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The «cell» according to the argument 4, is analogous to sphere of shadow. But, as a
substrate of the sphere of shadow, is the cultural structure: a «dissimulated» circlet on the
floor of the cell corresponds undoubtedly to a mathematical principle, an archetypical
integrated symbol, «dissimulated» in the scheme of a Relation.

The allegory permit us to comprehend, then, that the Liberators Gods with their
charismatic message, discover a mathematical principle which remained unconscious in the
cultural structure, which we named «principle of the enclosure». Thereby:

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c - The «circlet» in the cell of the prisoner is analogous to the «principle of the enclosure»,
mathematical principle, or Collective Archetype which remained unconscious in the asleep man

and that the message of the Liberators Gods dis-cover.

I demonstrated, days ago, that in the mental process that give place to the «scientific
idea» of a phenomenon concurs elements of two main sources: the «mathematical principles»
and the «preeminent cultural premises». This can be verified mainly when formulating a «law of
the nature», which explains the behavior of a phenomenon establishing casual relations
between aspects of the same. I will give a simply example: to «measure» the side of a regular
polyhedron. Here the phenomenon is a corpus with the form of a regular polyhedron; it means
a «phenomenic entity». It takes for it the «graduated rule», which is, a flat surface where are
engraved the longitudinal units and from which we are secure that one of its sides if perfectly
straight. We make it coincide with the zero in the ruler with the «beginning» of the object that
we will measure. It is observed now that the «end» of the side coincides with the number five of
the ruler and it is affirmed without more that «in the polyhedron, the side measures five
centimetres». It has been realized, as will be seen, a series of subjective operations which
conclusions, however, can be confirmed by others observers; this possibility of testing is what
gives the designation of «law of the nature» to the mentioned fact.

But it occurs that in the ruler, that we believe numbered, are really engraved signs that
represent numbers, not numbers themselves. The numbers are mathematical principles
property of the cultural structure, subjective elements, which intervene in the act to «recognize
that the limit of the side coincides with the sign «5». When we say «measures five centimetres»
we make the affirmation of an empirical quality: «exists a proportion (it means, a mathematical
relation) between the longitude of the side of the polyhedron and longitude of the earth
meridian». This proportion is inert or constant (=5cm.) and constitutes a «relation between
aspects of a phenomenon», that’s to say, a «law of the nature».

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