What to Do When the Trisector Comes (1983) [pdf]
ufv.caAlso relevant to this topic:
Fred Gruenberger's Measure for Crackpots (1962):
https://www.rand.org/content/dam/rand/pubs/papers/2006/P2678...
John Baez's Crackpot Index (1998):
That Gruenberger piece is a fantastic read and still applicable today.
These are fantastic. Thank you
Related:
What to Do When the Trisector Comes (PDF, 1983) - https://news.ycombinator.com/item?id=34404927 - Jan 2023 (1 comment)
Beware of Cranks: Misguided attempts to solve impossible mathematical problems - https://news.ycombinator.com/item?id=21206633 - Oct 2019 (61 comments)
What to Do When the Trisector Comes (1983) [pdf] - https://news.ycombinator.com/item?id=14446708 - May 2017 (28 comments) (<-- hello!)
The sheer amount of dedication is awe-inspiring. In the 80s, at Imperial College, London, Theoretical Physics Group, we came across some correspondence intended for one of the professors, I think. This person had evidently "translated" his native Spanish into English, laboriously, via some dictionary we thought. We spent many tea breaks puzzling over phrases such as
"Is well-knew the refran: of the said to made it has a good road."
In the same vein is the talk Pathological Physics: Tales from 'The Box' [1] which talks about various physics papers written by amateurs and sent in to the physics department at the university the speaker was in.
Underwood Dudley has written more comprehensive books about mathematical cranks (in general) and trisectors (in particular) which are a delight to read.
For some reason the article made me think about this quote from one of the 2025 MacArthur Fellowship videos, "I think there are some mathematicians who are kind of like the hiker who choose this massive peak they want to scale and they do everything they can to make it up the mountain. I'm more like the kind of hiker who wanders through the forest and stops to look at a pretty stone or flower and reflect on whether it's similar to a stone or flower that I've seen before."
It’s interesting to me that Augustus DeMorgan’s view of “a paradoxer” is someone who “attacks the consequences, direct and indirect, of the mathematical method.” (gentle paraphrase)
Why is that the central tenet of being a paradoxer? To me, that’s how I learn and internalize things. I take the premise under study, find some consequence that feels absurd, and turn it this way and that in my mind until the flaw in my own previous thinking becomes clear to me.
Are there better ways of learning?
Does this make me more prone to being a paradoxer?
It makes you a paradoxer if you stopped after the step of finding the consequence that feels absurd.
I had a lot of contact with computer science students coming from the other side, meaning they used Z3 or other (SMT) solvers as blackboxes which they just use at a certain point in their algorithm without having thought what theories they are using (the T in SMT) and what's undecidable in general or in that theory.
So I had quite a few "groundbreaking" approaches end in disappointment.
It's important to know the capabilities and limits of your tools.
I found the writing, and the descriptions of the types of trisectors, strangely poignant. Most of us do not attempt to trisect an angle with straightedge and compass; but surely many of us have other irrational obsessions with which we waste our time (I have certainly been guilty of this). I hope people can find time to look up from their interactions with social media and LLMs for enough healthy introspection to avoid these traps.
I was briefly a trisector in middle school but at least I was fortunate enough to have access to Geogebra which quickly showed me the error in my procedure. I wonder what other tools we can give a curious but potentially misguided person so they too do not fall too deep into the rabbit hole.
The advice here is now increasingly out of date in the era of LLMs. Trisectors are more numerous and voluminous than ever, while being less obvious and more effective at wasting your time, and approaching a far greater variety of subjects, and any kind of response to one has a much greater risk of outright aggressive and even threatening responses as sycophantic AIs escalate their users otherwise benign hyperfocus into outright paranoid delusions.
Out of date?
If what you say is true, shouldn’t that make the understanding of trisectors more urgent and important? If anything, this is more relevant than before.
I'm not sure. I think LLMs makes different people into trisectors and they trisect in different ways-- so not just much more numerous but also somewhat different in character.
LLMs are trisector factories.
Reads as if written by a Brontosaurus expert.