
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 8^{th}
ENLIHPE.
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
Ψ^{v→∞}
,
or W
= En lim^{
}_{v}_{→∞}
(Ψ^{v}
) ,
(1)
where W
is the total
energy of the
thought, En
the neuronal
energy (of the
brain), and
Ψ^{v}
the psychic
energy of the
soul.
Ψ^{v}
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
Ψ^{v}
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}_{→∞}
(Ψ^{v}
).
(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
Ψ^{v}.
So, making
the calculation
of the limit of
Ψ^{v}
when v tends to
infinity
is nothing more
than making the
analysis of to
which numeric
values the
operation
Ψ^{v}
(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}_{→∞}
(Ψ^{v}
) = 1
if
Ψ
= 1
,
(3a)
lim^{
}_{v}_{→∞}
(Ψ^{v}
) = 0
if 1 <
Ψ
< 1 ,
(3b)
lim^{
}_{v}_{→∞}
(Ψ^{v}
) = +∞
if
Ψ
> 1
,
(3c)
lim^{
}_{v}_{→∞}
(Ψ^{v}
) =
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}_{→∞}(Ψ^{v}
) 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
nonspiritists
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
Alexandre Fontes
da Fonseca is a
teacher of
physics at the Universidade
Estadual
Paulista "Júlio
de Mesquita
Filho", Bauru
(SP).
