Since 1970, when I drew for the first time this cosine curve for the masses of individuals, I have often interrogated myself about its origin. It seems fundamental because it bears on the structure of living beings. But I never found in modern science any material for an answer to this question : By which physical process the living matter builds itself thus ?

The explanation must take into account this curve and the fact that it is valid only for discrete values. The discontinuity arises from the disposition of individuals in organisation levels, each of them resulting from this going back : gathering of a great number of similar individuals in order to form assemblies, and setting up of a small number of different assemblies for creating upper level individual. The masses of individuals regroup themselves by level around the same order of magnitude.
An other important aspect of this curve is that it bears as much on beings that constitute biological edifice as we have just seen, as on those which form the cosmos. It is the same curve that supports the breakdown of these two categories of beings : It has an universal span.

It took me more than thirty years to arrive at the beginning of explanation I display here ; meanwhile I laid down a certain number of stakes (the elements of order
and the ontostat, the repositioning theorie) which are now important pillars of it.

Mathematical aspects. One interesting model could be that generated by the beat of two waves (figure 1). The red curve is the beat curve, which summarizes the two others, sin p in black and sin q in green ; its outlines take up a sinusoidal form (cos(p-q)/2) on account of the relation :

sin p + sin q = 2 sin(p+q)/2 . cos(p-q)/2

for the discrete values where sin(p+q)/2 is equal to + or – 1. That agrees with the maximums or minimums of the red, beat curve.

Figure 1

The curve that interests us is the envelope curve. It is discontinuous and valid only for the extremums of the beat curve it joints.

Let's see that in more details on the following figure 2, where I removed both basic waves (sin p and sin q). The beat curve remains in red and the envelope curve is reproduced in blue. I kept for it a continuous plotting, only for the clearness of the demonstration.

Figure 2

The explanations we can give. This blue curve reproduces the cosine curve of masses by levels already presented in previous chapters. It is graphically got here by the beat of two waves. Each period of the beat wave (in red) standing for a level, parameters are chosen so that we have effectively 10 levels for a half period of the blue curve. So we get back a cos(Nπ/10) which squares, disregarding temporarily the constants, with our formulation of individuals masses according to levels.

All that is astonishing. This mathematical and graphic work is likely to bring us the explanation of our first, empirically obtained, results, and then of the breakdown of masses and of the organisation by levels of heavenly bodies and living beings.

The hypothesis could be this : The universe is swept by two waves, of slightly different wavelengths. It is this double wave model that I have already presented, in smaller size of course, for elementary particle and which allowed me to make a certain number of interesting demonstrations in physics. On it, too, is built the ontostat. So we are on the good way, and whith this lighting I am able to complete the hypothesis on this set of waves at the origin of the contents of the Universe :

These are probably dilatation - compression waves, like sound waves ;

They are of opposite direction :

one retarded, divergent, coming from the past and going to the futur wave, like all those we see every day on the surface of a stretch of water;

and an advanced, information wave, coming from the futur;

These two waves associate in a beat wave, or phase wave, the role of which is determinant.

As they beat, these two waves are out of phase, differently according to places and times.
This creates zones with different influences between causality and information, more or less favorable to developpement
of organized structures, like living matter or heavenly bodies.

There is still much to say and numerous pages to put on the web. In a still in preparation work, I will show the existence of a relationship between complexity and masses of individuals. The link being the possibility of establishing feed-back controls of present by future, more and more important as rising in the level ladder and in relation with the variable shift of the two waves.