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 One can construct a model of two independent Turing machines allowing of a series of relevant interpretations: Language Quantum computer Representation and metaphor Reality and ontology In turn that model is based on the concepts of choice and information

1. How to make a home quantum
computer

2. • 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

3. 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

4. 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

5. 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

6. 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

7. 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 ...

8. 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

9. 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)

10. 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)

11. 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

12. 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

13. 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

14. 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

15. 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)

16. 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

17. 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

18. 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)

19. 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

20. 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

21. 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”

22. 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

23. 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

24. 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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