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@ Luiz Castrese
2025-04-25 11:31:08As is well known, mathematics is a form of logic — that is, it is characterized by the ability to generate redundancy through manifestations in space. Mathematics is unrestricted from the human perspective, since it is what restricts us; it is descriptive rather than explanatory, unlike physics, chemistry, biology, etc. You can imagine a world without physics, chemistry, or biology in terms of how these occur, but you cannot conceive of a world without mathematics, because you are before you do anything. In other words, it encompasses all possibilities.
You may be left without an explanation, but never without a description. Lies can be suggested with mathematics — you can write that “5+2=8,” but we know that’s wrong, because we are beings capable of manipulating it. Explanations are not necessary; it stands on its own. It is somewhat irreverent in its form, and this elicits its truth.
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An interesting way to think about mathematics is that it consists of “points,” where the only variation is their position. It is possible to conceive of a drastically different world, no matter how it differs, but we can only treat them as such because they are the same — except for their location. That is, the creation of a plane becomes possible. This leads us to infer that mathematics is the decoupling of space-time, allowing one to play emperor. In this sense, something that is independent of time can be considered as an a priori truth.
As Wittgenstein put it:
Death is not an event in life: we do not live to experience death. If we take eternity not as an infinite temporal duration but as timelessness, then eternal life belongs to those who live in the present. We can summarize what has been said so far using the following logic:
We are limited by time. You, as a being, can only be in one place at a given moment. Mathematics is independent of time. Therefore, its elements (points) encompass all locations simultaneously. If its elements exist throughout all logical space at once, mathematics transcends time; and if things vary according to time, then mathematics is sovereign. Thus, the point is this: since nothing distinguishes one point from another except position, a point can become another as long as it has a location. That is, it only requires the use of operators to get there.
Operators = act
To clarify: there is no such thing as a distance of zero, because it does not promote redundancy. It’s as if the condition for something to qualify as a mathematical problem is that it must be subject to redundancy — in other words, it must be capable of being formulated.
An interesting analogy is to imagine yourself as an omnipresent being, but with decentralized “consciousness,” that is, corresponding to each location where your “self” is. Therefore, people anywhere in the world could see you. Given that, when you inhibit the possibility of others seeing you — in a static world, except for yours — nothing happens; this is represented by emptiness, because there is no relationship of change. It is the pure state, the nakedness of logic, its breath.
You, thinking of your girlfriend, with whom you’ve just had an argument, see a woman walking toward you. From a distance, she resembles her quite a lot. But as she gets closer, you suddenly see that it isn’t her, and your heart sinks. Subtext: You are alive.
Diving deeper, “0” stands to redundancy as frustration stands to “life”; both are the negation of a manifestation of potential — of life. Yet they are fundamental, because if everything is a manifestation of potential, what value does it have if there is nothing to oppose it?
Corollary: There are multiple locations — and this configuration is the condition for redundancy, since for something to occupy another position, it must have one to begin with, and zero represents this.
A descriptive system
The second part of this essay aims to relate mathematics to what allows it to be framed as a “marker” of history: uncertainty — and also its role as an interface through which history unfolds.
From a logical assumption, you cannot claim the nonexistence of the other, because to deny it is to deny yourself.
As Gandalf said:
Many that live deserve death. And some that die deserve life. Can you give it to them? Then do not be too eager to deal out death in judgment. The issue is that we are obsessed with the truth about how the human experience should be — which is rather pathological, given that this experience cannot be echoed unless it is coupled with a logical framework coherent with life, with the factors that bathe it. That is, a logically coherent civilizational framework must be laced with both mathematics and uncertainty. We can characterize this as a descriptive plane, because it does not induce anything — it merely describes what happens.
Thus, an explanatory framework can be seen as one that induces action, since an explanation consists of linking one thing to another.
A descriptive framework demands a decentralized system of coordination, because for a story to be consistent, it must be inexpressible in its moments (temporal terms) and yet encompass them all. A valid analogy: History = blockchain.
To be part of history, certainty must outweigh uncertainty — and whoever offers that certainty must take on a corresponding uncertainty. Pack your things and leave; return when you have something to offer. That is the line of history being built, radiating life.
Legitimacy of Private Property
As previously woven, there is something that serves as a precondition for establishing conformity between the real plane and the mathematical one — the latter being subordinate to the logical, to life itself. The existence of the subject (will/consciousness) legitimizes property, for objects cannot, by principle, act systematically — that is, praxeological. It makes no sense to claim that something incapable of deliberate action possesses something that is not inherently comprehensible to it as property, since it is not a subject. An element of a set has as its property the existence within one or more sets — that is, its existence, as potential, only occurs through handling.
The legitimacy of private property itself is based on the fact that for someone to be the original proprietor of something, there must be spatiotemporal palpability between them, which is the mold of the world. Therefore, private property is a true axiom, enabling logical deductions that allow for human flourishing.