The (P_N = NP_1) bug that triggered 0.7 -> 0.8 isn't so bad.

Added notes to that effect.  Still, it's better for having thought it
out more clearly ;).

diff --git a/src/sawsim.nw b/src/sawsim.nw
index 96a786b964753a98438c92b28f7bbc1db1b30f67..850e7a9e913c47ffd7d3d225d75af347150b5ca0 100644 (file)
--- a/src/sawsim.nw
+++ b/src/sawsim.nw
@@ -153,11 +153,10 @@ Version 0.7 added tension model inverses, which seems to reduce
 computation time by about a factor of 2.  I was expecting more, but
 I'll take what I can get.
 
-Version 0.8 fixed a \emph{major} bug in unfolding probability for
+Version 0.8 fixed a minor bug in unfolding probability for
 multi-domain groups.  The probability of at least one domain unfolding
-had been calculated as $P_N=NP_1$, rather than $P_N=1-(1-P_1)^N$.  I
-dunno how that slipped by before.  Now there are multi-domain tests in
-testing to check for this sort of mistake.
+had been calculated as $P_N=NP_1$, rather than $P_N=1-(1-P_1)^N$.
+However, for small $P$ the two are equivalent.
 
 <<version definition>>=
 #define VERSION "0.8"
@@ -564,6 +563,10 @@ so the probability that \emph{at least one} domain unfolds is
 $$
   p(n>0) = 1-(1-P)^N.
 $$
+Note that for small $P$,
+$$
+  p(n>0) = 1-(1-NP+\mathcal{O}(P^2)) = NP - \mathcal{O}(P^2) \approx NP.
+$$
 We take some time to discuss the meaning of $p(n>1)$
 (i.e. multi-unfolding timesteps) in Section \ref{sec.timescales}.