How to make world monoidable
We, humans, are constantly creating ranks and hierarchies.
ABCDEFGHIJKLMNOPQRSTUVWXYZ
letter -> word -> sentence -> paragraph -> text -> book -> library -> library system
scene -> episode -> season -> TV show
private -> sergeant -> lieutenant -> captain -> ... -> Commander in Chief
minute -> hour -> day -> week -> month -> year
Genesis 1:26
And God said: 'Let us make man in our image, after our likeness; and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.'
We particularly like the concepts of space and time because they have two types of ranks: sequential and hierarchical.
Human history is a history of rank-making.
Abstraction works because it creates a hierarchy of types, which makes world monoidable.
A partially ordered set or a poset is a category, whose objects are elements of the poset and whose arrows are 'less than or equal' relations.
In greater detail, a preorder is a category in which there is at most one arrow from any object {\displaystyle A\,}
to any object {\displaystyle B\,}
.
upd: the invention of 0 (zero) enabled us to create neat hierarchies from numbers: 0.1 -> 1 -> 10 -> 100 -> 1000
ABCDEFGHIJKLMNOPQRSTUVWXYZ
letter -> word -> sentence -> paragraph -> text -> book -> library -> library system
scene -> episode -> season -> TV show
private -> sergeant -> lieutenant -> captain -> ... -> Commander in Chief
minute -> hour -> day -> week -> month -> year
Genesis 1:26
And God said: 'Let us make man in our image, after our likeness; and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.'
We particularly like the concepts of space and time because they have two types of ranks: sequential and hierarchical.
Human history is a history of rank-making.
Abstraction works because it creates a hierarchy of types, which makes world monoidable.
A partially ordered set or a poset is a category, whose objects are elements of the poset and whose arrows are 'less than or equal' relations.
In greater detail, a preorder is a category in which there is at most one arrow from any object {\displaystyle A\,}
to any object {\displaystyle B\,}
.
upd: the invention of 0 (zero) enabled us to create neat hierarchies from numbers: 0.1 -> 1 -> 10 -> 100 -> 1000