Representation & Realityby Language (How to make a home quantum computer)

Representation & Realityby Language

How to make a home quantum computer

Vasil Penchev• Bulgarian Academy of Science: Institute for the Study

of Societies and Knowledge:Dept. of Logical Systems and [email protected]

16:45 - 17:15, June 27th , University of Istanbul, Room “C”5th Congress in Universal Logic, University of Istanbul, Turkey, 25-30 June 2015

From Reality to Doubling

Reality as if is doubled in relation to language

We will model this doubling by two Turing machines (i.e. by usual computers) in a kind of “dialog”: the one for reality, the other for its image in language

The two ones have to reach the state of equilibrium to each other

At last, one can demonstrate that the pair of them is equivalent to a quantum computer

The concept of information as “twins”

The one counterpart of reality is within the language as the representation of the other counterpart of reality being outside the language and existing by itselfThey are represented as two Turing machinesAny state of the pair of them is a value of informationThen they turn out to be in one and the same state at last: that information is minimal and equal to entropyFurthermore, this is the state of equilibrium for the difference between the states of the two computers converges to zero

Representation & Metaphorin terms of Information

Both representation and metaphor are called to support the correspondence between the two twins as an “image and simile”

Representation being an “image” means that the computers are absolutely independent of each other, or “orthogonal to each other”.

Metaphor being a “simile” means that is not the case: the computers are partly dependent on each other and thus non-orthogonal to each other

The model of & by Language

The mechanism of that correspondence and its formal conditions are investigated as a formal and ontological model of language

One can use the metaphor that reality and its image in language “speak to each other” in a dialog in order to “agree with each other”

Reality is just the state of “agreement”, which is modeled by the state of equilibrium of the two computers

Language as potential infinity

Language is modeled by reducing to any infinite countable set (A) of its units of meaning, either words or propositions, or whatever othersThat language is furthermore modeled in the computers in a few steps:The units of meaning are reduced to the minimal possible ones, bitsThe infinite countable set is modeled by the independence of the same pair of each other: So infinity is represented by its “gap” to finiteness just a second dimension ...

The Tandem over the “Gap”

That infinite countable model of language includes all possible meanings, which can be ever expressed rather than the existing till now, which would always a finite set

This corresponds to the independence, the “gap” between the computers, which can be overcome by each of them only in an infinite set of working steps determining the value either “0” or “1” for each cell of an infinite “tape”

However, the tandem of both, i.e. in dialog can overcome that gap in finite set of steps

The set-theory modelThe external twin of reality is introduced by another set such that its intersection with the above set of language to be emptyThe union of them exists always so that a one-to-one mapping should exist under the condition of the axiom of choiceThe mapping produces an image of the latter set within the former set . That image serves as the other twin of reality to model the reality within the language as the exact representation of that reality out of language (modeled as the set )

The set-theory modelOne designates the image of B into A through f by “B(f)” so that B(f) is a true subset of A

A

B(f) Bf

Defining :f

The Axiom of ChoiceIn the model, the necessity and sufficient condition of that representation between reality both within and out of the language is just the axiom of choice

Indeed one needs only two well-ordered infinite series equivalent to the axiom of choice by the meditation of the so-called well-ordering theorem (or “principle”)

The pair of the two Turing machines though each of them being finite can represent effectively the two infinite series by the relation of independence to each other

The axiom of Choice between Representation & Metaphor

If the axiom of choice does not hold, the relation between the sets B (f) and B cannot be defined unambiguously Then the vehicle between the two twins can be only metaphor

This corresponds to the case where the Turing machines depend partly on each other or share some infinite segment of their “tapes”:

Any operation of any of both machines within that segment is necessarily valid for the other one, and this is not true out of that segment

Metaphor asa Set of Representations

The metaphor can be anyway defined to a set of one-to-one representations of the only similar external twin into a set of internal “twins”Then each of them is a different

interpretation of the external “twin” so that a different metaphor is generated in each case

This means an infinite set of Turing machines, each of which “interprets” the external “twins” differently

Metaphor as a Bifurcation of Representation

The representation seems to be vague, defocussed, after which the image is bifurcate and necessarily described by some metaphors within the language

Only the infinite set of Turing machines, each of which is a different interpretation of the external “twin”, can be exhaustedly represented as the two initial Turing machines being independent of each other

That is the case because “two infinities” can be equated to a single one

Uncertainty of Reality to Language

Consequently reality is in an indefinite, bifurcate position to language according to the choice formalized in the axiom of choice:oAs ontology, it is within languageoAs reality properly being represented in language, it

is out of language

That extraordinary property of the relation of reality and language can be modeled as involving o Infinity, or oTwo independent “finitenesses” (for the two Turing

machines)

Choice between Image & Simile

If choice is granted, the language generatesan exact image of reality in itself, and reality is outside of it

If not, only some simile can exist expressible within it only by metaphors, and reality and language merge into each other into ontology

The two above cases correspond in the Turing- machines model to their independence and partial dependence according to zero or nonzero correlation between the alternatives of choice

The axiom of choice between Reality and Ontology

If the axiom of choice does not hold, language and reality converge, e.g. as ‘ontology’

This corresponds to some common infinite segment between the “tapes” of the two Turing machines

In that segment, both machines as if merge into a single one for the operation of each of the predetermined the operation of the other one

Then the gap of independence modeling that gap between finiteness and infinity does not exist

Ontology as the Unification of Language and Reality

Ontology utilizing metaphors can describe the being as an inseparable unity of language and reality within language

This abandons both representation and conception of truth as the adequacy of language to reality

However, the state of equilibrium of the two Turing machines can be interpreted both in terms of representation (reality) and metaphor (ontology)

Metaphors as Reality

Those metaphors in ontology should coincide with reality (and with physical reality in particular) just in virtue of the ontological viewpoint

Thus the state of equilibrium between the two Turing machines can be interpreted as both:oContinuous transition between themoSynchronization between them

Language as a Set of Representations

Representation can be defined as a one-to-one mapping between two infinite sets:

The one for reality

The other for its image

Than language can be formally defined by the representation

This means that pair of the two independent Turing machines can defined a formal model of language at all

The Things and WordsAnd vice versa: Language is the natural interpretation of that modelIf there are available any infinite set whether “numbers” or “words”, one can utilize it to build a languageHowever this can realize even practically sidestepping for infinityAny two finite sets merely postulated as independent are sufficientThose two finite sets are interpreted in philosophy as the “things” and “words”

Representation as a Linkbetween Human Being and Machine

The advantage of that approach is to link the representation of the human being to the representation by a machine (e.g. a computer)

Furthermore, the pair of Turing machines can be interpreted as a single quantum computer (quantum Turing machine, in which all bits are replaced by qubits)

Then, the concepts of language, reality, and ontology can be thoroughly defined it terms of that quantum computer

Mathematics groundedon Language

Mathematics turns out to be a kind of language literally

It can be grounded formally on language asa theory of language at all

The concept of information as the quantity of choices is what links language and mathematics fundamentally

If information is granted both mathematics and language can be inferred rigorously from its properties if they are relevantly axiomatized

A Few Main Conclusions:

One can construct a model of two independent Turing machines allowing of a series of relevant interpretations:o Languageo Quantum computero Representation and metaphoro Reality and ontology

In turn that model is based on the concepts of choice and information

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