<story><title>Grothendieck’s use of equality</title><url>https://arxiv.org/abs/2405.10387</url></story><parent_chain><item><author>generationP</author><text>This is probably better known here under the name of implicit type conversions. Strictly speaking, the rational number 1 is not the same as the integer 1; we just have a conversion map that preserves all the relevant properties. It&amp;#x27;s all fun and games until there are 1000 types and 10000 conversion maps involved and the relevant diagrams no longer commute (i.e., it depends what order you go).</text></item></parent_chain><comment><author>reaperman</author><text>&amp;gt; (i.e., it depends what order you go)&lt;p&gt;At the risk of utterly derailing this with irrelevant discussion: path-dependent systems are particularly tricky for some people IMHO. I think in a more state-based way, and my first rigorous dive into path-dependent calculation was during my chemical engineering degree -- I learned to be extremely vigilant about memorizing what was path-dependent and triple-checking if that affected the situation I was calculating.&lt;p&gt;I do wish there was more rigorous exposure to them at lower levels of education and younger age. Because while I&amp;#x27;m perfectly capable of handling path-dependent systems with proper focus and effort, my brain doesn&amp;#x27;t feel &amp;quot;native&amp;quot; when deriving solutions around those spaces - it feels similar to being &amp;quot;fluent enough&amp;quot; in another language. I feel this way about a lot of things -- I really feel I&amp;#x27;d have been happier and more fulfilled if I&amp;#x27;d been immersed in super rigorous first-principles education beginning around age 8-9. I didn&amp;#x27;t do well with things like &amp;quot;memorize this procedure for doing long division&amp;quot; and did much better with conceptual derivations of physics&amp;#x2F;math&amp;#x2F;science&amp;#x2F;historical arcs, etc.</text></comment>
<story><title>Grothendieck’s use of equality</title><url>https://arxiv.org/abs/2405.10387</url></story><parent_chain><item><author>generationP</author><text>This is probably better known here under the name of implicit type conversions. Strictly speaking, the rational number 1 is not the same as the integer 1; we just have a conversion map that preserves all the relevant properties. It&amp;#x27;s all fun and games until there are 1000 types and 10000 conversion maps involved and the relevant diagrams no longer commute (i.e., it depends what order you go).</text></item></parent_chain><comment><author>actionfromafar</author><text>I assume you mean any random enterprise codebase? Because that is any random enterprise codebase.</text></comment>