<story><title>Math and Analogies</title><url>https://betterexplained.com/articles/math-and-analogies/</url></story><parent_chain><item><author>butisaidsudo</author><text>For Roman numerals to make sense you need to remove access to convenient writing tools. In a world without paper and pens, Arabic numerals are the ones that seem unwieldy.&lt;p&gt;I was on a multi-day hiking trip with a friend where we just had a pack of cards and some spiced rum to keep ourselves entertained in the evening. The first night we decided to play cribbage, but we didn&amp;#x27;t have paper or the like to keep score on.&lt;p&gt;At first I tried using a stick to scratch out numbers in the dirt. It was doable, but very awkward. The low light of the camp fire made it hard to see, and I quickly ran out of undisturbed soil within arms reach.&lt;p&gt;I then gathered a few twigs to shape into numbers, using the patterns you&amp;#x27;d see on an LED clock. That worked reasonably well, but took more effort than I liked.&lt;p&gt;I switched to Roman numerals thinking that the simpler shapes would be easier to work with. This turned out to be true, but I discovered it had the added benefit of being really easy to increment numbers.&lt;p&gt;In most cases, incrementing is incredibly simple. To go from 0 -&amp;gt; 1 -&amp;gt; 2 -&amp;gt; 3, you simply add a stick each time. To go from 3 -&amp;gt; 4, you pinch together the bottoms of the 2nd and 3rd sticks. Then you take the first stick away, then later drop it on the other side of the V. Add another stick, cross some sticks, etc.&lt;p&gt;There are a lot of things that seem poorly done at first glance, but make total sense when you understand the environment they were developed in. I&amp;#x27;ve heard younger folks wonder why old TV shows are so poorly written. When you&amp;#x27;ve always been able to watch on demand (or rent episodes on DVD), it&amp;#x27;s hard to understand the restrictions on writing when there was no way for your audience to watch previous episodes if they hadn&amp;#x27;t seen them when they had aired. And of course this is true for most software I&amp;#x27;ve ever worked on.</text></item></parent_chain><comment><author>sovietmudkipz</author><text>I like your thought experiment to illustrate why Roman numerals make sense for the time. I think you&amp;#x27;re right! It is more practical given the tools than Arabic numerals.&lt;p&gt;To respond to the hiking story; I would opt to use binary if I were in the same situation. I think it&amp;#x27;s a superior system to use especially out in the woods. It&amp;#x27;s hard to read for many folk unexposed to binary but it allows you to encode lots of base 10 numbers using a few items. For example, a twig rotated 0 degrees could signify 0, and a twig rotated 90 degrees could be 1. 5 twigs gets you 0 - 31!&lt;p&gt;To bring it back to the Romans... I realize Binary wasn&amp;#x27;t commonly used in the Ancient World and that is something I find a little baffling. Base 2 seems like it would be more useful in a pre-pen and paper world, especially when you have to etch something. The closest thing I can find is the Inca Quipu (&amp;quot;talking knots&amp;quot;) but even that encodes base 10 numbers into base 4 knots.&lt;p&gt;If base 2 was widely used by human beings our fingers could have encoded up to 1024 digits.&lt;p&gt;How did base n &amp;gt; base 2 evolve?</text></comment>
<story><title>Math and Analogies</title><url>https://betterexplained.com/articles/math-and-analogies/</url></story><parent_chain><item><author>butisaidsudo</author><text>For Roman numerals to make sense you need to remove access to convenient writing tools. In a world without paper and pens, Arabic numerals are the ones that seem unwieldy.&lt;p&gt;I was on a multi-day hiking trip with a friend where we just had a pack of cards and some spiced rum to keep ourselves entertained in the evening. The first night we decided to play cribbage, but we didn&amp;#x27;t have paper or the like to keep score on.&lt;p&gt;At first I tried using a stick to scratch out numbers in the dirt. It was doable, but very awkward. The low light of the camp fire made it hard to see, and I quickly ran out of undisturbed soil within arms reach.&lt;p&gt;I then gathered a few twigs to shape into numbers, using the patterns you&amp;#x27;d see on an LED clock. That worked reasonably well, but took more effort than I liked.&lt;p&gt;I switched to Roman numerals thinking that the simpler shapes would be easier to work with. This turned out to be true, but I discovered it had the added benefit of being really easy to increment numbers.&lt;p&gt;In most cases, incrementing is incredibly simple. To go from 0 -&amp;gt; 1 -&amp;gt; 2 -&amp;gt; 3, you simply add a stick each time. To go from 3 -&amp;gt; 4, you pinch together the bottoms of the 2nd and 3rd sticks. Then you take the first stick away, then later drop it on the other side of the V. Add another stick, cross some sticks, etc.&lt;p&gt;There are a lot of things that seem poorly done at first glance, but make total sense when you understand the environment they were developed in. I&amp;#x27;ve heard younger folks wonder why old TV shows are so poorly written. When you&amp;#x27;ve always been able to watch on demand (or rent episodes on DVD), it&amp;#x27;s hard to understand the restrictions on writing when there was no way for your audience to watch previous episodes if they hadn&amp;#x27;t seen them when they had aired. And of course this is true for most software I&amp;#x27;ve ever worked on.</text></item></parent_chain><comment><author>thaumasiotes</author><text>&amp;gt; To go from 0 -&amp;gt; 1 -&amp;gt; 2 -&amp;gt; 3, you simply add a stick each time. To go from 3 -&amp;gt; 4, you pinch together the bottoms of the 2nd and 3rd sticks.&lt;p&gt;The subtractive part of Roman numerals is an innovation the Romans generally didn&amp;#x27;t use. (Which is why clocks say IIII and not IV.) It adds significant complexity for no benefit.</text></comment>