From Critical Path (1981) , Part 2, Chapter 6 "The World Game" , Richard Buckminster Fuller & Kiyoshi Kuromiya make the Claim :
It has been found that within a 100 mile radius a wind is always blowing.
It is known that there exists The Hairy Ball Theorem which has as a corollary that at any given time on the Earth there is a cyclone happening somewhere. Was R. Buckminster Fuller aware of another mathematical theorem when he made this statement?
reference :
https://en.wikipedia.org/wiki/Critical_Path_(book)#Chapter_6_-_World_Game
https://en.wikipedia.org/wiki/Hairy_ball_theorem
Posting a longish comment here :
(0) Putting all the following Points together (TLDR) , what Fuller said is Empirical & Physical & Meteorological , not Mathematical. There is not much of a Connection to the Hairy Ball Theorem.
(1) The Hairy Ball Theorem applies to the Whole Sphere , not to 100-mile Patches.
There may be no Cyclone in the Purple Patch.
The left Pole & the Right Pole have Discontinuities.
(2) The Statement about Earthly Cyclones might be called Observation , not Theorem or Corollary.
Approximating the Earth with a Sphere is not very Exact , Mathematically.
Consider Sea Arches & land Arches :
It might look like topological handles on Sphere or torus , where the Hairy Ball Theorem is not Mathematically applicable & it is hence not valid.
(3) The Hairy Ball theorem is valid when every Point on the Sphere has Exactly 1 tangent vector.
The Wind on the Earth is not like that. It might flow in multiple Speeds/Directions at various altitudes at the very Same Point (latitude & longitude) on the Earth.
Eg , Wind might move very very slowly on ground level , while it might move moderately fast on tall tower tips & the hot air balloon over-head might experience fast winds , while the Aeroplane might encounter very high Speed Wind , all at the Exact Same Point on the Earth.
Wind Direction might matter too , changing with altitude.
Such Considerations are out of scope of the Hairy Ball theorem & hence we can not apply that here.
(4) There is no connection to 100 miles in the Hairy Ball theorem , which is Scale-Independent. We are then left with the Statement that the wind is moving in a Patch of 100 mm radius , which is not true.
(5) Physically , Wind is the outcome of heating (by Sun & Moon) & rotation & revolution (of Earth) , hence it is true that there is wind movement throughout the Earth. That there is always wind is additionally ensured by Human Constructions & Activities , Sea-Land Borders , Polar Ice, Volcanoes , Lakes , Dust , ETC , not by Hairy Ball Theorem.
(6) Putting all these together , what Fuller said is Empirical & Physical & Meteorological , not Mathematical. There is not much of a Connection to the Hairy Ball Theorem.