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What's really great about this is Terry Tao, a mathematician known primarily for analytics and combinatorics, can, in the space of two blog comments, completely

What's really great about this is Terry Tao, a mathematician known primarily for analytics and combinatorics, can, in the space of two blog comments, completely filet a Princeton prof's flawed argument in the largely unrelated field of mathematical logic.

mhh__ 5y ago
You're not wrong but as a professional mathematician it's not like Tao is exactly stumbling in blind. Logic is the basis of the bases
- catgary 5y ago
  Yeah, my understanding is that analysts are often quite strong in that domain of mathematical logic (there’s a similar where algebraic topologists are often incredibly comfortable with categorical logic).
lvs 5y ago
Fileting someone's argument is not a positive goal. It's an egotistical one. Finding truth is a good goal. That seems to be what is praiseworthy here.
- treyhuffine 5y ago
  And allowing one's ego to not get in the way of accepting the truth, even when it contradicts your original belief.
- civilized 5y ago
  Easy, there. It's just evocative language. I could have said "spot the core flaw" to the same effect.
  - ameister14 5y ago
    Not trying to attack you, just an aside - I don't know that 'spot the core flaw' is the same as 'filet someone's flawed argument.' The latter implies 'ooh, he won;' the former only 'ah, there was a problem and he spotted it.'
  - lvs 5y ago
    Then I apologize for responding to the language that you wrote and not other language you could have used.
    - deleted 5y ago
      [deleted]
- derefr 5y ago
  "Finding truth" isn't quite what happened here, though. Finding a contradiction/other invalidation of someone else's proof, doesn't advance the knowledge frontier. It means that there was a flaw in process of proving the original proof, but it doesn't disprove the idea behind the original proof. You'd need your own separate proof to do that—probably a proof by contradiction, of one of the main lemmas of the proof. The useful skill, here, is one shared by logicians and compilers: the ability to quickly find flaws that invalidate a proof, without needing to fully understand what the proof is trying to prove. Said skill, if it could be more widely-learned, would be very helpful in iterating toward sound proofs (or impossibility proofs for such.) But when it's only a skill in the hands of another party external to the one writing the proof, that iterative aspect isn't really there.
  - Cogito 5y ago
    Proving that one branch of a tunnel system does not lead to the open air is advancing the knowledge frontier. It's not as 'advancing' as finding a tunnel that does lead to the surface, but it is still useful. I think I agree with the rest of what you have said.
    - derefr 5y ago
      Sure, but I think the wrong image is conjured by saying "a branch of a tunnel system", since while branches in a real tunnel may themselves branch, they don't tend to branch every few millimeters, the way proofs can branch with every character in possibility space. Invalidating a proof is essentially what a compiler does when it blows up over a typo in the code you've fed it. The thing is, most of the time, it is just a typo. The code as-is is wrong, but the code with one character different — the code if "branched" in an alternate direction for just a few millimeters, and then course-corrected back onto the original existing path — is right, and the semantic meaning of the code isn't changed/compromised by that correction. Finding a logic-level flaw in a (presented) mathematical proof is usually similar: 99% of the time, it's something fixable. That 1% of the time does still exist; there can be "fatal flaws" in proofs, where the proof's author can't find a way to salvage their proof. But it's not the invalidation of the particular proof, where the knowledge that the proof is unsalvageable (i.e. that there's no path that follows the general "plan" of the branch to get from A to B) gets created. That knowledge is only discovered after much more work by the proof's author, to try to "dig around" the problem, that all turns out to hit other walls. (Note here that I'm assuming that the proof isn't already believed to be true when it's invalidated. Which it usually isn't; most proofs that get invalidated are invalidated when they're still being circulated as something novel and for-scrutiny, rather than when they're already generally-accepted. If a proof was already thought to be true, then invalidating it would temporarily create "negative" knowledge — it would retract a previous consensus assertion of the truth-value of the proof.)
tomjakubowski 5y ago
Tao is respectful in his criticism. And Nelson returns the respect in humbly withdrawing his claim. That is the great thing about this exchange to me.
- civilized 5y ago
  The tone of the exchange is great, although normal in the company of accomplished pure mathematicians.
SquishyPanda23 5y ago
Tao also writes about how to do this sort of error spotting in a proof you suspect to be wrong: https://terrytao.wordpress.com/advice-on-writing-papers/on-local-and-global-errors-in-mathematical-papers-and-how-to-detect-them/ https://terrytao.wordpress.com/advice-on-writing-papers/on-l... In general he thinks a lot about tool kits and I think what we're seeing here is the math equivalent to being great at debugging.
CTmystery 5y ago
What I find most admirable is not the complete fileting, but the humble acceptance of error on something that proof author had obviously put much effort into. It sucks to hear that something you've worked hard on is fundamentally flawed, especially on such public display
- Causality1 5y ago
  It sucks to hear that something you've worked hard on is fundamentally flawed, especially on such public display Exactly what I say at parent-teacher conferences.
  - quercusa 5y ago
    Are you the teacher or the parent? I can't decide which I think would be funnier.
deleted 5y ago
[deleted]
Rioghasarig 5y ago
Even the smartest people can be wrong and it can take an outside perspective for them to realize this. This isn't an example of someone "fileting" another's argument. It's an example of two professionals have a conversation and arriving at an agreement. Nelson was making an extraordinary claim so the odds were definitely against him.

mhh__ 5y ago

You're not wrong but as a professional mathematician it's not like Tao is exactly stumbling in blind. Logic is the basis of the bases

catgary 5y ago
Yeah, my understanding is that analysts are often quite strong in that domain of mathematical logic (there’s a similar where algebraic topologists are often incredibly comfortable with categorical logic).

lvs 5y ago

Fileting someone's argument is not a positive goal. It's an egotistical one. Finding truth is a good goal. That seems to be what is praiseworthy here.

treyhuffine 5y ago
And allowing one's ego to not get in the way of accepting the truth, even when it contradicts your original belief.
civilized 5y ago
Easy, there. It's just evocative language. I could have said "spot the core flaw" to the same effect.
- ameister14 5y ago
  Not trying to attack you, just an aside - I don't know that 'spot the core flaw' is the same as 'filet someone's flawed argument.' The latter implies 'ooh, he won;' the former only 'ah, there was a problem and he spotted it.'
- lvs 5y ago
  Then I apologize for responding to the language that you wrote and not other language you could have used.
  - deleted 5y ago
    [deleted]
derefr 5y ago
"Finding truth" isn't quite what happened here, though. Finding a contradiction/other invalidation of someone else's proof, doesn't advance the knowledge frontier. It means that there was a flaw in process of proving the original proof, but it doesn't disprove the idea behind the original proof. You'd need your own separate proof to do that—probably a proof by contradiction, of one of the main lemmas of the proof. The useful skill, here, is one shared by logicians and compilers: the ability to quickly find flaws that invalidate a proof, without needing to fully understand what the proof is trying to prove. Said skill, if it could be more widely-learned, would be very helpful in iterating toward sound proofs (or impossibility proofs for such.) But when it's only a skill in the hands of another party external to the one writing the proof, that iterative aspect isn't really there.
- Cogito 5y ago
  Proving that one branch of a tunnel system does not lead to the open air is advancing the knowledge frontier. It's not as 'advancing' as finding a tunnel that does lead to the surface, but it is still useful. I think I agree with the rest of what you have said.
  - derefr 5y ago
    Sure, but I think the wrong image is conjured by saying "a branch of a tunnel system", since while branches in a real tunnel may themselves branch, they don't tend to branch every few millimeters, the way proofs can branch with every character in possibility space. Invalidating a proof is essentially what a compiler does when it blows up over a typo in the code you've fed it. The thing is, most of the time, it is just a typo. The code as-is is wrong, but the code with one character different — the code if "branched" in an alternate direction for just a few millimeters, and then course-corrected back onto the original existing path — is right, and the semantic meaning of the code isn't changed/compromised by that correction. Finding a logic-level flaw in a (presented) mathematical proof is usually similar: 99% of the time, it's something fixable. That 1% of the time does still exist; there can be "fatal flaws" in proofs, where the proof's author can't find a way to salvage their proof. But it's not the invalidation of the particular proof, where the knowledge that the proof is unsalvageable (i.e. that there's no path that follows the general "plan" of the branch to get from A to B) gets created. That knowledge is only discovered after much more work by the proof's author, to try to "dig around" the problem, that all turns out to hit other walls. (Note here that I'm assuming that the proof isn't already believed to be true when it's invalidated. Which it usually isn't; most proofs that get invalidated are invalidated when they're still being circulated as something novel and for-scrutiny, rather than when they're already generally-accepted. If a proof was already thought to be true, then invalidating it would temporarily create "negative" knowledge — it would retract a previous consensus assertion of the truth-value of the proof.)

tomjakubowski 5y ago

Tao is respectful in his criticism. And Nelson returns the respect in humbly withdrawing his claim. That is the great thing about this exchange to me.

civilized 5y ago
The tone of the exchange is great, although normal in the company of accomplished pure mathematicians.

SquishyPanda23 5y ago

Tao also writes about how to do this sort of error spotting in a proof you suspect to be wrong: https://terrytao.wordpress.com/advice-on-writing-papers/on-local-and-global-errors-in-mathematical-papers-and-how-to-detect-them/ https://terrytao.wordpress.com/advice-on-writing-papers/on-l... In general he thinks a lot about tool kits and I think what we're seeing here is the math equivalent to being great at debugging.

CTmystery 5y ago

What I find most admirable is not the complete fileting, but the humble acceptance of error on something that proof author had obviously put much effort into. It sucks to hear that something you've worked hard on is fundamentally flawed, especially on such public display

Causality1 5y ago
It sucks to hear that something you've worked hard on is fundamentally flawed, especially on such public display Exactly what I say at parent-teacher conferences.
- quercusa 5y ago
  Are you the teacher or the parent? I can't decide which I think would be funnier.

deleted 5y ago

[deleted]

Rioghasarig 5y ago

Even the smartest people can be wrong and it can take an outside perspective for them to realize this. This isn't an example of someone "fileting" another's argument. It's an example of two professionals have a conversation and arriving at an agreement. Nelson was making an extraordinary claim so the odds were definitely against him.