Notes for 8/28/2026

  

8/27/2026

Have you ever seen the Milky Way when looking at the night sky? (Apparently 90% of people have not.)

 

Some significant events making up the “scientific revolution”

 

-      Printing press

-      Mercantilism and the rise of state sovereignty

-      Geographic exploration

-      Protestant revolution(s)

-      Developments in Mathematics

 

 

Galileo’s discoveries

-      Moon

-      Sunspots

-      Moons of Jupiter

-      Saturn

-      Phases of Venus

-      Milky Way is made of stars

-      Stellar parallax

 

 

 

 

Galileo also conducted experiments involving motion

 

Rolling, swinging, falling, floating things

 

An interesting mystery: Galileo endorsed Copernicanism as true (rather than as a mere hypothesis) BEFORE his telescopic observations. Why?

 

 

Galileo was among those who rejected teleological causation in science.

 

Instead, he endorses mechanism which lends itself to mathematical representation in ways teleology does not.

 

“Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.”

 

Whether mechanism motivated Galileo’s “mathematism” or the other way around is unclear.

 

For Galileo, “mathematics” primarily meant geometry.

 

It was largely Descartes who was responsible for advancing math beyond geometry. (Invented Cartesian coordinate geometry)

 

 

 

Opposition to Descartes’ mathematics

 

 

What happened to Galileo (house arrest)

Also (possibly) Giordano Bruno (burned at the stake)

 

 

 

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