The Alliance of Science and Religion:
A contribution from Mathematics
English translation
of a paper published in Fidelidade Espírita, October 2003
Recent
research in Mathematics is showing that solidarity and cooperation lead
a social group to evolve faster than selfishness. It constitutes an
important scientific result favoring the essential lessons of the
Gospel.
Unfortunately,
a good part of our society does not enhance the religious teachings
considering them as product of fanatism. The most scientists only see
the selfishness as the only one reason for all acts of the human being
and they say that it is in Nature when consider the idea given by the
expression “the selfish gene”[1] that states that the evolution
promotes the individuals that have higher capacity of proliferating
themselves. In other words, the genes that reduce the success of being
spread tend to disappear.
Despite the idea of the selfish gene be verified in several processes
in Nature there is an intricate question for which the scientists does
not have an answer yet. It is about the strange cooperative behavior
and altruism between animals of different species and families [2,3].
The human altruistic behavior cannot be understood in terms of the
gene-based evolutionary theories [4]. It is known [3] that Charles
Darwin [5,6], the father of the Theory of Evolution, noted that the
process of natural selection could not promote by itself the altruistic
behavior where some individuals reach the point of reducing their
abilities so as to favor other members of the species. We shall present
here an interesting scientific research, motivated by these questions,
whose solutions we interpret in a moral sense.
The subject of this paper agrees with some of Allan Kardec’s statements
found in the issue 8 of chapter one of The Gospel According to
Spiritism, with the title: “The Alliance of Science and Religion”[7].
We transcribe the following part:
“Science and Religion are the two levers of human intelligence, one
revealing the laws of the material world, the other revealing the laws
of the moral world. But seeing that these laws have the same principle,
which is God, they cannot contradict themselves.”(Original remarks).
This statement is a fundamental idea that reveals the divine character
of all creation. As Kardec says if Science and Religion contradict one
each other than one or another will be incorrect because God, “the
Supreme Intelligence, first cause of all things” (question 1 of the
Spirit’s Book [8]. Our remarks.) did not intent the destruction of His
own creation. We, spiritists, knew that it is in vain that the
scientists, politicians and sociologists look for formulas for the
social progress out of the Christian essential principles. Kardec [7]
also said that:
“We have now reached a phase upon this planet when the teachings of
Christ must be completed and the intentional veil cast over some parts
of these teachings lifted. A time when science must desist in its
exclusive materialism, so taking into consideration the spiritual
element; when religion must cease to ignore the organic and immutable
law of matter, so that both may become two forces, each learning one
the other and advancing together in mutual concourse. Then religion, no
longer discredited by science and no longer being able to oppose the
overwhelming logic of the facts, will acquire an unshakable power
because it will be in agreement with reason.”
Therefore, when the results of scientific research cannot be used
against the religious teachings, these will acquire a strong power
because they will be in accord to reason. But, if these scientific
results start showing that the religious teachings are correct or
sensible, the materialistic and selfish people will not have excuses
anymore to regard the religious teachings to the plane of the blind
faith.
So, who could imagine that just the most abstract science, Mathematics,
could give rise to some results that verify some of the Jesus’
essential moral teachings? In this paper, we shall present the news
about a research in Mathematics and Statistics where subjects like
“cooperation” and “non-cooperation”, “altruism”, “selfish”, etc., are
analyzed numerically using statistical models that reflect the behavior
of a given population. We explain that these models do not say anything
about a human behavior because the free will is not a mathematic
function. These models only reflect the statistical behavior of a group
of people where a given percentage, for example, cooperates, other
percentage does not-cooperate, and so on. Despite the obtained results
are amazing, the scientists usually try to explain them in terms of an
acquired behavior in thousands of years of evolution, in the sense
given by the Darwin’s Theory of Evolution.
The so-called Theory of Games [9] is the basis of the research [10,11]
we shall present in this paper. This theory was developed to study the
behavior of social groups interacting together, for example, in
economic investments. There is a game called “The Public Goods Game”
that is defined as follows. A group of players receives a given amount
of money to invest in a common pool. The rules are: in each step the
sum of invested money is doubled and then shared equally to all
participants, independent of how much money each one put in the pool.
Each player can invest the value he or she wants including the
possibility of not investing anything. The maximum profit occurs if all
players invest all money they have (all cooperate). But there is a
temptation: do not invest anything and receive the other players’
interest (attitude of non-cooperation). The temptation occurs because
who does not-cooperate always gains more money than who cooperates
after each step of the game (see table 1). However, by seeing that
someone did not-cooperate, the other players tend also to not-cooperate
and the final consequence is that all players do not-cooperate, anyone
gaining anything (table 1). Therefore, in common public goods, actions
based on purely selfishness lead to own prejudice (is this thinking not
familiar in the Gospel?). It is a social dilemma appearing in the
dynamics of several social activities as, for example, the Health Plan.
If each person, that belongs to a Health Plan, thinks that he or she
have to use the service all time only because it is being paid, the
consequence will be the increasing of the price or the bankruptcy of
the company. If all cooperate using the Health Plan only when it is
really needed, it will be possible to make the service to get better
and even the price to get down. Therefore, all participants will have
the advantage of the cooperative behavior.
| Players |
Strategy 1: All
Cooperate |
Strategy 2: All Do
Not-Coperate
|
Strategy 3: Player A
Does Not-Cooperate |
Before
|
After
|
Before
|
After |
Before
|
After |
A
|
10,00
|
20,00
|
10,00
|
10,00
|
10,00
|
25,00
|
B
|
10,00
|
20,00
|
10,00
|
10,00
|
10,00
|
15,00
|
C
|
10,00
|
20,00
|
10,00
|
10,00
|
10,00
|
15,00
|
D
|
10,00
|
20,00
|
10,00
|
10,00
|
10,00
|
15,00
|
Table 1: Examples of
different strategies in the Public Goods Game, where the invested money
is doubled and then shared equally to the participants. Players A, B, C
and D received, initially, US$10,00 to invest in the common pool.
“BEFORE” and “AFTER” mean the values that each player owns before and
after a step of the game. In the strategy 1, all cooperate investing
all money, gaining the double of what they had before playing one step
of the game. In the strategy 2, all do not-cooperate not investing
anything and therefore, not gaining anything. In the strategy 3, only
the player A does not-cooperate and his or her interest was higher than
that of the other players that invested all money they had. If the
player A does not invest anything, the sum of invested money by the
other players is equal to US$30,00. After doubling this value, the
total amount to be shared with all players is US$60,00. After dividing
by the 4 players, in accord to the rules of the game, it results in
US$15,00 for each player. As the player A did not invest anything he or
she owns US$25,00, while the other players own only US$15,00. That is
the reason of the temptation of not investing anything and receiving
the interest from the others’ investments. But if all players act like
that, nobody gains nothing.
Numerical
simulations in a computer machine showed how the social groups evolve
where each individual, in order to make the most profit, may choose
changing of strategy among the possible ones as cooperate,
not-cooperate, or even, not-play (in the last case the player does not
receive anything from the common pool). Under varied conditions as, for
example, the payment of a tax to make an investment, after some time
(or after running the game for various times), several situations are
verified that predominate within the social group as the cooperative or
non-cooperative behavior. In an interesting scientific work,
Szabó e Hauert [12] showed that, in these computational
simulations, voluntary participations of whom usually does not-play,
prevent the group from increasing the number of the non-cooperators
(the ones that do not invest anything and receive part of the total
interest).
But, the main purpose of such a research is not to see the Christian
teachings. We note that there exist economic motivations behind that.
However, it is impossible not seeing the moral consequences that the
results of this research present. It is interesting to note how these
moral results rise naturally from the computational simulations of this
game without consider them as hypotheses. We see that when the society
really follows the Christian teachings, summarized in the phrase: “you
must love God and your neighbor as yourself”, then the humanity will
evolve much more quickly, in all senses, because all cooperate and all
will fell the good consequences of this cooperation. What do we think
is important to see is that this conclusion is becoming a mathematical
certainty.
Figure 1: Picture
that represents the consequences and results of the research in
Mathematics. For example, we have equations and numbers. Who could say
that Mathematics is verifying the consequences of the lessons of the
Gospel?
The
dynamics of the Public Goods Game has some similarity with the process
of evolution of a spirit. After many selfish steps, that represent
non-cooperative attitudes of the spirit during the life, the principle
of cause and effect (Chap. V of The Gospel According to Spiritism [7]),
returns to us the consequences of our acts and decisions, compelling us
to “play” in a charitable and kind way (i.e., to cooperate) in the next
opportunities of the life. We suggest the reading of a great article of
Richard Simonetti [13], that stimulate us to invest in the “Bank of the
Providence, assisting all people who lives in material difficulties,
people who needs every kind of help, assisting them in these
needs.”[13](Our translation from the original in Portuguese).
We call the spirit of Emmanuel, in answer to the question 69 of the
book called O Consolador [14], to conclude our paper (by talking about
the spiritual value of the abstract sciences. Mathematics is one of
them):
“We cannot neglect the cooperation of the abstract sciences to the
educative postulates, by training the intelligences, dilating the
spontaneity in the spirits, in order to establish the facility of
understanding of the value of the planetary life, but we have to
acknowledge that its activities, almost always related to the world
problems, are processes or means by which man reaches the science of
life in its deepest spiritual revelations, science that symbolizes the
divine aim of all investigations and analysis of the organization of
the Earth.”(Our remarks and our translation from the original in
Portuguese).
The results of the above research reflect each individual’s choices
with respect to the acts performed during the life. This choice depends
on each one’s degree of evolution. Therefore, all efforts in our
innermost reform constitute the greatest investment for a real good
future life, with peace and love. May God continue helping us to make
this effort!
*
The author would like
to thank Mr. Renato Costa and Mrs. Marcia for correcting the
translation of this paper from the original in Portuguese into English.
Referênces
[1]
R. Dawkins, The Selfish Gene, Oxford University Press, (1989).
[2]
K. Sigmund e C. Hauert, Current Biology, Vol. 12, p. R270 (2002)
[3]
F. Michor e M. A. Nowak, Nature (London), Vol. 419, p. 677 (2002).
[4]
E. Fehr and U. Fischbacher, Nature, Vol. 425, p. 785 (2003).
[5]
The reader will find a complete description of the Charles Darwin’s
Theory of Evolution and its connection to Spiritism in the book of the
reference [5].
[6]
H. M. L. de Souza, Darwin e Kardec Um Diálogo Possível,
Centro Espírita Allan Kardec Dep. Editorial, (2002).
[7]
A. Kardec, The Gospel According to Spiritism, The Headquarters
Publishing CO LTD (London), 1st. Edition, (1987).
[8]
A. Kardec, The Spirits’ Book, Editora FEB (Brasília), 2a.
Edição, (1996).
[9]
J. von Neumann e O. Morgenstern, Theory of Games and Economic Behavior,
Princeton Univ. Press, New Jersey, (1944).
[10]
M. A. Nowak, R. M. May e K. Sigmund, Scientific American, Vol. 272, p.
76 (1995).
[11]
K. Sigmund, E. Fehr e M. A. Nowak, Scientific American, Vol. 286, p. 83
(2002).
[12]
G. Szabó e C. Hauert, Physical Review Letters, 89, p. 118101
(2002).
[13]
R. Simonetti, Reformador, Agosto, p. 14 (2003).
[14]
Emmanuel, Psicography of F. C. Xavier, O Consolador, Editora FEB, 20a.
Edição (1999).