# A Turing Network?

Where did this idea come from? From reading papers on the smart-grid and imagining self-healing smart-grid infrastructure.

Imagine your standard Turing Machine, but something a bit different. Instead of maintaining program state in the a tape with discretized values, this Turing Network instead processes waveforms where state can be encoded in various ways, including in spectral transformations. And this is a network, not a simple machine, where state is distributed amongst various autonomous Turing Machines.

#### Your Standard Turing Machine Animation or the Google Doodle for Turings 100th Birthday

### Why Does The Turing Network Matter?

If you are a computer scientist, then a Turing Network is a fascinating thought experiment. It’s a generalization of a problem that seems relevant to quantum computing, where some state is entangled amongst otherwise autonomous processes.

The traits distinguishing this hypothetical programming problem from a simple Turing Machine are:

#### (1) There is a network or graph of devices: a Turing Network

#### (2) They are connected together signaling using only electronic waveforms, so the speed of transfer of information is optionally relevant

#### (3) There is optionally, a universal clocking mechanism which can be assumed to be accurate.

#### (4) The electronic components and signaling used are optionally relevant, but should only be considered relevant by masochists.

#### (5) Optionally add to each node a quantum FTL networking connection that surpasses the speed of light

So you have a network of variously connected devices sharing the distribution of a waveforms between various electric channels. Again, the tape in this Turing Machine is the waveform, which the nodes of the network are programmed to modify. The nodes are connected in a graph that allows them to communicate using the waveform. It

The programs in this case are the behaviors of each node in response to inbound data from a waveform, which modify it and retransmit it along outbound edges to other nodes. The timing/positioning of the nodes on the electric network matter. Like any Turing program, the values encoded onto the wire depend on how the program processes values previously read into the program.

### Questions posed for a Turing Network:

#### (1) How difficult is it to get the assumptions from Turing Machines to hold for a Turing Network?

#### (2) How does one architect and program a Turing Network to simulate a single Turing Machine?

#### (3) Can a turing network, with nodes paired with the appropriate programs, always have a formulation that allows for Turing Completeness and/or Turing Equivalence?

#### (4) How do the traits mentioned above affect the design of Turing Networks?

This Turing Network is an incredibly useful thought experiment for engineers considering a career designing the Smart Grid. There are tons of papers on the smart grid that discuss various means of coordinating electric infrastructure. Many papers mention the usage of machine learning. If you think about it, the smart grid is very similar to this problem. The nodes receive signals that inform them of grid state and then signal coordinated changes to the grid, altering network behavior, sometimes resulting in dramatically variant network graphs.

An incredibly complicated problem: true self-healing smart-grid that dynamically identifies the most efficient circuits to act as a conduit for electrical power while maintaining security and redundancy. Such a smart grid requires distributing state across millions of devices to coordinate concerted network behavior to distribute power and accurately collect analytics, which are critical for Climate Change policy.

### An Extension to Programming in Dynamical State Machines

How does one extend this Turing Network idea to the idea of a probabilistic, genomic program based on dynamical state machines? In the case of the Turing Network, the nature of the “space” is very different than the cartesian space used in genomic programs: one is operating inside the topological space within the graph representing the Turing Network.

So, since topological spaces are analogous to cartesian space, what connections can be made from Turing Networks based in graph theory to Dynamical State Machines that spatially distribute state over a kind of state space mapped on top of 3D cartesian space.

This Dynamical State Machine Programming paradigm should carry over to networks where space is not cartesian and, in this case, the paradigm will be incredibly useful for artificial intelligence. A proper name for this paradigm escapes me. Stochastic Programming is a thing. Probabilistic Programming is a thing. Dynamic Program is a thing, so all the good names are taken. This thing is different and it’s utility and applicability to AI and genomics cannot be adequately stated. The nature of this programming paradigm is likely why Roger Penrose states that “human consciousness is non-algorithmic”. This programming paradigm can never guarantee infinite loops because everything is an event with probability between zero and one.

In the case where a Dynamical State Machine program is distributed across nodes in a Turing Network, it would seem that the “rules” for program behavior are tightly coupled to the structure of the network itself. That is the behavior is coupled to the the spatial fabric of the graph itself. This ties into representation theory (i think), where one can represent any graph as a mapping to other graphs, such as Cayley graphs or Complete Graphs. The program would need to adapt itself to various network topologies. If the underlying network topology changes, this would cause vastly different behavior unless the program could anticipate the change.

### The Turing Network is Closely Related to Quantum Computing

This thought experiment, the Turing Network, is closely linked to quantum computing and is an interesting analog to a Turing Machine for quantum computing. Thinking about his makes me appreciate how powerful technology is and makes me wonder where all the hyperintelligent people are in my life.

### TODO:

- turing network used by neurons to communicate data encoded into spectral components of neural spikes?
- can any program be converted into a probabilistic program that approximates the program?
- can any combinations of particles in space be represented as a special type of graph?

#### Wherefore Erdős Number? There for nothing?

“Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper…” Paul Erdős

What am I here for, anyways? Why am I tormented for the gifts of creativity, intelligence and perseverence? Why does it appear that I’m fated for oblivion?