counting cycles

From: George Greene (greeneg_at_greeneg-cs.cs.unc.edu)
Date: 06/20/04 

Date: 20 Jun 2004 17:18:59 -0400

"Peter Olcott" <olcott@worldnet.att.net> writes:

 : > B-->B has four words
 : >
 : > has the exact same structural problem and yet
 : > its meaning is perfectly clear and non-controversial.
 : > Having this alleged "infinitely recursive structure"
 : > IS NOT a bar to being meaningful in natural language.
 : > More to the point, there is nothing infinitary about
 : > the structure anyhow. If you try to graph it, the graph
 : > is quite perfectly finite; the problem is that it never
 : > gets down to any leaves, as it is not a tree; it contains a
 : > cycle. But cycles in general are NOT infinitary and they
 : > are also NOT -- not NECESSARILY -- even problematic.
 :
 : Except that this cycle IS infinite.

No, it isn't. It just has 1 node and one arrow.

 : Infinite cycles are produced in directed graphs
 : when the cycle is not based upon a conditional
 : test.

Oh, shut up. You don't know *** about graphs.
Graphs have NOTHING WHATSOEVER TO DO with conditional tests.
There ARE NO TESTS, conditional or otherwise, in ANY graph.
Graphs have vertices and edges, PERIOD.
They DO NOT HAVE tests!

 : Infinite cycles in directed graphs are analogous to
 : unconditional (as opposed to conditional) branch instructions.

We are not talking about a graph as a flowchart for a computer
program. We are JUST talking about the graph BY ITSELF.

 o__
| \ is NOT an INFINITE cycle. It is JUST a cycle.
 \__/ It has ONE node and ONE edge and that is AS finite
       as you can POSSIBLY get, for a cycle! You could have
5 nodes and 5 edges or 99999999999999999 nodes and 99999999999999999999
eges if you wanted to but it would STILL be a FINITE cycle.
It's hard to know what you even COULD mean by an infinite cycle.

But whatEVER it might be, it certainly doesn't have a damn
thing to do with computer programming.

More to the point, in trying to evaluate the truth of this statement
(B), YOU DON'T WIND UP in an infinite cycle.
B: B has 4 words

IS JUST TRUE
and that's VERY easy to see, and it DOESN'T require
cycling. The point being that you don't have to evaluate
the inner B to know how many words B has; THAT'S not
DEPENDENT on th value of B. So there IS an implicit conditional test.
But that's not really the point either. The point is that the GRAPH
of the statement would be the same IRrespective of the test. 

-- 
 --- The history of our nation has demonstrated that separate is seldom, if ever, equal.
 --- (Feb.3,2004) Supreme Judicial Court of Massachusetts (4-3), adv.Sen.#2175