Essay Abstract
This paper looks at the expression of physical realities in terms of mathematics as the problematic relationship as it has been regarded throughout and attempts to offer an explanation.
Author Bio
Undergraduate student, Bachelor of Arts.
Dear Mr. Uplap,
I thought that your essay was exceptionally well written and I certainly hope that your essay fares well in the competition.
Warm regards,
Joe Fisher
Dear Sarvesh,
I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.
All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.
Joe Fisher
Dear Sarvesh,
It is interesting to see you attempt to tie the contest topic to the chicken-or egg question. While I agree with some of your characterizations of physics and mathematics, I would like to make two points:
1) Mathematics may not be quite as culture-independent as you think. It is certainly true that propositions like 1+1=2 are not culture-dependent, but how such propositions are expressed may very well be. A good example is the comparison between Newton and Lagrange. Newton explained his theory in the Principia essentially using geometry, requiring him to have many pictures, while Lagrange took pride in having formulated Newton's theory in his book without the help of a single picture. Another example, recently I found out about Bhaskara, the ancient Indian mathematician who derived many results which were much later re-discovered by western mathematicians. Some of his results were stated in terms that are entirely unfamiliar and hard to understand for me because of my very different cultural upbringing. A final example involving the ancient Romans: Their inefficient notation of numbers surely made it much more difficult to recognize the truth of certain basic results, and it is almost certain that even in contemporary mathematics we fail to see some straightforward relationships because of the way we conceptualize and record mathematics, based on how we learned it from our teachers, a cultural factor.
2) You said: "Physics implies mathematics and mathematics implies physics". I think this reflects only a perspective that is thoroughly steeped in the current paradigm. Before Galileo, physics (which was Aristotelian at the time) had almost nothing to do with mathematics. On the other hand, there were (and are) Mathematicians who in their entire lives had nothing to do with physics (one example who comes to mind is Ramanujan), and these would seem to serve as counterexamples.
Nevertheless, you did make some salient points regarding the roles and relationships of physics and mathematics to each other.
I hope you found my criticism useful.
Best wishes,
Armin
