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Year 6 - N° 289 – December 2, 2012

Bauru, SP (Brasil)

O próprio autor


Scientific Analysis of Apometry

Alexandre Fontes da Fonseca

I. Introduction

         Apometry is a technique of projection of the soul into the spiritual world developed by Dr. José Lacerda de Azevedo with the aim of healing people from healthy and spiritual problems [1,2]. This technique is presented as a scientific theory which intends “to show a new world” through a set of “scientifically formulated” hypotheses [1]. According to the Apometry, the medium’s soul is taken to the spiritual world so as to observe sick people or disincarnated Spirits; to perform commands from a group leader; and to report the activities performed in the spiritual world. The efficiency of these techniques are based on the hypothesis that a mental process of counting together with a given set of commands are capable to agglutinate energies from physical body and empty space and use them in healing tasks or holding obsessor Spirits.

As the theory of Apometry is based on concepts from Physics and Mathematics presents itself as an innovative technique whose consequences in helping incarnate and disincarnate Spirits, are much more efficient than the Spiritism [1], the main objective of this paper is to present a rigorous scientific analysis of the use of concepts of Physics and Mathematics into the formulation of the theory of Apometry.

The spiritist movement already knows that Apometry is a technique incompatible with the spiritist orientation (see, for example, the papers in O Consolador, Refs. [3,4,5]). However, several spiritist groups have adopted and are adopting Apometry practices in spiritist centers. The reason is the belief that Apometry practices produce stronger and better results than the Spiritism, and that Apometry is based on important scientific theories like the Modern Physics. So, many spiritists think that Apometry would be more actual or modern than the Spiritism.

In order to verify the real importance of Apometry as a scientific theory, we will analyze the use of concepts and equations of Physics and Mathematics in the formulation of the theory of Apometry in the same way that all scientific works in the field of Physics and Mathematics are analyzed. The main criterion of scientific analysis used here is the existence of inconsistencies, i. e., the existence of conflicts, errors and contradictions between the concepts of the theory of Apometry and Physics. Logical consistence and interpretation will be also used to analyze one equation of the theory of Apometry.

II. Scientific analysis of two concepts and one equation of Apometry

Because of space, only the analysis of two concepts and one equation of Apometry will be presented. The concepts were chosen in view of their simplicity to be explained in terms accessible to all readers. An article containing a full analysis of additional concepts and equations of Apometry will be published soon in a book of papers presented at the 8th ENLIHPE[1]. In what follows, we will reproduce the chosen concepts of Apometry as presented in Ref. [1], and then present their scientific analysis.

Concept 1. Immaterial astral body

At the section entitled “8 – Properties and functions of astral body”, in chapter “III – Astral Body” of Ref. [1], it is said “This facility of moving itself from the physical body is characteristic of the astral body, immaterial and of magnetic nature, not having a fluidic constitution as the etheric double ...”. Ahead in the text, in the section entitled “9 – Food and "death" of astral body” in the same chapter, it is said that “Our astral body constantly loses energy, needing energetic supply for its sustenance, as the physical body. But the nature of this food varies a lot; it goes from the protein soups needed by the materialized Spirits, given by the houses of help in the astral, to the quintessence energies that feed the superior Spirits, (...)”.

Scientific analysis: In the above words we find inconsistencies and contradictions because if the astral body is “immaterial” and “does not have fluidic constitution”, it cannot lose “constantly energy, needing energetic supply (...) as the physical body”. In both philosophic and scientific terms, an immaterial thing does not contain neither depends on energy, since energy is a property related to material objects, bodies or particles.

Concept 2. Time and Space do not exist in mental dimension

The concept above is the title of section 7 of chapter “IV – Mental Body” of Ref. [1].

Scientific analysis: The title is a direct example of a scientific and philosophic incoherency and contradiction constantly found in the theory of Apometry [1]. For this case, the incoherency and contradiction comes from the fact that if time and space do not exist in the mental dimension, then it is not possible to speak about frequency, vibration or propagation of mental waves because the concepts of frequency, vibrations and propagation strongly depend on concepts of time and space. Reader is referred to the book of Ref. [6] for more details about wave equations and properties.

Equation 1.  Energy of psyche – W and Ψ

This part will take the most extension of this paper, because it is important to carefully explain the reader the details involving the equation. In the chapter entitled “”Nohtixon – The thought as the work of the Spirit” of Ref. [1], Dr. Azevedo presents an analysis of how the thoughts can act on the matter. Then, he proposes the following law for the thought of a Spirit: “The energy of the thought expressed in the physical world is equal to the product of the electric neuronal energy (En) by the psychic (of the soul) energy - Ψ elevated to the potency v, when v tends to infinity.” In mathematic terms, this law can be written in one of the two equivalent formulas:

  W = En Ψv       ,        or         W = En lim v (Ψv ) ,                 (1)

where W is the total energy of the thought, En the neuronal energy (of the brain), and Ψv the psychic energy of the soul. Ψv means: “Ψ elevated to the potency v”.

Scientific analysis: The first error of this law is the lack of theoretical inconsistency since the definition and meaning of the variable Ψ do not exist. Every variable in a mathematic equation requires the definition of a domain or a set of mathematical objects to which the variable is related. In simple words, the theory of Apometry does not present any values of reference for the variable Ψ. It only says that Ψ is of psychic nature. What does that means in quantitative terms, since Ψ is part of a mathematical formula? Is Ψ equal, larger or smaller than 1? How to distinguish it amongst different beings or amongst different people? What experiments allow measuring Ψ ?

The second error of the law of thought of the Apometry is what in Mathematics is called a mathematic absurdity and consists of the direct analysis of the equation (1). According to the theory of Apometry, it is the value of the exponent v that differs for different beings. It values 1 (v = 1) for unicellular beings, larger than 1 (v > 1) for animals, and v tends to infinity in humans (v : this symbol means “v tends to infinity” or “taking the limit when v tends to infinity”) [1]. This law of Apometry proposes the equation (1) as the way to estimate the value of the energy of the thought of a human being through the calculation of the limit of the function Ψv when v tends to infinity (or v ). Here, in order to show the absurd of this formula of the Apometry, we will analyze the possible results for the following expression:

lim v (Ψv ).                                                           (2)

The calculation of this expression needs to be explained in a very simple way in order to help the reader not used to mathematical analysis. The calculation of limits as what we are going to do here is learnt on basic courses of Calculus [7] of the main courses at the superior or college level of Engineering and Exact Sciences careers.

In order to estimate the values for the limit defined by equation (2), we will first identify what is the parameter and what is the main variable in the calculation of the limit. The main variable is the one that will go to the infinity: in our case it is the variable v. The parameter is an element that is considered fixed (not variable) in the calculation of the limit: in our case, it is Ψ. The operation of “calculating the limit” is applied to a function that, according to equation (1) or (2), is Ψv. So, making the calculation of the limit of Ψv when v tends to infinity is nothing more than making the analysis of to which numeric values the operation Ψv (remembering: “Ψ elevated to the potency v”) would be or be close to, when the variable v acquires extremely high values, tending to infinity [7].

The estimates for the calculation of the limit given by equation (2) require the consideration of all possible values for the parameter Ψ. The possibilities are: Ψ = 1 (possibility 1); -1 < Ψ < 1 (possibility 2); Ψ > 1 (possibility3); and Ψ ≤ -1 (possibility 4).

- If Ψ = 1, then we know that 1 elevated to any value is equal to 1 [7]. Therefore, the limit of equation (2) when v tends to infinity, with the possibility 1, is just 1 (um).

- If -1 < Ψ < 1, then we observe that the magnitude of Ψ is smaller than 1 and we know from Mathematics that a number smaller than 1 elevated to a large exponent is a number as small as large the exponent is [7]. Therefore, the limit of equation (2) when v tends to infinity, with the possibility 2, is the smallest absolute number which is 0 (zero).

- If Ψ > 1, then we know from Mathematics that a number larger than 1 elevated to a large exponent results in a large number [7]. Therefore, the limit of equation (2) when v tends to infinity, with the possibility 3, is infinity, i. e., it tends to infinity as long as v tends to infinity.

- If Ψ ≤ -1, then Ψ has a negative value and we know from Mathematics that a negative number whose absolute value is larger than or equal to 1, elevated to a large exponent is undetermined, because the sign of the result depends of the exponent if it is odd or even [7]. Therefore, the limit of equation (2) when v tends to infinity, with the possibility 4, is undetermined.

We can summarize the above results for equation (2) as follows:

lim v (Ψv ) = 1                       if        Ψ = 1 ,                           (3a)

lim v (Ψv ) = 0                       if        -1 < Ψ < 1 ,          (3b)

lim v (Ψv ) = +                             if        Ψ > 1 ,                           (3c)

lim v (Ψv ) = undetermined   if        Ψ ≤ -1 .                (3d)

The interpretation of these results is the following:

- If the equation (3a) is the valid result, then the psychic energy of the soul does not have utility because the term related to the mental energy, En, will be directly multiplied by lim v(Ψv ) that, in this case, is equal to 1, and multiplying En by 1 does not change the result and the energy of the thought is only the neuronal energy of the brain.

- If the equation (3b) is the valid result, then the psychic energy of the soul is null because multiplying En by zero is equal to zero. This result, besides not having any utility as discussed for the previous case, is contradictory with the own theory of Apometry because according to it the energy of the thought of an amoeba (for which v has a finite value) would be larger than the energy of a human.

- If the equation (3c) is the valid result, then the psychic energy of the soul is infinity because multiplying En by infinity is infinity. This result, again, does not have utility because in Science no one works with infinity values which cannot be measured, calculated or used for comparison.

- If the equation (3d) is the valid result, then the psychic energy of the soul is undetermined because multiplying En by an undetermined number gives an undetermined result. Therefore, this possibility also does not have any utility.

From the above analysis, we conclude by absurd that the equation (1) and the law of the thought according to the Apometry do not have any validity.

III. Conclusions

The analysis performed in this paper allows us to see that the theory of Apometry has not any support from both Physics and Mathematics and cannot be considered as scientific. It has errors of incoherency, inconsistency, and contradiction between its own concepts and equations. Therefore, the Apometry does not represent a scientific advance and, on the contrary, it demonstrates the lack of knowledge about even simple concepts of Science.

It is important to clarify that this analysis did not intend to disrespect anyone who practices and follows the Apometry. As long as we have been oriented by Jesus that we should find the truth since the truth will set us free, (João 8:32), and that we should say “yes, yes, no, no” (Mateus 5:37), our goal here is to clarify spiritists and non-spiritists about the wrong bases of the theory of Apometry. If some of the practices of Apometry yield good results, these are due to causes different from those that the theory of Apometry describes. Any healing and other helps that eventually happen in the name of Apometry are due to other reasons like the merit of the people, presence of mediums of physical effects, faith, and other factors that Spiritism predicts. The orientations for the use of certain objects or mental counts that were proposed based on concepts of Physics are completely wrong and lack any support from Physics. As already shown elsewhere [8], Spiritism is the most actual and modern theory capable to treat and orientate the mediumistic practice.

References (in portuguese):

[1] José Lacerda de Azevedo, Espírito / Matéria – Novos Horizontes Para A Medicina, 7ª edição, VEC Gráfica e Editora Ltda, Porto Alegre (2002).

[2] José Lacerda de Azevedo, Energia e Espírito, 2ª edição, Comunicação Impressa, Porto Alegre (1995).

[3] Jorge Hessen, “A apometria e as práticas espíritas”, O Consolador 67 (3 de Agosto de 2008), link: http://www.oconsolador.com.br/ano2/67/especial.html 

[4] Astolfo O. de Oliveira Filho, “Apometria não é Espiritismo”, O Consolador 130 (25 de Outubro de 2009), link: http://www.oconsolador.com.br/ano3/130/especial.html 

[5] Gebaldo José de Sousa, “Apometria não convém às Casas Espíritas”, O Consolador 139 (3 de Janeiro de 2010), link: http://www.oconsolador.com.br/ano3/139/gebaldo_sousa.html 

[6] D. Halliday, R. Resnick e J. Walker, Fundamentos da Física – Volume 2 – Gravitação, Ondas e Termodinâmica, Editora LTC, 8a. Edição (2009).

[7] H. L. Guidorizzi, Um Curso de Cálculo – Vol. 1, Editora Livros Técnicos e Científicos Editora LTDA., 2a. Edição (1987). 

[8] A. F. da Fonseca, “Estaria o Espiritismo ultrapassado?... Ou muito na frente?”, O Consolador 271 (27 de Julho de 2012), link: http://www.oconsolador.com.br/ano6/271/especial.html


[1] 8º Brazilian National Meeting of Researchers in Spiritism, from August 18th to 19th, 2012, held at the head-quarter of the Centro de Cultura, Documentação e Pesquisa do Espiritismo, Eduardo Carvalho Monteiro, CCDPE-ECM, in Sao Paulo. A video of the presentation (in Portuguese) is in: http://www.youtube.com/watch?v=-3nsVYTPFyU

Alexandre Fontes da Fonseca is a teacher of physics at the Universidade Estadual Paulista "Júlio de Mesquita Filho", Bauru (SP).




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