1. interpret the structure.
2. filter the interpretable to the uni...
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1
INTERPRETATION DEPARTMEN
RESEARCH CENTER IN THE X
Partial-complete
mobile interpretation
method (PCMI)
X21, X65, X45, X56
MSCRFA: C (no ref)
Contact (sht): 1J
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DOLU: 20/360/1925
2
Abstract
This study explores the fundamental concepts and methodologies asso-
ciated with interpretation of a complex data construct called Taiga. Taiga
exhibits local interpretability and gradual uninterpretability, prompting
the proposal of the Partially Complete Mobile Interpretation Method
(PCMI). PCMI employs Neumann’s findings on phi constants and con-
ceptual dividers, offering a systematic approach to interpret Taiga.
Contents
1 Introduction 3
1.1 interpretability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Theory of Interpretations 5
2.1 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Efficiency of Interpretations . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Serial vs. One-time Interpretations . . . . . . . . . . . . . . 6
2.3 Creating Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Taiga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Partially Complete Mobile Interpretation Method (PCMI) 8
3.1 Theoretical Description of Taiga Interpretation . . . . . . . . . . . 9
3.1.1 Utilization of an Agent . . . . . . . . . . . . . . . . . . . . . 9
4 Conclusion 9
1 Introduction
Let f be the morphism interpretation that maps element A to B.
f ∶ A Ð→B (1)
Then we say that B is the interpretation of A, where B is the basic form, and A is
the simple form. The fundamental purpose of interpretation is to create a simple
form that is a set of information equivalent to the basic form. Interpretations
are then divided into valid and abstract. Valid interpretation is an interpreta-
tion that is interpretable by our devices [1], and abstract interpretation is not
interpretable by our devices.
3
1.1 interpretability
However, interpretability by our devices is a vague concept that needs to be
formalized. Let lambda constant [2] be a scalar characterizing each set of ele-
ments. Then, the difference in lambda constants between two distinct sets will
express their similarity.
∆λ
A,B
=∣λ
A
−λ
B
∣ (2)
The more similar, the smaller the difference in lambda constants; the more
dissimilar, the greater the difference in lambda constants. We will further refer
to the absolute difference in lambda constants as delta lambda. The lambda
constant of a set of elements A is the arithmetic average [3] of all lambda
constants of all possible combinations of sets of elements B that are subsets of
A. Thus, we introduce the real deviation of lambda constants, which expresses
the similarity of set B to set A, where B is a subset of set A.
∆
r
λ
A,B
=∣λ
A
−λ
B
∣ (3)
Let the lambda interval be a closed interval from the lowest value of the real de-
viation of the lambda constant of set A to the highest value of the real deviation
of the lambda constant of set A.
Λ
A
∶=[min ∆
r
λ
A,B
1
, max ∆
r
λ
A,B
2
] (4)
If we call the set of elements C similar to the set of elements A, then the
intersection of their lambda intervals is non-empty; therefore, C is interpretable
by the set A.
Returning to practical applications, it is important to calculate the lambda in-
terval of all elements interpreted so far [4]. This lambda interval will be referred
to as the Fundamental Interval. If the lambda interval of set B has a non-empty
intersection with the Fundamental Interval, then set B is interpretable by our
devices. For the sake of clarity, we introduce the relative lambda constant.
λ
∗
A
=
λ
A
λ
(5)
where the denominator represents the basic lambda constant, which is the arith-
metic average of all values in the basic interval. Subsequently, we express the
relative fundamental interval as:
Λ
∗
A
=
1
λ
Λ
A
(6)
which can be rewritten as:
Λ
∗
A
=[1 −∆Λ
1
, 1 +∆Λ
2
] (7)
4
where ∆Λ
1
= ∆Λ
2
⇐⇒ ∆Λ
2
≤ 1 and ∆Λ
2
≠ ∆Λ
1
= 1 ⇐⇒ ∆Λ
2
≥ 1. It follows
that we are interested only in the scalar ∆Λ
2
, so we define ∣Λ
∗
A
∣ ∶= ∆Λ
2
, which
we will call the second fundamental criterion.
2 Theory of Interpretations
2.1 Interpretation
Interpretation is performed precisely when the interpreted set of elements A is
not interpretable. The goal of interpretation is to shift the lambda interval of
the basic form A to a position where the difference in lambda constants between
the basic interval and the interval of A is lower. If the simple form is still not
interpretable, then interpretation is applied again. This process is repeated until
the simple form has a non-empty intersection with the fundamental interval.
2.2 Efficiency of Interpretations
It is necessary to measure the efficiency of interpretations. Let elements be sets
of information u
i
. These pieces of information represent the properties of the
corresponding element. During interpretation, there is an irreversible loss of
some information, given that interpretation inherently creates a lighter form of
the interpreted concept.
Let A be the basic form, B be the simple form, and f be the interpretation. The
amount of lost information is determined by the formula:
U
A,B,f
=100 −
λ
∗
B
λ
∗
A
×
1
Ψ
f
×100 [%] (8)
where Ψ
f
is the so-called psi constant, serving as a correction [5]. This constant
can only take real numbers greater than 1. An ideal interpretation is one where
the Psi constant equals one; however, this is a theoretical case and cannot be
found in nature. We will call an interpretation efficient precisely when the loss
is less than 10 percent. This value may vary depending on the purpose of using
the results, but 10 percent is given as the standard for a one-time interpretation.
From the information loss equation, we can derive the following inequality, which
we will call the classical inequality:
90 ≤
λ
∗
B
λ
∗
A
1
Ψ
f
×100 (9)
5
then
0.9 ≤
λ
∗
B
λ
∗
A
1
Ψ
f
(10)
0.9 < Ψ
f
×0.9 ≤
λ
∗
B
λ
∗
A
(11)
0.9 <
λ
∗
B
λ
∗
A
(12)
9
10
×λ
∗
A
<λ
∗
B
(13)
(14)
If we repeat the interpretation process omega times:
f ∶ A
1
Ð→A
2
Ð→... Ð→A
ω
(15)
then the inequality relationship looks like this:
(
9
10
)
ω−1
×λ
∗
A
1
<λ
∗
A
ω
(16)
2.2.1 Serial vs. One-time Interpretations
Serial interpretation is a method that involves repeated interpretation. One-
time interpretation is a single interpretation. Which method is more effective if
they have the same initial form and final form? We will create a mathematical
apparatus to answer this question.
Serial Interpretations Let’s consider a serial interpretation repeating omega
times:
f ∶ A
1
Ð→A
2
Ð→... Ð→A
ω
(17)
then, for each interpretation, we can create the classical inequality:
90 ≤
λ
∗
A
1
λ
∗
A
2
1
Ψ
f
1
×100 (18)
90 ≤
λ
∗
A
2
λ
∗
A
3
1
Ψ
f
2
×100 (19)
. . . (20)
. . . (21)
90 ≤
λ
∗
A
ω−1
λ
∗
A
ω
1
Ψ
f
ω−1
×100 (22)
6
Now, multiplying all these classical inequalities, we obtain the following rela-
tionship:
(
9
10
)
ω−1
ω−1
∏
i=1
Ψ
f
i
≤
λ
∗
A
1
λ
∗
A
ω
(23)
One-time Interpretation Suppose we have a one-time interpretation:
F ∶ A
1
Ð→A
ω
(24)
then the classical inequality, in its adjusted form, will look like:
(
9
10
)Ψ
F
≤
λ
∗
A
1
λ
∗
A
ω
(25)
Comparison Two scenarios may occur:
A ∶(
9
10
)
ω−2
ω−1
∏
i=1
Ψ
f
i
<Ψ
F
(26)
B ∶(
9
10
)
ω−2
ω−1
∏
i=1
Ψ
f
i
>Ψ
F
(27)
In scenario A, it is more efficient to use the one-time method, and in scenario
B, the serial method is more effective.
2.3 Creating Interpretation
Interpretation is, in theory, the simplification of the original concept for per-
ception by our devices. This implies that we need to know the original concept
without fully understanding it. For these purposes, an interpretor tool is used.
It converts axiomatic systems of uninterpretable sets of elements into interpre-
tations containing information about axiomatic systems in the form of encoded
parameters. These parameters are then used to create a simple form of inter-
pretation, either through a serial or one-time method, depending on the case
when the final form is a valid interpretation.
2.4 Taiga
All data structures except Taiga have a certain degree of homogeneity. [6] Taiga
is a data construct that has unusually different properties, preventing its inter-
pretability [7]. Many observers consider this a failure of current knowledge [8].
Others see it as another possible step in exploring the interpretational bound-
aries, metaphorically enclosing all data constructs into one structure, which is
one of the hypotheses explaining Neumann’s paradox ”If we observe data con-
structs created independently, why are they similar?”. [9][10] Many observers
7
do not consider this form of the paradox as valid, assuming that data constructs
were created independently [11], which is not the correct direction for interpret-
ing this paradox. The point it tries to convey is ”Where are the uninterpretable
objects?”. [12]
It has been found that Taiga is locally interpretable, meaning only a certain part
of this structure can be interpreted. [13] It has also been found to be gradually
uninterpretable, meaning the degree of uninterpretability increases as we go
deeper into the structure. [14] Based on these findings, I propose a method for
interpreting Taiga. Subsets of Taiga will be called Omega structures.
3 Partially Complete Mobile Interpretation Method
(PCMI)
PCMI is a method that utilizes the conceptual divider technology [15]. This
method is known to almost all observers, so I won’t delve into the mathematical
apparatus that describes it. This method uses Neumann’s results on differences
in similarities and the distribution of the phi constant of the interpretation
device Alfa-02 [16]. I quote, ”The graph of differences in interpretations to
the original structure dependent on the phi constant shows the occurrence of
sectors that meet the relative basic interval. Practical sectors are Alpha, Beta,
and Gamma sectors. Due to the probability distribution of the phi constant,
Alpha is the most effective and hard to reach, Beta is generally harder to reach
than Alpha, and at the same time less effective than Alpha but still usable.
Gamma is the most probable sector, and therefore the least efficient.”
The method consists of 5 fundamental steps that can be spatially adjusted to
increase efficiency for specific utilization situations.
1. Step C: One-time interpretation, in case there was a step P before this
step, it is a one-time interpretation of all subsets of the structure before
step P.
2. Step P: Using the interpretation divider to divide the structure into any
number of subsets.
3. Step E
n
: A filter that filters interpretable structures from the product of
the previous step; in case they are not in the relative basic interval, they
are sent back as the product of the n-th step.
4. Step F
n
: This step filters structures based on their phi constant values;
if they do not meet the mode of the currently used method, they are
returned as the product of the n-th step.
5. Step T: This step is the opposite of P; in this case, however, we combine
all subsets and create a single structure.
8
The most effective method for exploring Taiga is P CE
1
F
1
T [17], in this exact
order. [18] Modes of settings are filters that filter structures with a phi constant
having a value falling into a specific interval. There are two modes. Alpha
mode, which allows structures with a phi constant in the alpha sector to pass
through. Gamma mode, which lets structures with phi constants in the alpha,
beta, and gamma sectors pass through.
3.1 Theoretical Description of Taiga Interpretation
The goal of this mission is to test the interpretative capability of the local
environment using our current devices. The expected result is the impossibility
of interpreting the local environment.
Under standard conditions (100 Sg, 25 j, 0 tk) on 00/000/1927 of rotational
time, 10 - 15 carriers will be released, who will evaluate the current state of the
union of all omega structures and send the necessary number of agents of type
P CE
1
F
1
T according to Neumann’s algorithm [19], to be evenly distributed with
dependence on local interpretation.
3.1.1 Utilization of an Agent
An agent is a mobile interpreter [20] with the ability to create its optimized
clones. After the agent intersects with an interpretable omega structure, we call
this omega structure a zero iteration. The interpreter creates an interpretation
anchor, which creates a copy of the agent containing information about the
previous iteration. It then interprets the next iteration and creates another
anchor, and so on. These anchors then create a complete interpretation of
Taiga and send it to receivers that will move above the critical interpretational
boundary of Taiga. These receivers will create locally global interpretations,
which will be sent to the British Sea for final evaluation.
U
C
=100 −
⋃
∀p
λ
∗
p
⎛
⎝
ω
p
⋃
u=0
i
∏
j=0
λ
∗
j+1
λ
∗
j
1
Φ
j
A
j
⎞
⎠
−1
1
Φ
p
×100[%] (28)
U
C
is the amount of information lost during the entire method. p in the subscript
refers to the receiver. ω
p
is the number of agents released in an individual carrier.
A
j
is the agent’s correction.
4 Conclusion
This study contributes not only to the theoretical foundations of interpretation
but also offers practical insights for addressing real-world challenges in data
interpretation. As technology evolves, and the complexity of data structures
increases, a deeper understanding of interpretation becomes paramount. The
9
proposed methodologies and criteria provide a stepping stone for further ad-
vancements in the field of interpretation, paving the way for more effective and
nuanced approaches in diverse contexts.
References
10
1. interpret the structure.
2. filter the interpretable to the uninterpretable.
3. then send the interpretable will be sent back.
4. Check their $\phi$ constants. If it diverts from the normal concept it will be sent back.
5. We use the context we know to create (an assumption of) the structure.
hey they didn't cite their sources with proper APA formatting