**Links to**: [[Sameness]], [[Difference]], [[Homotopy Type Theory]], [[Ontology]], [[Analogy]], [[Homotopy]], [[Identity]], [[Reflection]], [[Univalence principle]], [[Equivalence and difference]], [[Generalization]], [[Abstraction]], [[Platonism]], [[Lying]], [[Likeness]], [[Repetition]], [[Difference]]. %% [[Equivalence notes]] %% ### [[Postulate]]: _Equivalence_ in this research means that things^[All the way to Pauli’s _exclusion principle_ level of analysis: where no two particles can have the same qualities at the same time, they necessarily differ because of qualities such as location, etc.] can be made to hold the same identity (can be made predictable in the “same” way) even if they don’t have it, even if this is a lie. _Mutatis mutandi_ holds here.^[In the mathematical sense: implying that we don’t lose the abstractive; generalizing (predictive) capacity of a structure.] But what types of differential engines, what types of infrastructures, support the bifurcation of paths? In natural language, as we saw in “[[04 Concepts as pre-dictions]]”, we observe _negation_ as a foundational bifurcator. But what about other structures, such as certain mathematical or logical principles? These explorations lead us to the writing of the entries: _Equivalence_ / _Equivalence and Difference_, which we have not finished yet. Here, we will contemplate the question of **difference** in terms of equivalence in computation. It will be first argued that, at the level of social dynamics, this question bottoms out, antisocially abstractly, at the question of: is difference compressible to something more foundational than itself (i.e., can we ever get out of individualist traps? Is this dilemma the root of the one and the many? Is the concept of “people”/homo/man/whatever the distracting abstraction that gave rise to not needing to spend energy on understanding an-other?)? This entry explores difference and equivalence as universal, inevitable, inseparably relational _first predictive principles_ in social computation. At least, this is what is argued can be said at this point in history. We thus merge mathematics with the social, and the social with mathematics. Some brief points I want not to forget, because most things related to equivalence are treated in [[Equivalence and difference]] and [[Homotopy Type Theory]]. This note is highly unfinished. #todo. 1) Hofstadter & Sander say, in _Analogy..._: the equal sign… #todo 2) _Equivalence_ in all analogical reasoning is based on the acknowledgement and purposeful effacement of _difference_ (Kant); a) Equivalence is _not_ equality (Voedvodsky), we remove **identity** as a possibility; b) Also in this sense that all speaking is _lying_ (Nietzsche); b) Lying here implies the Aristotelian move of metaphors “giving something the name of something else”, see also: [[Likeness]] and [[Schein]]. 3) The only thing that has no equivalence/analogical-relation to other things is nothingness (Priest), which is why it has historically confused and continues to confuse (its ontological status is fuzzy: it does and does not exist at the same time); a) In this sense nothingness can be understood as _pure difference_ (Deleuze). b) But there are many more things to say about nothingness, see [[Nothingness]], [[Nothing]]. 4) If we relate nothingness to 0 as a _function_ (not always as a set, but _also_ as the empty set), some of the confusions can be cleared (_nothingness_ mathematized becomes a reference point, a relative relation holding for several operations, etc.), but not many would accept that 0 holds the same ontological space/ground as nothingness. 5) The implication that homotopy-typing across scales results in _different types of equivalence_ perhaps hints at the fact that _difference_ is a more fundamental or primordial basic principle than equivalence. However, as the two are somehow mutually-defining, they can be considered a fundamental basic principle in unison, _together_, but that doesn’t feel right to me for some reason. That’s all I can say about it until I understand/apply (i.e., make _equivalent_) these abstract-predictive structures _differently_. ### For the ethicists: Nietzsche. Sameness, for humans understanding each other as the “same” type of creature. As we know: equality is not _equity_ (and Marx: each according...). Difficult questions about equivalence: how to organize equity in society? We cannot define so many things, and if we do: this is not equity. ### Footnotes