ON THE NATURE OF EXISTENCE- PART II
Previously, in the first part of this continuing exposition on the nature of existence(https://medium.com/@raphaelmaz1/on-the-nature-of-existence-c485a97e8d41), a connection between the meaning of existence and of space-time was suggested. Part II delves deeper into a conjecture that pre-supposes a generative state of existence.
Finding the Generative Pre-cursurial State :
Finding the Generative Pre-cursorial State: Where do we look to find this pre-cursorial state that is somehow generative of the present moment, that is the antecedent of ‘Absence’ and ‘Presence’, that furthermore completes the void in our perceptions of existence and, thus, of space, time, and of a deeper understanding of these ideas?
Eugene Wigner, a twentieth century scientist, commented on the ‘unreasonable effectiveness of mathematics to explain nature’, as have many others. There is a mystique surrounding this question of effectiveness of logical systems to align so well with natural phenomena. It is there, but no one has satisfactorily explained the origins, the synthesis of this effectiveness. Let us presuppose that ‘existence’ comes before mathematics; in other words, mathematics is subordinate to existence. Let us pre-suppose that, whatever ‘existence’ is, the world of existence is in some way foundational to logical systems and mathematical formulations. Newton, Maxwell, Planck, Einstein, and all the great quantum originators have aligned reality with mathematics. Others, like Noether, Dirac, and more contemporary mathematical scientists have aligned mathematics with reality and, in doing so, have predicted new phenomena, new realities. The alignment between logical abstraction and reality seems to be a bilateral connection, a commonality founded in something deeper than themselves.
The 15th and 16th centuries are when that ‘something else’ began to reveal itself. Until that era, certain solutions of polynomial equations could not be logically completed given the extent of knowledge of the number system at that time. Cardano and others realized that in order to attain all the solutions of certain polynomial equations, there was a necessity to admit solutions based upon a construct that mysteriously was not a part of the number system; and, furthermore, that mysterious construct could not be created from the then known number system, but that the mysterious construct could only be inferred as a necessity to the completion of the solution space of their equations. That mysterious something ultimately became known as the imaginary number ‘i’.
The nomenclature ‘imaginary number’ is the greatest disservice ever given to revolutionary discovery in the history of science and mathematics. There is nothing ‘imaginary’ about the number ‘i’. It is a reality that not only completes the number system; it is a functional reality that appears in Schrodinger’s equation for time evolution of a quantum system. Quantum systems can be modeled and then experiments setup to measure the quantum system’s behavior. The alignment of quantum predictions with quantum measurements is one of the great triumphs of 20th century science. ‘i’ appears in relativity theory. The spacetime interval properly stated can be expressed as Δx2 + c2Δ(it)2 (delta x square plus speed of light squared times delta (it)squared) . We know relativity theory’s predictions are correct; should we not suspect that there is something different about time, t, with the modifier ‘i’ attached.
‘i’ is not among the real numbers, nor can it be generated from the reals. Casper Wessel, realized that this independence of the imaginary numbers from the reals could be visualized as an orthogonal relationship, thus created the complex plane. The salient point to be made is that this dichotomy of numbers which was found necessary for mathematical solutions exhibits itself in mathematical expressions that describe nature and natural phenomena. Nature reveals itself in real numbers, or at least our measurements do so. The necessity to extract real number data from complex expressions is driven by the need to extract real results from theories that otherwise are born from or do involve complex number considerations. However, the process has been somewhat myopic. The ontological significance of those other than real number formulations in expressions that are derived to explain natural phenomena has been fully overlooked.
Mathematical logic and reality appear to have a sibling relationship. The one can so well portray the other and the second so well abides by the first. Certainly, there must be a common parentage. This portion of this narrative began with a quest to complete the attribute set of which ‘Presence’ and ‘Absence’ form a sub-set with a hope to find a generative precursory element. Let us embrace ‘i’ to that end. Furthermore, let’s denude ‘i’ of its mathematical connotations. Let us rename ‘i’ as ’S’, where ‘S’ signifies, for lack of better nomenclature, ‘Sur-Real’. Furthermore, let us look to the multiplication progression of the powers of ‘i’ for a hint of the meaning we seek.
Finding the Existential Set
The table of operations shown above mirrors the multiplication table for the imaginary number with one very major exception; ‘Ø’, the element that aligns with i3 ( i to the third power), has been modified to satisfy an intuition, a mind perception. The perception is that ‘Ø’ negates all elements. It is an annihilator. One must depart from the rigor of mathematical analogy here to think intuitionally. A.S → Ø. This relationship may be construed in this interpretation as the absence of S, our generative element, infers a condition of existence where absolute void prevails. If there is no generative element S, then none of the three S dependent elements, {A, Ø, P}, can exist. We can then surmise that void, the annihilator, ‘Ø’, operating on all elements of the existential set yields void, ‘Ø’. This is reflected in the 3rd row of the table of set operations, which is the departure from the analogy with the multiplication table of the imaginary number ‘I’.
An important consequence of the modification of the 3rd row of the table of set operations is that if one wishes to consider the existential set as a group, the group is non-Abelian- there are non-commutative elements. (A,Ø) and (S,Ø) no longer commute. Moreover, the alteration reveals a new sub-group.
Prior to the intuitively driven alteration of the interactive table’s 3rd row, it was determined that (A,P) form a sub-group; this can be easily verified. For the sake of identification, let us name this group as ‘State’, G2 . The alteration of the table’s 3rd row does not affect or destroy this relationship of group identity. The postulated modification of the interactive table’s 3rd row creates a 2nd sub-group consisting of (Ø,P). The multiplication table for this group mirrors the multiplication table of the binary numbers (0,1). Let us name this group as ‘Information’, G1. Putting all naming conventions together, we can identify S, A, Ø, P, G1 , G2 , and {S, A, Ø , P}- the existential set E. For the sake of brevity, let us refer to this collection of elements and sets of elements as D7, the Seven Primitives of Discernment.
To summarize where we have come, it has been asserted that there is a deep connection between the usage of the thought ‘to be’ with the essence of space and time. By analogy with the generative effect of the so-called imaginary number, ‘i’, we have imputed a generative pre-cursory element of existence, S. We have departed from a strict analogy with the multiplication table for ‘i’ by modification of the i3 (i to the third power) row ( the ‘Ø’ row of the existential set). Seven primitives of existence have been identified. Further on, it will be suggested how appropriate interpretation of the elements of a 7 x 7 table of interaction defined by D7 x D7 infers the existence of 6 hierarchies of existence.
In the next segment of this exposition, 4 pairs of non-self extinguishing sequences will be generated whose interpretation will be aligned with the nature of space and time.