Graph Theory and the Tree of Life

No one, to my knowledge, has ever applied the techniques of graph theory to examine the Tree of Life. Thus, being into graph theory as I am, I'm doing it.

A few definitions. A graph G is a collection of vertices (nodes) V(G), and a set of edges E(G). A node is generally represented by a dot or circle, and an edge by a line between two nodes. Thus the Tree is a graph, with each sephira as a node and each path as an edge.


Now, if we can find a set of nodes and edges between two nodes on a graph, then there is a path between them. If we can do this and then take a different set of edges and nodes to get back we have a cycle. A Hamiltonian Cycle is such a cycle that uses all node sin the graph only once (except the first/last node which is the same node).

The Tree of Life has a Hamiltonian cycle... which is also the Path of the Flaming Sword (among others) [note: lost my notes... again, not so sure on this]. Early inspections seem to indicate that all subgraphs (same Tree with removed sephira) have Hamiltonian cycles as well, which doesn't always happen.

there is a perfect matching on the Tree... ie, we can also pair off all the sephiroht without using an edge more than once. Obviously subgraphs don't have this property, as it requires an even number of nodes.

The Tree is 3/2-tough, which means that the best possible result we can get is by removing 3 nodes and yielding 2 disconnected components... remove Tiphareth and Netzach and Hod. Two parts with just Yesode and Malkuth and the rest in separate parts.

The Tree of Life is also 4-partite, meaning the nodes can be grouped into 4 parts and have no edges between any node and the other nodes in its part. Took me a minute to figure this one out, until i drew it in Word and started dragging around the nodes and the edges could move with me.

The girth of the graph (shortest cycle) is 3, as there is a triangle.

*sigh* I'll add more to this at another time, when I have more time for deeper study.

Stillness and Knowledge

I had always wondered what it was about walking around late at night on campus that I loved. I especially loved to watch the light on our old castle-like buildings and on the trees and grass. This year I discovered that it is the stillness. Go out around your house or on campus or down the road late at night at 1AM and look at the trees. They are very calm and very still. Absolute silence and darkness except for whatever lights may lie nearby.

This is not how life is. Life is truly not static at all, not even the objects are static during the day, but at night everything seems to stumble to a crawl. I have sat out many an evening and can never pinpoint exactly when the trees stop.

This post doesn't really have much to do about anything, other to say that life is dynamic and that any peace and goal we may obtain are changeable. The only constant is variable. Time never stops, for it never really existed to begin with, not in the way we'd imagine or would like it to. The only thing to do is press on as if this makes sense. In that respect I agree with Camus' ideas on the absurdity of life, in short that the human mind desires to know the sense of things and the world disappoints with a senselessness that is enfuriating. Yes, Ody, I do agree that sometimes not everything has an answer, some things you can't "know" in the usual sense, but then I've always told you that and never seemed to explain the differences in "knowing" properly. For the many futile arguments over that, I apologize, and even though you probably haven't caught on that this is here yet, I'm going to explain a little more.

This isn't an uncommon idea, that there are different means to knowledge. Knowledge is obtained through many avenues, through experience, through reason and logic, through God and deity, and just plain random inspiration (which differs in source from God and deity, but is similar in effect). There is also a knowledge that we can never know consciously (it is this kind that arguments seem to arise from with me).

The knowledge that the Qaballah gives is available through all these routes, but not all knowledge is available through all routes. For example, the correspondences, as in why the Divine Name (otherwise regarded as the Atziluthic Title) of Kether is Eheieh (I Am), and why Malkuth's is Adonai ha-Aretz (The Lord of the Earth), are reason knowledge. Scholarly knowledge. Books can give this information or it can be taught and passed on. What Malkuth means, how it feels, how it functions, how it "exists" are things that cannot be passed on, they can be experienced to an extent, but most of the experience is never shown consciously. It may influence further conscious thought and action, but is never directly known. The human mind is a many-faceted thing, whose facets may break. We can only take in so much and our minds can only directly understand little.