##### volume **II:** Synopsis

#### section IV: Divine Dynamics

### page 27: Alan Turing

(1912-1954)

What Gödel did for the 'static' structure of the Cantor Universe, Turing did for its dynamics. He showed that, given a reasonable definition of a computer, there are some computation problems which can be solved, but there are many other 'incomputable' problems which cannot. Gödel's result shows that there will always be incompleteness, no matter how big the system. We can interpret Turing's result to mean that there will always be incomputable problems, no matter how big the computer. From this we conclude that if the whole Universe may be modelled as a computer, there are some computations it will never complete. The Universe is in this sense eternal. Kurt Goedel I

Turing's place in history is guaranteed by his paper 'On computable numbers, with an application to the *Entscheidungsproblem*'. The* Entscheidungsproblem *(German 'decision problem') was posed by Hilbert in 1928: did there exist a definite method by which any mathematical assertion could be classified as true or false? Hilbert himself felt that there were no undecidable assertions. Alan Turing, Davis

Turing modelled the 'definite method' of Hilbert's problem with an abstract computer now called a Turing machine. Turing was able to show that there are definable numbers which are not computable, thus showing that Hilbert's expectation was wrong. Further, Turing noted that the class of computable numbers is
denumerable (ie its cardinal number is ℵ_{0}), whereas the class of real numbers is non denumerable (its cardinal number is ℵ_{>0}). This means that the computable portion of the real numbers is infinitesimally small compared to the total class of real numbers.

Our model of the Universe comprises an address space modelled by the transfinite numbers with operations on this space modelled by computers. The question then arises, how can computers which can only compute a countable infinity of different functions deal with an address space whose higher cardinals are uncountably large? Transfinite numbers - Wikipedia

The solution to this problem lies in the concept of correspondence, in different contexts called mapping, naming or, in the physical world, binding or bonding. The first step in the workings of bureaucracies of all sorts is to establish the identities of their clients so that they can be certain that all the paperwork with the same name on it applies to the same individual. Personally identifiable information - Wikipedia

We assume that a human person is a transfinite object, but we know that the bureaucratic manipulation of that person is effectively computable, since the bureaucratic process of drawing files (elements of memory), updating them and returning them to their position in an ordered filing system is quite definite and finite. By handling the file, the bureaucrat is effectively handling the person, in a very limited way, of course.

We are imagining a dynamic universe that begins as a totally simple point analogous to the classical God documented by Aquinas. By mapping onto itself (analogous to the procession of the Word in the Christian doctrine of the Trinity), this Universe generates stationary fixed points which can be observed and documented scientifically. Trinity - Wikipedia, Aquinas 161, Brouwer fixed point theorem - Wikipedia

Turing's machine is a relatively complex device, having a finite number of internal states, being able to write and erase a 'tape' of memory squares, and to move itself along the tape in two directions. A maximal Turing machine requires a countably infinite number of memory locations.

Like Gödel's theorem, Turings theorem is a fixed point in the mathematical community. Although it is a model of a universal computer, the Turing machine is very inefficient, since it spends many operations stepping up and down its tape to reach the data it needs to perform its operations. Modern computers, with random access memory, are far more efficient: they use fewer processing operations to complete the same algorithm. Because of their enormous utility a large community of programmers has arisen to increase the efficiency of computers. The discovery of new algorithms can often yield an enormous benefit. Asymptotically optimal algorithm - Wikipedia

Hamilton's variational principle can be used to derive classical mechanics (including relativity), quantum mechanics and quantum field theory. The essence of this principal is the minimization of action which is modelled as the time integral of the Lagrangian. If we consider each operation of a computer as a quantum of action, we can guess that the optimization of computing algorithms and the minimization of action are closely related. Hamilton's principle - Wikipedia

In a universe where energy is conserved (ie the rate of action is constant) we have the necessary conditions for an evolutionary process: competition for the resource of energy or computing power by a population some of whose variations can compute more effectively than others.

Computer codes are fixed points in the software community, being created and annihilated in that community. We see this process as analogous to the evolution of genotypes in the biological community, and imagine an analogous evolution of the computable functions that quantum theory uses to explain the operation of the world. Computer programming - Wikipedia

(revised 25 May 2013)