Something seems out of kilter about this, Eliezer.
When I was 13, I thought I had a proof in principle that there must be a minimum possible distance—because to move is to move a finite distance, but no sum of infitesimal distances can compose a finite distance. I shared my idea with a professional physicist, who dismissed my idea using an appeal to authority. I don’t care how fabulous the authority was, nor how ignorant I may have been, it was a terrible thing to for him to do that. It killed my enthusiasm for questioning physics, or math, at the time.
Reasoning, even mathematical reasoning, is not about just about right and wrong. It’s also about how we model the world and apply our models to it. See Imre Lakatos’s wonderful Proofs and Refutations for a look at how proofs are not just proofs, they are assertions about what’s worth talking about and what we mean by our words.
And reasoning is also about honing our skills. We must develop the guts to recognize when we are wrong, but also the guts not worry so much about being wrong that we give up before we learn very much.
I once discovered a way to trisect an angle with a compass and straight edge. This has been proven to be impossible, apparently, but I did it. Later I discovered that I used an operation that wasn’t “allowed” (an approximation maneuver), even though I performed the maneuver with only a compass and straight edge. To me, the proof that it can’t be done is obviously incorrect, by any practical standard. Show me an angle and I can trisect it to an arbitrarily high degree of accuracy with my mechanical procedure. I challenge the “rules” set out by whomever thinks he’s the know-all on what can be done with a compass and straight edge.
I hope other 13 year-olds don’t read your essay and decide that the rational attitude is never to try to reinvent or challenge the Ancient Ones.
Something seems out of kilter about this, Eliezer.
When I was 13, I thought I had a proof in principle that there must be a minimum possible distance—because to move is to move a finite distance, but no sum of infitesimal distances can compose a finite distance. I shared my idea with a professional physicist, who dismissed my idea using an appeal to authority. I don’t care how fabulous the authority was, nor how ignorant I may have been, it was a terrible thing to for him to do that. It killed my enthusiasm for questioning physics, or math, at the time.
Reasoning, even mathematical reasoning, is not about just about right and wrong. It’s also about how we model the world and apply our models to it. See Imre Lakatos’s wonderful Proofs and Refutations for a look at how proofs are not just proofs, they are assertions about what’s worth talking about and what we mean by our words.
And reasoning is also about honing our skills. We must develop the guts to recognize when we are wrong, but also the guts not worry so much about being wrong that we give up before we learn very much.
I once discovered a way to trisect an angle with a compass and straight edge. This has been proven to be impossible, apparently, but I did it. Later I discovered that I used an operation that wasn’t “allowed” (an approximation maneuver), even though I performed the maneuver with only a compass and straight edge. To me, the proof that it can’t be done is obviously incorrect, by any practical standard. Show me an angle and I can trisect it to an arbitrarily high degree of accuracy with my mechanical procedure. I challenge the “rules” set out by whomever thinks he’s the know-all on what can be done with a compass and straight edge.
I hope other 13 year-olds don’t read your essay and decide that the rational attitude is never to try to reinvent or challenge the Ancient Ones.