Modelagem termodinâmica da reflexão e meditação humana

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Progress in Biophysics and Molecular Biology xxx (2017) 1e11
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Progress in Biophysics and Molecular Biology
journal homepage: www.elsevier .com/locate/pbiomolbio
Theoretical modeling of the subject: Western and Eastern types of
human reflexion
Vladimir A. Lefebvre
University of California at Irvine, Irvine, CA 92697, USA
a r t i c l e i n f o
Article history:
Received 27 April 2017
Accepted 2 June 2017
Available online xxx
Keywords:
Reflexion
Meditation
Neural network
Thermodynamics
Chakra
E-mail address: valefebv@uci.edu.
http://dx.doi.org/10.1016/j.pbiomolbio.2017.06.006
0079-6107/© 2017 Published by Elsevier Ltd.
Please cite this article in press as: Lefebvre, V
Biophysics and Molecular Biology (2017), ht
a b s t r a c t
The author puts forth the hypothesis that mental phenomena are connected with thermodynamic
properties of large neural network. A model of the subject with reflexion and capable for meditation is
constructed. The processes of reflexion and meditation are presented as the sequence of heat engines.
Each subsequent engine compensates for the imperfectness of the preceding engine by performing work
equal to the lost available work of the preceding one. The sequence of heat engines is regarded as a chain
of the subject's mental images of the self. Each engine can be interpreted as an image of the self that the
engine next to it has, and the work performed by engines as the emotions that the subject and his images
are experiencing. Two types of meditation are analyzed: The dissolution in nothingness and union with
the Absolute. In the first type, the initial engine is the one that yields heat to the coldest reservoir, and in
the second type, the initial engine is the one that takes heat from the hottest reservoir. The main con-
cepts of thermodynamics are reviewed in relation to the process of human reflexion.
© 2017 Published by Elsevier Ltd.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00
2. Brain, mental phenomena, and thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00
3. Heat engines and reflexion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00
4. Meditation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00
Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00
1. Introduction
In the West, the concept of reflexion appeared in the XVIIIs
century as the ability of a human to have the image of the self in the
mental domain. In the East, two millennia earlier, meditation exis-
ted already, which allowed a human not only to see himself in the
mental domain, but also to govern his body and mental world
conditions. In this paper, we will show that reflexion and medita-
tion can be considered from the single point of view. To do this, we
construct the thermodynamic model of reflexion and meditation.
The second section contains a brief review of works on
.A., Theoretical modeling of th
tp://dx.doi.org/10.1016/j.pbio
thermodynamic processes in large neural networks and introduces
the basic thermodynamic concepts. The third section describes the
thermodynamic model of reflexion, and the fourth section is
devoted to the model of meditation. These constructions represent
the development of the mathematical model of the subject with
reflexion making bipolar choice (Lefebvre, 1992, 1997, 2014). The
model is given by the two equalities:
X1 ¼
x1
x1 þ x2 � x1x2
; (1.1)
e subject: Western and Eastern types of human reflexion, Progress in
molbio.2017.06.006
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V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e112
X2 ¼
x2
x1 þ x2 � x1x2
; (1.2)
where 0 < х1,х2 � 1.
Х 1 is the probability with which the subject is ready to choose
the positive pole; X2 is the probability with which the subject
evaluates his preparedness to choose the positive pole; that is, we
consider that the subject may have an image of the self.
х1 is the probability that the environment makes a push toward
choosing the positive pole at the moment of choice, and х2 is the
average probability of pushes toward the positive pole in the past.
The image of the self may have its own image of the self and so on
(Lefebvre, 1967, 2014).
The diagram of reflexion is given in Fig. 1. The bottom square
represents the subject; the square above it is the subject's image of
the self; the next one is the image of the self that the image of the
self has. Square 2 is what square 1 “knows”; square 3 is what square
2 “knows” and, at the same time, what square 1 “is aware of.” Thus,
in our scheme, “knows that knows” is equal to “is aware of”;
thereby, we distinguish knowledge and awareness. The input to odd
squares is х1, and the output Х 1. The input to even squares is х2, and
the output Х 2. The mathematical model of reflexion allows us to
explain a number of psychological phenomena (see Adams-
Webber, 1987; Lefebvre, 1997).
2. Brain, mental phenomena, and thermodynamics
We all know that human cognition is somehow connected with
the brain, because distortion of the brain's functioning leads to
mental pathology. We also believe, at least in the framework of
science, that the brain's functioning is governed by physical laws.
All this leads us to assume that it is possible to establish a direct
connection between consciousness and the laws of physical reality.
In this section, wewill elaborate a theoretical construction showing
the evident formal correlation between thermodynamic processes
and the model of the reflexive subject introduced in our earlier
Fig. 1. The diagram of reflexion (k � 0).
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work (Lefebvre, 1997). It allows us to suggest a hypothesis con-
cerning the nature of the relationship between the brain's
computational systems and the aspect of our individual existence
which we call “inner experience,” “subjectivity,” “consciousness” or
“mental phenomena.” Our hypothesis is as follows: mental phe-
nomena are a “form of existence” of the thermodynamic charac-
teristics of neural nets in their performance of computational
processes. In other words, the connection between a mental pro-
cess and the functioning of real neural nets is similar to the
connection between the temperature of a gas and the movements
of particles constituting it. We will presentlyshow that this state-
ment is more than just a metaphor.
The main question concerns whether it is right, in principle, to
talk about the thermodynamic characteristics of neural nets. The
first to answer this question was Cowan (1968); he indicated the
possibility of establishing a parallel between the statistical behavior
of a microparticle and computational processes in formal neural
nets. Following this, Bergstrom and Nevanlinna (1972) suggested
the characterization of a system consisting of a large number of
neurons by its total energy and by the distribution of entropy in its
subsystems. They assumed that the first and second laws of ther-
modynamics would hold in such a system, and this allowed them to
describe the system's evolution using thermodynamic concepts.
The next important step was taken by Hopfield (1982), who
connected Ising's model, constructed for the theoretical represen-
tation of physical processes in solid bodies, with both parallel and
asynchronic computational processes in neural nets. When the
activity of the brain neural system is schematized according to
thermodynamic concepts it appears to consist of two levels. The
first or micro-level characterizes functioning of a single neuron or
of a small group of connected neurons. The second or macro-level
characterizes the functioning of nets consisting of huge number
of neurons (see Ackley, 1985; Cadieu et al., 2007). These nets ac-
quire stable statistical characteristics, and at this level the func-
tioning of neural nets can be connected with thermodynamic
values (temperature, entropy).
Our hypothesis is that the macro-level of such a system is not
only a convenient theoretical description but has the ontological
status of “existing reality” and that our inner experience is a form of
the existence of this thermodynamic level. If we accept this hy-
pothesis, we can expect the formal schemes of mental phenomena to
coincide with the formal schemes of thermodynamic processes. The
statement formulated above is a theoretical prediction resulting
from our hypothesis.
Imagine that we were studying a certain mental phenomenon
without the use of relations from thermodynamics or statistical
physics and then discovered that the formal model which we had
constructed described not only the mental phenomenon we were
studying but also a particular thermodynamic process. At that
moment we could consider that we had found an argument in favor
of the hypothesis articulated above.
We have done just that and constructed a formal model of a
mental phenomenon - human reflexion. In the following sections
we demonstrate that, from the formal point of view, this model is
isomorphic to an elementary thermodynamic process, and in this
way we obtain support for our hypothesis on the general nature of
mental phenomena.
The following gives a brief sketch of classical thermodynamics.
Thermodynamics is constructed as an abstract field. Imagine that
we have the means to measure heat and work, that is, we have the
capacity to tie these characteristics of physical processes to non-
negative numbers. Let the heat be transformable into work and
work into heat, and let there be a universal unit for measuring
them. At this moment we move to the concept of energy, and
consider work and heat as two forms of the transmission of energy.
e subject: Western and Eastern types of human reflexion, Progress in
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V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e11 3
Suppose that we can compare a pair of bodies A and B and make
statements of the type: “A is hotter than B,” or “B is hotter than A,”
or “A and B are equally hot.” We assume that this relation is tran-
sitive, that is, if “A is hotter than B” and “B is hotter than C” then “A
is hotter than C,” and if “A and B are equally hot” and “B and C are
equally hot” then “A and C are equally hot.”
Thus, we can begin the construction of thermodynamics
without introducing the concept of temperature. We assume,
however, that there is an ordered relation in the set of all bodies,
and that for any two bodies we can say which one is hotter or that
they are equally hot. Let us introduce now the second law of
thermodynamics:
The production of work is impossible without transmission of heat
from a hotter body to a cooler one.
Since the second law of thermodynamics is formulated as a
negative statement and since we believe that everything which is
not prohibited is allowed, then we have the following principle for
receiving work from heat:
It is possible to create an engine which receives heat from a hotter
body, yields heat to a cooler body, and performs work W > 0.
The simplest heat engine performing work can be represented
as follows (see Fig. 2):
The two reservoirs 1 and 2 are given, with 1 hotter than 2. In
accord with the principle of receiving work from heat, it is possible
to construct an engine which takes heat Q1 from reservoir 1, yields
heat Q2 to reservoir 2, and performs work W. The connection be-
tween Q1, Q2 and W is given by the first law of thermodynamics or
the law of the conservation of energy:
W ¼ Q1 � Q2: (2.1)
Since the second law requires Q2 > 0, only part of the heat taken
from a hot reservoir can be transformed into work. This limitation,
however, is absent when work is transformed into heat. The entire
work performed by a heat engine can be transformed into an equal
amount of heat.
A reversible engine is an engine for which the diagram in Fig. 2
can be reversed, that is, the same engine can work in accord with
diagram 2.1a and with diagram 2.1b. In other words, when the
engine is reversible, we can take heat Q2 from a cool reservoir by
using work W. In accord with the first law, Q1 ¼ W þ Q2. A non-
reversible engine is an engine for which the diagram in Fig. 2 is
not reversible, that is, we cannot, using work W from an external
agent, take heat Q2 from a cool reservoir and yield heat Q1 to a hot
reservoir.
We will assume that the reservoirs are so large that during the
engine's functioning their “temperatures” do not change. Since we
Fig. 2. Diagram of an abstract heat engine. Vertical lines depict heat reservoirs;
reservoir 1 is hotter than reservoir 2. (a) The direct diagram. The engine takes heat Q1
from reservoir 1, yields heat Q2 to reservoir 2, and performs work W. (b) Reversed
diagram. The engine receives work W from an external agent, takes heat Q2 from the
cold reservoir, and yields heat Q1 to the hot reservoir.
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do not have a measure for temperature, we say that transmitting
heat from a hot reservoir to a cool one does not change the order of
heated bodies. We will call such reservoirs unchangeable. The value
r ¼ Q1 � Q2
Q1
(2.2)
is called efficiency. This parameter shows what portion of heat
which comes from the hot reservoir is transformed into work. The
following statement is true:
Statement 1. For any two given unchangeable reservoirs (one
hotter than the other) there is no engine whose efficiency is greater
than that of a reversible engine.
Proof. Consider Fig. 3.
Let engine 1 be reversible, and engine 2 be another engine (not
necessary reversible); let each engine receive heat Q1; the revers-
ible engine performs work W1 and the other engine work W2 (see
Fig. 3). Let W2 > W1. The reversible engine corresponds to the
reversible diagram, and we can build the following construction
(Fig. 3). A portion of the work performed by engine 2 is spent to
return heat Q1 into the hot reservoir (the heat taken from it by
engine 2). Since W2 > W1, the additional work W2 - W1 is per-
formed. In this case there is no transmission of heat from a hotter
body to a cooler one since we returned the heat, but we performed
workW2 -W1 > 0, which is prohibited by the second law. Therefore,
our presumption that W2 > W1 is wrong, and the following
expression holds:
W1 >W2 (2.3)
Carnot Theorem. Allreversible engines working between the
same two reservoirs have the same efficiency.
Proof. Let both engines in Fig. 3 be reversible. Since engine one
is reversible, than in accord with Statement 1, W1 � W2, and since
engine 2 is reversible, then in accord with Statement 1, W2 � W1.
These two inequalities lead to
W1 ¼ W2 (2.4)
It follows from the Carnot theorem that if an engine is reversible,
its efficiency does not depend either on its principle of work or on
the fuel it consumes.
Let us now introduce a concept of temperature. We distinguish a
reservoir which we call basic and consider a set of reservoirs hotter
than the basic one. Then we choose a heat Q* and call it a unit of
heat. Finally, we establish a reversible engine between each reser-
voir and the basic reservoir and take from each reservoir the
amount of heat in order that the reversible engine yields heat Q*
into the basic reservoir. We will call the temperature of a given
Fig. 3. Engine 1 is reversible; engine 2 may be either reversible or non-reversible; we
suppose that W2 > W1.
e subject: Western and Eastern types of human reflexion, Progress in
molbio.2017.06.006
Fig. 4. Definition of temperature. Reservoir 2 is basic. Reservoir 1 is hotter than the
basic one. Q is the heat which must be taken from reservoir 1 to make the reversible
engine yield heat Q* to reservoir 2.
V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e114
reservoir the number
T ¼ Q
Q*
(2.5)
where Q is the heat taken from the given reservoir (Fig. 4). The
temperature of the basic reservoir is equal to 1 (Feynman et al.,
1966).
Statement 2. Reservoir 1 is hotter than reservoir 2 if and only if
the temperature of reservoir 1 is higher than the temperature of
reservoir 2.
Proof.
(1) Necessity. Let reservoir 1 be hotter than reservoir 2 and each
engine, 1 and 2, yield heat Q* to the basic reservoir (see
Fig. 5).
Because engine 2 is reversible, the diagram in Fig. 5(b) can be
transformed into the diagram in Fig. 5(a). Now the amount of heat
taken from the basic reservoir is equal to the amount of heat yiel-
ded to it. The work performed by the system in Fig. 5(b) is equal to
W ¼ W1 �W2
¼ ðQ1 � Q*Þ � ðQ2 � Q*Þ
¼ Q1 � Q2:
(2.6)
Since the amount of heat yielded to the basic reservoir is exactly
the same as that taken from it, a given system can be considered as
working between reservoirs 1 and 2. Because engines 1 and 2 are
reversible, this system is also a reversible engine receiving heat Q1
from reservoir 1 and yielding heat Q2 into reservoir 2. And since a
reversible engine performs the maximumwork out of heat Q1, then
in accord with the principle of receiving work from heat
W ¼ Q1 � Q2 >0; (2.7)
which implies that
Fig. 5. Engines 1 and 2 are reversible. Reservoir 3 is basic.
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T1 ¼
Q1
Q*
>
Q2
Q*
¼ T2 (2.8)
(2) Sufficiency. Consider the scheme in Fig. 5. Let T1 > T2. Then
(2.8) holds, which implies that W ¼ Q1 - Q2 > 0, which is
possible (in accord with the second law of thermodynamics)
only when reservoir 1 is hotter than reservoir 2
It follows from (2.8) that the following equation holds for the ef-
ficiency of a reversible engine
Q1 � Q2
Q1
¼ T1 � T2
T1
(2.9)
Since the efficiency of the reversible engine is greatest under the
given conditions of functioning, then for the efficiency of any other
engine working between reservoirs with temperatures T1 and T2
the following is true:
Q1 � Q2
Q1
� T1 � T2
T1
: (2.10)
Suppose that we choose another basic reservoir and in this new
scale the temperatures of reservoirs 1 and 2 are equal to T10 and T20
respectively. It follows from (2.9) that
T1 � T2
T1
¼ T1
0 � T20
T1
0 : (2.11)
Thus the temperature scales T and T 0 are connected by equation
T ¼ cT 0; (2.12)
where c > 0 is constant. Therefore, we have defined a function
establishing a temperature scale in the set of reservoirs, accurate up
to multiplication by a positive number.
Let us note that we can choose expression (2.10) as a formula-
tion of the second law of thermodynamics. All the statements cited
in this section, including the formulation of the second law of
thermodynamics at the beginning, can be deduced from (2.10).
Indeed, it follows from (2.10) that Q2 > 0, i.e., it is impossible to
product work without transferring the heat from a hotter body to a
cooler one.
Consider now some correlates necessary for the construction of
a model. Let engine M be located between reservoirs with tem-
peratures T1 and T2, where T1 > T2; the engine receives heat Q1 from
the hotter reservoir and yields heat Q2 to the cooler one. Engine M
performs the work
W1 ¼ Q1 � Q2: (2.13)
Let a reversible engine be located between the same reservoirs. It
performs the work
W0 ¼ Q1
T1 � T2
T1
(2.14)
which is a theoretical maximum for the given ratio of reservoir
temperatures. The value
DW1 ¼ W0 �W1 (2.15)
is called lost available work. If engine M is not reversible,
e subject: Western and Eastern types of human reflexion, Progress in
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V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e11 5
DW1 >0 (2.16)
The lost available work is the energy lost by a heat engine because
its construction is not perfect. It is the work which engine Mwould
additionally perform if it were reversible. Thus,
DW1 ¼ Q1
T1 � T2
T1
� ðQ1 � Q2Þ
¼ Q2 �
T2
T1
Q1
¼ T2
�
Q2
T2
� Q1
T1
�
(2.17)
Value
DH ¼ Q2
T2
� Q1
T1
(2.18)
is called a change of entropy of the system, which appears as a result
of production of the work W1. Therefore,
DW1 ¼ T2DH (2.19)
Further, an essential role will be played by the two values:
r1 ¼
Q1 � Q2
Q1
(2.20)
u1 ¼
r1
r0
(2.21)
where
r0 ¼
T1 � T2
T1
(2.22)
The value of r1 is the efficiency of engine M; r0 is the efficiency
of a reversible engine, and u1 is relative value of this efficiency in
comparison with the efficiency of a reversible engine working un-
der the same conditions.
Let us consider the construction in Fig. 6. It consists of two en-
gines. The first engine works between reservoirs T1 and T2, and the
second between reservoirs T2 and T3. We assume that (T1/T2) ¼ (T2/
T3) > 1. Engine 1 performs work W1 ¼ Q1 - Q2 and yields heat Q2 to
reservoir 2. Since we do not require this engine to be reversible, it
may lose work DW1, given by (2.15). Engine 2 compensates for the
imperfection of engine 1. It takes from reservoir 2, exactly the same
amount of heat which engine 1 yielded to it, and performs work
exactly equal to the work which engine 1 could not perform
because of its imperfection.
Let us find now the efficiency of engine 2, designated r2.
Fig. 6. Engine 1 takes heat Q1 from reservoir 1 and yields heat Q2 to reservoir 2. Engine
2 takes heat Q2 from reservoir 2, performs works equal to the lost available work of
engine 1 and yields heat Q3 to reservoir 3.
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According to the definition of efficiency,
Q2r2 ¼ DW1 (2.23)
Because of (2.17)
r2 ¼
Q2 � T2T1Q1
Q2
(2.24)
and analogously to (2.21)
u2 ¼
r2
r0
(2.25)
In the next section we will begin construction of a model based
on the scheme in Fig. 6
3. Heat engines and reflexion
Let us consider a sequence of heat reservoirs whose tempera-
tures decrease in geometrical progression:
T1
T2
¼ T2
T3
¼ T3
T4
¼ … (3.1)
where T1/T2 > 1.
We place a heat engine between every two reservoirs; the en-
gine takes heat Qm from the reservoir with temperature Tm, per-
forms work Wm, and yields heat Qmþ1 to the reservoir with
temperature Tmþ1, where m ¼ 1, 2,… (see Fig. 7).
Let this sequence be structured in such a way that every engine
included in it except the first compensates for the imperfectness of
the preceding engine by performingwork equal to the lost available
work of the preceding engine. And let eachfollowing engine take
from a hot reservoir the amount of heat yielded to it by the pre-
ceding engine (see Fig. 6).Engine m performs work
Wm ¼ Qm � Qmþ1 (3.2)
Its lost available work is (see 2.17):
DWm ¼ Qmþ1 �
Tmþ1
Tm
Qm ¼ Qmþ1 �
T2
T1
Qm (3.3)
Engine (mþ1) receives from reservoir (mþ1) heat Qmþ1, performs
work
Wmþ1 ¼ DWm (3.4)
and yields heat Qmþ2 ¼ (T2/T1)Qm to reservoir (mþ2).
Statement 1. Engine (mþ2) performs work
Wmþ2 ¼
T2
T1
Wm (3.5)
where m ¼ 1, 2 . …
Proof. The work performed by engine (mþ2) is equal to the lost
available work of engine (mþ1):
Wm ¼ Qm � Qmþ1;Wmþ1 ¼ Qmþ1 �
T2
T1
Qm;Wmþ2
¼ T2
T1
ðQm � Qmþ1Þ ¼
T2
T1
Wm (3.6)
Engines 1 and 2 perform, respectively, work
e subject: Western and Eastern types of human reflexion, Progress in
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Fig. 7. Sequence of heat engines.
V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e116
W1 ¼ Q1 � Q2 (3.7)
and
W2 ¼ Q2 �
T2
T1
Q1 (3.8)
Therefore, for the odd numbers m ¼ 2k þ 1
Wm ¼
�
T2
T1
�k
ðQ1 � Q2Þ (3.9)
and for the even numbers m ¼ 2k þ 2
Wm ¼
�
T2
T1
�k�
Q2 �
T2
T1
Q1
�
(3.10)
where k ¼ 0, 1, 2,. …
Note that it follows from (3.5), (3.7), and (3.8) that the engines
with odd numbers m ¼ 2k þ 1 receive from the hot reservoir heat
Qm ¼
�
T2
T1
�k
Q1 (3.11)
and engines with even numbers m ¼ 2k þ 2 receive the heat
Qm ¼
�
T2
T1
�k
Q2 (3.12)
where k ¼ 0, 1, 2, . …
We will supplement the sequence of engines with two tapes,
divided into boxes in such a way that each engine has two boxes,
one at each tape (see Figs. 8, 9)
Let each engine in the heat machine measure the work per-
formed as a portion of the heat received from the hot reservoir and
let it print the figure on the bottom tape. On the upper tape each
engine prints its work, measured as a portion of the work which
would be performed by a reversible engine under the same
Fig. 8. A heat machine with two tapes. Each engine prints its efficiency, rm, in the bo
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conditions. Thus, the following value is printed on a bottom tape:
rm ¼
Wm
Qm
¼ Qm � Qmþ1
Qm
(3.13)
that is, the efficiency of engine m. The following value is printed on
a top tape:
um ¼ WmW0m
(3.14)
where
W0m ¼ Qm
T1 � T2
T1
(3.15)
is the work which would be performed by a reversible engine
located between reservoirs m and mþ1. Thus,
um ¼ Wm
QmT1�T2T1
¼ rmT1�T2
T1
(3.16)
is the relative efficiency of engine m.
We will further show that such a machine can be considered a
“self-generating” diagram of reflexion (see Fig. 9).
Statement 2. Sequence rm is periodical and
rm ¼
�
r1; if m is odd
r2; if m is even
(3.17)
Where
r1 ¼
Q1 � Q2
Q1
; r2 ¼
Q2 � T2T1Q1
Q2
(3.18)
and m ¼ 1, 2,.
Proof. Dividing (3.9) by (3.11) and (3.10) by (3.12) we obtain
(3.17)
It follows from (3.17) that
xes of a lower tape and its relative efficiency, um, in the boxes of a higher tape.
e subject: Western and Eastern types of human reflexion, Progress in
molbio.2017.06.006
Fig. 9. Self-generating diagram of reflexion (m ¼ 2k þ 1).
V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e11 7
um ¼
�
u1; if m is odd
u2; if m is even
(3.19)
where
u1 ¼
r1
T1�T2
T1
; u2 ¼
r2
T1�T2
T1
; (3.20)
Statement 3.
u1 ¼
r1
r1 þ r2 � r1r2
(3.21)
u2 ¼
r2
r1 þ r2 � r1r2
(3.22)
where
r1r2s1 and r1 þ r2 >0 (3.23)
Proof. Using direct calculations we find that the following
identity holds for r1 and r2 from (3.18):
r1 þ r2 � r1r2 ¼
T1 � T2
T1
(3.24)
Thus,
r1
r1 þ r2 � r1r2
¼ r1T1�T2
T1
¼ u1 (3.25)
r2
r1 þ r2 � r1r2
¼ r2T1�T2
T1
¼ u2 (3.26)
Note also that neither r1 nor r2 can be equal to 1 because of the
second law of thermodynamics.
It follows from (3.24) that variables r1 and r2 are connected with
(T2/T1) by the equality
ð1� r1Þð1� r2Þ ¼
T2
T1
(3.27)
Therefore, for each pair r1 and r2 we can always find a ratio of
temperature (T1/T2) allowing the machine in Fig. 8 to function. Let
x1; x2s1 and x1 þ x2 >0 (3.28)
Under these conditions equations (1.1) and (1.2) are equal to
equations (3.21) and (3.22), if there is one-to-one correspondence
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x14r1
x24r2
x14u1
x24u2
9>>=
>>;
(3.29)
In this way we obtain two pairs of equivalent correlations
x1 ¼
x1
x1 þ x2 � x1x2
; u1 ¼
r1
r1 þ r2 � r1r2
(3.30)
x2 ¼
x2
x1 þ x2 � x1x2
; u2 ¼
r2
r1 þ r2 � r1r2
(3.31)
Let us now choose arbitrary x1 and x2 for which inequalities
(3.28) hold and construct a machine consisting of m ¼ 2k þ 1 en-
gines (k ¼ 0, 1, 2,…) with the efficiency of the two first engines
equal to
r1 ¼ x1; r2 ¼ x2 (3.32)
and the temperature ratio given by (3.27).
In accordance with (3.30) and (3.31) this machine will generate
on its tapes, the same sequences of numbers X1, X2, X1 … X1 and x1,
x2, x1, …, x1, which are present in the diagram of reflexion (Fig. 1).
We can establish a one-to-one correspondence between the set
of engines M1, M2,…Mm-1, Mm and the set of subjects S1, S2,… Sm-1,
Sm as follows:
M1 M2 Mm�1 Mm
S1 S2 Sm�1 Sm
(3.33)
Note that the production printed by the machine on its tapes is
symmetrical between left and right. Thus, we can also establish the
following one-to-one correspondence:
M1 M2 M3 Mm�1 Mm
Sm Sm�1 Sm�2 S2 S1
(3.34)
Let us agree to denote engines by the symbols of the subjects
corresponding to them. If the orientation of the engines is given,
then the machine printing on the top tape the sequence X1, X2,…,
X1, and on the bottom tape the sequence x1, x2,…, x1, is isomorphic
to the corresponding diagram of reflexion. Such a machine can be
considered a “self-generating” diagram of reflexion.
In the framework of our analytical considerations, we ascribe to
the subject the capability for multiple self-awareness. From the
formal point of view, each step of awareness consists in adding two
squares (see Fig. 1). In the heat model, the analogue to the act of
awareness is the addition of two new engines to the machine. With
orientation (3.33) the two engines are added on the left, and with
orientation (3.34) they are added on the right. The awareness cor-
responding to the left-hand additions will be called ascending
reflexion, and awareness corresponding to the right-hand additions
e subject: Western and Eastern types of human reflexion, Progress in
molbio.2017.06.006
Fig. 10. Left and right addition. (I) the machine after adding two engines on the left;
(II) the machine after adding two engines on the right. The heat spreads in the systems
from the left to the right in both cases.
V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e118
will be called descending reflexion.1 Fig. 10 shows two machines
consisting each of three engines and representing a performing one
act of awareness.
Fig. 11 shows machines corresponding to performing k consec-
utive acts of awareness (where k ¼ 0, 1, 2 …):
4. Meditation
Meditation is a special type of human activity whose main
characteristic is concentration either on an external object or on an
inner thought or feeling. This high level of concentration results in
changes both of mental and physiological states. Meditation has
been traditionally associated with various world religions, each of
which has its own inner language for describing mental phenom-
ena. The main difficulty for scientific research into meditation lies
in the near-impossibility of separating mental experience from the
traditional religious forms of its description and interpretation. A
great number of these forms exist, and each of them has a language
which not only describes mental realities, but generates them as
well (see Tart, 1975; Naranjo and Ornstein, 1971).
We can distinguish two large classes of meditation. In the first
one, the goal which the guru or instructor sets before the learner is
to attain a psychologicalstate that feels like dissolving into
emptiness. This state is reached by means of step-by-step elimi-
nation of external perception, thoughts, feelings, and, finally,
awareness itself. This meditation is called sometimes “emptiness.”
The declared goal of meditation of the second type is to reach a
feeling of union with the Absolute, God, or “Super-I.”
Meditation of the first type is found in the traditions of Bud-
dhism, and meditation of the second type is found mainly in Hin-
duism, but also in Christianity and Islam.
Let us consider in more detail the “emptiness” meditation,
which is practiced in Zen-Buddhism and particularly widely spread
in China (see, for example, Abaev, 1983; Radcliff & Radcliff 1993;
Owens, 1992). In the first stage the pupil must learn to stay
immobile for long periods of time. Then his ability to concentrate is
developed. After that, comes a stage devoted to controlling one's
own attention: a person must learn how to move smoothly from
one aspect of his inner world to another. Next, the ability to “clean”
one's inner world from concrete thoughts and feelings is acquired.
This “cleaning” looks at first like a “dialectical game.” The learner
suppresses all feelings, to the point where he can describe his inner
state by words, “I have no feelings.” At the same time he is aware of
experiencing joy from reaching this success, so that he must
describe his state with the words, “I have feelings,” in contradiction
with his previous statement. In the next step the person again
1 Another version of choosing engines is given in Lefebvre (2014). In adding
engines at the left, the rightmost one represents the subject, and in adding engines
at the right, the leftmost one is the subject.
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Biophysics and Molecular Biology (2017), http://dx.doi.org/10.1016/j.pbio
suppresses the feelings that he is aware of in himself. This pro-
cedure is repeated many times until the fixation on feelings dis-
appears and together with it the fixation on the task of eliminating
them. Progress through these stages can produce the sensation of a
vanishing self. At first this is discouraging, and the learner asks, “Is
it me or not me?” At higher levels of meditation everything van-
ishes from the mental sphere: worry, dialectical oscillations, and
even the fixation on self's disappearance (see Suler, 1993).
After self's disappearance all questions connected with this
disappearance also vanish, including those which concern the
relation of one's own intentions to oneself (which is the conse-
quence of the vanishing of one's self). Intention is sensed as an
alienated stream flowing into cognition from the outside. Then this
sense is also deleted from cognition and thememory of it as well. At
this stage the subject's inner world represents a form without
content, that is, it is structured emptiness. Then the meditator
senses emptiness without form; in the final stage this sense is also
lost and sense of emptiness is perfected. Continuous practice allows
one to combine all the steps necessary for reaching the “higher”
states into a short procedure and to attain this state quickly at any
moment.
Let us recap the psychological changes taking place in the pro-
cess of emptiness meditation.
(1) “Switching off” of the perceptive sphere step-by-step.
(2) Fading of inner thought and verbal activity.
(3) Loss of the ability to experience emotions.
(4) Fading of the sense of self.
(5) Dissolution in nothingness.
Let us now consider meditation of the second type. In Chris-
tianity, the most sophisticated meditative technique for “touching
the Divine Light”was created by the Hesychasts in Byzantium in the
IV-VII centuries. The Hesychasts' process of meditation begins in
the same way as that of the Buddhists, with deep concentration.
Further on, however, something very different from emptiness
meditation begins to occur. Feelings do not fade but rather increase.
The meditator becomes increasingly aware of his sinful nature. At
the same time he experiences rising excitement and feels himself
approaching God. At the climactic moment a light appears before
his eyes, a light which is interpreted as the radiance of God. This
state ends leads to a catharsis, tears, the sense of atonement with
God, and finally relaxation.
A similar meditative technique was developed by Sufimystics of
Islam in the eighth century (see Ornstein, 1992). In many schools of
Sufism the path to unity with God consists of three stages. The first
stage corresponds to seeing the self as an outside observer. This
stage is described by the metaphor of “a fly burnt in a candle's
flame.” The second stage is deep understanding on one's own
sinfulness (“I am burning myself”). The third stage is unity with
God, a state which cannot be expressed in words.
The perfect technique for meditation of the second type appears
within the framework of Hinduism. Let us consider one of the most
advanced Hinduist systems of meditation, Raja-Yoga. This system
consists of eight steps. The first two are devoted to the moral and
ethical preparation necessary for meditative exercises. In the third
and fourth stages, the pupil learns concentration, correct body
position and breathing, which in this system are the necessary
means for reaching the higher states. In the fifth stage one learns
how to switch off one's own perceptive system and, in this way,
“liberate mind” from external obstacles. The sixth stage is devoted
to exercising deliberate control over one's own attention. This al-
lows a person to concentrate easily on any element of the inner
world and to maintain this concentration for a long time. At the
seventh stage begins the deep meditation. The merging of one's
e subject: Western and Eastern types of human reflexion, Progress in
molbio.2017.06.006
Fig. 11. Ascending (I) and descending (II) reflexion. In ascending reflexion, the leftmost engine after a k-th act of awareness is S1. In descending reflexion, the rightmost engine after
a k-th act of awareness is S1.
V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e11 9
own self with the object of attention is the goal of this stage. Finally,
the last, eighth stage, is union with the Absolute, whose name is
Brahman. The metaphorical statement “I am a Brahman” corre-
sponds to this stage.
Therefore, in process of meditation Raja-Yoga contains the
following psychological changes:
(1) Step-by-step switching off of the perceptive sphere
(2) Step-by-step strengthening of the feeling of one's self
(3) Subordination of the perceptive sphere to the will of one's
self
(4) Union of the self with the Absolute
If we compare this list with that for Zen-Buddhism we can see
essential differences. The main one is that, in Zen-Buddhism, a
person experiences the disappearance of one's self, whereas in
Raja-yoga the self is strengthened and its culmination is unionwith
the Absolute. Note also that in Zen-Buddhism, individual will
follow a stream of natural changes, while in Raja-Yoga, a person
feels himself in control and even the creator of all changes occur-
ring within him.
Let us construct a model of meditation. The main idea is that in
emptiness meditation we connect with the descending reflexion,
Fig. 12. Two types of meditation. The length of arrows symbolizes the work of engines. The v
appears.
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Biophysics and Molecular Biology (2017), http://dx.doi.org/10.1016/j.pbio
and in the one which leads to union with the Absolute, with the
ascending (see Fig. 12).
The work performed by the engines is interpreted as emotion
intensities of the subject and of the subject's image of the self.
During each act of awareness the emotion of the subject S1 changes:
in pursuit emptiness it diminishes, and in a tendency to Absolute it
rises, in both cases in geometrical progression as follows from (3.6).
Many types of meditation practices are based onthe teaching
about the energy centers in a human body called chakras. The
followers of this doctrine believe that chakras are channels in
which the vital energy moves. Each chakra corresponds to a special
place in the human body, and these places are the centers to focus a
person's attention during meditation. Various teachings present a
different number of chakras, for example, in Tantrism, there are six
(Woodroffe, 1928).
Meditation begins with concentration on the first, the lowest
chakra located in the area of reproduction part of human body. The
declared goal is to relax it. The second chakra is located in the lower
part of the abdomen. The goal of concentration on it is legs’
relaxation. The third chakra is in the center of the abdomen. The
concentration on it must lead to controlling digestion. The fourth
chakra is located on the chest; concentration on it allows a person
to control his own emotions. The fifth chakra is on the neck;
alue of n denotes the number of the acts of awareness, as a result of which a given state
e subject: Western and Eastern types of human reflexion, Progress in
molbio.2017.06.006
Fig. 13. Centers of energy in Tantrism. Chakras' system is shown in the right (Woodroffe, 1928).
V.A. Lefebvre / Progress in Biophysics and Molecular Biology xxx (2017) 1e1110
concentration on it leads to control over the entire upper part of the
body. And the sixth chakra is located in the center of the forehead
and is considered to be the center of consciousness (Fig. 13).
We may notice certain similarities between this representation
of human energy centers and the thermal unit in Fig. 12. The heat
engines correspond to the five lower chakras, and the energy
source - to the sixth one located on the forehead.
In what relation is the set of heat engines to the human body? If
we do not want to move beyond today's science, we have to pre-
sume this set to be connected with the brain functional structures.
But the Eastern notion of chakras claims that they are located in
several parts of human body. Although the multi-year debates did
not find correspondence between chakras and human physiology
(see Mishlove, 1993), in some Eastern teachings, chacras are shown
as large nodes in acupuncture maps of a human. Medical effec-
tiveness of acupuncture makes us think that our internal organs are
projected to the skin (see Motoyama, 1990). Brain parts are also our
internal organs, so, they too may be projected onto the skin. In this
case, chakras are the glares of heat engines realized by the brain.
5. Conclusion
What have we done? The course of our work was as follows.
First, we constructed a mathematical model of a certain psycho-
logical process - bipolar choice - and tested the model. Then we
demonstrated that this model corresponds to a chain of ideal heat
engines, functioning of which may explain the phenomenon of
bipolar choice. In addition, this chain of heat engines explains a
number of other psychological phenomena unrelated to bipolar
choice (Lefebvre, 2014).
Our hypothesis poses a question: is the connection between the
chain of ideal heat engines and some phenomena in mental life of
humans only a coincidence? To answer this question we have to
analyze those features of formal theories, which convince us their
predictions are not coincidental. At the beginning of the twentieth
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century, Niels Bohr constructed a model of a hydrogen atom
(Levitin, 1990). He represented it as a solar system consisting of a
nucleus - the Sun - and an electron - a planet, which can leap from
orbit to orbit and, in so doing emit or absorb light quanta. This
theory would not have been accepted by other physicists if it did
not explain complicated patterns in the hydrogen spectrum. So, in
saying that the prediction is not accidental we are concerned not
only with its correctness, but also with its complexity. Does our
theory predict complex phenomena? Yes, it does. It predicts the set
of attractive intervals in music, which we obtained by solving the
Diophantine equations deduced from our thermodynamic model
(Lefebvre, 2014). This set consists of eighteen intervals, fourteen of
which coincide with Helmholtz set of harmonic intervals
(Helmholtz, 1877).
Acknowledgment
I am deeply grateful to Victorina Lefebvre, a professional psy-
chologist, for clear and specific suggestions and for technical
preparation this paper for print.
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	Theoretical modeling of the subject: Western and Eastern types of human reflexion
	1. Introduction
	2. Brain, mental phenomena, and thermodynamics
	3. Heat engines and reflexion
	4. Meditation
	5. Conclusion
	Acknowledgment
	References