From 8f049ad6d4ffab5bd7b758b7133f5fae7c29e7bb Mon Sep 17 00:00:00 2001 From: Andrew Date: Sat, 12 Nov 2022 16:55:17 +0800 Subject: Change into for pandoc math. --- article/math-science-and-philosophy.html | 40 ++++++++++++++++---------------- 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/article/math-science-and-philosophy.html b/article/math-science-and-philosophy.html index d4d2240..3c2f723 100644 --- a/article/math-science-and-philosophy.html +++ b/article/math-science-and-philosophy.html @@ -88,10 +88,10 @@ or would it possibly be buggy?

is calculations, often as an abstraction of experimental experience into a general formula, which is then applied to specific questions. With the knowledge that F = ma and that +class="math inline">F = ma and that a = 10 m/s2, m = 1 kg, -we conclude that F = 10 N. But +class="math inline">a = 10 m/s2, m = 1 kg, +we conclude that F = 10 N. But many times this involves or implies the second role of math in physics, because calculations depend on corresponding concepts, and sometimes the mathematical utilities themselves are developed from physics but are @@ -124,9 +124,9 @@ results. But there are tons of logistical issues that prevent us from doing so, not to mention the inherent downside to experiments: a limited number of attempts cannot derive a general-case theory (take the Borwein integral as an example: a limited number of experiments may easily -conclude that it's always π +conclude that it's always π while it's actually less than π after the 15th +class="math inline">π after the 15th iteration). So then, we turn to logical proof. But then because mathematical logic is incomplete, we are not guaranteed to be able to prove a given conjecture, which may be otherwise indicated by @@ -141,13 +141,13 @@ discussion about these topics.

theories with mathematical logic?

  • Under what circumstance shall mathematical logic be ``trusted'' in physics?

    • -

  • How is it possible to know anything in physics? +

  • How is it possible to know anything in physics? Experiments can be inaccurate or conducted wrongly or can be affected by physical properties completely unknown to us, and mathematical proof can be erroneous because of systematic flaws and/or false assumptions about the representation of physical entities in math.

    • -

  • Gödel's theorems only tell us that there are true -statements that we cannot prove, and there may be +

  • Gödel's theorems only tell us that there are true +statements that we cannot prove, and there may be inconsistencies. My intuition suggests that these statements and inconsistencies would be in the highly theoretical realm of math, which if accurately identified and are avoided in physics, would not pose a @@ -155,20 +155,20 @@ threat to applied mathematics in physics.

    However, it shall be noted that any single inconsistency may be abused to prove any statement, if consistencies were to be found in math: Suppose that we know a statement A (i. e. physics is squishy) is both -true and false. Thus, A = 1 -and A = 0 are both true. Then, -take a random statement B +class="math inline">A (i. e. physics is squishy) is both +true and false. Thus, A = 1 +and A = 0 are both true. Then, +take a random statement B (let's say ``my friend likes humanities''). Thus we have A + B = 1 where A + B = 1 where + is a boolean ``or'' operator because A = 1 and 1 + x = 1 (x is any statement). But then -because A = 0, thus 0 + B = 1, which means that B must be 1 (if B is zero, then A = 1 and 1 + x = 1 (x is any statement). But then +because A = 0, thus 0 + B = 1, which means that B must be 1 (if B is zero, then 0 + 0 = 0). Thus, if we can prove that ``physics is squishy'' and ``physics is not squishy'' (without differences in definition), then we can literally prove that ``my friend likes -- cgit 1.4.1-2-gfad0