What to Do When the Trisector Comes (1983) [pdf] (opens in new tab)

(ufv.ca)

93 pointsrobertvc2mo ago18 comments

18 comments

lambdaone2mo ago

Also 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):

https://math.ucr.edu/home/baez/crackpot.html

cenazoic2mo ago

That Gruenberger piece is a fantastic read and still applicable today.

quotemstr2mo ago

These are fantastic. Thank you

dang2mo ago

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!)

theodorethomas2mo ago

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."

EdwardCoffin2mo ago

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.

[1] https://www.youtube.com/watch?v=HXSgp755DSA

lbruck2mo ago

Underwood Dudley has written more comprehensive books about mathematical cranks (in general) and trisectors (in particular) which are a delight to read.

conditionnumber2mo ago

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."

gcr2mo ago

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?

talyian2mo ago

It makes you a paradoxer if you stopped after the step of finding the consequence that feels absurd.

maweki2mo ago

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.

awanderingmind2mo ago

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.

saagarjha2mo ago

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.

nullc2mo ago

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.

gcr2mo ago

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.

nullc2mo ago

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.

filoeleven2mo ago

LLMs are trisector factories.

user____name2mo ago

Reads as if written by a Brontosaurus expert.

j / k navigate · click thread line to collapse

18 comments

lambdaone2mo ago

Also 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):

https://math.ucr.edu/home/baez/crackpot.html

cenazoic2mo ago

That Gruenberger piece is a fantastic read and still applicable today.

quotemstr2mo ago

These are fantastic. Thank you

dang2mo ago

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!)

theodorethomas2mo ago

"Is well-knew the refran: of the said to made it has a good road."

EdwardCoffin2mo ago

[1] https://www.youtube.com/watch?v=HXSgp755DSA

lbruck2mo ago

Underwood Dudley has written more comprehensive books about mathematical cranks (in general) and trisectors (in particular) which are a delight to read.

conditionnumber2mo ago

gcr2mo ago

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)

Are there better ways of learning?

Does this make me more prone to being a paradoxer?

talyian2mo ago

It makes you a paradoxer if you stopped after the step of finding the consequence that feels absurd.

maweki2mo ago

So I had quite a few "groundbreaking" approaches end in disappointment.

It's important to know the capabilities and limits of your tools.

awanderingmind2mo ago

saagarjha2mo ago

nullc2mo ago

gcr2mo ago

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.

nullc2mo ago

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.

filoeleven2mo ago

LLMs are trisector factories.

user____name2mo ago

Reads as if written by a Brontosaurus expert.

j / k navigate · click thread line to collapse