(A name for the three-way tension you will find a lot: trilemma.)
If you have to budget something, it becomes a soft trilemma: I have 24 hours for work + leisure + sleep, so any given combination will be a point inside a triangle whose vertices are (0, work), (0,leisure), (0, sleep). This structure is called a (2-)simplex.
BTW: a regular dilemma (should I spend or save) is a 1-simplex, and is a simple linear combination asave + (1-a)spend.
Now, this is fun for two reasons:
- You can have (n)-lemmas (i.e. n-fold tradeoff structures) that are modeled as (n-1)-simplices. Actually useful: you can do statistical inference on simplices using the Dirichlet distribution.
- A simplicial complex (basically, a set of simplices) can be used to build topological spaces part by part. This kind of maths (algebraic topology) is a whole "south part of the mountain" climb towards abstract mathematics that bypasses a lot of Cantorian handwringing on the ultra-local structure of topology. Instead, you're computing stuff from the get go -- and indeed one of the emerging machine learning techniques goes precisely from building a simplicial-like complex from data and computing characteristics of its topology.
If you have to budget something, it becomes a soft trilemma: I have 24 hours for work + leisure + sleep, so any given combination will be a point inside a triangle whose vertices are (0, work), (0,leisure), (0, sleep). This structure is called a (2-)simplex.
BTW: a regular dilemma (should I spend or save) is a 1-simplex, and is a simple linear combination asave + (1-a)spend.
Now, this is fun for two reasons:
- You can have (n)-lemmas (i.e. n-fold tradeoff structures) that are modeled as (n-1)-simplices. Actually useful: you can do statistical inference on simplices using the Dirichlet distribution.
- A simplicial complex (basically, a set of simplices) can be used to build topological spaces part by part. This kind of maths (algebraic topology) is a whole "south part of the mountain" climb towards abstract mathematics that bypasses a lot of Cantorian handwringing on the ultra-local structure of topology. Instead, you're computing stuff from the get go -- and indeed one of the emerging machine learning techniques goes precisely from building a simplicial-like complex from data and computing characteristics of its topology.