Comment by aleph_minus_one
2 months ago
> Would you assign a large sum of money to a group that cannot present their design clearly, neatly, and concisely? If they are struggling even with that, would you trust them to be good at actually designing a spacecraft soundly, economically, and in a reasonable time?
This mentality seems very US-Amercian to me.
> "If you can't explain it to a five-years-old, you likely do not understand it yourself", said one of the greatest modern scientists, who also was notoriously good at explaining things.
OK, challenge: explain A1 homotopy theory to a 5-year old child: https://en.wikipedia.org/wiki/A%C2%B9_homotopy_theory
Lesson learned: very commonly you need a deep knowledge of a topic to understand advanced scientific theories.
What problem in the physical world does a knowledge of A1 homotopy theory enable you to solve?
https://www.ecfr.gov/current/title-7/subtitle-B/chapter-XVII...
A¹ homotopy is currently still a research area, but if you read the linked Wikipedia article:
"The underlying idea is that it should be possible to develop a purely algebraic approach to homotopy theory by replacing the unit interval [0, 1], which is not an algebraic variety, with the affine line A¹, which is."
In other words: it's a novel approach towards homotopy theory, which does have applications in the physical world.
Even better (Wikipedia article):
"[A¹ homotopy theory] has also recently revolutionized the theory of enumerative geometry problems."
Enumerative geometry does have applications in the physical world.