Mathematical definition of public language and modeling of will and consciousness based on the public language Hana H ebishima Mina Arakaki Chikako Dozono Hanna Frolova Shinichi Inage

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Mathematical definition of public language, and modeling of will and consciousness

based on the public language

Hana Hebishima, Mina Arakaki, Chikako Dozono, Hanna Frolova, Shinichi Inage

To propose a mathematical model of consciousness and will, we first simulated the inverted qualia

with a toy model of a neural network. As a result, we confirmed that there can be an inverted qualia

on the neural network. In other words, the qualia were individual-dependent and considered difficult

as an indicator of consciousness and will. To solve that difficulty, we introduce a probability space and

a random variable into a set of qualia and define a public language for events. Based on this idea of

public language, consciousness and will are modeled. In this proposal, future actions are randomly

selected from the comparison between "recognition of events" by external observation and past

episodic memory, and the actual "recognition of actions" is regarded as the occurrence of consciousness.

The basic formula is also derived. This proposal is compared with other past philosophical discussions.

Key words: conscious, will, mathematical model, probability space, information entropy

1. Introduction

This paper is concerned with the mathematical definition of public language and the model of

consciousness derived from it. Modeling of consciousness is an important topic, and the relationship

between the conscious realm and its physical realm has been studied and developed over the centuries,

involving not only scientists but also philosophers and theologians (Bill Faw, 2014). Examples of

models of consciousness include the Global Workspace Theory (Stanislas Dehaene et al., 1998),

Multiple Draft Theory (Daniel C Dennett, 1993), Higher Thought Theory (Peter Carruthers, 2016),

Dehaene - Changeux model (Dehaene S, Changeux JP, 2000), Integrated Information Theory (Tononi

G, 2004, Masafumi Oizumi aet al., 2014) and many others. There are also many good reviews of those

models (Leonid I. Perlovsky, 2006, Christopher Durugbo et al., 2013), and we won't be introducing

each model sequentially here.

Among those theories, the integrated information theory was proposed by Tononi to quantify

consciousness - especially using the concept of information in information theory. The main purpose

of the program is to quantitatively evaluate the perception of a person as a first-person. Integrated

information theory does not keep in mind the so-called "hard problem of consciousness" but starts

from "consciousness exists" and adopts "information," "integration," "structure" and "exclusion" as

axioms. This system of theories is also of great interest, especially in terms of quantifying the

functions that complex networks produce. The basic concept is that consciousness appears when much

information is integrated, and the degree of integration is expressed by the integrated information

quantity:Φ. The Φ is defined for a set of variables that interact and evolve over time, and is a

quantification of how much more information the entire original network produces compared to the

sum of the information produced by the subnetworks that divided the network. For quantification,

we use the concept of Kullback–Leibler divergence, which is also used in this paper.

These many models of consciousness complement metaphysical theories of consciousness, such

as functionalism, identity theory, dialogic dualism, and neutral monism. The following is a summary

of the topics related to this paper.

1.1 Qualia

"A unique texture that cannot be explained by words felt by each individual, caused by subjective

experiences and senses" is qualia. Even if we express our thoughts and feelings in words, they are

essentially things only we can know. For example, let's say a person gets a "bad vibe" when they see

a particular color. It is impossible to communicate and share that specific "bad feeling" with others by

any means. And a hideous color for one person may be a favorable color for another. However, while

we can explain why it is preferable, we cannot verbalize how it is preferable. In other words, because

qualia refer to the very feeling of everyone, it is impossible for others to feel qualia generated within

them in the same way.

Qualia is told with the following two characteristics.

1) Qualia is a subjective feeling gained through individual experience and the difficulty of verbalizing

everything correctly

2) Qualia are extremely personal and subjective and cannot be shared with others, and even if we go

through the same experience, the qualia we gain is incomprehensible to others

Thus, all sensations take place in an individual's brain and do not achieve the exact same qualia

as others.

1.2 Philosophical Zombies

The "philosophical zombie" is a thought experiment designed to counter the physicalism of

qualia and perceptions of consciousness. used by Chalmers, D., to describe qualia (Chalmers, D., 1996).

A philosophical zombie is a thought experiment defined as "a being who behaves like a normal human

being but in fact has no inner feelings." A major characteristic of philosophical zombies is the lack of

qualia. For a philosophical zombie, all emotions and sensations are just part of a brain activity. To put

it simply, a philosophical zombie is an entity that has sensations and emotions as a function but no

sensations and emotions as a reality. Philosophical zombies are said to be unrecognizable because

they look and behave no differently from humans. This is because, as mentioned above, qualia refer

to "the sensations and emotions felt by an individual," and it is impossible to prove whether the other

person has qualia. If it exists but can't be recognized, no one can prove it.

Physicism for consciousness is a monism that ascribes all phenomena to physics. The position is

that the human mind and senses fluctuate due to some physical phenomenon and can be observed as

an activity of the brain, and for this reason, in physicalism, the human mind and qualia are also

regarded as "physical objects."

An opposing position is the dualistic idea that there are objects that can be physically observed

and objects that cannot be physically observed. Even if we try to physically analyze emotions and

sensations, what we can observe is the physical phenomena of the brain, and we can't observe whether

there is "something" other than the physical phenomena of the brain. This leads to the idea that the

essence of the human mind and consciousness cannot be expressed in modern physics, and this is

called the "hard problem of consciousness."

In physicalism, the "mind," such as consciousness and qualia, is taken as a physical phenomenon

of the brain - that is, "the mind is the same as the senses and emotions as functions." If physicalism

is right, we can say that philosophical zombies are unimaginable and "improbable." Physicism,

however, cannot prove why philosophical zombies are improbable, because the physical phenomena

of the brain do not explain why or how the mind arises. Based on this logic, the argument is that

"Physicism is wrong if philosophical zombies are imaginable, and their existence cannot be denied."

1.3 Inverted qualia

Consider, for example, the color red. Observers watching the same sunset: Even if A and B each

recognize the color of the sunset as "red," they cannot confirm whether the private "red" that A and B

recognize is the same. For example, even if A's perceived "red" is considered "blue for A" to B, there is

no problem with A and B's claim that "the setting sun is red." This "inverted qualia" thought

experiment argues that the idea of physicalism cannot explain differences in internal experiences,

such as the appearance and perception of colors among observers.

1.4 Existence of free will

B. Rivett attached a device that measured brain electrical signals to participants in the

experiment and had them move their wrists freely to measure brain electrical signals at that time (B.

Rivet, 1980). When we move our bodies, it is known that electrical signals, commands to move our

muscles, come out of our brains shortly before we move. The results of the experiment were in the

following order.

1)The brain produces electrical signals to move the wrist

2)Conscious to move the wrist

3)Wrist moves

This means that the brain is sending electrical signals to move the wrist before the person is

conscious of moving the wrist, and the wrist is already set to move before the person is conscious of

moving the wrist. In other words, the wrists did not move because he was conscious of moving them.

The normal human feeling that the wrist has moved because he or she wanted to move the wrist by

his or her own will is an "illusion," and before that will, the wrist has been determined to move by

something unconscious, and the command is coming out of the brain unconsciously. In the middle of

the process of moving the wrist, it is a state in which the conscious mind is aware in the pursuit of

"let's move." B. Rivet, between 2) and 3) above, there is a short time left for refusing to move the wrist,

within which man can stop the action at his own will. So, he concludes that human beings have free

will. However, there is no harm in interpreting the results of this experiment by thinking that it is

"consciousness" - i.e., that there is no free will - to recognize the results of unconscious random

processing in the brain as an afterthought. B. Rivet's interpretation of the experiment has been

criticized by dualistic interpreters and others. However, if we take the view of "consciousness" in the

absence of free will, we can assume that the brain unconsciously and randomly processes certain

options based on physicalism. If we consider the post-processing recognition at the stage when the

processing is determined to be "consciousness," we believe that it does not go against physicalism and

does not cause a "hard problem of consciousness.". In dualism, apart from physical phenomena, there

is non-physical "consciousness" that cannot be measured by physics. However, it fails to explain why

and how non-physical consciousness can influence our behavior and the processing of the brain, which

is a physical phenomenon. If consciousness, which is non-physical, can affect physics, we must also

consider the existence of so-called "telekinesis" and the possibility of consciousness in all things, which

seems to make interpretation more complicated.

1.5 Isolated Brains

Isolated brain is a condition in which the corpus callosum connecting the left and right sides of

the brain is removed for the purpose of treating epilepsy, etc. This prevents information from being

exchanged between the left and right sides of the brain. The left side of the brain is primarily

responsible for language areas, while the right side is responsible for imaging areas. If we ask a

subject with a separate brain, showing the subject only to his right eye, which is processed by his left

brain, "What is it?" he can tell. Conversely, if the left eye, which connects to the right side of the brain,

is seen alone, the right side of the brain, which connects to the right side of the brain, answers "I can't

see anything" because it can't process language. On the other hand, if we let him draw a picture of

the subject, his right brain, which controls the image area, can draw without any problem. It is

sometimes said that this separate brain subject has two personalities = consciousness. Considering

this, we think that consciousness is physically dominated, or at least influenced, by the physical state

of the brain.

1.6 Short-term and Long-term Memory

Memories are divided into short-term and long-term memories because of differences in their

temporal duration. Tulving further subdivides this long-term memory into "episodic" and "semantic"

memories. "Episodic memory" is a memory of a personal experience associated with a specific time

and place, and "semantic memory" is defined as a memory unrelated to a specific time and place

(Tulving, 1976). As a classification of long-term memory, "episodic memory" and "semantic memory"

may be combined into "declarative memory" and classified into two separately defined categories of

"procedural memory" (Squire, 1987). Procedural memory, for example, is said to be the memory of

how to ride a bicycle.

FIG. 1: Neural Network Configuration

Table 1: Color representation by RBG

No.

Reference colors

Red

255

Green

255

Blue

255

White

255

Black

Table 2: Learning results when Table 1 is used as input and output teacher signals

No.

Simulated Colors

Input

Output

Red

229

Green

227

Blue

231

White

254

255

253

Black

Table 3: Learning results considering color weakness

No.

Simulated Colors

Input

Output

Red

124

128

Green

124

115

Blue

185

202

255

White

255

Black

Table 4: Learning results when complementary colors in Table 1

are used as teacher signals for output

No.

Simulated Colors

Input

Output

Red

238

Green

245

Blue

236

161

White

255

Black

FIG 2: Comparison of neural network weight coefficients

Many existing models of consciousness seem to focus on first-person consciousness. In this paper,

we first think of the neutral network as a Toy Model of a brain, and we performed a simulation of the

inverted qualia using it. As a result, we show that color blindness and inverted qualia can occur even

in the same network structure only with different values and arrangements of coefficients. On that

basis, we defined second-person consciousness - especially qualia - mathematically and used the

results as axioms to examine the process of creating a physically possible consciousness. We aim to

build a model that can provide some answers to the above 1.1－1.6 questions. Here are the details:

2.Mathematical definitions and modeling of consciousness

2.1 Simulations of Inverted qualia

The possibility of 'inverted qualia' mentioned in the introduction is explored through a

simulation based on a neural network. Neural networks, a type of machine learning that mimics the

function of neurons in the brain, have many applications and achievements as so-called artificial

intelligence. Now consider the three primary colors of red (R), green (G) and blue (B) and the five

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Mathematicaldefinitionofpubliclanguage,andmodelingofwillandconsciousnessbasedonthepubliclanguageHanaHebishima,MinaArakaki,ChikakoDozono,HannaFrolova,ShinichiInageToproposeamathematicalmodelofconsciousnessandwill,wefirstsimulatedtheinvertedqualiawithatoymodelofaneuralnetwork.Asaresult,weconfirmedthat...

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Mathematical definition of public language and modeling of will and consciousness based on the public language Hana H ebishima Mina Arakaki Chikako Dozono Hanna Frolova Shinichi Inage

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