Notes
[Notebook Turkey, DB 55]
[Sunday 3 November 2002 - Saturday 9 November 2002]
[page 128]
Sunday 3 November 2002
Monday 4 November 2002
Tuesday 5 November 2002
Time to make the network concept more precise. Tanenbaum, chapter 2, Network Topology, Tanenbaum.
(Chapter 1 details ISO Protocol - ie the atomic layer delivers services to the molecular layer while remaining essentially invisible. Molecular layer provides services to the cellular layer, and so on.
We are talking about computer networks, ie information processing networks.
Tanenbaum p 32: Network topology - design is NP complete.
Fundamental property of networks is possibility of goal directed behaviour. Thomas proved the existence of God by postulating the need for a final goal which induced order in the rest of the world. Aquinas 13. Aristotle also saw the outermost heaven as the end/goal of the lower world.
Sport provides us with a good model of the way goals (the need to score) influence behaviour. We can see a soccer game as a network of servers dealing with one packet. There are two sets of servers which try to serve to one another but sometimes lose possession.
Neural and other networks induce goal directed behaviour by feedback. How is the goal encoded? By a structure that decides what has to be done as a consequence of the current input. The goal, which may exist in a
[page 129]
space of any dimension, is the 'set point' (which may be a point on the 'set line' (or generalized geodesic)), a point or set of points singled out from a space of 'peer points' which are nevertheless not set points.
This project is goal directed, although the goal is defined at only a low level of resolution. (I seek a 'new theology', the next step in the evolution of theology.)
tij = traffic flow from i to j
cij = cost of sending a packet from i to j.
Tanenbaum page 33: "performance optimization using only an allowed set of speeds is a difficult integer programming problem.
page 34: "every pair of sites shall be able to communicate even if an arbitrary collection of three IMP's and four lines are down."
Network design parameters: (topology, flow assignment)
These may be adjusted by designers to optimize cost.
Brute force search for topology cannot work. n nodes allow n(n-1)/2 lines. Since each line may be present or absent, the possible designs are 2n(n-1)/2.
n = 1, topologies = 0
n = 2, topologies = 1
n = 3, topologies = 8
n =4, topologies = 64
n = 5, topologies = 1096 . . .
These grow as fast as the transfinite numbers in the limit of ℵ0 nodes.
One way to construct a Universe is from a 'dust' of ℵ0 nodes to give ℵ1 network topologies.
The creative power of the Universe is manifested in the search for the densest possible coding = most efficient use of events
[page 130]
to realize a certain goal [productivity]
Aristotle's causes are useful mnemonics
final = GOAL
efficient = SELECTION to match goal
formal = ORDERINGS = MATHEMATICS
material = SYMBOLS
Good play = leading to a score (our side) or prevent scoring (their side).
The heuristic considerations used to generate candidate models are not necessarily reflected in the final model, just as the scaffold used to erect a building is not seen in the end but its erstwhile presence may be inferred by an experienced builder.
To design networks we consider ensembles of networks at various levels of coarse and fine graining eg macro and micro-management.
page 34: hierarchical networks
"the basic principle on which all networks are based is that the customers are not spread around uniformly.
page 35: Backbone vs local access.
Tree has no routing problem. TOPOLOGY can TRADE OFF against ROOTING.
36: Connectivity analysis => reliability
graph = {node, edge} + terminological variations.
adjacency, directed, undirected.
[page 131]
arc weights (cf synaptic weight)
GRAPH can easily be represented by a matrix, Mij is the capacity from i to j = frequency, = energy
What is the momentum measure of a graph?
Exclude parallel lines (this is true in a closed Universe) and self loops (which lead to renormalization problems). We can exclude self looping at the lowest level because the selves are not complex enough to carry a representation of themselves.
Degree of node is the number of arcs ending there.
Euler: The sum of the degrees of all nodes in a graph is equal to twice the number of arcs since each arc contributes one degree to each of two nodes.
regular = all nodes same degree.
shortest path = geodesic«diameter = length of longest geodesic.
circuit = sequence of adjacent nodes that comes back to the starting point.
connected = every point can be reached from every other point = one component
Reliable networks remain connected despite the loss of nodes and links.
spanning tree - minimum spanning tree.
[page 132]
Here we come to the big issue : LABELLING
Transmission Control Protocol proves CONNECTION and RELIABILITY
page 42: Feasible flow is graph condition corresponding to div j = 0 - axiomatic definition.
1. source has no inward arcs;
2. sink has no outward arcs;
3. no arc overloaded;
4. inflow and outflow balance at source and sink (this is the
definition of source and sink)
5. outflow at sink = inflow at source.
To imitate multiple sources and sinks we superpose diagrams with one source and sink. LINEAR SUPERPOSITION.
FEASIBLE FLOW is related to UNITARITY
Why does physics use complex numbers; which means why is the behaviour of the world isomorphic to the mathematical construct we call Z? Because representation requires duality, and this is the simplest available duality square root(n) <> square root(-n)
page 43: Max flow min cut Ford and Fulkerson 1962: The maximum flow between two arbitrary nodes in a graph cannot exceed the capacity of the minimum cut separating the two nodes.
Always a feasible flow that saturates the minimum cut (assuming that source and sink can saturate network).
44; max flow algorithm
46: reference node, reference potential.
[page 133]
arc connectivity(i,j) = minimum cut between i and j.
Wednesday 6 November 2002
Thursday 7 November 2002
A night of firefighting and a short sleep induce a pleasing weariness conducive to dreamlike thought. A night of watching God burn and drawing lines on God beyond which the burn may not go. Lefty is on the dozer making a break up some pretty steep country. Sailor is watching him and keeping an eye out for problems that may not be obvious to the driver of a big and heavy machine working near the limits of its stability but nevertheless an extremely powerful weapon against wildfire. The line of bare earth provides a starting line for the backburn which will meet the wildfire so that they annihilate one another by exhaustion of fuel. Then Forestry sausages and rissoles. Ugh. Boarding school circa 1955s catering.
The incessant traveller moves because she/he has somewhere to go.
PEER / NOT PEER == CONTROL / NOT CONTROL == possess / not possess.
Peers negotiate rather than command and respect one another's needs (protocols) as the price of effective communication.
Friday 8 November 2002
Our interface with survival is encoded as pleasure and pain. Our psychic landscape is populated with attractors and repellers which shapes the potential field that guides our actions. Detailed actions are determined by a superposition of potentials = superposition of communication networks.
POTENTIAL = POTENTIAL
ACT = ENERGY
Network = superposition of trees. Tree = {source, sink}
Sum (source) = Sum (sink)
