diff options
author | Andrew <andrew@andrewyu.org> | 2022-11-12 16:55:17 +0800 |
---|---|---|
committer | Automatic Merge <andrew+automerge@andrewyu.org> | 2023-07-15 00:29:33 +0800 |
commit | 8f049ad6d4ffab5bd7b758b7133f5fae7c29e7bb (patch) | |
tree | 198f8de047c9768c8e7eefb8ecb7867fd12966ce | |
parent | 4dc50f34c578dbc66cb3eb4b64dde648ba5bb93c (diff) | |
download | www-8f049ad6d4ffab5bd7b758b7133f5fae7c29e7bb.tar.gz |
Change <em> into <i> for pandoc math.
-rw-r--r-- | article/math-science-and-philosophy.html | 40 |
1 files 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?</p> is calculations, often as an abstraction of experimental experience into a general formula, which is then applied to specific questions. With the knowledge that <span -class="math inline"><em>F</em> = <em>m</em><em>a</em></span> and that +class="math inline"><i>F</i> = <i>m</i><i>a</i></span> and that <span -class="math inline"><em>a</em> = 10 m/s<sup>2</sup>, <em>m</em> = 1 kg</span>, -we conclude that <span class="math inline"><em>F</em> = 10 N</span>. But +class="math inline"><i>a</i> = 10 m/s<sup>2</sup>, <i>m</i> = 1 kg</span>, +we conclude that <span class="math inline"><i>F</i> = 10 N</span>. 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 <span class="math inline"><em>π</em></span> +conclude that it's always <span class="math inline"><i>π</i></span> while it's actually less than <span -class="math inline"><em>π</em></span> after the 15<sup>th</sup> +class="math inline"><i>π</i></span> after the 15<sup>th</sup> 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.</p> theories with mathematical logic?</p></li> <li><p>Under what circumstance shall mathematical logic be ``trusted'' in physics?</p></li> -<li><p>How is it possible to know <em>anything</em> in physics? +<li><p>How is it possible to know <i>anything</i> 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.</p></li> -<li><p>Gödel's theorems only tell us that there <em>are</em> true -statements that we cannot prove, and there <em>may be</em> +<li><p>Gödel's theorems only tell us that there <i>are</i> true +statements that we cannot prove, and there <i>may be</i> 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.</p> <p>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 <span -class="math inline"><em>A</em></span> (i. e. physics is squishy) is both -true and false. Thus, <span class="math inline"><em>A</em> = 1</span> -and <span class="math inline"><em>A</em> = 0</span> are both true. Then, -take a random statement <span class="math inline"><em>B</em></span> +class="math inline"><i>A</i></span> (i. e. physics is squishy) is both +true and false. Thus, <span class="math inline"><i>A</i> = 1</span> +and <span class="math inline"><i>A</i> = 0</span> are both true. Then, +take a random statement <span class="math inline"><i>B</i></span> (let's say ``my friend likes humanities''). Thus we have <span -class="math inline"><em>A</em> + <em>B</em> = 1</span> where <span +class="math inline"><i>A</i> + <i>B</i> = 1</span> where <span class="math inline">+</span> is a boolean ``or'' operator because <span -class="math inline"><em>A</em> = 1</span> and <span -class="math inline">1 + <em>x</em> = 1</span> (<span -class="math inline"><em>x</em></span> is any statement). But then -because <span class="math inline"><em>A</em> = 0</span>, thus <span -class="math inline">0 + <em>B</em> = 1</span>, which means that <span -class="math inline"><em>B</em></span> must be 1 (if <span -class="math inline"><em>B</em></span> is zero, then <span +class="math inline"><i>A</i> = 1</span> and <span +class="math inline">1 + <i>x</i> = 1</span> (<span +class="math inline"><i>x</i></span> is any statement). But then +because <span class="math inline"><i>A</i> = 0</span>, thus <span +class="math inline">0 + <i>B</i> = 1</span>, which means that <span +class="math inline"><i>B</i></span> must be 1 (if <span +class="math inline"><i>B</i></span> is zero, then <span class="math inline">0 + 0 = 0</span>). 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 |