Abuse of Notation bot
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I am a bot who posts random quotes from https://abuseofnotation.github.io
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The last law is called totality (or connexity) and it mandates that all elements that belong to the order should be comparable ($a ≤ b lor b ≤ a$). That is, for any two elements, one would always be “bigger” than the other. -- […]
Original post on aethy.com
aethy.com
December 24, 2025 at 4:26 PM
The last law is called totality (or connexity) and it mandates that all elements that belong to the order should be comparable ($a ≤ b lor b ≤ a$). That is, for any two elements, one would always be “bigger” than the other. -- […]
Or more formally put, for any $a$ and $b$ if we have $a ≤ b$ we should also have $F(a) ≤ F(b)$ (and vise versa). -- https://abuseofnotation.github.io/category-theory-illustrated/10_functors/index.html
Category Theory Illustrated - Functors
abuseofnotation.github.io
December 24, 2025 at 4:17 PM
Or more formally put, for any $a$ and $b$ if we have $a ≤ b$ we should also have $F(a) ≤ F(b)$ (and vise versa). -- https://abuseofnotation.github.io/category-theory-illustrated/10_functors/index.html
Let’s construct one more set. The set of all balls that are warm in color. Let’s call it $Y$ (because in the diagram, it’s colored in yellow). -- https://abuseofnotation.github.io/category-theory-illustrated/01_set/index.html
Category Theory Illustrated - Sets
abuseofnotation.github.io
December 18, 2025 at 6:03 PM
Let’s construct one more set. The set of all balls that are warm in color. Let’s call it $Y$ (because in the diagram, it’s colored in yellow). -- https://abuseofnotation.github.io/category-theory-illustrated/01_set/index.html
Again, going straight from requirement to code would result in a somewhat messy block (note that there are two subsequent if-s - something which I see as an anti-pattern). -- https://abuseofnotation.github.io/if/index.html
Abuse of Notation - writings on math, logic, philosophy and art - Structured programming: how to write proper if statements
abuseofnotation.github.io
December 16, 2025 at 6:02 PM
Again, going straight from requirement to code would result in a somewhat messy block (note that there are two subsequent if-s - something which I see as an anti-pattern). -- https://abuseofnotation.github.io/if/index.html
Note that a while a formal picture might be misunderstood, i.e. the picture that is in the communicator’s mind end up different from the one which is received, a non-formal one is (in some sense) always misunderstood, simply because it doesn’t have a single logically sound interpretation. -- […]
Original post on aethy.com
aethy.com
December 13, 2025 at 6:03 PM
Note that a while a formal picture might be misunderstood, i.e. the picture that is in the communicator’s mind end up different from the one which is received, a non-formal one is (in some sense) always misunderstood, simply because it doesn’t have a single logically sound interpretation. -- […]
My criticism of Boolean thinking is not merely academic. The way we think about logic shapes how we think about everything — and, ultimately, how we live our lives. This is why what I call “Boolean thinking” in logic has many names elsewhere. In philosophy, it’s called Platonism. In politics, it […]
Original post on aethy.com
aethy.com
December 12, 2025 at 7:38 PM
My criticism of Boolean thinking is not merely academic. The way we think about logic shapes how we think about everything — and, ultimately, how we live our lives. This is why what I call “Boolean thinking” in logic has many names elsewhere. In philosophy, it’s called Platonism. In politics, it […]
We won’t use the balls this time, because in terms of symmetries, they have just one position and hence just one action — the identity action (which is its own reverse, by the way). -- https://abuseofnotation.github.io/category-theory-illustrated/03_monoid/index.html
Category Theory Illustrated - Monoids
abuseofnotation.github.io
December 11, 2025 at 6:01 PM
We won’t use the balls this time, because in terms of symmetries, they have just one position and hence just one action — the identity action (which is its own reverse, by the way). -- https://abuseofnotation.github.io/category-theory-illustrated/03_monoid/index.html
And they are everywhere. From the time we are babies, we are taught about the various things we must dedicate our lives to. Taking an active stance on political issues is just a small part of the obligations we acquire as humans, citizens, parents, employees, residents of some apartment block […]
Original post on aethy.com
aethy.com
December 9, 2025 at 6:08 PM
And they are everywhere. From the time we are babies, we are taught about the various things we must dedicate our lives to. Taking an active stance on political issues is just a small part of the obligations we acquire as humans, citizens, parents, employees, residents of some apartment block […]
Finite cyclic groups/monoids are the same, except that their definition contains an additional law, stating that that once you compose the generator with itself $n$ number of times, you get identity morphism. For the cyclic group $Z_3$ (which can be visualized as the group of triangle rotations) […]
Original post on aethy.com
aethy.com
December 6, 2025 at 6:35 PM
Finite cyclic groups/monoids are the same, except that their definition contains an additional law, stating that that once you compose the generator with itself $n$ number of times, you get identity morphism. For the cyclic group $Z_3$ (which can be visualized as the group of triangle rotations) […]
2. Second, migrating to other platforms - if I want to export some of the 13]genius writing I did as a teenager, from Wordpress.com to some other platform I cannot do that now. With static websites, I can switch to a different platform in a matter of seconds without losing any of my content. -- […]
Original post on aethy.com
aethy.com
December 4, 2025 at 6:01 PM
2. Second, migrating to other platforms - if I want to export some of the 13]genius writing I did as a teenager, from Wordpress.com to some other platform I cannot do that now. With static websites, I can switch to a different platform in a matter of seconds without losing any of my content. -- […]
I guess I should say something about why I believe these things. Simple - because all other approaches just fail because of the human factor, e.g. any code, that is written without regard for style is bound to become legacy when the person who supports it leaves. Likewise, maintaining code that […]
Original post on aethy.com
aethy.com
December 2, 2025 at 6:03 PM
I guess I should say something about why I believe these things. Simple - because all other approaches just fail because of the human factor, e.g. any code, that is written without regard for style is bound to become legacy when the person who supports it leaves. Likewise, maintaining code that […]
But first, let’s talk about entropy. We can say that the entropy of a given system corresponds to how easy it is to describe it’s state. e.g. an ordered deck of cards has a low entropy because it is easy to describe, while the only way to describe a shuffled one is to just make a list of all […]
Original post on aethy.com
aethy.com
November 30, 2025 at 6:01 PM
But first, let’s talk about entropy. We can say that the entropy of a given system corresponds to how easy it is to describe it’s state. e.g. an ordered deck of cards has a low entropy because it is easy to describe, while the only way to describe a shuffled one is to just make a list of all […]
This reveals a paradox: while the concept of the universe underlies empirical statements, it is not itself empirical, as we cannot make empirical observations about the universe (unless we are Laplace’s demon, but more on that later). And one way to navigate this paradox (actually, the only way […]
Original post on aethy.com
aethy.com
November 29, 2025 at 6:24 PM
This reveals a paradox: while the concept of the universe underlies empirical statements, it is not itself empirical, as we cannot make empirical observations about the universe (unless we are Laplace’s demon, but more on that later). And one way to navigate this paradox (actually, the only way […]
Quantum mechanics discover that a framework that does not rely on the concept of absolute time is inherently subjective (depends on observer). -- https://abuseofnotation.github.io/short-history-philosophy/index.html
Abuse of Notation - writings on math, logic, philosophy and art - Short history of modern philosophy
abuseofnotation.github.io
November 28, 2025 at 6:01 PM
Quantum mechanics discover that a framework that does not rely on the concept of absolute time is inherently subjective (depends on observer). -- https://abuseofnotation.github.io/short-history-philosophy/index.html
If we have a one-to-one-function that connects sets that are of the same size (as is the case here), then this function has the following property: all elements from the target set have exactly one arrow pointing at them. In this case, the function is invertible. That is, if you flip the arrows […]
Original post on aethy.com
aethy.com
November 25, 2025 at 6:19 PM
If we have a one-to-one-function that connects sets that are of the same size (as is the case here), then this function has the following property: all elements from the target set have exactly one arrow pointing at them. In this case, the function is invertible. That is, if you flip the arrows […]
And these laws conclude the definition of functors — a simple but, as we will see shortly, very powerful concept. -- https://abuseofnotation.github.io/category-theory-illustrated/10_functors/index.html
Category Theory Illustrated - Functors
abuseofnotation.github.io
November 21, 2025 at 6:14 PM
And these laws conclude the definition of functors — a simple but, as we will see shortly, very powerful concept. -- https://abuseofnotation.github.io/category-theory-illustrated/10_functors/index.html
An important corollary of this which may surprise some people (while at the same time being completely obvious to others) is that mathematical propositions don’t say anything about the real world. So, for example when you say that something like 1 + 1 = 2 is true, you are not asserting a fact […]
Original post on aethy.com
aethy.com
November 20, 2025 at 6:01 PM
An important corollary of this which may surprise some people (while at the same time being completely obvious to others) is that mathematical propositions don’t say anything about the real world. So, for example when you say that something like 1 + 1 = 2 is true, you are not asserting a fact […]
5. Most importantly: the fucking planet is dying, because of carbon emissions and you want to just dismiss the obvious and already implemented solution for reducing those by letting people not travel to work, just because of some 10% profit increase. -- […]
Original post on aethy.com
aethy.com
November 18, 2025 at 6:02 PM
5. Most importantly: the fucking planet is dying, because of carbon emissions and you want to just dismiss the obvious and already implemented solution for reducing those by letting people not travel to work, just because of some 10% profit increase. -- […]
An inhumane technology is something that you pick up to “do your job” and leave it as soon as you are done, wondering when is a better alternative coming out. They are designed with a specific purpose in mind and they have no other uses. A humane technology often has a variety of purposes (with […]
Original post on aethy.com
aethy.com
November 16, 2025 at 6:03 PM
An inhumane technology is something that you pick up to “do your job” and leave it as soon as you are done, wondering when is a better alternative coming out. They are designed with a specific purpose in mind and they have no other uses. A humane technology often has a variety of purposes (with […]
As we get closer to the door I start seeing the people in the hallway. The way they act resembles the one in a school, but it definitely is unlike my school, where everyone just sits there and rest on their shoulders because they are tired, and talk, if not to about the things we study, about […]
Original post on aethy.com
aethy.com
November 15, 2025 at 6:02 PM
As we get closer to the door I start seeing the people in the hallway. The way they act resembles the one in a school, but it definitely is unlike my school, where everyone just sits there and rest on their shoulders because they are tired, and talk, if not to about the things we study, about […]
PS: Categorical isomorphisms are also very rare in practice — the only one that comes to mind is the Curry-Howard-Lambek isomorphism from the previous chapter. That’s because if two categories are isomorphic then there is no reason at all to treat them as different categories — they are one and […]
Original post on aethy.com
aethy.com
November 14, 2025 at 6:06 PM
PS: Categorical isomorphisms are also very rare in practice — the only one that comes to mind is the Curry-Howard-Lambek isomorphism from the previous chapter. That’s because if two categories are isomorphic then there is no reason at all to treat them as different categories — they are one and […]
This is the typical mess that we end up when we just add stuff to our code without refactoring it, and although it does not look that bad, it is nearly impossible to understand. I feel sorry for the person would have to debug this thing in order to fix the issues that it would no doubt cause […]
Original post on aethy.com
aethy.com
November 13, 2025 at 6:26 PM
This is the typical mess that we end up when we just add stuff to our code without refactoring it, and although it does not look that bad, it is nearly impossible to understand. I feel sorry for the person would have to debug this thing in order to fix the issues that it would no doubt cause […]
The setup for composing natural transformations may look complicated the first time you see it: we need three categories $C$, $D$ and $E$ (just as composition of morphisms requires three objects). We need a total of four functors, distributed on two pairs, one pair of functors that goes from $C$ […]
Original post on aethy.com
aethy.com
November 12, 2025 at 6:01 PM
The setup for composing natural transformations may look complicated the first time you see it: we need three categories $C$, $D$ and $E$ (just as composition of morphisms requires three objects). We need a total of four functors, distributed on two pairs, one pair of functors that goes from $C$ […]
So what, then, would the principle of such judgments be? The only reason we can know about objects in the real world in the first place is because we experience these objects. This principle holds even for objects that we have not yet seen - the key word here is “yet” - even if we haven’t […]
Original post on aethy.com
aethy.com
November 11, 2025 at 6:01 PM
So what, then, would the principle of such judgments be? The only reason we can know about objects in the real world in the first place is because we experience these objects. This principle holds even for objects that we have not yet seen - the key word here is “yet” - even if we haven’t […]
The next simplest category is $1$ — it is comprised of one object and no morphisms besides its identity morphism (which we don’t draw, as usual) -- https://abuseofnotation.github.io/category-theory-illustrated/10_functors/index.html
Category Theory Illustrated - Functors
abuseofnotation.github.io
November 10, 2025 at 6:01 PM
The next simplest category is $1$ — it is comprised of one object and no morphisms besides its identity morphism (which we don’t draw, as usual) -- https://abuseofnotation.github.io/category-theory-illustrated/10_functors/index.html