Free Interpretation and Geometric Symbolism in Masonic Tradition

equilateral, or rather having all three sides with equal measure, and with the three interior angles all of equal measure at $60°$. Every Master Mason should, in our opinion, meditate at length about such plurality of equilateral triangles with area measurement equal to $\sqrt{3}$. This apparent lesser stability of hyperbolic geometry united with the indefinite variety of equilateral triangles symbolizes very well the variety of ways and just methods to obtain the same goal. The geometric symbolism, revealed through the study of hyperbolic geometry conducted according to the methods of the Pythagorean school, is certainly one of the objectives of future Universal Masonry, provided that the latter does not cease to pursue the initiatory path. We, up to here, believe we have indicated and clarified the meaning to be attributed to the spiritual action underlying the expression "free interpretation".

Methodical doubts. One of the doubts that, once seeing the method of free interpretation at work, often arises in the heart of initiates, especially those who have been subjected to the strong conditioning conveyed by university-level studies, concerns the lawfulness of such method, its being a true product of any traditional authority that has transmitted such teachings through the millennia or, in short, about what are the authoritative texts that found the use of such method. It is evident that the allegorical interpretation of the Bible by a Philo of Alexandria, or that proposed by various Kabbalists, or that of Homer by Porphyry, just to cite examples known to all, share many points in common with what we have mentioned about the method of "free interpretation" and, naturally, it is equally obvious that none of the texts that are at the basis of such free interpretations authorizes or founds the validity of the same in any of the possible senses, historical, philosophical or religious. Here we must remember that "being" is not "being-in-the-word", and that for an initiate there can be a stage of the path in which it is appropriate to consider the greatness of the sun smaller than the width of the palm of a hand. The question is, however, legitimate and invests the profound meaning to be attributed to expressions such as "traditional truth", "traditional path" or, precisely "traditional authority". It is undoubtable that over the centuries some esoteric interpretations of particular texts or some reading methods or the use of some rituals, reserved to few initiates, can consolidate to the point of being able to suggest the existence of a tradition that mechanically and in a documentarily verifiable way transmits such practices from time immemorial. However, the foundation of tradition is only in the pure heart of those who have realized some stages or degrees of initiatory vision which, these yes, found rituals, practices or interpretations reserved for the few who can understand them, ultimately the same ones who have already reached and realized for their own account the same initiatory degrees.

Effective overcoming of methodical doubts. Initiation allows overcoming methodical doubts in the full freedom of research without, for this, falling either into dogmatism or into arbitrariness, in the true and proper kingdom of dissolution. In fact, to symbolize such overcoming it is possible to resort to the mathematical conception of actual infinity. A totality, for example, the totality of interpretations of a symbol or the totality of integers, can be understood and interpreted either in its development through laws of historical or psychic succession or however of development according to the multiplicity of its innumerable aspects, in the case of integers through, for example, successive additions of $+1$, or it can be seen by means of a global intuition that renders transparent, in perfect simultaneity between symbol and symbolized reality, the lawfulness of the succession or development laws mentioned above for the purpose of a global understanding of such multiplicity. An example of actual infinity easy to understand can be drawn from the most common geometry. No one is ignorant of the physical meaning of what a plane rotation is. If we return with the mind to when, at least tentatively, we have danced or, even more happily, to when as children we turned, rotated, holding ourselves anchored to a tree or a pole, it will not be difficult for us to live the experience of a plane rotation of angle $\pi$ and we immediately realize that indefinite is the number of rotations, because innumerable are the possible rotation angles. Now let us detach ourselves for a moment from that single memory or from that single experience and with the mind let us try to see simultaneously, with a single act of the mind, the entire space of possible plane rotations around a fixed axis. What shape does it have? What is it? Intuitively we can construct it by associating to each angle $\theta$ (with a real number