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I’m not completely happy with this interview with Micah Zarin. It was nothing he did, it was me. I forgot to say that current-day AI wastes a lot of energy, and companies hope to use it to lay off people, and oligarchs are using it to extract lots of money from everyone. While obvious, these things are tremendously important and I should have emphasized them.
I...
The sum of the reciprocals of the primes diverges, but very slowly. The sum of the reciprocals of the first 100 primes is
2.106…The sum of the reciprocals of the first 1,000 primes is
2.457…For the first 10,000 it’s
2.709…And it keeps creeping up, ever more slowly. To get the sum to reach 6, you need to add up the reciprocals of the first 3 × 10¹...
I recently showed you that if you take the regular icosahedron:
I never knew what was so great about the ‘great icosahedron’. Now I do.
Take a regular icosahedron whose vertices have coordinates in the field ℚ[√5], which consists of numbers a + b√5 with a and b rational.
Apply the nontrivial element of the Galois group of this field: that is, simply replace √5 by -√5 in all your formulas. You get the
This post starts with the the slides of an elementary talk I gave at Sloans Bar and Grill, in Glasgow, as part of a wonderful series called A Pint of Science. At the end I include some fascinating details which I only had time to briefly touch on in my talk.
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