The Standard Model
I noticed a pattern in the pedagogy of certain difficult fields: often, the entire world gets &quot;stuck&quot; on a single teaching approach, a single method, or a single point of view. This happens when the subject is difficult enough by itself that <i>reframing</i> it is decidedly non-trivial, so people don&#x27;t bother. They slog through the one path available, get to a point of understanding, and then they&#x27;re so exhausted and relieved that they got there at all that they cling to their mountaintop of success for dear life and refuse to contemplate re-taking that journey by some different path.<p>My pet peeve is asymmetric numeral systems (ANS), which used the <i>exact same too-busy diagram</i> in literally every explanation of it I&#x27;ve ever seen: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Asymmetric_numeral_systems#Basic_concepts_of_ANS" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Asymmetric_numeral_systems#Bas...</a><p>I&#x27;ve seen diagrams like this before, made by two of my fellow students who&#x27;s brains were... rather odd, let&#x27;s just say. I can&#x27;t grok diagrams like this. They&#x27;re too busy. Animations would help, or labels, or even just a legend explaining the random and meaningless colour choices.<p>But there aren&#x27;t any other diagrams. There&#x27;s <i>this one</i>, and only this one. It was the one in the original paper, and was copied into every blog, every other paper, and Wikipedia as well.<p>The Standard Model is the same kind of thing. Its maths is <i>atrocious:</i> a horrific blend of Einstein summation convention, matrices chosen out of thin air, and complex numbers sprinkled on top just for fun. Then it gets worse.<p>There&#x27;s a reason for this: history. The linked article walks through the steps we took over the last century building up to the Standard Model.<p>The problem is that those steps were <i>the pinnacle of human thought</i>. The greatest minds climbed to each of those peaks through decades of effort.<p>Nobody can just wave their hand and reframe the maths, or explain it a different way -- <i>rotating the topology</i> to show a difference face to new students. It&#x27;s just too hard. It&#x27;s Everest, not the local forest path.<p>If you keep at it long enough, you&#x27;ll see some partial attempts. I&#x27;ve seen most (but maybe not all?) of the associated maths rephrased into the language of Geometric Algebra. Most of the complexity just <i>evaporates</i>. The magical matrices disappear, and the reason for their historical usage becomes clear. The complex numbers disappear. The summation convention vanishes. Etc...<p>But nobody flies the helicopter to the top of Mount Everest, even though we <i>can</i> do that now. The point is to climb up there. So we suit up students every year, and make them go through each base camp, suffering through altitude sickness and frostbite on the way up.