Beware of Cranks: Misguided attempts to solve impossible mathematical problems
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Beware of Cranks: Misguided attempts to solve impossible mathematical problems
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Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#2I've talked with a bunch of cranks and my experience resonates with this article. I believe in reasoned argument and persuasion, probably to a fault, but I never managed to change any of their opinions in the slightest.
One of them had a theory that every electron was made of two photons going round and round. After pointing out a few of the many problems with that he tracked down where I live to try to report me for "censorship".
Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#3> 3. They don’t understand what it means for something to be mathematically impossible.
This one gets a lot of technically competent people.
I spent a very unsatisfying 45 minutes vainly trying to explain to an eminent biologist that no, really, some statements really are _undecidable_ -- and no, that doesn't mean that at some future time we'll figure out a new approach that lets us decide them.
Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#4If you can put the points of the compass against the straightedge, which gives you a marked straightedge, you can trisect an angle. But that's considered cheating. Archimedes is credited with figuring out this approach.
Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#5Super curious---I actually never took trig (complicated story), so I don't understand the trisecting an angle thing at all. What is it that makes measuring the angle and then dividing that measurement by 3 impossible?
Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#6Super curious---I actually never took trig (complicated story), so I don't understand the trisecting an angle thing at all. What is it that makes measuring the angle and then dividing that measurement by 3 impossible?
It's not the actual measurement, it's the physical act of dividing an angle graphically into thirds using nothing but a compass and a ruler.
Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#7Super curious---I actually never took trig (complicated story), so I don't understand the trisecting an angle thing at all. What is it that makes measuring the angle and then dividing that measurement by 3 impossible?
While dividing by three is easy, dividing an angle by three with just a compass and a straight edge is impossible. Numberphile[1] did a video on this a few years ago
[1] https://www.youtube.com/watch?v=6Lm9EHhbJAY (Euclid's Big Problem - Numberphile)
Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#8Super curious---I actually never took trig (complicated story), so I don't understand the trisecting an angle thing at all. What is it that makes measuring the angle and then dividing that measurement by 3 impossible?
"Measuring" is not permitted. You are granted access only to an idealized compass and straight edge. There's a mobile game called Euclidea based on this which I'd recommend.
Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#9Super curious---I actually never took trig (complicated story), so I don't understand the trisecting an angle thing at all. What is it that makes measuring the angle and then dividing that measurement by 3 impossible?
"Measuring" is not permitted. You are granted access only to an idealized compass and straight edge. There's a mobile game called Euclidea based on this which I'd recommend.
Oooh. I was imagining a compass like you're given in school, with labels on it, and ditto a ruler. :-)
Re: Beware of Cranks: Misguided attempts to solve impossible mathematical problems
#10> 3. They don’t understand what it means for something to be mathematically impossible. This one gets a lot of technically competent people. I spent a very unsatisfying 45 minutes vainly trying to explain to an eminent biologist that no, really, some statements really are _undecidable_ -- and no, that doesn't mean that at some future time we'll figure out a new approach that lets us decide them.
I encountered something similar almost a decade ago on this forum when discussing the halting problem: https://news.ycombinator.com/item?id=1322901