On Dec 6, 2007 12:15 PM, Ed Murphy <[EMAIL PROTECTED]> wrote:
> In CFJ 1813, Goethe argued that VVLOP is defined as a "parameter",
> implicitly treated as a number, but could also be interpreted as a set
> of numbers (added up whenever the value of VVLOP is queried). In this
> hypothetical context, "decrease by -1" is interpreted as "remove -1 from
> the set". However, this only works if the set contains a -1 to be
> removed. This is sufficiently unworkable to shoot down the implicit
> application of this interpretation. Even if this interpretation were
> explicitly stated, the AFO's VVLOP set did not contain enough -1's to
> remove 104 of them.
Now that you've got me thinking about it, what about this one:
d) A player may spend N+2 VCs of different colors to multiply
another player's VVLOP by (10-N)/10, where 1 <= N <= 10.
Multiplication by a number isn't normally defined on multisets. If we
want to force one, the simplest interpretation would be that
multiplication by a number is equivalent to joining that many copies
of the multiset together; but that doesn't work here, because the
multiplication factor isn't necessarily an integer.
Alternatively, we could interpret it as multiplying each element of
the multiset by the multiplication factor, which just feels strange;
it's not the sort of operation I would expect on a multiset.
If we look back at the electric charge example, multiplication by a
non-integer does make sense in that context: if a chemist prepares a
solution with a charge of q, then pours out half of that solution, e
will have two solutions each with charge q/2. This suggests that, to
multiply VVLOP by (10-N)/10, we remove N/10 of everything in the
multiset in proportion.
That seems to solve the problem, but what happens if the actual
quantities of each summand aren't exactly in proportion? In
chemistry, this isn't a problem; the charge of a few individual
electrons is negligible. With VVLOP, it is a problem; suddenly a
player's VVLOP is a whole point or two more or less than what it
should be, and since we don't track the actual contents of the
multiset, we don't even notice.
-root
