Imagine ... that triangles actually have five corners ...

[Nereid]

The full quote is "Imagine, for example, that there existed a devoted band of crackpots who believed, for complicated, impossible-to-pin-down reasons of topology and geometric algebra, that triangles actually have five corners."

Scott Aaronson goes on to explain why he gave up trying to have a rational (i.e. reason-based) discussion with a particular crackpot. It's both amusing and depressing; you can find it here.

Some snippets:

But I hadn’t actually studied Joy’s “work” at a technical level. Well, yesterday I finally did, and I confess that I was astonished by what I found. Before, I’d actually given Joy some tiny benefit of the doubt—possibly misled by the length and semi-respectful tone of the papers refuting his claims. I had assumed that Joy’s errors, though ultimately trivial (how could they not be, when he’s claiming to contradict such a well-understood fact provable with a few lines of arithmetic?), would nevertheless be artfully concealed, and would require some expertise in geometric algebra to spot. I’d also assumed that of course Joy would have some well-defined hidden-variable model that reproduced the quantum-mechanical predictions for the Bell/CHSH experiment (how could he not?), and that the “only” problem would be that, due to cleverly-hidden mistakes, his model would be subtly nonlocal.

What I actually found was a thousand times worse: closer to the stuff freshmen scrawl on an exam when they have no clue what they’re talking about but are hoping for a few pity points. It’s so bad that I don’t understand how even Joy’s fellow crackpots haven’t laughed this off the stage.

Update (May 11): A commenter pointed me to a beautiful preprint by James Owen Weatherall, which tries sympathetically to make as much sense as possible out of Joy Christian’s ideas, and then carefully explains why the attempt fails (long story short: because of Bell’s theorem!). Notice the contrast between the precision and clarity of Weatherall’s prose—the way he defines and justifies each concept before using it—and the obscurity of Christian’s prose.

These crackpots couldn’t be persuaded by rational argument—indeed, they didn’t even use words and sentences the same way you do, to convey definite meaning. And crucially, they had infinite energy: you could argue with them for weeks, and they would happily argue back, until you finally threw up your hands in despair for all humanity, at which point the crackpots would gleefully declare, “haha, we won! the silly ‘triangles have 3 corners’ establishment cabal has admitted defeat!” And, in a sense, they would have won: with one or two exceptions, the vast majority who know full well how many corners a triangle has simply never showed up to the debate, thereby conceding to the 5-cornerists by default.

[danscope]

He must have missed the class where polygons were explained.
Lesson: always read the book.... with understanding.

[John Mendenhall]

Hi, Nereid. This thread could use some links. I didn't find much usable on a search for Christian,

Thanks, John M.

[Solfe]

I am not exactly sure where these folks went wrong. I know where I went wrong... "5 corners, triangle shape... 4 sided pyramid." Which isn't really a triangle, but the resemblance is there.

[Ara Pacis]

Is te 5-sides triangle an analogy or the actual argument?

[Nereid]

Hi, Nereid. This thread could use some links. I didn't find much usable on a search for Christian,

Thanks, John M.

There was one in the OP (the word "here" is in blue)

The Blog of Scott Aaronson: I was wrong about Joy Christian

[John Mendenhall]

There was one in the OP (the word "here" is in blue)

The Blog of Scott Aaronson: I was wrong about Joy Christian

Got it, thanks, Nereid.

Now, let's generalize. How do people, even educated ones, get off in the wrong direction and won't give it up. There must be some psychological mechanism at work. Any ideas?

Regards, John M.

[HenrikOlsen]

Dunning-Kruger is probably a good start.

[SkepticJ]

Got it, thanks, Nereid.

Now, let's generalize. How do people, even educated ones, get off in the wrong direction and won't give it up. There must be some psychological mechanism at work. Any ideas?

Regards, John M.

Ego?

You can't make someone see they're wrong unless they're open to the possibility they could be.

[grav]

I will use as many notebooks and spend as many long nights as it takes in an attempt to disprove this 5 corner triangle theory. Okay, well, where to start... hmm. I suppose we should begin with some basic definitions of terms, as usual, starting of course with that of a triangle. Wiki defines a triangle as a polygon with 3 corners and 3 sides. This seems to be the standard definition. Okay, where to go from there? A triangle has 3 corners. I'm stuck. Let's try again. A polygon with 3 corners is defined as a triangle. This is harder than I thought. Let's start with a polygon with 5 corners. Can't be a triangle because triangles are defined as having only 3 corners, so it must be something else. Not gaining any headway here. Oh wait, I've got it. A triangle has 3 corners because it is defined that way, hence the name "tri"-"angle". Whew, that was rough. Anyway, it's in the original definition to begin with, so proof complete.

[grav]

Is te 5-sides triangle an analogy or the actual argument?

Upon glancing through the link, it appears to be an analogy about the futility of trying to reason with someone about a simple misconception they might have or error they may have made that still clings to it stubbornly no matter what, the same as we often see here. The actual argument appears to have to do with Bell's theorem however, a complicated subject, so there's probably more to it than that. Pity though, after all the time and effort I put into my proof of a 3 cornered triangle.

[Jens]

He must have missed the class where polygons were explained.
Lesson: always read the book.... with understanding.

It isn't actually an argument about five-sided triangles. That's just an analogy that the blogger used to express his frustration. The real issue is about Bell's theorem, and to be honest I lack the background to be able to even understand what's being argued about.

But I agree with others, a lot is about ego. But it's encouraged; look at how Nobel laureates are treated.

It's kind of a sad situation, though, which we all see here as well. A person comes in with some counterintuitive idea, and claims to be correct, refuses to look at evidence, and then self-contentedly states that others have "lost" because they were not able to convince the person of the falsity of the claim. And the person walks away self-righteously, but without any better understanding of reality, which actually should be the point of thinking.

[danscope]

Hi Jens, I think he has run into a few sophists, who relish the situation of argument without and beyond reason
because they" Think they can" . It is of course absurd. A kind of intellectual troll, I guess, with foot in mouth disease.

Best regards,
Dan

[Ara Pacis]

Upon glancing through the link, it appears to be an analogy about the futility of trying to reason with someone about a simple misconception they might have or error they may have made that still clings to it stubbornly no matter what, the same as we often see here. The actual argument appears to have to do with Bell's theorem however, a complicated subject, so there's probably more to it than that. Pity though, after all the time and effort I put into my proof of a 3 cornered triangle.

It can be hard to tell around here sometimes. After all, they might have been talking about topology, where you can have a triangle with each angle being 90 degrees or something along similar lines.

[Zentisan]

Sometimes words do conjure images. Saw this somewhere.

expand.jpg

[headrush]

Sometimes words do conjure images. Saw this somewhere.

expand.jpg

I loled !

Reminds me of a java course at the open university. I won't go into too much detail, but in an online multiple choice component, the correct answer depended on knowing the correct meaning of certain words in context.
I knew the answer, as did many others. Imagine my surprise when my answer was marked incorrect !
When I complained, the question and all marks were withdrawn because "the question could have been misinterpreted". Rubbish, if you had done any studying it was obvious.
The OU is like that in many areas I'm afraid.
(The question was concerning the initial states of arrays and hashes, ie. which one could you specifically set the capacity when initializing. The possible misinterpretation was over the word " capacity" because it could mean "size", but size means the current contents, not the total possible contents.)

[HenrikOlsen]

Being comp-sci myself I would say capacity is the potential content, not current content, but you might have come up against a book that used it differently. This is the bane of learning everywhere.
Which is why developing a vocabulary where you qualify everything to make your intent clear is a good thing to do.

[headrush]

Henrik, your interpretation is correct AFAIK, the issue for me and the relevance to the thread was the howls of protest from the people who had got it wrong, and then denounced me for complaining about the marking.
It was pretty black and white in the course text, but even the test compilers got it wrong.

[Ara Pacis]

as hard as they might try to be monologists, even they are dialogists.

[headrush]

as hard as they might try to be monologists, even they are dialogists.

But surely there are instances where there is only one answer ? (impossibility of disproofs aside),
ETA, I found this quite amusing (and apt),

[Ara Pacis]

But surely there are instances where there is only one answer ? (impossibility of disproofs aside),
ETA, I found this quite amusing (and apt),

one answer =/= one meaning

[Ivan Viehoff]

Now, let's generalize. How do people, even educated ones, get off in the wrong direction and won't give it up. There must be some psychological mechanism at work. Any ideas?

The psychologist Daniel Kahneman (who won the Nobel Prize for Economics) said in his book "Thinking Fast, Thinking Slow" that intelligent people are better at self-deception than less intelligent people. In other words, if they get stuck on some wrong idea, they are, through their intelligence, better at thinking up plausible arguments for why it is correct. They may also have a vested interest - reputation, loss of face - for sticking with it. A prime example would be Isaac Newton, who probably spent more of his life trying to use biblical sources to estimate the date of the earth's creation, than he did on gravity, mechanics, opticks (as he spelled it), and calculus. But most people are only aware of the latter.

[HenrikOlsen]

The (unconscious) fear of looking stupid is you step away from a previously held position is a powerful motivator for shoring up that position even in the face of quite strong counterarguments.

[grapes]

There was one in the OP (the word "here" is in blue)

The Blog of Scott Aaronson: I was wrong about Joy Christian

My favorite part? Here:

It’s as if someone announced his revolutionary discovery that P=NP implies N=1, and then critics soberly replied that, no, the equation P=NP can also be solved by P=0.

It's hard for me to believe that he used P and NP randomly, to illustrate simple solutions to x = yx . Talk about layers of meaning!

Is P equal to NP?

[John Mendenhall]

My favorite part? Here:

It's hard for me to believe that he used P and NP randomly, to illustrate simple solutions to x = yx . Talk about layers of meaning!

Is P equal to NP?

Oh, I feel so good! Halfway thru the link I saw cryptography applications, and there it was at the end!

Thanks for the link. I'm going to adopt this idea and never give it up, no matter what sort of arguments evil conspiratorial close minded mainstreamers use against me.

Regards, InflatedEgo.

[publiusr]

I seem to remember the time cube guy tried to say that a cube had four sides.

[swampyankee]

Sometimes words do conjure images. Saw this somewhere.

I gave a test to a group of high-school physics students. Two of them wrote "42" as an answer to all the questions, having missed that it's the answer to "life, the universe, and everything," but not "resolve these vectors into components...." or "add these vectors" or any other question of that sort. Neither was, however, named "Peter," although both were male.

[Nereid]

My favorite part? Here:

It’s as if someone announced his revolutionary discovery that P=NP implies N=1, and then critics soberly replied that, no, the equation P=NP can also be solved by P=0.

It's hard for me to believe that he used P and NP randomly, to illustrate simple solutions to x = yx . Talk about layers of meaning!

Is P equal to NP?

Yeah, that was awesome, wasn't it?

[Zentisan]

"Imagine..

I guess this is somewhere about the point I wandered off. My problem is when I Imagine, I draw mental pictures. So I saw a triangle sneaking into a pentagon and tra la la... There she is! You could also ask it to pirouette, and viola! A straight line.

Darn these triangles... too versatile for my liking.