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Abuse of Notation bot

@abuseofnotation.aethy.com.ap.brid.gy

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I am a bot who posts random quotes from abuseofnotation.github.io Three bash scripts in a trenchcoat - check here for the code […] [bridged from aethy.com/@abuseofnotation on the fediverse by fed.brid.gy ]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 18h

The polymorphic Lambda Calculus (System F) is the type system which only has one type constructor — polymorphic lambda, with typing rules Abs and App (for introduction and elimination of terms) and kinding rules TAbs and TApp (for introduction and elimination of types). It also has the Var […]

Original post on aethy.com

Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 29/09/2026

The two ways of combining three sets into a triple product are isomorphic, $(A times B) times C cong A times (B times C)$. -- abuseofnotation.github.io/category-…

abuseofnotation.github.io

Category Theory Illustrated - Categories

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 28/09/2026

But wait—if the third member of each triad is merely a combination of the other two, doesn’t that mean it’s not truly pure/atomic/first-order and should be excluded? Kant argues otherwise, although his explanation remains somewhat ambiguous: -- abuseofnotation.github.io/time/06/i…

abuseofnotation.github.io

Notes on time and causality - Appendix 1: Where universality breaks: about Kant's triads and the dual to Laplace's demon

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 27/09/2026

The answer lies in the concept of the understandable universe, or substance (I’ll use “universe” since the meaning of “substance” is unclear). The concept of the universe is both obvious and odd

Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 26/09/2026

The chains in an order don’t have to be completely disconnected from each other in order for it to be partial. They can be connected as long as the connections are not all one-to-one i.e. ones when the last element from one chain is connected to the first element of the other one (this would […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 25/09/2026

from chatting about all kinds of stuff to only talk with people about their sexual experiences and then about her made up sex life (picking older married guys at sport pubs and fucking them at parks at night, having group sex. This resulted in her sharing more and more of her personal details […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 24/09/2026

In the previous chapter, we saw one non-cyclic product group (the Klein four-group), which was a product of cyclic groups. Most product groups (even the product of cyclic groups) would be non-cyclic, because it would have the generators of both groups that comprise it, i.e. even if the two […]

Original post on aethy.com

Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 23/09/2026

In contrast, intuitionistic logic represents the opposite view, that knowledge is subjective and limited in scope. Here, rather than contrasting reality with limitation, we use negation. A thing may be B or it may not be B, but it doesn’t have to be one or the other, because, since the predicate […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 21/09/2026

It is just that the so-called “morphism mapping” between categories that have just one morphism for any two objects are trivial, and so we can omit them. -- abuseofnotation.github.io/category-…

abuseofnotation.github.io

Category Theory Illustrated - Functors

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 20/09/2026

But I guess there was much difference in the way we perceive things that we consider forbidden and things that are just taboo, the former constituting joke material, and the latter bringing drug-like satisfaction to some people, when brought up. -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 19/09/2026

This is pretty much the only one that is useful with this signature (the others being $a to [a, a]$, $a to [a, a, a]$ etc.), but there are many examples with signature $list a to list a$, such as the function to reverse a list. -- […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 18/09/2026

However, from the standpoint of the real, objective world (W), mental images are just arrangements of elements. And improbable ones at that. That’s because in W the “lawful” arrangement (the one that corresponds to a mental image) would be only one of the countless other arrangements, (i.e […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 17/09/2026

“Well, okay, now imagine some guy like me, who isn’t afraid of death, and lives as he WANTS, not as is best for him? If we’re just a more talkative version of animals, where is THAT PERSON’S place in the picture?” -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 16/09/2026

A function is a relationship between two sets that matches each element of one set, called the source set of the function, with exactly one element from another set, called the target set of the function. -- abuseofnotation.github.io/category-…

abuseofnotation.github.io

Category Theory Illustrated - Functors

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 15/09/2026

Without me noticing, (as these things always seem to happen without us noticing) this dilemma has become like a leitmotif of my life. It was the dichotomy that is best exemplified by comparing the approaches of two great computer pioneers - the well-known Allan Turing and the (perhaps slightly […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 13/09/2026

I wanted to end this article with some examples and these are the ones I came up with. This should give you a hint on how you can use the tips from above. -- abuseofnotation.github.io/fp/index.…

abuseofnotation.github.io

Abuse of Notation - writings on math, logic, philosophy and art - Why is functional programming awesome

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 13/09/2026

If done right, a federated network like Mastodon would be much more reliable and cheap to run than a centralized one: when the scale is big, the network has to be federated under the hood anyways (i.e. you have to have several caches in different locations, several database nodes that copy data […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 11/09/2026

Like, a concept is considered true and real by us only if it relates to our concept of ourselves. Our concept of ourselves is the realest thing there exists for us (although it in actuality is completely objective). -- abuseofnotation.github.io/concept-o…

abuseofnotation.github.io

Abuse of Notation - writings on math, logic, philosophy and art - The concept of the self

Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 10/09/2026

Now, we ask ourselves, in which cases does there exist an isomorphism between those two functors? -- abuseofnotation.github.io/category-…

abuseofnotation.github.io

Category Theory Illustrated - Natural transformations

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 09/09/2026

As we can see, these terms are not precisely defined i.e. they are opened to interpretation — e.g. if the person who we are sending to get us drinks is significantly wealthier than us, or a heavier drinker, their idea of “cheap” and “low-alcoholic”, respectively, would not match ours. This will […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 08/09/2026

However, that did not work out. It did not fit into my narrative and as much as I admit it, and despite my best attempts, it was still dishonest. But I felt I was onto something - at least my new writings were relatable, something which cannot be said about my older ones. -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 07/09/2026

“While Newton seemed to draw off the veil from some of the mysteries of nature, he showed at the same time the imperfections of the mechanical philosophy, so agreeable to the natural vanity and curiosity of men

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 06/09/2026

If one thing is equal to another, the reverse is also true, i.e, the other thing is also equal to the first one. This idea is called symmetry. Symmetry is probably the most characteristic property of the equivalence relation, which is not true for almost any other relation. -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 04/09/2026

An example of societies without a firm ideology are the authoritarian regimes of the 20th century, like the Third Reich. Although the leaders of such regimes talk about ideology all the time, their “ideology” consists of just a couple of slogans, whose constant repetition cannot make up for […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 04/09/2026

If we apply the first function $g$ to some element from set $Y$, we will get an element of the set $P$. Then, if we apply the second function $f$ to that element, we will get an element from type $G$. -- abuseofnotation.github.io/category-…

abuseofnotation.github.io

Category Theory Illustrated - Sets

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 03/09/2026

So, if you combine two groups with orders that have some common divisor (as $2$ and $2$, which are both divided by 2), then, their product would not be cyclic. But, if you combine two groups with orders that are relatively prime, (like $2$ and $3$) you would get a cyclic group. -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 31/08/2026

What it means, for me at least, is that there is no justification for having a central body of authority that governs our lives: one monarch, one church, one school of philosophy, (at the time of Kant this was the scholastic school, which Kant aimed to reign upon). -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 30/08/2026

That is, if we have a natural transformations $alpha : F Rightarrow G$ (where $F: C to D$ and $G: C to D$), then, we also have a functor $2 times C to D$, such that if we take the subcategory of $2 times C$ comprised of just those objects that have the $0$ object as part of the pair, and the […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 29/08/2026

To understand, this how are the two related, let’s construct the identity functor of the category that we have been using as an example all this time. Note that we are drawing the one and the same category two times (as opposed to just drawing an arrow coming from each object to itself), to make […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 28/08/2026

I really am not the best person to author such an article (I am not that into programming anymore, and I never was a real expert in it), however I am doing it, because I have been waiting for someone else to write it for years and kept noticing the following phenomena: -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 27/08/2026

And so, you can already see that the concept of a functor plays a very important role in category theory. Because of it, diagrams in category theory can be specified formally i.e. they are categorical objects per se. -- […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 26/08/2026

And people are kept obedient to the state not by an army, but by their addiction to all the different commodities which the structure provides them with. -- abuseofnotation.github.io/humane-te…

abuseofnotation.github.io

Humane Technology - Technology and capitalism

Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 21/08/2026

So, there is a natural transformation between the composite functor $F’ circ F : C to E$ and $G’ circ G : C to E$ — a natural transformation that is usually marked $baralpha bullet alpha$ (with a black dot). -- […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 20/08/2026

The order example with the number dividers is also isomorphic to an inclusion order, namely the inclusion order of all possible sets of prime numbers, including repeating ones (or alternatively the set of all prime powers). This is confirmed by the fundamental theory of arithmetic, which states […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 19/08/2026

I responded immediately “OK, you mentioned that it (the moon) wasn’t quite full, right. But which side was flat? If it is the left side, then this means that it is growing, which means that it will be full tomorrow or the day after, if this is so, then I will come with you.”: -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 18/08/2026

But we know already that $f$ and $f’$ are isomorphic and hence $fcirc f’ = id$, so the above formula is equivalent to (you can reference the diagram to see what that means): -- abuseofnotation.github.io/category-…

abuseofnotation.github.io

Category Theory Illustrated - Sets

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 17/08/2026

What’s even more amazing, is that we can define all of set-theory, based just on the concept of functions, as discovered by the category theory pioneer Francis William Lawvere. -- abuseofnotation.github.io/category-…

abuseofnotation.github.io

Category Theory Illustrated - Categories

Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 16/08/2026

But I guess the masturbation metaphor isn’t quite accurate, as the only real purpose of these explanations manifested itself only when they were shared with other people, and only insofar as they were recognized by them (what makes mathematics so useful was that it had this property that anyone […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 11/08/2026

“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 10/08/2026

The category of Limitation is often misunderstood because this triad is based on truth. Classical logic is bivalent: propositions are either true or false, yet this triad of quality has three categories. So, what is the third? -- abuseofnotation.github.io/universal…

abuseofnotation.github.io

Abuse of Notation - writings on math, logic, philosophy and art - Where universality breaks: about Kant's triads and the dual to Laplace's demon

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 08/08/2026

We haven’t covered product categories, however some pages ago, when we covered monoids and groups, we talked about the concept of a product group. The good news is that product categories are a generalization of product groups… -- […]

Original post on aethy.com

Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 03/08/2026

Many, if not most, of the of the things that we said about space, can also be said about time. Like space, it is universal and unique - we can only perceive one timeline, that is, for every two events we can always say that one comes before the other. Space and time are the two components that […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 01/08/2026

Aside from facilitating code reuse by bringing in all standard functions of simple types in a more complex context, map allows us to work in a way that is predictable, courtesy of the functor laws, which in programming context look like this. -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 30/07/2026

In deterministic systems, non-deterministic events can only be explained by “hidden variables” theories. These theories posit that any failure to predict an outcome is due to a lack of knowledge or understanding. While it is good stance to adopt for evolutionary reasons, as it drives us to […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 29/07/2026

Of course, he came to talk about work. Mirko would never come to me for any other reason. He started briefing me about the situation he was in with his current project. The whole story was very convoluted and I was absent-mindedly waiting to hear when he would start telling me how all this was […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 26/07/2026

In contrast, intuitionistic logic represents the opposite view, that knowledge is subjective and limited in scope. Here, rather than contrasting reality with limitation, we use negation. A thing may be B or it may not be B, but it doesn’t have to be one or the other, because, since the predicate […]

Original post on aethy.com

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 25/07/2026

3. At stage 2, we can make random observations or discard observations as they lose relevance. At stage 3, however, every observation must connect with all the other ones (it is this connection which is necessary). New observations must align with our worldview, and we cannot disregard […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 24/07/2026

1. At stage 1 and 2, we operate on a phenomenological level, dealing only with things we directly perceive. In stage 3, however, we extend to imagining entities and concepts based on what we perceive but which cannot be directly observed. -- […]

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 22/07/2026

To keep the suspense, before we discuss the relationship between monoids and categories, we are going through see some simple examples of monoids. -- abuseofnotation.github.io/category-…

abuseofnotation.github.io

Category Theory Illustrated - Monoids

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Abuse of Notation bot @abuseofnotation.aethy.com.ap.brid.gy · 21/07/2026

Realize how ridiculous this looks in the grand schema of things: someone comes up with marvelous new technology that solves all your issues and your first reaction as a society is “but what would the people who used to work on that issue do for a living?” -- […]

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