INTRODUCTION:
There are many studies reporting differences between
the female and the male brain1-3. However, it has also been reported
that the existence and direction of sex/gender differences may depend on
environmental events and developmental stages4,5. Moreover, human
brains do not belong to one of the two distinct categories: female or male5.
There is a strong possibility that the functional gender differences of the
brain may be attributable more to environmental factors than to one's gender.
Here, the processes of adapting to one's environment have been demonstrated
through Piaget's developmental theory6 and explained by the chaos
theory7.
A conclusive type thought such as the male
brain is equivalent to a fixed state in chaos theory, and a default type
thought such as the female brain is equivalent to a chaotic state. Both fixed
state and chaotic state change according to changes in the variables of chaos
theory. Thoughts change with environment because the changes in variables are
equivalent to changes in the environment. For example, Nightingale's brain was
the fixed type. This is an example of how using "gender" to describe
the types of thoughts in the brain is incorrect. And the conclusion that
Nightingale's brain was the male type should not be permitted.
In human life, the ability to adapt to
environments may be more useful than gender differences. In this report, gender
differences of the brain are explained as fixed type thoughts and chaotic type
thoughts.
METHOD:
Definition of female/male type brain:
Sexual differences in the human brain
functioning have been reported8. According to the traditional
viewpoint, female brain is the default type, and male brain is a deviation from
the default type. The former is called the "female brain" and the
latter the "male brain." The sexually dimorphic views about human
behavior, cognition, personality, attitudes, and other gender characteristics
have also been reported2. In this paper, these definitions of the
female brain and the male brain are used.
Definition of chaos theory:
The definition of chaos theory was reported
as below7.
Chaos theory can be defined as "the
qualitative study of unstable a periodic behavior in deterministic non-linear
dynamical systems"9. Chaos theory is a part of complexity
theory that concerns itself with nonlinear dynamic systems whose behavior does
not follow clearly predictable and repeatable pathways. In linear systems, the
relationship between an environmental factor and system behavior is predictable
and easily modeled.
As the presence of an environmental factor
increases, system behavior changes linearly in response to it. In contrast,
behavior in chaotic systems might be perceived as unpredictable10.
In this regard, it is important that such a chaotic state is not confused with
the term "random." In mathematical terms, "random" means
the "statistics governed by or involving equal chances for each item"
(New Oxford American Dictionary).
Relation between continuous co variation
and chaos theory:
A necessary condition of chaos theory is
continuous co variation and more than three variables. In Yanagisawa's paper10,
continuous co variation is related to chaos theory. The basic concepts are
outlined below. A representative chaos equation is expressed as:
(1)
In Equation (1), three variables are Y (n +
1), Y (n) and "p." The relation between Y(n + 1) and Y(n) is a
continuous co variation. Equation 1 is equal to the following two equations:
(2)
(3)
Here, since the calculations in Equations 2
and 3 are alternately repeated, the solutions to X (n) and Y (n) are in an
ordered spiral state. Once Y (n) is a determined, Y (n + 1) change according to
Equation 1. However, once Y (n + 1) moves to the position of Y (n) in Equation
1, Y (n + 2) also changes. Thus, Y (n) can never settle into its original
pre-chaotic value. This relation indicates that once a variable has changed
into another, it cannot return to its original value, and the correlated
variable relationship (equivalent to covariation) becomes unsettled. Hence, the
covariant relation between Y (n) and Y (n + 1) in Equation 1 may sustain the
chaotic state. If the variables are uncorrelated, a chaotic state cannot be
established. As the parameter p changes from 3.0 to 3.56995 [called the
Feigenbaum point11], the number of fixed points in Equation 1 varies from 1 to
2 and eventually to 4. Below the Feigenbaum point, the solution Y (n)
converges, while above the point, it splits into a localized state and a proliferating
chaotic state. The solution does not converge in the chaotic state.
A logistic map of Equation 1 is shown in
Figure 17. The vertical axis is Y (n), and the horizontal axis is
"p." The border point between convergence and a chaotic state is
called the "Feigenbaum point" in the dotted vertical line M in Figure
111. The number of fixed points in Equation 1 changes to 1 (Part P),
2 (Part Q), and 4 (Part R). Fixed points are equivalent to "linear"
in the definition of chaos theory. When "p" is less than the
Feigenbaum point, the answer converges. When "p" is greater than the
Feigenbaum point, the answers change to the localized (near the right part of
point M) and proliferated (Part S) chaotic states. In Figure 1, when
"p" is 3, points A and B are 0.16 and 2/3, and when "p" is
4, points D and E are 0.16 and 2/3.
Definition of complete and incomplete fixed
state:
The phenomena with absolutely no change are
considered to be complete fixed state. The 5W1H (who, when, what, why, where,
and how) is unnecessary in it. Mathematics and past facts including
descriptions are examples of fixed state phenomena.
(4)
In Equation 4, "p" of Equation 1
is 3. Because the solutions led from Equation 4 cannot change to chaotic state
with other variables, they are complete fixed state. There is no variable being
equivalent to environment factor such as "p" of Equation 1.
Therefore, Equation 4 exists outside chaos theory.
However, the fixed state within the
framework of chaos theory can change into the chaotic state. In Equation 1, the
solutions of Y (n) are fixed state when "p" is smaller than the
Feigenbaum point, but they are considered to be chaotic state when
"p" is larger than the solutions. Therefore, fixed state within chaos
theory is incomplete.
Social laws and physical laws are examples
of this. Social law and physical phenomena change with environmental change;
however, the 5W1H is almost unnecessary in incomplete fixed states when the
environmental change is very less. The difference between complete fixed state
and incomplete fixed state was explained with Equation 1 and 4 in this report.
However, the solutions led from Equation 1 do never change with environmental
factor and are always shown as Figure 1. The existence of incomplete fixed
state and chaotic state is merely shown in chaos equations being complete fixed
state. Chaos theory was proved with mathematics existing outside it.
Relation between chaos theory and the
female/male brain:
The female/male brain paradigm is
equivalent to chaotic/fixed type thoughts. Some representative examples of
chaotic/fixed type thoughts are shown below. In reality, chaotic/fixed type
thoughts cannot be separated into two categories because they coexist in individuals.
People who have fixed type thoughts are
more interested in fixed factors such as mathematics, law, price, position in
society, position in space, point in time, and common consensus, compared with
variable factors. They try to achieve a specific solution as fixed state.
Therefore, positions in space and time are strictly observed, and the content
of thoughts is most important in fixed type thoughts. A common consensus is
pursued in communication. In contrast, people with chaotic type thoughts attach
greater importance to continuation of communication. A common consensus is not
always necessary in continuation of chaos phenomena; therefore, people with
fixed type thoughts will likely be confused by chaotic contents with no
specific solutions. As a result, they may not be open to the viewpoint of
others who claim that a specific solution may be unnecessary.
In Figure 1, when "p" is 3, point
B is the correct solution and point A is incorrect. The presence and lack of
common consensus are equivalent to the points B and A, respectively. It means
that people with fixed type thoughts judge the content with no common consensus
as wrong. Therefore, the question "Why men don't listen?"12
should be corrected to "People with fixed type thoughts are not interested
in chaotic contents with confusion."
On the other hand, people with chaotic type
thoughts are interested in variable factors such as fashion, color, and speech.
In the chaotic state, there is always continuous co variation and solutions
always change with the change in environment. No solution is ever the same;
therefore, variable factors are very important in chaotic type thoughts. Fixed
factors are unimportant because of the constantly changing state. Only 5W1H
with high degrees of change are recognized as important. As people with chaotic
type thoughts have no fixed conceptions, their own opinion is decided in
relation to other people person. They seek opinions from their partners; they
consider something that they hear numerous times as the truth. An act of
communication is most important in chaotic type thoughts, as it sustains the
continuous co variation that is the necessary condition of chaos phenomena. A
common consensus is not always pursued in communication, because, in chaotic
type thoughts, the continuation of communication is the most important and
communication of completely different contents is forgiven. Therefore, it is
possible that domestic violence is misunderstood as an outcome of
communication. What is important is that communication does not stop in a
chaotic state. Since continuous co variation is required in chaos phenomena, a
chaos phenomenon is destroyed with an interruption in communication.
Individuals with chaotic type thoughts are most afraid of the interruption of
communication, so they never willingly stop communicating. Moreover, it is
understood that people with chaotic type thoughts can listen. In this context,
"listening" means "no interrupting hearing with no understanding
contents." Time and position in space are recognized very loosely in
chaotic type thoughts.
Points D and E are the correct solutions
when "p" is 4 in Figure 1. Point E is equivalent to the fixed correct
solution when "p" is 3. Point E is merely one of the many correct
solutions in chaotic state. It means that people with chaotic type thoughts are
not always interested in the fixed phenomenon. Therefore, the question
"Why Women Cannot Read Maps? 12 should be corrected to "People with
chaotic type thoughts are not interested in the strict space position."
The solutions of Y (n) exist from 0 to 1
when "p" is 4 in Figure 1. All numbers of "n" are
completely different. In this case, "n" is equivalent to time, and
differences across the "n"'s are unnecessary because all solutions
are correct. Therefore, people with chaotic type thoughts can understand all
solutions with different times as those with the same time. People with chaotic
type thoughts can collect many parts with different space and time and draw a
picture from their medley, even though the picture may look unrealistic.
Different recognitions of responsibility in
chaotic/fixed type thoughts:
Any solution except it is considered
incorrect because only fixed solution is correct in the fixed state. Therefore,
people with fixed type thoughts feel responsible for incorrect results. However,
all solutions of a predetermined range are correct in the chaotic state. There
is hardly any incorrect solution for people with chaotic type thoughts.
Therefore, they do not always feel responsible for the incorrect results. They
rarely feel responsible and dislike bearing any responsibility. They may say
something like "I am not causing the problem," and they very much
dislike being a villain. People with fixed type thoughts need to exert
particular effort to exercise this trick. The person causing the problem could
be anyone except the one with chaotic type thoughts uttering this sentence.
A person with fixed type thoughts must
always bear the responsibility of a person with chaotic type thoughts; however,
because people with fixed type thoughts have poor communication skills, people
with chaotic type thoughts must always facilitate the communication of those
thoughts.
Explanation of chaos theory for the
acquisition of sexual differences:
Every individual with fixed type thoughts
has different conclusive opinions. If these individuals do not compromise,
their community will be destroyed. Differences in opinion with no compromises
lead to battles. Unification of opinions is demanded in society, and each
person must compromise to a certain degree in order to continue communication.
The degree to which compromises are made is decided in relation to others.
In Figure 1, each possible compromising
degree in part P, the right part of M, and part S is none, small, and large.
Part S with very large compromising degree is equivalent to the female brain;
however, there is no social unification in the female brain because of
unnecessary common consensus. Therefore, a society where there are only female
brains appears to be in peace; however, a society with no leadership is
vulnerable to destruction by an outside enemy. A leadership with male brains is
always necessary for the continuation of society; it is very difficult for the
female or the male brain to sustain a society without each other.
Both the female and the male brain are
necessary in human life, and they cannot be classified in two distinct
categories. In Figure 1, the right part of M with a small compromising degree
is located midway between the fixed state and the proliferating chaotic state,
and change to each state is continuous. Therefore, change in human thought is
continuous and is related to environmental factors, including other people.
Such change process was reported to have equilibrium and convergence to the
environment in Piaget's developmental theory13.
Human development is a process of
adaptation to converge with the environment. Its process is shown as change
from part S to part P in Figure 1, and Piaget's theory was explained by the
chaos equation7.
Relationship between Nightingale's work and
the female/male brain:
Nightingale reformed the social system in
the nursing profession14. She implemented a method that altered the
practice of medicine by applying the scientific method to describe hospital
conditions using statistics. Her influence extended beyond Britain and spread
across the world and into the future.
All types of thoughts are permitted during
the chaotic state. If Nightingale's brain was the chaotic type, she would have
permitted the miserable state of the Crimean War to continue. However, she
changed the social system in Britain. Therefore, it is concluded that
Nightingale's brain was the fixed type. Because of her high influence, the
author concludes that Nightingale's brain was the super-fixed type. If she was
described using the old gender stereotypes of the brain, her brain would be equivalent
to the male brain.
However, the conclusion that Nightingale's
brain was the male type should not be permitted. This is an example of how
using "gender" to describe the types of thoughts in the brain is
incorrect. Nightingale demonstrated excellent communication skills with many
patients and nurses during the Crimean War. This indicates that she had
fixed-type brain and also used the skills of chaotic-type brain.
DISCUSSION:
Gender differences of the brain in the
traditional sense are conclusive because gender cannot be changed. According to
this conclusive understanding, an individual may feel that trying to change
his/her ability would be a challenge.
However, gender differences are part of
environmental differences and chaos theory. Apart from one's gender, there are
many factors that a person can change in one's environment. According to a
non-conclusive understanding of chaos theory, a person may feel that it is
easier to develop a different ability. This author believes that the brain's
ability to adapt to environments is more powerful than gender differences, a
hypothesis that does not contradict Piaget's theory7.
According to chaos theory, imbalanced
social thoughts will be corrected over time. People with the female brain can
contribute to the society without females, while people with the male brain can
contribute to the society without males. The concept of female/male brain is
required in society, and having a single type is disadvantageous to the
continuation of society. Communication will be destroyed in only fixed type
thoughts.
On the other hand, society will be confused
because it will not be unified solely with the thoughts of the proliferating
chaotic type. There is peace inside; however, the society is vulnerable to
attacks from the outside. Chaos theory's claim that change between the fixed
type and the proliferating chaotic type is possible with environmental change
is more beneficial to society than the traditional biological view of the
brain.
Brain type will never be decided solely
based on gender differences; therefore, it seems right that the distinction
between the female and the male brain is replaced with a distinction between
chaotic versus fixed type thoughts.
Nightingale is equivalent to a male brain
because of her grand works. However, the expression that Nightingale's brain
was a male type will not be permitted. Using "gender" to describe the
types of thoughts in the brain is incorrect.
CONCLUSIONS:
Gender differences of the brain in the
traditional view have become conclusive because gender cannot be changed. In
this new research, an alternative to the traditional view was reported. In
chaos theory, gender differences of the brain are understood as part of one's
adaptations to the environment. The ability of the brain to adapt to various
environments is more powerful than gender differences. It does not contradict
Piaget's theory. From a chaos theory viewpoint, a person may find it easier to
try to develop a different ability. Nightingale's brain was the fixed type. Using
"gender" to describe the types of thoughts in the brain is incorrect.
To avoiding misunderstandings, the female brain and the male brain should be
referred to as chaotic type thoughts and fixed type thoughts.
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