n-dimensional sweetener

Well, I couldn't wait - I had this:

In my head all afternoon so I worked up a quick and dirty set of functions to deal with a n-dimensional pair of lists.

; sub-list, a function to subtract one list from the other
(define (sub-list xlist ylist)
(let* ((blah (list 'head)))
(let iter ((i 0))
  (if (>= i (length xlist)) (cdr blah)
     (begin
       (set! blah
         (append blah
           (list (- (list-ref xlist i)
           (list-ref ylist i)))))
       (iter (+ i 1)))))))

; sum of squares
(define (sum-of-squares xlist)
(let* ((sum 0))
(for-each (lambda (x) (set! sum (+ sum (square x))))
  xlist) sum))

; n-euclidean distance
(define (n-euclidean n n1)
(/ 1 (sqrt
       (sum-of-squares
         (sub-list n n1))) 1)))

Combined with the square() function from previously today one now has the ability to do such things as the following:

1. Use a standardised list of questions to create "compatibility" charts
2. Use this as a performance metric - using the final result as a range from 0-1.0 with regards to predictions vs realities
3. Plot the distance between objects in n-dimensional space
   

#1 would be useful for creating teams -as in, ask a bunch of questions and find the best matching partners.

#2 is used in Build Your Own Expert System which is a book I have read, marked up, and re-read so many times it is looking very much worse for the wear.

#3 - well how many n-dimensional spaces do you know?