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authorAndrew <andrew@andrewyu.org>2022-11-12 16:55:17 +0800
committerAutomatic Merge <andrew+automerge@andrewyu.org>2023-07-15 00:29:33 +0800
commit8f049ad6d4ffab5bd7b758b7133f5fae7c29e7bb (patch)
tree198f8de047c9768c8e7eefb8ecb7867fd12966ce /article
parent4dc50f34c578dbc66cb3eb4b64dde648ba5bb93c (diff)
downloadwww-8f049ad6d4ffab5bd7b758b7133f5fae7c29e7bb.tar.gz
Change <em> into <i> for pandoc math.
Diffstat (limited to 'article')
-rw-r--r--article/math-science-and-philosophy.html40
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