# Towards the Development of an Einstein/Turing Machine:

## I.   The Turing Machine:

The Turing Machine is a fundamental conceptual model for the Computational Process. In Principle, it is capable of Simulating any process that can be described in terms of a Computational Model.

Basically, the Turing Machine comprises two main components:
• A Memory (environment) which is processed
• A (three part) Process which modifies the contents of the memory/environment:
• Substitution Rule    (determining the nature of the modification)
• Write Rule              (determining the position of the "Write" Pointer)
In principle, the "Process" is continued until it is terminated (for some external or internal reason) . Originally, the Turing machine was seen as a model for the process of  Problem Solving -and so the "Computability Problem" (deciding if a specific "Problem" could be solved within a finite number of steps" was an important issue. Later, as Computational Models were increasingly applied to non-terminal processes (such as controlling a continuously operating electricity generating plant) the Computability Problem became a more specialised concern.

## II.   Understanding the Turing Machine:

### 1.0   Simulation and Understanding:

A.  Including the Infinite:

Clearly, there is an element of tautology in the description of the Turing Machine as a "Universal Simulation Machine" -simply because it is assumed to be capable of "Simulating" any processes that can be "Described" in terms of a Turing Machine (which is assumed to be a synonym for "Computational Model").

To a certain extent, this tautology could be resolved through the "Computability Problem" -which eliminated processes that could not be terminated (because the "problem" was never solved). However, the price for this was the (conceptual) elimination of all non-terminal processes.

So are there other (more suitable) criteria which can specify the limits (and value) of the simulation?

B.  Simulation and Marketing:

Postmodernism has apparently fallen in love with "Simulacra" -which (conform with its consumerist bias) it loves to equate with that which is being simuulated. Apparently, postmodernists have never really understood that although one might gain nourishment from eating an apple -one cannot remain healthy on a diet of "Virtual Reality" apples.

Consumerism requires that "Simulacra" can be marketed as if they were real -and postmodernism seems to be the philosophy which is principally designed to market this somewhat dangerous concept. Within this perspective, objects are alienated from their functional context -and have no other function other than to be marketed as (basically meaningless) status symbols intended to improve the (presumably low) self-esteem of the purchaser.

C.  Simulation and Description:

Outside the marketing perspective, Simulacra are less useful as objects in themselves -but gain their meaning through a (usually pedagogical) context.

Within the context of the Turing machine one can perhaps see that (with the Computability Problem eliminated) the question of "Describability" becomes the key factor determining if a process can be simulated or not.

D. The Value of Simulations (Models)

i.   Clarifying the  Concept:
One can perhaps argue that the value of a Computational Model lies less in its practical application than in the insights gained in its creation -simply because of the need to clarify these concepts in terms of an explicit (and testable) description.

ii.   Experiencing the External:
In many cases it is difficult to imagine situations from a perspective other than our own. Traditionally "Art" has been a way of simulating (through visual imagry, play acting and story telling) the human condition from various viewpoints which are not usually available to us.

iii. Experienceing the Internal (Self Reflection):

As the Bible remarks -it is often easier to see the plank in someone else's eye than it is to see the splinter in one's own. Indeed, in many cases our own (internal) functioning is at least as mysterious (and sometimes even more) to ourselves as it is to others. Sometimes we need a form of externalising "mirror" in order to see ourselves more clearly.

iv.  Simulating the Impossible:
Some forms of knowledge involve situations that are difficult or even impossible for us to experience directly. These situations may be too big or too small, too distant, too expensive or too dangerous. However, they can still be studied if they can be simulated in some form or other (not neccessarily in hi-fi "sensory" terms). In many cases, A mathematical Formula, Classical Greek drama -or Indonesian shadowpuppets can simulate a situation just as effectively as modern cinema or expensive digital "virtual reality" systems can.

### 2.0    Einstein and Turing:

In the "Newtonian" view of space, there is no (theoretical) interaction between the (environmnetal) space and the objects that "move" through it ("Friction" can be seen as the influence of the "environment" on the moving object -but this is not a "reciprocal" action which involves bi-directional interaction between the object and its environment).

In the Einsteinian view of space, objects moving through space are not only influenced by the environmental space through which they move -in turn, they also modify it.

Clearly, the Turing machine modifies the environmental memory space through which the "Read" and "Write" pointers move. The main difference between a Turing Machine and an Einsteinian Time/Space Machine would therefore appear to be concerned with the number of Dimensions of space involved. A Turing machine is generally assumed to be operating in a one-dimensional space -while the dimensions of Time/Space are unspecified (but presumably generally assumed to be larger than one).

### 3.0   Organic and Inorganic

A.  The Inorganic Machine:

There seems to be a common tendency to concider "Einsteinian Time/Space" as something extraordinary which does not exist in the more mundane universe of daily (earth-bound) experience.

However, if we concider the difference between "Newtonian" and "Einsteinian" space to be based on the absence or presence of interaction between the objects involved and the environmnetal space through which they travel -then it becomes easier to concider Newtonian space as being "Mechanical" and Einstineinian/Turing space as being "Organic".

Initially, this seems counter-intuitive -because our experience of artificiality (in particular as manifest by the machines produced in the industrial revolution) has, up until now, always been limited to experience with Newtonian machines -and so we assume that the concept "Machine" is always synonymous with the concept "Inorganic".

On the other hand, we do seem to associate "organic" intuitively with "Interaction" (or feedback): While the interaction with the environment exhibited by, for example, an (inorganic) fence seems to be limited to decay -however, all the organisms living in the area of the fence will respond in a variety of ways. Contrary to the behaviour of the fence, a row of (organic) trees will be in constant interaction with the environment (both influencing it and being influenced by it).

B.   Homogenity and Diversity:

The second law of thermo-dynamics claims that in a system exhibiting different energy levels, the energy will gradually disipate throughout the system until it becomes homogenous. This is known as "Entropy".

"Decay" is a natural condition of all inorganic systems. But all systems are not "inorganic" -so we should be carefull in applying the laws of physics (which esentially deals with inorganic systems) to "organic" systems.

In practice, it seems that "organic" systems have an anti-entropic tendency -which involves taking (diffuse) energy and dissipated nutrients and converting them into differnentiated organisms. It also seems that "organic" systems are not stable -that in general they exhibit both an "organic" (living, anti-entropic) phase and an "inorganic" (dead, entropic) phase.

C. Chaos Theory:

Information Theory also uses the concept of entropy -and defines it (contrary to physics) as the degree of "uncertainty" resolved by recieving the message. So in Information theory -"diversity" (unpredictability) increases entropy while in physics "diversity" (differentiation) reduces it.

In practice, it is generally so that the longer a (repetitive) "mechanical" system operates -the less uncertainty there is as to which transformation will come next. The parallel with physics seems to hold good. However, the behaviour of a living organism is generally less predictable -so perhaps differnt rules apply to "organic" systems here too.

Chaos Theory claims that some systems do not degenerate into simple repetition -but continue to generate "uncertainty" as to their next state. Is "Chaos Theory" a parallel "Information Theory" for  "organic" (Einsteinian Time/Space) systems?

D.   Decay and Abundence:

The distinction between "organic" and "inorganic" might also have implications for economics.

It seems that politicians generally refer to economic systems as if they were "inorganic" systems (subject to decay) -as if income was a static "pie" that can only be divided and distributed once. The "economics" of scarcity often operates as the "stick" used to "beat" the public into cooperating in a system of economic exploitation.

However, in practice, it appears that (as the economist Keynes pointed out) organic systems can increase (as well as decrease) and so the income is not fixed but dependant on how it is re-invested in the system. If one has a couple of cockroaches hiding under one's fridge -then one soon discovers that sometime the problem with organic systems is not their tendency to decay and become scarce -but their tendency to reproduce and multiply themselves into abundance. Perhaps, in an economy based on "organic" systems -an economy of abundance would be more appropriate.

### 4.0   Linear and Non-Linear Systems:

In Euclidian/Newtownian space the characterisitcs of the space involved does change over time -wheras in time/space the state of the space itself changes over time and this in turn can affect the way objects behave as they pass through the space. The time/space becomes both modified and modifier.

If the main difference between Euclidian/Newtownian space and Einsteinian/Turing space involves an interactive feedback between the space and the process or object that "navigates" that space -then a change in the conceptual nature of space must have some implications for our traditional (mechanistic) view of cause and effect which generaly sees a rigid conceptual distinction between "that which is moved" and "that which does the moving".

If cause and effect become intertwined (and constantly fed back into each other) then the outcome is not so easilly predicted. Just as an interaction between observer and observed -an interaction between cause and effect does not deny the importance of the principle of "causality" -but it does make its outcome less obvious.

A simple "linear" extrapolation is not so reliable in time/space as it is in Euclidean space -although even there, there may be an infinite number of curves that connect any set of specified points.

### 5.0    Computational Space:

(Multi-Dimensional) Space Thinking:
(The periodic Table of Elements)

The "computability" problem perhaps lies at the heart of the difference between "artistic' and "scientific" problem solving..... because "scientific" questions are supposed to be decidable in terms of 'true" or "false" -while artisitc problems are generally more ambigous as to both their interpretation and their truth value  -and may not  be interested at all in the question of  "proof"....

### 6.0   Mapping Spaces:

A separation of the "read" and "write" procedures allows the concideration of "mapping" between different spaces by "reading"in one (conceptual) space and "writing" in another.

### 7.0   Conscious Intelligence:

Presumably, the process of mapping between different conceptual space and the use of "computational models" for prediction and control brings us into the realm of intelligence.

If "Consciousness" is a (perhaps primitive) form of feedback based "self-awareness" which is linked to "intelligence" -then the time/space machine may prove to be a useful model for exploring conciouness and intelligence.

Indeed, practical experience with the human "thinking" process suggests that perhaps the human mind operates more in terms of complex interactions between various (emotional and intellectual) "force-fields" -and less on the basis of "rational (binary) logic" than our (Classical Greek) cultural heritage seems to assume.

## III. Constructing the Turing Machine (Defining the Space):

Basic Implementation Process:
•    -Space Definition    (Creative Process -Epistemology -Taxonomy)
•    -Space Processing   (Transformational Process -Projection, Calculus and Prediction -Rules and Patterns)
•    -Space Mapping      (Interpretation Process  -Converting data to Information -Ontology)

### 1.0     Space Definition(s):

Defining the Universe (Taxonomy):
(number of dimensions/components)
(domain/viewpoint)

### 2.0     Space Processing:

Transformations within Space

### 3.0   Space Mapping:

i.  Defining Domains
- Contexts & Contents
- Self & Others
- Organism & Environment
- Inside & Outside
- Figure and Background
- You and Me

- Perception
- Cognition

- Active,  Passive
- past, present, future
- natural, artifical
-  known, unknown
- real, imaginary
- physical, mental

ii.  Transformations between Spaces
-Changing Dimensions
-Changing Metric and Scale
-etc...

iii.  The Interpretation Process (Transformations between Domains)
- Data
- Information
- knowledge
- Understanding
- Wisdom

("spirituality", "conciousness" and "intelligence -including the relationships between them)

## IV. Implementing the Turing Machine (Articulating Space)

Different Models of Articulation and Application:

The Sonological Process:
-Data Aquisition  (Problem Definition)
-Data  Reduction (Theory Forming)
-Theory Testing   (Mapping into "subjective" Space) (interpretation, testing,  creative feedback)

Other (Potential) Parameter Systems:
- Ends (Dreams) and Means (Realisations)
- Pragmatic Striving for:
-the Existing
-the Potential
-the Desirable
-the Undesirable (for others)
- Media, Methods, Meanings
- Tool, Medium, Metaphor
- Alphabet, Grammar, Interpetation
- Stomach, Mind, Language
- Space, Articulation, Mapping
- Actors, Goals, Environments
- Aims, Strategies, Logistics

### Towards a Generalised Model:

• - Specifications:    (Taxonomy of Alphabets, Topology of Spaces and sub-Spaces, Connectivity of  Concepts, etc.)
• - Articulations       (Process, Grammar, Calculation and Divination, etc.)
• - Interactions         (Control systems, Interpretational systems,  Ecological, and Social systems, etc.)
• - Equilibria            (Aesthetics, Entropy, Sustainability, etc.)

Trevor Batten
<trevor at tebatt.net>
July 2003
September 2005/
Feb/April 2006