How to make a home quantum computer

• Bulgarian Academy of Science: Institute for the Study of Societies and Knowledge: Dept. of Logical Systems and Models vasildinev@gmail.com

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

eality as if is doubled in relation to language

e 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

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

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

he one counterpart of reality is within the language as the representation of the other counterpart of reality being outside the language and existing by itself

hey are represented as two Turing machines

ny state of the pair of them is a value of information

hen they turn out to be in one and the same state at last: that information is minimal and equal to entropy

urthermore, this is the state of equilibrium for the difference between the states of the two computers converges to zero

oth representation and metaphor are called

to support the correspondence between the two twins as an “image and simile”

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

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

he mechanism of that correspondence and its

formal conditions are investigated as a formal and ontological model of language

ne 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”

eality is just the state of “agreement”, which is

modeled by the state of equilibrium of the two computers

anguage is modeled by reducing to any infinite countable set (A) of its units of meaning, either words or propositions, or whatever others

hat language is furthermore modeled in the computers in a few steps:

he units of meaning are reduced to the minimal possible ones, bits

he 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 ...

hat 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

his 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”

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

he external twin of reality is introduced by another

set (𝐵) such that its intersection with the above set of language to be empty

he union of them (𝐶 = 𝐴 ∪ 𝐵) exists always so that a one-to-one mapping (𝑓: 𝐶 ↔ 𝐴) should exist under the condition of the axiom of choice

he mapping (𝑓) produces an image (𝐵 (𝑓)) of the latter set (𝐵) within the former set (𝐴).

hat image (𝐵 (𝑓)) 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 𝐵)

One designates the image of B into A through f by “B(f)” so that B(f) is a true subset of A

Defining : 𝑨 ∪ 𝑩

(𝟏:𝟏)

n 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

ndeed 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”)

he 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

f the axiom of choice does not hold, the relation

between the sets B (f) and B cannot be defined unambiguously

hen the vehicle between the two twins can be only metaphor

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

ny 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

he 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”

hen each of them is a different

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

his means an infinite set of Turing machines,

each of which “interprets” the external “twins” differently

he representation seems to be vague, defocussed,

after which the image is bifurcate and necessarily described by some metaphors within the language

nly 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

hat is the case because “two infinities” can be

equated to a single one

onsequently reality is in an indefinite, bifurcate

position to language according to the choice formalized in the axiom of choice:

s ontology, it is within language

s reality properly being represented in language, it is out of language

hat extraordinary property of the relation of reality and language can be modeled as involving

nfinity, or

wo independent “finitenesses” (for the two Turing machines)

f choice is granted, the language generates

an exact image of reality in itself, and reality is outside of it

f not, only some simile can exist expressible within

it only by metaphors, and reality and language merge into each other into ontology

he 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

f the axiom of choice does not hold, language

and reality converge, e.g. as ‘ontology’

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

n 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

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

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

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

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

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

hus the state of equilibrium between the two Turing machines can be interpreted as both:

ontinuous transition between them

ynchronization between them

epresentation can be defined as a one-to-one

mapping between two infinite sets:

he one for reality

he other for its image

han language can be formally defined by the representation

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

nd vice versa: Language is the natural

interpretation of that model

f there are available any infinite set whether

“numbers” or “words”, one can utilize it to build a language

owever this can realize even practically

sidestepping for infinity

ny two finite sets merely postulated as

independent are sufficient

hose two finite sets are interpreted in

philosophy as the “things” and “words”

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

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

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

athematics turns out to be a kind of language

literally

t can be grounded formally on language as a theory of language at all

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

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

ne can construct a model of two independent Turing machines allowing of a series of relevant interpretations:

anguage

uantum computer

epresentation and metaphor

eality and ontology

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

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