Weird or "no shit" moments in Star Trek

[Discofan]

^I know that (being a mathematician myself by education), that's why I explicitly talked about things that would be immediately obvious to another species, otherwise not more intelligent than us. I don't expect those theorems would fall into that category, unless there is a fundamentally different way to prove them, a way we cannot conceive of, not even in principle.

Could it be that there are truths that elude us, and that we also won't discover by any (future) A.I. built by us, since the same limitations wouldn't allow us to build an A.I. that could grasp them -- somehow transferring our own limitations into the very construction of such A.I.'s without even realising it ?

Well, we are the products of our environment, basically, we are wired to survive predators, competing predators, elusive preys, etc... Unfortunately for us, that does not mean being very good at finding deep abstract truths about the Universe. That's probably why as a species we are really bad at it. Just think about how much harder it is for a child to learn basic mathematical principles than it is to learn their mother language (something arguably a great deal more complex!!!).

 

[matthunter]

When Picard said that Fermat's Last Theorem was never solved. I thought :

"For once that they genuinely tried to say something real, they still got it wrong, although they couldn't know it at the time."

Oh, that wasn't their only foray into predicting the real world. The whole ep The High Ground couldn't be shown on UK television for many years because of Data's line announcing that the IRA militarily defeated the British Army to end the Irish Troubles...

 

[at Quark's]

Wouldn't it be fun if it turned out that that episode actually inspired Wiles to give proving the theorem yet another try? (since it is often described as his life's work, most probably not true, I know)


Later addition to post: (separate point, but don't want to post twice in row)

Just rewatched part of Year of Hell. In it, Chakotay tells Annorax they made a course correction to avoid a rogue comet, and that otherwise they never would have entered Krenim space at all.

So they have to avoid an ice rock of about 60 miles diameter max (that's the size of the largest comet known today), yet this leads to them deviating lightyears off their original course?

The only way I can explain that is to assume that they were too lazy to revert back to their original heading after having avoided that comet, and that those precise headings don't matter that much, as long as they keep heading in the same general direction ...but that imho clashes with the beginning of the very same episode where they open astrometrics, dedicated to finding a more efficient route ...

 

[Discofan]

Wouldn't it be fun if it turned out that that episode actually inspired Wiles to give proving the theorem yet another try? (since it is often described as his life's work, most probably not true, I know)


Later addition to post: (separate point, but don't want to post twice in row)

Just rewatched part of Year of Hell. In it, Chakotay tells Annorax they made a course correction to avoid a rogue comet, and that otherwise they never would have entered Krenim space at all.

So they have to avoid an ice rock of about 60 miles diameter max (that's the size of the largest comet known today), yet this leads to them deviating lightyears off their original course?

The only way I can explain that is to assume that they were too lazy to revert back to their original heading after having avoided that comet, and that those precise headings don't matter that much, as long as they keep heading in the same general direction ...but that imho clashes with the beginning of the very same episode where they open astrometrics, dedicated to finding a more efficient route ...

I'll play the devil's advocate for a short while here and say that that course correction predated the opening of astrometrics maybe by a lot and considering that Voyager also moves willy nilly depending on the ores and the different resources they find, a change of several light years could be amplified to much more and ending (why not) in another sector than the one they would initially have passed through. Basically, the butterfly effect applied to Voyager.

 

[Timo]

When Picard said that Fermat's Last Theorem was never solved. I thought :

"For once that they genuinely tried to say something real, they still got it wrong, although they couldn't know it at the time."

Actually, Picard never said that.

What Picard said was that Fermat's own proof was never found. This remains 100% true today. And no doubt will remain true in the 24th century, too. Fermat simply never had the proof - either it was all a big joke on his part, or then he didn't realize he was all wrong about the proof he thought he had.

The search for Fermat's proof can still continue, of course. Wiles' proof wasn't it - Fermat would never have understood a word of it. And clearly Tobin's wasn't it, either, and we don't know if it was any closer to it than Wiles', or if it even attempted to be. It may simply have been an attempt at more elegant but still decidedly non-Fermat proof. Was it a success? We don't know that, either - it might have been elegant but not proof, or proof but not elegant.

Timo Saloniemi

 

[Timo]

Basically, the butterfly effect applied to Voyager.

...Regarding weird and "oh shit" moments, I just rewatched "Statistical Probabilities", and realized something. The supergenius mutants there discover that they can do accurate Seldonian psychohistory, that is, predict the course of history, because "the fluctuations cancel out in the long term", instead of accumulating. These are clever folks - this is exactly how time works in Trek! It's robust and self-repairing and converges towards "strange attractors" such as the same people always getting born. It just takes unnatural genius to see that this seemingly impossible thing underlies the very nature of time.

In Trek, the butterflies never stood a chance...

Timo Saloniemi

 

[Discofan]

Actually, Picard never said that.

What Picard said was that Fermat's own proof was never found. This remains 100% true today. And no doubt will remain true in the 24th century, too. Fermat simply never had the proof - either it was all a big joke on his part, or then he didn't realize he was all wrong about the proof he thought he had.

The search for Fermat's proof can still continue, of course. Wiles' proof wasn't it - Fermat would never have understood a word of it. And clearly Tobin's wasn't it, either, and we don't know if it was any closer to it than Wiles', or if it even attempted to be. It may simply have been an attempt at more elegant but still decidedly non-Fermat proof. Was it a success? We don't know that, either - it might have been elegant but not proof, or proof but not elegant.

Timo Saloniemi

I just checked it and you're wrong that's not what he said:

Here's the quote:

PICARD: For the eight hundred years people have been trying to solve it.

He never said anything about Fermat's own proof other than the words written on the book and that's nothing new.

Nobody is trying to find Fermat's own proof as it's quite obvious now that that proof doesn't exist. Not only was Fermat no math genius but he didn't have a hundredth of the mathematical tools necessary to solve it.

Besides, even the ST people realized their error as they tried to correct it with Jadzia's remark on DS9. So I don't see why you put so much effort into trying to rationalize it.

 

[Discofan]

...Regarding weird and "oh shit" moments, I just rewatched "Statistical Probabilities", and realized something. The supergenius mutants there discover that they can do accurate Seldonian psychohistory, that is, predict the course of history, because "the fluctuations cancel out in the long term", instead of accumulating. These are clever folks - this is exactly how time works in Trek! It's robust and self-repairing and converges towards "strange attractors" such as the same people always getting born. It just takes unnatural genius to see that this seemingly impossible thing underlies the very nature of time.

In Trek, the butterflies never stood a chance...

Timo Saloniemi

Actually, they didn't invent the "the fluctuations canceling out in the long term" concept. It was already present in Asimov's excellent "The End Of Eternity" which predates the first Star Trek airing by more than a decade but even Asimov admitted much later that it was a mistake, necessary for a story like that though.

Come to think of it Poul Anderson's Time Patrol works the same way. How would you explain that a temporal base in the Cretaceous doesn't screw up the timeline otherwise?

 

[Timo]

I just checked it and you're wrong that's not what he said:

Umm, no, I'm not.

He never said anything about Fermat's own proof other than the words written on the book and that's nothing new.

Very much to the contrary, Fermat's own proof is the one and only thing Picard talked about. "Solve it" refers to the mystery of Fermat's own proof - grammatically and contextually, it follows directly after Picard presents the thing enthralling him, which (extremely explicitly, just listen to his words!) is Fermat's own proof, the one the man came up without computers and colleagues and skills and whatnot.

Nobody is trying to find Fermat's own proof as it's quite obvious now that that proof doesn't exist.

But here Picard is. He may be an idiot, akin to those otherwise reasonable people devising perpetual motion machines today (and, inevitably, tomorrow). Or then he just enjoys the challenge - there being nothing decidedly impossible about finding Fermat's proof as such, even though the odds are almost nonexistent.

Besides, even the ST people realized their error as they tried to correct it with Jadzia's remark on DS9. So I don't see why you put so much effort into trying to rationalize it.

There's no rationalization. I'm just pointing out what was actually said in "The Royale". If you want to find conflict in it for some reason, feel free. I have no respect for that pursuit. But I do have a soft spot for the idea that Picard would be one of those folks trying to come up with Fermat's proof, or the perfect moment, or any other elusive and irrelevant thing to enrich his existence.

Timo Saloniemi

 

[Discofan]

Umm, no, I'm not.



Very much to the contrary, Fermat's own proof is the one and only thing Picard talked about. "Solve it" refers to the mystery of Fermat's own proof - grammatically and contextually, it follows directly after Picard presents the thing enthralling him, which (extremely explicitly, just listen to his words!) is Fermat's own proof, the one the man came up without computers and colleagues and skills and whatnot.



But here Picard is. He may be an idiot, akin to those otherwise reasonable people devising perpetual motion machines today (and, inevitably, tomorrow). Or then he just enjoys the challenge - there being nothing decidedly impossible about finding Fermat's proof as such, even though the odds are almost nonexistent.



There's no rationalization. I'm just pointing out what was actually said in "The Royale". If you want to find conflict in it for some reason, feel free. I have no respect for that pursuit. But I do have a soft spot for the idea that Picard would be one of those folks trying to come up with Fermat's proof, or the perfect moment, or any other elusive and irrelevant thing to enrich his existence.

Timo Saloniemi

I am sorry but I can't agree with that. Picard never says that he's seeking Fermat's own proof. It's just not possible to deduce that from what he says. You can't just pull things out of thin air. Picard is seeking A proof, anyone. Nothing in his words says otherwise.

If you wish we can just agree to disagree at this point as this discussion is leading to nowhere.

 

[DanGussin]

Not a Math proof example here but -

Tal in "The Enterprise Incident" Looking at the gapping hole in the control panel "The Cloaking device is gone ! "

I could almost see the comic book bubble above everyone in the rooms head saying "No S**T "

 

[Finn]

I am sorry but I can't agree with that. Picard never says that he's seeking Fermat's own proof. It's just not possible to deduce that from what he says. You can't just pull things out of thin air. Picard is seeking A proof, anyone. Nothing in his words says otherwise.

If you wish we can just agree to disagree at this point as this discussion is leading to nowhere.

The subtitles seem to include lines that doesn't appear in the script as shown via Trekcore.com. I don't know what you all hear in that episode so. The script does imply they are searching for Fermat's proof. But the subtitles I see on Netflix just suggest people are trying to solve the equation Fermat came up with....

 

[Timo]

Yes, the penultimate script refers to "rediscovering" Fermat's proof explicitly. But the actual episode dialogue has it worded like this:

Picard: "When Pierre de Fermat died, they found this equation scrawled in the margin of his notes. X to the nth plus Y to the nth equals Z to the nth, where n is greater than 2, which he said had no solution in whole numbers. But he also added this phrase... 'Remarkable proof".
Riker: "Yeah, that's starting to come back to me. There was no proof included."
Picard: "For the eight hundred years people have been trying to solve it."

The grammatical and contextual relationship between the "it" and the specific "remarkable" version of the proof seems clear-cut to me. But even outside that, the two heroes aren't discussing the theorem. They are discussing the mystery, the "but" bit.

And Picard would be qualified to try and solve the mystery, since it doesn't take all that much to be on par with Fermat there. Picard wouldn't be qualified to tackle the theorem's deeper mathematical implications, as he's no mathematician in any onscreen version of his skill set. But he can pretend to be Fermat, just like he loves to pretend to be Dixon Hill. Indeed, Picard himself sets the goalposts in his next phrase:

Picard: "...unravel a simple knot tied by a part-time French mathematician working alone, without a computer."

Picard is playing a game, hobbling himself by the same constraints that applied to Fermat. He isn't asking Data, say. So the theorem being proven by his time would be neither here nor there, not by the rules of the game.

Timo Saloniemi

 

[Discofan]

Yes, the penultimate script refers to "rediscovering" Fermat's proof explicitly. But the actual episode dialogue has it worded like this:



The grammatical and contextual relationship between the "it" and the specific "remarkable" version of the proof seems clear-cut to me. But even outside that, the two heroes aren't discussing the theorem. They are discussing the mystery, the "but" bit.

And Picard would be qualified to try and solve the mystery, since it doesn't take all that much to be on par with Fermat there. Picard wouldn't be qualified to tackle the theorem's deeper mathematical implications, as he's no mathematician in any onscreen version of his skill set. But he can pretend to be Fermat, just like he loves to pretend to be Dixon Hill. Indeed, Picard himself sets the goalposts in his next phrase:



Picard is playing a game, hobbling himself by the same constraints that applied to Fermat. He isn't asking Data, say. So the theorem being proven by his time would be neither here nor there, not by the rules of the game.

Timo Saloniemi

I am sorry but "solve it" automatically refers to the theorem, not the proof.

You solve a theorem and FIND a proof, you don't solve a proof. That would be nonsense. A proof is already a solution, it doesn't have to be solved. Picard's own words say that you are wrong, sorry.

 

[James Vines]

"Contagion", when they turn the Enterprise off and on again to purge the Iconian virus and act as though doing so is some revolutionary computer science

Maybe its windows reboot that makes it difficult. In any case I was telling folks as technical support on call at 2AM to reboot in 1973.

 

[Timo]

I am sorry but "solve it" automatically refers to the theorem, not the proof. You solve a theorem and FIND a proof, you don't solve a proof. That would be nonsense.

Yes, what you are saying is certainly nonsense, alas.

A "theorem" cannot be "solved". This doesn't compute grammatically or logically. Fermat's theorem involves an equation that can be solved, trivially so outside the parameters specified by Fermat to make the equation be of any interest, but this solution is uninteresting in the terms of the theorem, and if that is what some people try to solve for 800 years without success, we're talking about seriously disturbed people. The theorem is in no need of a solution, but of deductive proof, which is a completely different thing.

In comparison, the mystery of Fermat's theorem can be solved, grammatically speaking. And logically speaking, and although there again a trivial solution (Fermat never had any proof) readily presents itself, it is not the only solution this time around.

Now, there are obvious three layers to this: writer intent, writer output, and interpretation. It's very seldom that the first survives till the third, and here there are two major issues. One, the writer may or may not have been thinking that the theorem lacked proof as of the 2360s because it did as of the 1980s, and two, the writer (or, rather, the rewriter) may not have been all that good with English (or with understanding what the original writer wanted to say). But the sum total seen in the output nicely eliminates the need to ponder whether there's proof or not, because nothing in the dialogue refers to the search for proof as such, while specific elements of grammar and mathematical terminology steer the dialogue away from the issue of proof. All that remains is the search for Fermat's proof and the associated mystery, whether the writer intended that or not. Which of course is for the best.

Equally obvious alternatives, from the in-universe point of view, involve Picard and Riker being no good at English, or at least fumbling it every now and then (a good assumption with all real people, but perhaps less so for characters in drama); or them having a poor understanding of the theorem and the general issue at hand; or there having been no Wiles and no proof in their reality so far. Some may find one of those the most satisfactory one. I'd rather ditch the first two, for the love of the characters, and DS9 forces me to ditch the third. What remains is the grammatically consistent bit that (thanks to TrekCore and its preference for penultimate scripts rather than transcripts) we also know was the writer intent, FWIW.

Timo Saloniemi

 

[Discofan]

Yes, what you are saying is certainly nonsense, alas.

A "theorem" cannot be "solved". This doesn't compute grammatically or logically. Fermat's theorem involves an equation that can be solved, trivially so outside the parameters specified by Fermat to make the equation be of any interest, but this solution is uninteresting in the terms of the theorem, and if that is what some people try to solve for 800 years without success, we're talking about seriously disturbed people. The theorem is in no need of a solution, but of deductive proof, which is a completely different thing.

In comparison, the mystery of Fermat's theorem can be solved, grammatically speaking. And logically speaking, and although there again a trivial solution (Fermat never had any proof) readily presents itself, it is not the only solution this time around.

Now, there are obvious three layers to this: writer intent, writer output, and interpretation. It's very seldom that the first survives till the third, and here there are two major issues. One, the writer may or may not have been thinking that the theorem lacked proof as of the 2360s because it did as of the 1980s, and two, the writer (or, rather, the rewriter) may not have been all that good with English (or with understanding what the original writer wanted to say). But the sum total seen in the output nicely eliminates the need to ponder whether there's proof or not, because nothing in the dialogue refers to the search for proof as such, while specific elements of grammar and mathematical terminology steer the dialogue away from the issue of proof. All that remains is the search for Fermat's proof and the associated mystery, whether the writer intended that or not. Which of course is for the best.

Equally obvious alternatives, from the in-universe point of view, involve Picard and Riker being no good at English, or at least fumbling it every now and then (a good assumption with all real people, but perhaps less so for characters in drama); or them having a poor understanding of the theorem and the general issue at hand; or there having been no Wiles and no proof in their reality so far. Some may find one of those the most satisfactory one. I'd rather ditch the first two, for the love of the characters, and DS9 forces me to ditch the third. What remains is the grammatically consistent bit that (thanks to TrekCore and its preference for penultimate scripts rather than transcripts) we also know was the writer intent, FWIW.

Timo Saloniemi

Nothing in this changes the fact that "solve it" can't refer specifically to Fermat's "own proof" as you don't solve a proof, you FIND it. Picard was obviously not referring to that specific proof but to ANY proof that would solve the problem, which is likely what he meant. Plus it's not how mathematicians work. They don't try to find specific solutions to unsolved problems. They're very happy to find ANY solution. When Wiles solved the Fermat problem, no one objected that his solution wasn't good enough because it couldn't be the one Fermat was talking about.

As for Fermat, there are two possibilities:

1) He sincerely thought at the time that he was onto something and when later he tried to put it in writing he realized that it didn't work, which is why he never published it. Also, he must have forgotten about the inscription or was afraid to look like a boob if he struck it out.

2) He lied about having a solution in the hopes of stimulating research in that domain (which makes him a visionary but also a liar).

 

[Timo]

Nothing in this changes the fact that "solve it" can't refer specifically to Fermat's "own proof" as you don't solve a proof, you FIND it.

Well, no, and this is exactly what rules out Picard speaking about merely proving the theorem in the first place. But you can solve the mystery, and neither the proof nor the theorem are mysteries that can be solved - only what happened to Fermat's proof is one of those. So it's the easy way out.

Picard was obviously not referring to that specific proof but to ANY proof that would solve the problem, which is likely what he meant.

Well, we know there is no problem to solve in terms of the theorem now. This is also true in-universe now, and retroactively in "The Royale" as well. So saying the heroes are enthralled by the mystery rather than the theorem is not only the easy way out, but also the one that dodges the dodgy grammar and maintains in-universe and out-universe continuity. Plus it's what the original writer intended. Indeed, it swipes the desk clean: there's no remaining grammar or logic problem there, no misuse of terminology, no contradiction between the capabilities and aims of Picard.

Plus it's not how mathematicians work. They don't try to find specific solutions to unsolved problems. They're very happy to find ANY solution. When Wiles solved the Fermat problem, no one objected that his solution wasn't good enough because it couldn't be the one Fermat was talking about.

Which is why it would be Picard interested in Fermat's proof, and not some mathematician. And Picard obviously would have a range of solutions to his problem of Fermat's proof, just as you say (and more): Fermat had it and failed to write it down, Fermat didn't have it and was mistaken, Fermat didn't have it and was kidding, Fermat had it and the Denosumbians stole it from him, Fermat didn't have it but the Fagmoblastians promised to sell it to him... Finding out afterwards would be challenging and interesting and might not require much maths in the end.

(But again, it's wrong to refer to "proof" as "solution" in mathematics, just as it would be to refer to "solution" as the answer to a question in chemistry. The grammar works in several ways except for the one where Picard tries to outdo Wiles.)

Timo Saloniemi

 

[Discofan]

Well, no, and this is exactly what rules out Picard speaking about merely proving the theorem in the first place. But you can solve the mystery, and neither the proof nor the theorem are mysteries that can be solved - only what happened to Fermat's proof is one of those. So it's the easy way out.



Well, we know there is no problem to solve in terms of the theorem now. This is also true in-universe now, and retroactively in "The Royale" as well. So saying the heroes are enthralled by the mystery rather than the theorem is not only the easy way out, but also the one that dodges the dodgy grammar and maintains in-universe and out-universe continuity. Plus it's what the original writer intended. Indeed, it swipes the desk clean: there's no remaining grammar or logic problem there, no misuse of terminology, no contradiction between the capabilities and aims of Picard.



Which is why it would be Picard interested in Fermat's proof, and not some mathematician. And Picard obviously would have a range of solutions to his problem of Fermat's proof, just as you say (and more): Fermat had it and failed to write it down, Fermat didn't have it and was mistaken, Fermat didn't have it and was kidding, Fermat had it and the Denosumbians stole it from him, Fermat didn't have it but the Fagmoblastians promised to sell it to him... Finding out afterwards would be challenging and interesting and might not require much maths in the end.

(But again, it's wrong to refer to "proof" as "solution" in mathematics, just as it would be to refer to "solution" as the answer to a question in chemistry. The grammar works in several ways except for the one where Picard tries to outdo Wiles.)

Timo Saloniemi

I find your arguments specious at best but responding to them one by one is more effort than I am willing to devote to this question which is starting to nauseate me, so let's just say that we disagree and leave it at that. If you wish you can start a poll to see how many people agree with your version, versus the opposite but I doubt it'll get many answers, if any.

 

[at Quark's]

Plus it's not how mathematicians work. They don't try to find specific solutions to unsolved problems. They're very happy to find ANY solution. When Wiles solved the Fermat problem, no one objected that his solution wasn't good enough because it couldn't be the one Fermat was talking about.

Well.... yes and no. While it's true that when a theorem is proved for the very first time, it doesn't matter much how, it's also true that there is some ongoing interest in finding simpler and shorter proofs for complicated ones-to find a shorter and clearer route to the theorem, so to speak. This still can (and does) advance mathematics in some cases (though usually it is a consequence of a new piece of theory allowing a shorter route), and also, a more succinct proof is more satisfying.

In the case of Fermat's last theorem, supposing the (extremely unlikely) event that an amateur today would suddenly come up with a correct proof that uses only basic mathematics and that fits on a single page (let's be generous here instead of only allowing a margin), I doubt the proof itself could advance mathematics very much by now, but I'm still convinced the mathematical world would take significant notice- if only to see which simple key ideas and in which connection were overlooked by all those professionals working on it over 4 centuries- and then if those key ideas could also be applied elsewhere.