Alfred North Whitehead is a Brit who famously practiced philosophy at Harvard. However prior to becoming a “full time” philosopher, he was an oxford educated mathematician!
Consequently, the AOK of Math had a massive influence on his thinking and philosophy. Whitehead went on to formalize some of his musings on Math as an AOK and below are linked some excerpts from his famous work, An Introduction to Mathematics published in 1911.
After we’ve read about Simulation Theory, Expansionary theory and now watched the incredible “Fabric of the Cosmos” by NOVA and Brian Greene, your mind is probably (and hopefully) spinning.
If you began our math unit certain that the laws of physics and mathematics were “in there somewhere” and it was only a matter of time before we discovered them, do you feel the same way now? Are you still a Platonist in regard to mathematics? Or, have you started to sway towards empiricism (generalizations about the observed world) and Formalism (Mathematical truths are true by definition)?
Some reasons you may be swayed:
1. Newton’s laws were considered “perfect” as they described what we could observe.
2. However as our powers of observation increased, we realized that what we were observing were but “shadows on the wall of the cave” to use a Plato reference thus
3. Einstein created his theories of relativity and space time. DRASTICALLY different than newtonian physics. This was a scientific revolution
4. If Newton’s laws, which stood for 100s of years, could be proven wrong, what else can?!?!?!?! Will Einstein’s theories be proven wrong as well?!?!?! IF so,
5. WHAT CAN WE REALLY SAY WE KNOW FOR CERTAIN!?!?!?!?!?!
This of course brings us to Descartes who asked this very question…we’ll move into his philosophy later….
Euclid’s Geometry seemed pretty immutable…that is until Riemann came along in the mid 19th century and created new axioms of geometry. They were as follows:
A. Two points may determine more than one line
B. All lines are finite in length but endless– i.e. circles
C. There are no parallel lines
A. All perpendiculars to a straight line meet at one point (lines of longitude are perpendicular to the equator but meet at north pole)
B. Two straight lines enclose an area (Any two lines of longitude meet at both north and south pole, thus enclose an area)
C. The sum of the angles of any triangle is greater than 180 degrees.
Einstein further muddled (or clarified) the picture with his new Laws Of Physics embodied in Relativity. Here, he too saw space as curved and not flat. Thus, the geometry that applied to Einsteins’ physical laws are more Riemann than Euclid.
Andrei Linde and his “Expansionary Theory” researchers made similar revolutionary claims that were rejected until they recently received amazing scientific evidence supporting their theories regarding the origins of the universe…more on that in a later post!!!!
LInk to “doodling in math part 2” How do these “natural patterns” that correspond to the Fibonacci sequence support or refute the Simulation Hypothesis?
Read the NYTimes article below:
This brings up amazing ideas regarding the platonic nature of math, reason and math as a #wok and issues of creation and #cosmology
For further information, listen to Nick Bostrom explain both his Simulation Argument and his Simulation Hypothesis
And below is an interview with Nick Bostrom from the New Yorker that you should read to further your understanding and intrigue your mind: