- #61
- 29,552
- 21,351
Does the formula $$\frac{\pi^2}{6} = \sum_{n = 1}^{\infty} \frac 1 {n^2}$$ depend on the local stress-energy tensor?DanielMB said:
You could write a paper on how to do real analysis in curved spacetime!
Can physics deal with the existence of Pi?
Click For Summary
Discussion Overview
The discussion revolves around the existence of the mathematical constant Pi (π) in relation to physics and cosmology. Participants explore whether Pi exists independently of physical reality, and if its existence is contingent upon the existence of space or geometry. The conversation touches on philosophical implications regarding the nature of mathematical entities and their relationship to physical phenomena.
Discussion Character
- Exploratory
- Debate/contested
- Conceptual clarification
Main Points Raised
- Some participants assert that Pi is a number that exists as a consequence of mathematical axioms, independent of physical reality.
- Others question whether Pi requires physical space to exist, suggesting that if space exists, then Pi must also exist.
- A few participants argue that the existence of numbers, including Pi, is tied to human cognition and does not imply physical existence.
- There is a discussion about the definition of Pi as the ratio of a circle's circumference to its diameter, with some noting that this definition may not hold in non-Euclidean geometries.
- Some contributions highlight that while Pi is a mathematical constant, its application in physics may vary depending on the curvature of space-time.
- Several participants express confusion over the implications of Pi's existence and its relationship to physical reality, leading to further questions and clarifications.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the nature of Pi's existence, with multiple competing views presented regarding its relationship to physical reality and mathematical abstraction. The discussion remains unresolved, with ongoing debate about the implications of these perspectives.
Contextual Notes
Some participants note that the discussion involves complex philosophical considerations about the nature of existence and the definitions of mathematical concepts, which may not be universally agreed upon.
Similar threads
- · Replies 7 ·
- · Replies 13 ·
- · Replies 7 ·
- · Replies 8 ·
- · Replies 13 ·
High School
Does Spacetime Have Physical Existence?
- · Replies 58 ·
Intro Physics
What is the best conceptual high school physics book?
- · Replies 2 ·
- · Replies 7 ·
- · Replies 1 ·
- · Replies 36 ·