. Dick's system to some extent now- be back!
Anything you agree with in the numbered para. post? E.g. origin of the 10 and the 6 curled up dimensions? Or: relevance of the philosophical look at "definition", to Dr. Dick's "Logical Consistency Analyser"?