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    <title>Rens</title>
    <link>https://rensoliemans.nl/</link>
    <description>Rens</description>
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      <title>Breathe With Me</title>
      <link>https://rensoliemans.nl/en/writing/breathe-with-me/</link>
      <guid>https://rensoliemans.nl/en/writing/breathe-with-me/</guid>
      <pubDate>Mon, 08 Dec 2025 00:00:00 +0000</pubDate>
      <description><![CDATA[&lt;p&gt;&lt;a href=&quot;https://en.wikipedia.org/wiki/Breathe_(The_Prodigy_song)&quot;&gt;Breathe&lt;/a&gt; is a song by the Prodigy in which their vocalist &lt;a href=&quot;https://en.wikipedia.org/wiki/Keith_Flint&quot;&gt;Keith Flint&lt;/a&gt; calls upon us to &amp;quot;Breathe with me&amp;quot;. Flint died in 2019, and this made me wonder, do I still breathe with him in a way?&lt;/p&gt;
&lt;p&gt;Flint died at age 49. Assuming he breathed at &lt;a href=&quot;https://en.wikipedia.org/wiki/Respiratory_rate&quot;&gt;the same rate as an average human&lt;/a&gt;, he took around 350 million breaths in his life&lt;sup&gt;&lt;a href=&quot;#fn-1&quot; id=&quot;fnref-1&quot;&gt;1&lt;/a&gt;&lt;/sup&gt;. The volume of a regular breath is about 500mL of air&lt;sup&gt;&lt;a href=&quot;#fn-2&quot; id=&quot;fnref-2&quot;&gt;2&lt;/a&gt;&lt;/sup&gt;, so Flint breathed 175 million litres of air overall, or about 215 tonnes&lt;sup&gt;&lt;a href=&quot;#fn-3&quot; id=&quot;fnref-3&quot;&gt;3&lt;/a&gt;&lt;/sup&gt;. Since the &lt;a href=&quot;https://en.wikipedia.org/wiki/Atmosphere_of_Earth&quot;&gt;total mass of the atmosphere is \(5.15 \times 10^{18}\) kg&lt;/a&gt;, about one part in every \(2 \times 10^{13}\) parts of the atmosphere has been in Flint&#39;s lungs&lt;sup&gt;&lt;a href=&quot;#fn-4&quot; id=&quot;fnref-4&quot;&gt;4&lt;/a&gt;&lt;/sup&gt;.&lt;/p&gt;
&lt;p&gt;In order to find out whether a breath of ours contains some part that has been in Flint&#39;s lungs, we need to see how many molecules of air we breathe. If its greater than \(2 \times 10^{13}\), we know that each breath contains at least one molecule of air that has been in Flint&#39;s lungs. We find that, &lt;a href=&quot;https://en.wikipedia.org/wiki/Density_of_air&quot;&gt;with an average molar mass of 0.029 kg/mol&lt;/a&gt;, we breathe about \(10^{23}\) molecules of air per breath&lt;sup&gt;&lt;a href=&quot;#fn-5&quot; id=&quot;fnref-5&quot;&gt;5&lt;/a&gt;&lt;/sup&gt;, that&#39;s nearly &lt;em&gt;5 billion molecules&lt;/em&gt; that were once in Flint&#39;s lungs with every single breath we take.&lt;/p&gt;
&lt;p&gt;This is wild. Each time you breathe, you are breathing air that has been breathed by &lt;em&gt;every person that has ever lived&lt;/em&gt;. &amp;quot;Breathe with me,&amp;quot; indeed.&lt;/p&gt;
&lt;h2&gt;Footnotes&lt;/h2&gt;
&lt;div class=&quot;footnote&quot; id=&quot;fn-1&quot;&gt;&lt;sup&gt;1&lt;/sup&gt; According to &lt;a href=&quot;https://en.wikipedia.org/wiki/Respiratory_rate&quot;&gt;Wikipedia&lt;/a&gt;, an adult typically breathes for about 12-15 breaths per minute. Children breathe more often, but also take smaller breaths, so I&#39;m going to assume Flint breathed like an adult for his entire life. He lived for 18,065 days, so he breathed \(18,065 \times 24 \times 60 \times 13.5 \approx 3.5 \times 10^{8}\) times. &lt;a href=&quot;#fnref-1&quot;&gt;↩&lt;/a&gt;&lt;/div&gt;
&lt;div class=&quot;footnote&quot; id=&quot;fn-2&quot;&gt;&lt;sup&gt;2&lt;/sup&gt; &lt;a href=&quot;https://archive.org/details/principlesofanat0000tort_f3y5&quot;&gt;Principles of anatomy &amp;amp; physiology by Gerard J. Tortora and Bryan H. Derrickson&lt;/a&gt;, page 874. &lt;a href=&quot;#fnref-2&quot;&gt;↩&lt;/a&gt;&lt;/div&gt;
&lt;div class=&quot;footnote&quot; id=&quot;fn-3&quot;&gt;&lt;sup&gt;3&lt;/sup&gt; Air weighs about 1.225 kg/m^3. So \(0.5 \times 351,183,600 \times 10^{6} \mathrm{L} \times 1.225 \mathrm{kg}/\mathrm{m}^3 \approx 215,100 \mathrm{kg}\). &lt;a href=&quot;#fnref-3&quot;&gt;↩&lt;/a&gt;&lt;/div&gt;
&lt;div class=&quot;footnote&quot; id=&quot;fn-4&quot;&gt;&lt;sup&gt;4&lt;/sup&gt; \(215,100/(5.15 \times 10^{18}) \approx 4.18 \times 10^{−14}\), which is the fraction of the atmosphere that has been in Flint&#39;s lungs. The reciprocal of that, \(1 / 4.18 \times 10^{-14} \approx 2.39 \times 10^{13}\) means &amp;quot;one in every \(2.39 \times 10^{13}\) atmospheric parts has been in Flint&#39;s lungs&amp;quot;. This makes the perhaps unrealistic assumption that each breath is a totally new volume of air in our atmosphere. In reality our number will be lower, but not orders of magnitudes lower. &lt;a href=&quot;#fnref-4&quot;&gt;↩&lt;/a&gt;&lt;/div&gt;
&lt;div class=&quot;footnote&quot; id=&quot;fn-5&quot;&gt;&lt;sup&gt;5&lt;/sup&gt; Using a density of 1.225 kg/m^3, each breath weighs \(500 \mathrm{mL} \times 1.225 \mathrm{kg}/\mathrm{m}^3 = 0.0006125\mathrm{kg}\). So, each breath contains \(0.0006125 \mathrm{kg} / (0.0289652 \mathrm{kg}/\mathrm{mol}) \times \mathrm{avogadro} \approx 1.27 \times 10^{23}\) molecules. &lt;a href=&quot;#fnref-5&quot;&gt;↩&lt;/a&gt;&lt;/div&gt;
&lt;div class=&quot;footnote&quot; id=&quot;fn-6&quot;&gt;&lt;sup&gt;6&lt;/sup&gt; At sea level, &lt;a href=&quot;https://en.wikipedia.org/wiki/Density_of_air&quot;&gt;air weighs 1.225kg/m^3&lt;/a&gt; &lt;a href=&quot;#fnref-6&quot;&gt;↩&lt;/a&gt;&lt;/div&gt;]]></description>
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      <title>Projects</title>
      <link>https://rensoliemans.nl/en/projects/</link>
      <guid>https://rensoliemans.nl/en/projects/</guid>
      
      <description><![CDATA[&lt;dl&gt;&lt;dt&gt;&lt;a href=&quot;https://kwantumkwestie.nl&quot;&gt;kwantumkwestie.nl&lt;/a&gt;&lt;/dt&gt;&lt;dd&gt;a mini website that plays around with some philosophical ideas that arise from quantum mechanics.&lt;/dd&gt;&lt;dt&gt;&lt;a href=&quot;https://vogelgeluidjes.nl&quot;&gt;vogelgeluidjes.nl&lt;/a&gt;&lt;/dt&gt;&lt;dd&gt;a website that helps you learn to recognize bird sounds using spaced repetition.&lt;/dd&gt;&lt;dt&gt;&lt;a href=&quot;https://rensoliemans.nl/aoc&quot;&gt;My Advent of Code solutions&lt;/a&gt;&lt;/dt&gt;&lt;dd&gt;literate programming solutions written in Clojure.&lt;/dd&gt;&lt;dt&gt;&lt;a href=&quot;https://addons.mozilla.org/en-US/firefox/addon/anna-goodreads/&quot;&gt;anna-goodreads&lt;/a&gt;&lt;/dt&gt;&lt;dd&gt;a Firefox extension that adds annas-archive links next to books on Goodreads.&lt;/dd&gt;&lt;dt&gt;&lt;a href=&quot;https://addons.mozilla.org/en-US/firefox/addon/vogelchecklist-vergelijker/&quot;&gt;vogelchecklist-vergelijker&lt;/a&gt;&lt;/dt&gt;&lt;dd&gt;a Firefox extension that helps compare &lt;a href=&quot;https://vogelchecklist.nl/bigyear&quot;&gt;vogelchecklist.nl/bigyear&lt;/a&gt; lists.&lt;/dd&gt;&lt;dt&gt;&lt;a href=&quot;https://codeberg.org/RensOliemans/randomshit&quot;&gt;randomshit&lt;/a&gt;&lt;/dt&gt;&lt;dd&gt;a collection of (mainly python) programs that I have created over the years to answer questions like &amp;quot;how many times do you have to riffle shuffle a deck to get it properly sorted?&amp;quot;, or &amp;quot;what is the average occupancy rate of parking lots in Amsterdam?&amp;quot;&lt;/dd&gt;&lt;/dl&gt;]]></description>
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