Quantum Gravity Via Expansion-Contraction 35.1: Permutations, Combinations, etc.
- From: "OsherD" <mdoctorow@xxxxxxxxxxx>
- Date: 16 Nov 2006 21:44:00 -0800
From Osher Doctorow mdoctorow@xxxxxxxxxxx
Aside from an idiotic comment by one of the loonie graffiti artists in
the last Section (perhaps he/she has returned from a prolonged
celebration of the November Election idiocy with MoveOn.Org types),
let's continue with more general aspects of permutations and
combinations in elementary and intermediate probability and
combinatorics.
The number of (unordered) combinations of n different things in groups
of size r < = n, C(n, r), is:
1) C(n, r) = n!/[(n-r)!r!] = (n-r+1)(n-r+2)...n/[(1)(2)...r]
while the number of (ordered) permutations corresponding to these is:
2) P(n, r) = n!/(n - r)! = (n-r+1)(n-r+2)...n
Thus, both C(n, r) and P(n, r) increase with n for fixed r, and if we
want to count them all with r ranging from 1 to n, the grand total
increases with n in a similar if partitioned way.
So we see that it is correct to regard n! as the fundamental measure of
Causal Knowledge for fixed r or for r = n, and that even the
modifications for r not equal n are in the same direction. Since the
length of an arbitrary Causal chain is better represented by general r
for 1 < = r < = n than by n, this is a useful fact, where n is the
number of different symbols.
How do combinations (unordered) occur instead of permutations in this
scenario? Where the Causal order is "interchangeable", as for example
ab and ba if both a Causes b and b Causes a.
The structure considered here has to be supplemented with Probabilities
to use the detailed machinery of Probable Influence/Causation (PI), but
the Foundational ideas still include the above ones.
Osher Doctorow
.
- Follow-Ups:
- Prev by Date: Re: T.J., See you Tuesday, Nov 28th.
- Next by Date: Re: What kind of seas should I avoid ?
- Previous by thread: Supernova Remnant Acts as a Particle Accelerator
- Next by thread: Re: Quantum Gravity Via Expansion-Contraction 35.1: Permutations, Combinations, etc.
- Index(es):
Relevant Pages
|
