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An Imaginary Rabbit Hole

Here is a rabbit hole for Saturday.

  • In the morning, I click on a few links that lead me to an article in Quanta magazine discussing how imaginary numbers might after all be essential elements of reality rather than mere mathematical conveniences. This is a big deal for me. It has consumed hours of my free time literally for years. I won’t go into it here (which I know you’ll thank me for). Let’s just say that I’m still shaking my head from reading the beginning of the article. I don’t finish reading because…
  • I click on a few links that lead me to Sabine Hossenfelder’s awesome physics videos, the most recent of which is (whaddaya know) “Do Complex Numbers Exist?” Her book is good. Her blog is great. Her video explanations are tremendous. I listen to her slowly, periodically pausing to do morning chores. I don’t finish listening because…
  • I stumble onto a brief (100 page) synopsis of General Relativity by Alan MacDonald. I have two his two little books on Geometric Algebra and Calculus. The synopsis is written with the intent of getting to the core ideas without too much mathematical complexity, seeking in particular to avoid long diversions into tensor analysis. I won’t go into the tensor analysis point (which I know you’ll thank me for) other than to say that my feelings on the subject turn out to be (strangely enough) tied up with the whole problem with imaginary numbers, but let’s just stop there. I don’t finish the synopsis because it’s 100 pages, and because…
  • MacDonald’s article talks about time (which any discussion of spacetime inevitably will), and I find myself browsing through links again and find a reference to Jorge Luis Borges’ essays on the refutation of time. I knew his name. I didn’t know his writing. Now I do. I love how he writes. And I find myself searching the public library hoping to find ebooks (to no avail, they are all checked out — a concept that defies rational explanation). But web searches are of course your friend, and I find the two essays I’m looking for in a PDF someone had stashed away. I don’t finish them, because…
  • In the first essay, Borges writes, “Two arguments led me to this …: Berkeley’s idealism and Leibniz’s principle of indiscernibles.” And not surprisingly, a web search of Liebniz’s principle leads me to the awesome Stanford Encyclopedia of Philosophy entry for “The Identity of Indiscernibles”. But I don’t finish reading it because…

… morning had become day. Breakfast and lunch had come and gone. The yard work was finished. Afternoon ended. Dinner done. Stars shining. 

And because I started writing this story about a rabbit hole I had stumbled down.