134
F. COLLOT
But if we want to write the reflected flow fjJr in terms of the number of cells
there arises a difficulty. Each cell, each tissue, each organ reflects a quantity
of energy which depends neither on its volume nor its weight but on its
degree of differentiation. Moreover, in a growing organism, this rate of
differentiation varies considerably from one tissue to another and perhaps
from one cell to another. Therefore, it is impossible to speak of average
differentiation at time t; in order to make the solution homogeneous, while
still assuring permanent growth, the notion of the cell has to be replaced by
that of the "bioton". We shall call "bioton" some volume of living matter
of arbitrary size not necessarily equal to each other but receiving a flow of
IE which is equal to each other and remains constant. Our approach is
similar to that of the physicist, who in the statistical mechanics renounces
to enter into more details and to calculate the trajectory and kinetic energy
of each individual molecule. Let us call w the number of "biotons". Thus,
equation (3) becomes:
fjJi = aw + c
(3')
We now postulate: To any increase of biotonic volume of an organism
corresponds a proportional increase of the rate of average specialization or
of the rate of average differentiation of its constituent parts. This postulate
can be understood intuitively by means of a sociological example. Let us
imagine a primitive community in a remote island composed of ten individuals who live very distant from each other. Each of them will have to
satisfy his proper needs and he will be therefore a fisherman, farmer, mason,
miller, baker and so on. Here the rate of specialization or differentiation
(we ascribe the same meaning to these words) is practically negligible, i.e.
a specialization once attained will remain unchanged. Suppose now that the
number of invididuals increase to one thousand. Consequently, various
trades are going to appear, and the rate of specialization will increase in
direct proportion to the number of individuals. If we apply this postulate
here under the conditions mentioned we have:
CPr
1
cPj
q;; = g _ b w or fjJr = g _ b w
(4)
By applying equations (2) (3') and (4) we get:
dw
aw + c
-
= (aw + c) - --:-dt
g - b w
(5)
Upon integration it results
A
B
t = ---;;-log(aw + c) - blog(g -1 - bw) + K
(6)
The examination of this equation reveals that the representative curve is a
sigmoid one with two asymptotes and a point of inflection. The position of
F. COLLOT
But if we want to write the reflected flow fjJr in terms of the number of cells
there arises a difficulty. Each cell, each tissue, each organ reflects a quantity
of energy which depends neither on its volume nor its weight but on its
degree of differentiation. Moreover, in a growing organism, this rate of
differentiation varies considerably from one tissue to another and perhaps
from one cell to another. Therefore, it is impossible to speak of average
differentiation at time t; in order to make the solution homogeneous, while
still assuring permanent growth, the notion of the cell has to be replaced by
that of the "bioton". We shall call "bioton" some volume of living matter
of arbitrary size not necessarily equal to each other but receiving a flow of
IE which is equal to each other and remains constant. Our approach is
similar to that of the physicist, who in the statistical mechanics renounces
to enter into more details and to calculate the trajectory and kinetic energy
of each individual molecule. Let us call w the number of "biotons". Thus,
equation (3) becomes:
fjJi = aw + c
(3')
We now postulate: To any increase of biotonic volume of an organism
corresponds a proportional increase of the rate of average specialization or
of the rate of average differentiation of its constituent parts. This postulate
can be understood intuitively by means of a sociological example. Let us
imagine a primitive community in a remote island composed of ten individuals who live very distant from each other. Each of them will have to
satisfy his proper needs and he will be therefore a fisherman, farmer, mason,
miller, baker and so on. Here the rate of specialization or differentiation
(we ascribe the same meaning to these words) is practically negligible, i.e.
a specialization once attained will remain unchanged. Suppose now that the
number of invididuals increase to one thousand. Consequently, various
trades are going to appear, and the rate of specialization will increase in
direct proportion to the number of individuals. If we apply this postulate
here under the conditions mentioned we have:
CPr
1
cPj
q;; = g _ b w or fjJr = g _ b w
(4)
By applying equations (2) (3') and (4) we get:
dw
aw + c
-
= (aw + c) - --:-dt
g - b w
(5)
Upon integration it results
A
B
t = ---;;-log(aw + c) - blog(g -1 - bw) + K
(6)
The examination of this equation reveals that the representative curve is a
sigmoid one with two asymptotes and a point of inflection. The position of