way to exert power over someone, was to make yourself the “normal” one in the face of others and them, the “weird” one, the deviating one. -- https://abuseofnotation.github.io/x-notes/permanent-confusion/13-dana/index.html

i.e. a transformation is natural when every morphism $f$ in $C$ is mapped to morphisms $F(f)$ by $F$ and to $G(f)$ by $G$ (not very imaginative names, I know), in such a way, that we have $alpha circ F(f) = G(f) circ alpha$ i.e. when starting from the white square, when going right and then down […]

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For example, if we again take the relationship between a person and his mother as a function with the set of all people in the world as source, and the set of all people that have children as its target, composing this function with other similar functions would give us all relatives on a […]

So, if there may exist another (simulated?) universe that is an exact copy of our universe, where there is another version of me who is doing exactly what I am doing, does that mean that I don’t have free will? For me, the answer is “No” — I am freely making all of my decisions, it is just that […]

It is often said that the definition of insanity is doing the same thing over and over and expecting different results. This saying embodies one of the main postulates of all human societies — in just a few words, it captures both the function that people have in society (making the world behave […]

In the contrast, in the category of sets where there are potentially infinite amount of functions from, say, the set of integers and the set of boolean values, as well as a lot of functions that go the other way around, and the existence of either of these functions does not imply that one set […]

One of the relationships that functions can represent is the one-to-one relationship, in which we have one element from the source set, pointing to one element from the target set. But for one-to-one functions the reverse is also true — exactly one element from the target set points to one […]

The morphism part might seem hard… until we realize that, once the connections between the object mappings are already established, there is only one way to connect the morphisms — we take each morphism of the source category and connect the two morphisms given by the two functors, in the target […]

This is the same viewpoint that we adopt in programming, especially when we work on the higher level — there might be many different implementations of pair, but as long as they work in the same way (i.e. we can convert one to the other and vice versa) they are all the same to us. -- […]

Here I want summarize the argument that David Deutch makes in “The fabric of reality” about quantum mechanics, non-determinism and life. He explains how DNA (which we can view as the embodiment of “free will”) has a special place in the universe because it copies itself in a way in a manner that […]

And because the monoid operation is always given in the context of a given monoid, we can view the element $2$ and the function $+2$ as equivalent in the context of the monoid. -- https://abuseofnotation.github.io/category-theory-illustrated/03_monoid/index.html

Too much of the left wing/right wing discussion is about which is better, when every ideology is bad when pushed to the extreme: If you lean to the far right you get wars, genocide, people dying on the street etc. and in the far left you get degrowth, free health care and education for everyone […]

Same argument as in the previous analogy applies - seeing several appearances at the same time is not enough to establish that these appearances correspond to simultaneously existing objects. In order to postulate that, we should observe some relation between the objects, indicating that they […]

But that’s nonsense. People don’t do bad things for money because they are evil, or extremely materialistic by nature, they do them because they are hostages to the system, because the belief in the fairy tale made a society where money is equal to life itself. -- […]

Let’s talk about Occam’s Razor. The most popular formulation of Occam’s Razor says that “the simplest explanation is usually right”, but I think this is a huge oversimplification of Occam’s razor. -- https://abuseofnotation.github.io/occams-razor/index.html

The first component of a functor is a mapping that converts one type (let’s call it A) to another type (B). So it is like a function, but between types. Such constructions are supported by almost all programming languages that have static type checking in the first place — they go by the name of […]

In the case of our color-mixing monoid, the identity element is the white ball (or perhaps a transparent one, if we have one). -- https://abuseofnotation.github.io/category-theory-illustrated/03_monoid/index.html

So Smith’s evidence for (d) is based on some other assumptions e.g. “the president of the company makes the decision all by himself”, “the president of the company will not lie to me.” “Jones’ pockets don’t have holes in them” etc. But how we justify those? If we keep God out of the picture, we […]

The one I use is called 7]vim, but since it takes time to getting used to I won’t be preaching it to you (you can click the link to read all about why I use it.) A more beginner-friendly editor is [8]Sublime text, for example. You can even get a Word-style editor that supports markdown or the […]

3. Translate all instances of the symbol in the program to pointers to that location in memory (because a symbol was actually interchangeble with a memory location). -- https://abuseofnotation.github.io/fp/index.html

“I proclaim that justice is nothing else than the interest of the stronger. [..] And the different forms of government make laws democratical, aristocratical, tyrannical, with a view to their several interests

Overall, orders (thin categories) are often used for exploring categorical concepts in a context that is easier to understand e.g. understand the order-theoretic concepts of meets and joins would help you better understand the more general categorical concepts of products and coproducts). -- […]

Note that most mathematical operations, such as addition, multiplication, etc. require two numbers in order to produce a result. This does not mean that they are not functions, it just means they’re a little fancier. Depending on what we need, we may present those operations as functions from […]

They don’t think collectively, so they are not concerned by the fact that they are creating a world that is incompatible with people: if you replace a worker with AI, your profit is up, but if all workers are replaced by AI then there can be no profits as there would be no one to buy (that’s the […]

We saw that for some groups, like the groups of symmetries and rotations, the group elements can be understood not as objects but as actions. This is actually true for all other groups as well, e.g. the red ball in our color-blending monoid can be seen as the action of adding the color red to […]

Further, assume that Laplace’s demon is still able to do its thing in some parallel universe, but that I am able to get a hold of its computations. If so, I can find the part where he says what I will do next and do something else (I can do that because the computation deterministic i.e. fixed) […]

And it so happens (actually for very good reason) that the join operation again corresponds to an operation that is relevant in the context of the objects — the join of two numbers in this partial order is their least common multiple. -- […]

What are ideas? According to Plato they are concepts, ones which are much bigger than anything that we can experience. An example of idea is the idea of justice that is discussed in the Republic (and the republic is itself a good example of an idea-driven approach). -- […]

“So let’s go,” Catherine said and we all went, breaking the exit rule, each for their own reasons: Catherine, because in her own words that breaking rules and not getting punished was the only privilege she had. Anna, because she preferred to trash her principles than to have them, but not to […]

The ultimate conclusion that you can reach when comparing their viewpoints is that causality is not a law, nor a meta law, but a belief which every thinking being must hold to some extend. -- https://abuseofnotation.github.io/kant-hume/index.html

Indeed, while we can model certain aspects of the world with some degree of accuracy, the notion that we could perfectly model the entire world suggests that it was designed specifically for us — a proposition that I find highly unlikely. The resemblance between our mental images and the world […]

A most recent example of this phenomena is the Facebook project to create a virtual world (called the Metaverse). This is a typical escapist technology which, instead of trying to address some shortcomings of our world, seeks to replace it completely by a very bad copy of it (and one that is […]

If you know about semiotics, you may view the source and target categories of the functor as signifier and signified. -- https://abuseofnotation.github.io/category-theory-illustrated/10_functors/index.html

When we should consider a green technology fake? I consider it fake if it fails to fulfill its promise to help us cope with the climate disaster. So, being slightly less-polluting than some of it’s alternatives does not qualify a technology as green. A good example of a fake green technology are […]

We saw how picking a different selection of laws gives rise to various types of monoids. But what monoids would we get if we pick no laws at all? These monoids (we get a different one depending on the set we pick) are called free monoids. The word “free” is used in the sense that once you have […]

This sentence contains the assumption that all objects in the universe are either mortal or immortal, which is questionable e.g. what about the objects that are not alive in the first place? e.g. is a chair mortal or immortal? -- https://abuseofnotation.github.io/time/06/index.html

The main problem with this principle is marketing - few people would sell you a 10$ product that can solve your problem for ever, when they can sell you a 1000$ product, with 10$ per month maintenance cost, that will become obsolete after 10 years. If you listen to the “experts” you would likely […]

“Do you want to see Dana?” Ann she asked me after a while (Dana was the nickname she used for that dirty profile in that social network that she told me about) and then she explained what she meant - she liked to show me the sexy outfits that she had bought in order to take the pictures she […]

My focus for the next year or so is to stop being so self-critical. No reason whatsoever to beat yourself for stupid shit, and it destroys your self-esteem, allowing you to be exploited by people who don’t even know what self-criticism means. -- […]

We can represent product groups this way too. Let’s take Klein four-group as an example, The Klein four-group has two generators that it inherits from the groups that form it (which we considered as vertical and horizontal rotation of a non-square rectangle) each of which comes with one law. -- […]

Conflating M with W, not recognizing that they are different things, can lead us to the mistaken belief that the world (W) is deterministic (i.e. everything we see that is not lawful is an illusion), when in reality, unpredictability is the defining characteristic of the world. When we fail to […]

It turns out that this property defines the singleton set uniquely i.e. there is no other set that has it, other than the sets that are isomorphic to the singleton set. This is simply because, if there are two sets that have it, those two sets would also have unique functions between themselves […]

In this installment, we will see that not only the way we think, but the way we communicate is formal, and that perhaps it is that very ability (to communicate) that makes our thinking formal. -- https://abuseofnotation.github.io/logic-communication/index.html

We can define a function that is the equivalent to performing the operation described above. That would be a function such that, if you follow the arrow $h$ for any element of set $Y$ you will get to the same element of the set $G$ as the one you will get if you follow both the $g$ and $f$ […]

would learn that Anna, although seemingly detached from reality, actually felt a very strong need to identify with someone else from it, a need that was probably inexplicable to her as it was to us. -- https://abuseofnotation.github.io/x-notes/permanent-confusion/05-fence/index.html

We all know that if statements should handle all possible cases and doing so is very easy, especially if we keep one condition per statement, we just have to ensure that every if statement has an else clause which would handle the cases where the other condition or conditions are not satisfied […]

Luckily, I was able to detect the “boring robot” behavior on time so I managed to stop myself on time and never said any of those at hindsight awful-sounding things that Anna had probably heard too many times (one is already too many), nor did I go at the equally easy-to-fall-into opposite […]

Many technologies that are not humane are justified with the following point: “Sure, I agree that tech X is unpleasant/polluting/ugly, but look how efficient it is. If we use it we would produce so much stuff/save so much time that it is worth it.” -- […]