A point of view is limited in itself.
It gives us a unidirectional view of the landscape.
Only when multiple complementary views
in the same reality add one has
full access to knowledge of things.
The more complex what we want to understand,
The more important it will be to have different pairs of eyes,
so that the light rays converge
and we can see the One through the multiplicity.
This is the nature of authentic vision:
Bringing together already known points of view
and show others hitherto unknown, teaching us that,
In fact, they are all part of the same Whole.
Alejandro Grothendieck
We often say that official science is coming to understand and explain what the ancients already knew through intuition or some type of revelation. This is true, but science has different times and ways of affirming the same truths as the ancients. Its process is much slower and more laborious. A path made of hard chisel work and small steps one after another, steps firmly planted in the earth because to look at the Cosmos of Uranus (the ordered sky of the ancients), it is necessary to have a solid foundation on which to stand and trust. . (1)
A simple example to understand it. We all “intuit” in some way that 1 + 1 = 2. The arithmetic that we study in school when we are children tells us this, but so does our daily experience, our empirical knowledge. For science, however, “intuition” is not enough, science advances through “formal demonstrations” and the formal demonstration that 1 + 1 = 2 occupies the first 300 pages of Whitehead and Russell's book. Mathematical principles, a monumental work whose (failed) goal was to formalize the foundations on which all mathematics is based. Why so much effort to say that 1 + 1 = 2? Because first of all you have to formally declare which actors are involved. What is “1”? What is “2”? What is “+”? And what is “=”? It may seem trivial, but when Whitehead and Russell asked themselves these questions, an abyss of unexpected depth opened before them, and to begin to answer them it was necessary to have a common language with which to define the basic concepts. . This common language in which all mathematics can be expressed is Cantor-Frege “Set Theory”. Towards the middle of the last century, Mac Lane expanded this language by founding “Category Theory”, which gave much more expressiveness to mathematics and its various disciplines such as geometry, algebra or topology. In the 1960s, Grothendieck further expanded this theory, generalizing it and taking it to its essence, introducing the concepts of “Motif” and “Topos”. But at the beginning, to prove that 1 + 1 = 2 and to answer the non-trivial questions we posed above, Whitehead and Russell used set theory and therefore “1”, in Mathematical principles, is “the Set of all Sets containing a single element”. Likewise, “2” is “the Set of all Sets that contain two elements.” “+” becomes an operation of logical union between sets and “=” is a non-trivial concept of equivalence that will reach, with Grothendieck and Morita, its maximum expression of beauty and elegance.
Alexander Grothendieck, who has been called the Albert Einstein of mathematics, used the tool of abstraction to probe the foundations of mathematics ever deeper until he reached its heart. For him, any dilemma could be simplified if analyzed in its essence. He was not interested in numbers, curves, lines or any other mathematical object in particular, but rather the relationship between them. He had an extraordinary sensitivity to finding harmony between things. One of his greatest strokes of genius was to expand the notion of a point. This ceased to be a dimensionless place and came to life with a complex internal structure that contained an infinite universe. All of this gave rise to the aforementioned concept of Topos. Looking at the world and reality through the lens of the Topoi is like abstracting ourselves to such a point that the words of natural language (which we humans invent, while the same does not happen with mathematics, as Plato had already intuited) are not enough to describe the experience. It is like observing the “everything” from the perspective of the “not everything”, or the finite from the 'perspective' of the non-finite or Infinite, defined in these pages as the “veil of the Absolute”.
These are fascinating and charming places of thought, but also extremely dangerous. Grothendieck himself wrote that: “even in mathematics certain things should remain secret forever, for the good of us all.” A statement of this type may seem exaggerated, but just as in physics there are cosmic monsters like black holes that literally destroy space and swallow anything, even time, in mathematics there are demons that are capable of engulfing and annihilating even thought. . Monsters that can drive erudite geniuses crazy, as happened to Gödel (we will talk about this in a moment) or to Grothendieck himself, who wrote: “Humanity lives in the shadow of a new horror”, that of the “dream of reason” (F. Goya). However, beyond the limits of the mind defined as concrete Through the esoteric Teachings, other vibrations wait to be received by the higher levels of intelligent intelligence.
Francisco Goya – The dream of reason produces monsters
And speaking of “essence,” one must be careful at what level to seek the heart of the phenomena that one wants to analyze. An example: we often say that Sound and Light have the same essence. But as physical phenomena, the only thing that sound and light have in common is that they are two vibratory phenomena. That’s all, the analogies end here.
Sound is the molecular vibration of a physical medium, whether gaseous, liquid or solid; in fact, in empty space (or, according to Ancient Wisdom, simply more subtle, considering Space as alive either full of life), outside the Earth's atmosphere, the deepest silence reigns and is inaudible by ordinary physical means.
Light is the vibration of something completely different from sound, it is the vibration of a field: the electromagnetic field that can propagate even in the “vacuum” of deep space; and the Universe itself has a vibration of a still different nature from sound and light, it is the vibration of another field: the Higgs field, responsible for everything that is in manifestation, including the Universe itself, which in turn is a manifest characteristic of the gravitational field. That is to say, stating that sound and light have the same essence presupposes a shared knowledge of the meaning of the word. Essence, which is not that of its physical manifestation, where the two entities are not interchangeable. In occult philosophy, the ideas of sound and light do not, therefore, mean their phenomenal or physical counterparts, but rather the Vibration of life at the various levels of spatial Substance.
Kurt Godel
Like Grothendieck, Kurt Gödel was also interested in essence, understood as abstract truth or the heart of mathematics, and to search for this essence he directed the power of mathematical formalism towards mathematics itself (2). What he discovered has forever marked the world of logic and mathematics, identifying in its 'essence' the very nature of “indeterminacy(3) that Heisenberg had found in the foundations of Physics a few years before. In short, what Gödel discovered is that in formal mathematical systems, like arithmetic, there are statements about numbers that are true, but whose truth cannot be proven using arithmetic itself. Therefore, any formal system, for example any numerical system, is by nature incomplete (which is why Whitehead and Russell's project failed). It presupposes the intervention of a level of observation or understanding different from that of the intellectual reasoning of mathematical research.
Math, maqhmatikov, As a term, it refers to everything related to study, learning and knowledge, but Grothendieck, Gödel and Heisenberg have drawn limits beyond which we are not allowed to go with this intellectual knowledge. There is “event horizons“beyond which everything – space, time, thought – loses its meaning. These great thinkers told us that no matter how deep and passionate our study, there will always be truths that are hidden from us in this manifestation, and science has learned this since the 1930s. No matter how hard humanity tries, there are barriers, veils, beyond which our physical the look cannot go away. We have to accept this and this applies to any type of “teaching” learned. only through certain levels of the mind. This does not mean, however, that science is limited with respect to intuition or the possibility of developing the tools of perception of everything that “in some way resonates with us.” Cognitive limits are universal or proportional to the various levels of 'reality' or consciousness and wisdom teachings state that: “Humanity will only be able to access certain levels of understanding when it is ready.”
The language that science uses to describe these limits is very complicated, for a few “disciples”, just as the language of esotericism is complicated and reserved for those who dedicate themselves to its study. All of us, scientists and esotericists, must strive so that these languages converge more and more and so that scientists do not see esotericists as charlatans and esotericists do not consider scientists blind and deaf. As Grothendieck wrote in the quote at the beginning of this article, only with a common look will it be possible to recognize that we are part of the same Whole.
It is important that, for each discipline of study and research, we proceed with an open mind and curiosity, in order to build bridges of thought, connections and therefore common languages that respect the categories of meaning of each “science”, leading to that unification of knowledge and studies that, over the centuries, we have forgotten.
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1. What is defined as “Scientific Method” is based on the observation of the phenomenon, the theorization of this phenomenon and experimentation to verify the hypothesized theory.
2. This is called a “metamathematical” process.
3. It is impossible to explain here exhaustively Gödel's formidable discovery, which are the “Syntactic incompleteness theorems”. In common language we could summarize their results by saying that any formal system S in which a certain amount of arithmetic can be developed and which satisfies some minimal conditions of coherence (there are no contradictions) is incomplete: one can construct an elementary arithmetical statement A such that neither A nor its negation is provable in S. In fact, the sentence so constructed is then true (in the sense of being possible) since it expresses its unprovability in S, through a representation in arithmetic of the syntax of S. Furthermore, one can construct in arithmetic a statement C which expresses the coherence of S, and C is not provable in S if S is coherent.
