Fixed Points and God

A Fixed Point is like that point on a map of England that is right over the place where the point on the map is. Easy to see that the operation making a map (which is shrinking and moving it around) has a fixed point for any location of the map within the map area.

Fixed points remain invariant under an operation. Some geometric operation have one like making a map. But due to Kleene there is a proof that all logical systems have a fixed point. I believe a Turing machine has a fixed point. And since a Turing machine can perform every computation possible, and can emulate every computable system possible it means that every system must have a Fixed Point (that argument needs serious work).

It means that every system has an invariant. ow suppose there are systems we make which are designed to discover points of invariance. They cannot discover their own points of invariance because they cannot operate on them. Fixed Points represent “meta” data about a system. Possibility the basis of the proof I need to show that systems cannot be total, because they cannot encompass their own meta data.

Bt vast analogy Religions speak of the invariant nature of God or True Self. And also that this invariance is beyond the power of individuals. It is the given. The presence of Fixed Points in out Existence would provide exactly this experience. The discovery of the Fixed Points that Religion speaks of is not a process that lies within the system but is a feature of the system itself. Human Being may be systems but they belong to a world which ha just one Fixed Point. It is the invariance of that which enables the world to see that it is not a particular System as is the view point of Human Beings. Seeing the meta data releases us from the common system of being a Human Being. We are not ourselves in the system, but rather the whole interconnected system itself. That was the original insight anyway. But back to something concrete and intellectual.

A quine is a fixed point of a computer program. You input the text of a particular program to a computer and it generates the text of that program. So if this (SRH) hypothesis is true then a program cannot find its own quine. Well obviously. A quine must output the program itself. But a search is a program that goes through all options until finds something matching a criterion. So if the output is just a list of possibilities until matching a criterion then so must the program be. But is that a search. Anyway try to write a quine that is both the output of a search and a program at the same time… something obvious I’m missing here?