Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker
Examples of alpha and b.
x y Formula log-log u v formula alpha b xshift
y=1/x v = -u -1 0 0
y = 1000/x v = 3-x -1 3 0
y = x 2 v = 2 * u 2 0 0
y = 10 x v = 10 u (need double
0
log paper)
y = K/square v = log(K) - 0.5*u -0.5 log(K) 0
root(x)
y = y 0 (x) alpha v =
alpha log(y 0 ) xshift
log(y 0 )+alpha*u
I wrote some examples of power laws on a piece of paper and lost them, so lets try
again.
x axis y axis Pairs... Formula
Size of
advance
10 7 , 1 10 6 , 10 10 5 , 10 2 10 2 , 10 5 v = 7-u;
y = 10 7 /x
Number of
links
Ordinal
rank of
word
popularity
Number of
writers
getting this
advance
Number of
websites of
this size
Probability
that a word
is this
word
1, 0.5 2, 0.5
(7) The rich get richer algorithm can account for power law clustering, it comes out
with an exponent of -3. Two key steps (a) growing network with new nodes arriving forever
and (b) new nodes form links with existing nodes with probability proportional to the number
of links the existing nodes have. I read his Science paper on this too. This is essentially the
only result in his whole book.
(8) In some networks one node wins and they become stars.
(9) Scale free networks are vulnerable in that if the highly linked hub nodes are
knocked out the network breaks into pieces.
(10) In a scale free network a virus can spread more easily because when the viruses
get to hubs they radiate out a lot.
(11) Can the internet become self aware? Don’t know.
(12) The Web actually breaks into pieces, given that links are directed. Central Core
is mutually linked. In continent has links into Central Core, but you can’t get back to it.
OUT continent has links from Central Core but no links back to Central Core. Islands have
mutual links but don’t like back to core. Tubes run from IN to OUT.
(13) Can make a network for the many biomolecules in a cell, saying that two are
linked if they participate in a reaction. Seems to be three degrees of separation typical in this
small world network. Also seems to have a scale free topology.
(14) If nodes are fat cats and a link is being on the board of a corporation we get a
scale free network.
p. 108