These articles go in-depth on specific topics, explaining where abstract mathematical and scientific concepts come from.
(Spoiler: all concepts are derived from things in the real-world)
Start from the first two articles, which introduce the key concept pair of abstraction and reduction.
The idea that line segments have an “infinite number of dimensionless points” is self-contradictory. I have a better idea (involving angels dancing on a pinpoint).
Showing how the concept of numbers arises from the act of quantitative comparison, and how it extends to include negative, irrational and complex numbers.
Explaining the mystery of how mathematical equations can predict things in the real world.
“Reduction” is an act-of-mind, where we take some abstraction (e.g. area of a square, 𝐴 = 𝑙2 ), and trace it back to its originating source in the physical world.
An introduction to “abstraction”, a mental process where we focus on certain aspects of a thing (a physical object or an idea), while ignoring all others.
Support the site by getting the eBook, a full introduction to the concept of reduction.
Get the eBook