Sometimes I feel that everything can be collapsed back to What Is, discarding all the socially constructed abstract bullshit, and a less wrong, less distorted observation can be made for a few seconds – a glimpse of a the Truth.
The task is quite simple – just to reconcile logic, math, programming and the Eastern philosophy of the mind, keeping the properly generalized patterns and tossing away abstract bullshit. Once you have done this a couple times…
Here is how it works. Every area of study, which once used to be called a Natural Philosophy, before it diverges in a distinct sub-disciplines, such as Mathematics and Physics, and then Chemistry and Molecular Biology, is the exactly one and the same Elephant being touched by a bunch of Blind Philosophers. This is the main universal principle – The Elephant is, indeed, the one and the same. What Is.
Everything else just follows – we have incomplete, partial views, strip away the bullshit, and put together the pieces of the Jigsaw Puzzle which cannot be discarded as socially constructed abstract bullshit. The actual facts cannot be falsified or simple dismissed, like the impermanent existence of molecular arrangements as the basic building blocks of everything around (and including) you.
The Intuitive insights – the most weaker but still correct and “less wrong” form of knowledge (of What Is – knowledge is always of some aspect of What Is) – has already arrived at the Ultimate Truths. The Buddha postulated the principles of Dependent Origination (which is what in the Western world is called The Causality principle) and also the ultimate principle of the Impermanence of all arrangements, whole the greatest Vedic insight was that, ultimately, everything is just manifestations (appearances) a single universal “vibration”.
Yes, these are just countless rewrites over rewrites – “moving” social constructions – a chain of transformations within a socially maintained “culture”, as a currently accented set of “memes”.
The “Chain Of Transformations”, however, is not an arbitrary wording. This is one of the Universal Forms, or Universal Shapes of a Process. Yes, processes have its shapes and these shapes constitute a Universal Geometry of not just What Is, but Everything What Is Actually Possible, apart and independent from what can be Observed by the mind (of an External Observer).
The “Forms” are simple. The atoms, which are “localized energy” (some people say “pockets of localized energy”, but just two words is better than three) will show you every possible form, shape and symmetry That Is, not what can be imagined or defined using abstract formulas.
Natural Numbers, Pairs, Symmetry, Sequences, Triangles, Angles, Length, Distance, etc – all the properly captured and properly generalized abstract notions are simply Out There, they Just Are.
If we follow the only pure Mathematics, we will arrive at the Exuberance of Pure abstract bullshit, like some parts of the Category Theory, Multi-dimensional Manifolds and bullshit parts of Topology, and the Theoretical Quantum Physics (with a new fundamental particle being “discovered” every week or so) in the department next door.
The problem is that they have been disconnected from What Is end went all the way into Platonic realms of pure imaginary abstract bullshits – whatever we can imagine or write in symbols “exists” – the core tenet of so-called Liberal Arts Education.
Anyway, what actually exists is the finite set of all possible molecular arrangements in so-called 3 dimensions and the generalization of the reoccurring patterns by the mind of an external observer, of which a [linear] Sequence is the Ultimate one.
The fact that mRNA is (has a form of) a linear sequence is not arbitrary. It tells an Observer that this is Universal Pattern.
The fact that Molecular Biology has evolved distinct necessary but otherwise arbitrary start and stop markers on the sequences it uses tells us about “rotation of an observer around the shape” or rotation of the shape around an imaginary axis, and that these two are “one and the same”.
To “read” a sequence one has to “know” from which end. It also shows that GTA is not the same as ATG, and yet, AA is the same as AA (and, of course, A is the same as A).
Nothing of this is arbitrary or invented or socially constructed. It is all has been discovered and properly abstracted out in non-bullshit branches of mathematics by the mind of an External Observer.
But mathematicians are always going too far and are always getting lost in the realm of socially constructed abstractions. They inevitable invent further abstractions, beyond What Is, and find the way to construct these.
Here is something to realize – everything beyond a Semigroups is socially constructed (Monoids, Groups, etc).
The Causality principle itself, the Modus Ponens, the Composition of Processes is a Semigroup, Not a Monoid. Reality (or What Is) does not have any “empty” values or “identity operations”. It just does not.
Moreover, the arrows of Causality (of What Is) are irreversible in principle – some energy which has been used in an energy-threshold reaction has been lost (from the locality or a “pocket”) as heat, so the inverse arrows is just a theoretical abstraction and simply “cannot be”.
The localized energy-threshold reactions explain the directedness (and in principle irreversibility of the arrows) of the Causality, the abstract notion of an Entropy (inevitable return to the “baseline”), and the ultimate principle of Impermanence Of All Arrangements – all structural arrangements (forms or shapes) are ultimately unstable, and thus impermanent.
This is it, so to speak. Mathematicians love to reverse arrows and do it all the time, but in reality you cannot. This is just a frivolity of an undisciplined mind, which lost its connection to What Is and lost in its illusory constructions.
This is exactly why the apparent (mathematical) duality of “product” and a “sum” feels bullshit – they just reversed the direction of the arrows and claimed a “duality”. But you can do it only inside your head (or only on paper). The arrows of reality are irreversible.
This simple observation collapses the whole Himalayas of socially constructed (and then written down) abstract bullshit.
The question of “time travel” even no longer arises – you cannot go back in Causality simply because it unidirectional in principle, just like any physical reaction, which is subject to (constrained by) It.
If we try to properly generalize, we shall ask “Which Exactly Arrows are Actually Possible, Out There” , which paths are not illusory and can actually to be taken.
And the answer is surprisingly simple – look at what pattern emerge from atomic arrangements – all the possible the forms and shapes are out there, all the non-bullshit, non-abstract geometric notions are out there.
By analyzing these captured patterns one can see the actual “constraints” of the Universe Itself – the recurring (re-emerging again and again at all levels of structural granularity) patterns of “arrows between dots”.
And guess what? A Semigroup, not a Monoid. Composition, but not Duality, Associativity, but without Identities. Functor (as distinct nested structural arrangements), but not Monoids. The notion of an Abstraction Barrier (Boundary) or of a Membrane or even distance-based boundary of Localized Physical Process and the composition (nesting) of such processes from a Monad, but, again, not a full Monoid, which is a theoretical abstraction.
There is more. Causality is directed because it is universally Nested. No reaction can occur before all the requirements are being Causally meet – the necessary atoms has to be present in the particular physical locality, the energy level has to exceed the sufficient threshold (yes, yes, the “necessary and sufficient” meme).
Distinct reactions (within distinct localities) can occur in parallel (having literally nothing in common), but each reaction has that particular (and universal) “a few arrows into a single dot” shape.
Now think of Currying and curried functions, and you will discover this universal shape at the “core” of the Universe. Modus Ponens, a function application, Gentzen’s Elimination are just different captures of the same universal shape.
It is not a random coincidence that these “abstract processes” come in pairs – Introduction and Elimination, Abstraction and Application, etc.
And there are the Universal Invariants – which has been properly captured as the “Laws of Conservation”, so the whole not blows up into infinity or shrinks into nothingness (This collapses another mountain of witter abstract bullshit, and praises the ancient Indian intuitive insight about Universe being “breathing” – expansion following by contraction, followed by expansion, and so on).
So, I promised you a brief glimpse of What Is. Here it is.
Consider a biological colony (of cells) actively maintaining a rigid thermodynamic boundary in a freezing, windy, high-altitude environment somewhere in Manang district. The internal structure—the carefully regulated heat, the physical clustering with distinct well-maintained boundaries—is a localized, high-energy state forced into existence against the ambient cold and void.
It requires a continuous, relentless chain of metabolic reactions or arrows (of causality) to maintain. The moment those causal arrows stop firing, the unstable equilibrium is lost forever, the unidirectional (DAG, Semigroup) nature of entropy takes over. The decomposition inevitably reclaims that heat (vibration, which is what you are), dissolving the boundary and returning the localized state to the raw baseline of the environment.
The very same “pattern” is for every single sub-process of the Universe at all scales “observed and imagined as a whole”. Any star has the same “Causal Shape” or “Form of a Process” as you – an unstable, self-maintaining process, subject to the constraints of the Universe, its symmetries and its geometries.
Notice how the abstract notions of Time and Entropy are intentionally absent, as being precisely just abstract notion of the Mind.
Okay, there is the “take home” message.
If we strip away all the socially constructed abstract bullshit in pure mathematics, and stick only to the properly captured and properly generalized abstractions, by tracing them back to What Is, to non-theoretical physics, atomic-table based chemistry and molecular biology (which are structurally just the same thing (arrangements) at different granularity) we could begin to See Things As They Really Are, or a less wrong glimple of What Is – an ideal of Upanishadic seers, which is a very opposite of the Platonist clowns, by the way.
The key principle is that not everything that can be imagined or expressed in symbols is real or existent, and only what is Real or Existent is worth knowing.
Yes, Monoids and Groups are beautiful abstractions, Products and Coproducts can be viewed as Duals, Isomorphism could be defined as just two arrows in opposite directions between two “objects”, but those are merely over-generalizations or over-abstractions, or, ultimately, subtle social constructs, which does not exist anywhere outside your heads and the shared culture which preserves these abstractions (social constructs) in a written form.
The way a society preserves and maintains its constructions is an another distinct pattern, and it is just imperative over-writing, instead of invariant-preserving nested transformations (which is what Universe consists off).
And finally, when the composition of Nested, Lawful (structure or invariant preserving) transformations has been put at the center (along with the universal notion of introduction/elimination) in the symbolic Logic, the untyped Lambda Calculus, and later Haskell, the Universal, “real” pattern of arrows between dots manifested themselves, and they show or “unveil” the underlying constraints and the “very” structure of the Universe.
Causality is (has a universal shape of) a DAG and the arrows are irreversible in principle. Every sub-process thus, subject to the Causality principle (or the principle of Dependent Origination), has to have exactly the same shape, and this, in turn, the shape of our programs (models) shall have.
This explains the Curry-Howard Isomorphism itself.
Yes, a bunch of arrows between dots. but not all the arrows which can be imagined or drawn on paper are “real” or “possible”, and none are actually reversible.
It is not random coincidence or a mere arbitrary abstract social construct that a DAG is, indeed, “Directed” and “Acyclic” and consist of just “forks, joins and steps” and their associative compositions and nothing else.