They also resolved not to accept proposals of perpetual-motion machines
October 13, 2019 7:10 PM Subscribe
The four impossible “problems of antiquity”—trisecting an angle, doubling the cube, constructing every regular polygon, and squaring the circle—are catnip for mathematical cranks. Every mathematician who has email has received letters from crackpots claiming to have solved these problems. They are so elementary to state that nonmathematicians are unable to resist. Unfortunately, some think they have succeeded—and refuse to listen to arguments that they are wrong.
Once I happened upon a coworker with a furrowed brow sketching on a note-card, over and over, different attempts at paths over the Bridges of Koenigsberg. I asked him who had put him up to that, thinking someone was pranking him. Thankfully it turned out that he knew it was impossible; he used it as a sort of meditation.
posted by a snickering nuthatch at 7:39 PM on October 13, 2019 [21 favorites]
posted by a snickering nuthatch at 7:39 PM on October 13, 2019 [21 favorites]
I had never heard of these problems before, but I just solved them. Unfortunately the comment is too small for the answers to fit.
posted by Literaryhero at 7:44 PM on October 13, 2019 [79 favorites]
posted by Literaryhero at 7:44 PM on October 13, 2019 [79 favorites]
I once emailed a former professor with a proof of the axiom of choice. My friends, there is no higher calling than that of the crank.
posted by vorpal bunny at 7:49 PM on October 13, 2019 [12 favorites]
posted by vorpal bunny at 7:49 PM on October 13, 2019 [12 favorites]
Physicists have their perpetual-motion inventors, historians their Holocaust deniers, physicians their homeopathic medicine proponentsI think when history is concerned, 'Holocaust denial' doesn't really belong in the same category; deniers of this and other historical crimes often understand and are able to practice historical discipline in a way that makes it very tiresome to refute, and very unlike the way perpetual-motionists don't understand physics—the thing is that denialists are factually wrong, have motivated reasoning, and are generally just hateful (and therefore boring), rather than cranks (who can be very interesting, despite being even more wrong about basic matters of historical fact).
There are far profounder historical cranks, like Fomenko, who was convinced that there were fake centuries, similar to the Phantom Time Hypothesis.
posted by Fiasco da Gama at 7:53 PM on October 13, 2019 [31 favorites]
When I was into math, when I was like, 14, I spent a lot of time trying to make division by zero possible, by using the fact that 0!=1. Didn't ever find a solution. You can't factorial the top and bottom like you can with other things...
posted by Windopaene at 7:55 PM on October 13, 2019 [5 favorites]
posted by Windopaene at 7:55 PM on October 13, 2019 [5 favorites]
This reminds me how I miss USENET.
posted by RobotVoodooPower at 8:23 PM on October 13, 2019 [20 favorites]
posted by RobotVoodooPower at 8:23 PM on October 13, 2019 [20 favorites]
When I was into math, when I was like, 14, I spent a lot of time trying to make division by zero possible, by using the fact that 0!=1.
I think it is defined that way so that you can have a recursive definition, n! = n*(n-1)!, although why you need 0 as a base case, I do not recall.
posted by thelonius at 8:31 PM on October 13, 2019 [2 favorites]
I think it is defined that way so that you can have a recursive definition, n! = n*(n-1)!, although why you need 0 as a base case, I do not recall.
posted by thelonius at 8:31 PM on October 13, 2019 [2 favorites]
Mmm, some sweet and tasty small-angle approximation in that non-proof of trisecting an angle (as any good engineer should know, as an angle approaches zero, sin(angle) ~= angle)
posted by muddgirl at 8:40 PM on October 13, 2019 [6 favorites]
posted by muddgirl at 8:40 PM on October 13, 2019 [6 favorites]
I think when history is concerned, 'Holocaust denial' doesn't really belong in the same category
I'm inclined to agree with this. A crank in the sense of the rest of this article isn't generally a liar, at least not in the sense that they know the truth and intend to deceive others. If there is deception, it is primarily self-deception, taking the form of delusions of grandeur and a refusal to consider that one's own intuitions can in fact be false, and that others may have greater knowledge and understanding that at the very least mean it's unlikely they haven't already thought of trying what you've thought of.
In contrast, Holocaust deniers typically know, or at least don't care, that the Holocaust really did happen. Their goal is to convince people of falsehoods, or at least confuse the issue. They are liars or bullshitters (in the technical sense of someone making truth claims without especially knowing or caring what the actual fact of the matter is) rather than cranks. In addition to Fiasco da Gama's example, you could probably place the "ley line" people and even the "ancient aliens" people in the category of historical cranks.
I think examples of medical cranks are useful both for considering a case where the line between crankdom and denialism can be blurry, but also maybe important to recognize. So for example, I think most homeopaths are cranks rather than liars; they genuinely believe in homeopathy, even if they are unable or unwilling to understand the evidence against it. Most vaccine deniers are true believers, if not full-on cranks, but leading anti-vaxxers like Andrew Wakefield are liars or bullshitters; they know their arguments are specious, but they receive tremendous personal gain for continuing to make them. Supplement manufacturers are bullshitters; if their products actually work, great, but they don't really care whether they do as long as people believe they do.
posted by biogeo at 8:42 PM on October 13, 2019 [16 favorites]
I'm inclined to agree with this. A crank in the sense of the rest of this article isn't generally a liar, at least not in the sense that they know the truth and intend to deceive others. If there is deception, it is primarily self-deception, taking the form of delusions of grandeur and a refusal to consider that one's own intuitions can in fact be false, and that others may have greater knowledge and understanding that at the very least mean it's unlikely they haven't already thought of trying what you've thought of.
In contrast, Holocaust deniers typically know, or at least don't care, that the Holocaust really did happen. Their goal is to convince people of falsehoods, or at least confuse the issue. They are liars or bullshitters (in the technical sense of someone making truth claims without especially knowing or caring what the actual fact of the matter is) rather than cranks. In addition to Fiasco da Gama's example, you could probably place the "ley line" people and even the "ancient aliens" people in the category of historical cranks.
I think examples of medical cranks are useful both for considering a case where the line between crankdom and denialism can be blurry, but also maybe important to recognize. So for example, I think most homeopaths are cranks rather than liars; they genuinely believe in homeopathy, even if they are unable or unwilling to understand the evidence against it. Most vaccine deniers are true believers, if not full-on cranks, but leading anti-vaxxers like Andrew Wakefield are liars or bullshitters; they know their arguments are specious, but they receive tremendous personal gain for continuing to make them. Supplement manufacturers are bullshitters; if their products actually work, great, but they don't really care whether they do as long as people believe they do.
posted by biogeo at 8:42 PM on October 13, 2019 [16 favorites]
Jpfed: Once I happened upon a coworker with a furrowed brow sketching on a note-card, over and over, different attempts at paths over the Bridges of Koenigsberg. I asked him who had put him up to that, thinking someone was pranking him. Thankfully it turned out that he knew it was impossible; he used it as a sort of meditation.
So that's why I was never able to solve that one.
posted by clawsoon at 8:56 PM on October 13, 2019 [1 favorite]
So that's why I was never able to solve that one.
posted by clawsoon at 8:56 PM on October 13, 2019 [1 favorite]
I think it is defined that way so that you can have a recursive definition, n! = n*(n-1)!, although why you need 0 as a base case, I do not recall.
There's a couple of good reasons to define 0!=1. One is to consider what n! is often used to represent, which is the number of ways a set of n elements can be rearranged. Then 0! denotes the number of ways the empty set can be ordered: exactly 1 way. Relatedly, the binomial coefficient (the number of ways to choose k items from a set of n without replacement, or equivalently the coefficient that appears in front of the k'th term in the expansion of (a+b)^2) is conveniently written as n!/(k!*(n-k)!) if 0!=1, but would need exceptions if 0! was defined any other way. And finally, it allows the identity n! = Γ(n+1) (Gamma function) for all natural numbers.
Mmm, some sweet and tasty small-angle approximation in that non-proof of trisecting an angle (as any good engineer should know, as an angle approaches zero, sin(angle) ~= angle)
Turns out "infinitesimal" is one of the special cases that can be solved!
posted by biogeo at 8:57 PM on October 13, 2019 [12 favorites]
There's a couple of good reasons to define 0!=1. One is to consider what n! is often used to represent, which is the number of ways a set of n elements can be rearranged. Then 0! denotes the number of ways the empty set can be ordered: exactly 1 way. Relatedly, the binomial coefficient (the number of ways to choose k items from a set of n without replacement, or equivalently the coefficient that appears in front of the k'th term in the expansion of (a+b)^2) is conveniently written as n!/(k!*(n-k)!) if 0!=1, but would need exceptions if 0! was defined any other way. And finally, it allows the identity n! = Γ(n+1) (Gamma function) for all natural numbers.
Mmm, some sweet and tasty small-angle approximation in that non-proof of trisecting an angle (as any good engineer should know, as an angle approaches zero, sin(angle) ~= angle)
Turns out "infinitesimal" is one of the special cases that can be solved!
posted by biogeo at 8:57 PM on October 13, 2019 [12 favorites]
I am still honestly half-convinced it [trisecting an angle] OUGHT to be possible!
It totally is possible. You just have to allow tools and techniques that go beyond a compass and an unmarked straightedge.
One technique I like was known to Archimedes and involves a marked straightedge and the willingness to allow arguments by continuity (i.e., sliding).
posted by leahwrenn at 9:20 PM on October 13, 2019 [6 favorites]
It totally is possible. You just have to allow tools and techniques that go beyond a compass and an unmarked straightedge.
One technique I like was known to Archimedes and involves a marked straightedge and the willingness to allow arguments by continuity (i.e., sliding).
posted by leahwrenn at 9:20 PM on October 13, 2019 [6 favorites]
Yeah, there's some nice solutions beyond the classical construction techniques. One of my favorites is origami.
posted by biogeo at 9:26 PM on October 13, 2019 [9 favorites]
posted by biogeo at 9:26 PM on October 13, 2019 [9 favorites]
the thing is that denialists are factually wrong, have motivated reasoning, and are generally just hateful (and therefore boring), rather than cranks (who can be very interesting, despite being even more wrong about basic matters of historical fact).I tend to find that the denialists and the cranks are often the same people. The world view of the crank is necessarily anti-expert, has a tenuous grasp on facts, and usually includes strong doses of persecution and superiority. This is super-fertile ground for bigotry and conspiracy theories.
Gene "Time Cube" Ray was a zealous homophobe, racist, and anti-Semite. Prominent flat-earthers are also Holocaust deniers. And anecdotally, so are a number of the persistent cranks I've run into in math/science sites on the internet.
posted by mbrubeck at 9:40 PM on October 13, 2019 [33 favorites]
Oh god. I think one of my husband's favorite things about getting out of academic physics was no longer being cornered by physics cranks. You never knew when you'd encounter one and it was always the MOST random scenario. You'd be, like, in a restaurant and the waiter would overhear some technical term in conversation as he passed your table and suddenly, oh no, twenty minutes of physics crankery emerges without warning and you just have to smile and nod.
posted by potrzebie at 9:54 PM on October 13, 2019 [15 favorites]
posted by potrzebie at 9:54 PM on October 13, 2019 [15 favorites]
It totally is possible. You just have to allow tools and techniques that go beyond a compass and an unmarked straightedge.
I don't see what's so hard about squaring the circle. You merely work out what the area of the circle is by measuring the radius, take the square root of that, and draw a square with that length side. Easy! I don't know why everyone else is so dim.
posted by Merus at 10:17 PM on October 13, 2019 [6 favorites]
I don't see what's so hard about squaring the circle. You merely work out what the area of the circle is by measuring the radius, take the square root of that, and draw a square with that length side. Easy! I don't know why everyone else is so dim.
posted by Merus at 10:17 PM on October 13, 2019 [6 favorites]
Sorry if off topic: does an infinitesimal exist?
posted by paladin at 10:23 PM on October 13, 2019 [2 favorites]
posted by paladin at 10:23 PM on October 13, 2019 [2 favorites]
only a little bit
posted by Merus at 10:29 PM on October 13, 2019 [69 favorites]
posted by Merus at 10:29 PM on October 13, 2019 [69 favorites]
It's a question worth looking closely at.
posted by cortex at 10:38 PM on October 13, 2019 [5 favorites]
posted by cortex at 10:38 PM on October 13, 2019 [5 favorites]
There is another sort of crank (of a partition) in mathematics.
posted by oonh at 10:41 PM on October 13, 2019
posted by oonh at 10:41 PM on October 13, 2019
I did Ramanujan’s circle-squaring with a good compass and rule. On a regular sheet of paper it was something like 99.64% accurate. I’m dying to try it on a large, flat, parking-lot with a surveyor’s steel tape and a chalk line.
posted by tayknight at 10:55 PM on October 13, 2019 [2 favorites]
posted by tayknight at 10:55 PM on October 13, 2019 [2 favorites]
There's another kind of squaring the circle which involves taking the circle apart into a number of disjoint pieces (no two have any points in common) and then reassembling those pieces into a square with no points left out or covered twice.
I remember reading that a very clever proof showed a way of doing this using a finite number of pieces during this century, but I can't find any reference to it.
Maybe it was countable rather than finite, but I feel like I'm thinking that only because doing it with a finite number of pieces seems so unlikely.
posted by jamjam at 11:45 PM on October 13, 2019 [1 favorite]
I remember reading that a very clever proof showed a way of doing this using a finite number of pieces during this century, but I can't find any reference to it.
Maybe it was countable rather than finite, but I feel like I'm thinking that only because doing it with a finite number of pieces seems so unlikely.
posted by jamjam at 11:45 PM on October 13, 2019 [1 favorite]
Sorry if off topic: does an infinitesimal exist?
I was reading about the good ol' 0.999...=1 argument recently, and if I remember right infinitesimals only exist in in the realm of hyperreals, which is a pretty specialized domain of math?
posted by rifflesby at 11:46 PM on October 13, 2019 [2 favorites]
I was reading about the good ol' 0.999...=1 argument recently, and if I remember right infinitesimals only exist in in the realm of hyperreals, which is a pretty specialized domain of math?
posted by rifflesby at 11:46 PM on October 13, 2019 [2 favorites]
This is common in physics as well. Typically the profile there is a retired engineer with the sort of mechanical mindset that physicists of the 19th century made good use of. He (it's always he) sits down and rolls his eyes at General Relativity or Quantum Mechanics and says "Guys, come on! You're making this way too complicated!"
There is usually a woman in his life who takes care of him and doesn't pay attention to his work but it seems intricate and she supports him and believes he must be smart so there is probably something to this. She gets a bit fed up of his complaints about the "idiots" who are part of a "conspiracy to bury this important development."
There used to be a semi-regular talk given at UC Berkeley based on anonymised copies of kook theories sent into the Berkeley and Livermore labs. My favourite was the one where the reason gravity happens is that everything is growing and this means the outward motion of the Earth's expanding surface exerts a 1G force on all of us.
posted by rum-soaked space hobo at 12:04 AM on October 14, 2019 [32 favorites]
There is usually a woman in his life who takes care of him and doesn't pay attention to his work but it seems intricate and she supports him and believes he must be smart so there is probably something to this. She gets a bit fed up of his complaints about the "idiots" who are part of a "conspiracy to bury this important development."
There used to be a semi-regular talk given at UC Berkeley based on anonymised copies of kook theories sent into the Berkeley and Livermore labs. My favourite was the one where the reason gravity happens is that everything is growing and this means the outward motion of the Earth's expanding surface exerts a 1G force on all of us.
posted by rum-soaked space hobo at 12:04 AM on October 14, 2019 [32 favorites]
A previously on physics cranks. May possibly be your talk, rum-soaked space hobo.
There's definitely something distinctive about the motivation of the crank. They're usually not just pursuing something out of interest and a desire to find some truth in the universe or mathematics. They have to do it as the lone outsider like it's a key part of the process to have the hope of creating that kind of story. The applecart has to be upset and dogma overturned.
A physics crank once wrote to me telling me that quasars were actually powered by supermassive black holes, and he never mailed back when I told him this was correct and we had known this for some time.
posted by edd at 12:20 AM on October 14, 2019 [50 favorites]
There's definitely something distinctive about the motivation of the crank. They're usually not just pursuing something out of interest and a desire to find some truth in the universe or mathematics. They have to do it as the lone outsider like it's a key part of the process to have the hope of creating that kind of story. The applecart has to be upset and dogma overturned.
A physics crank once wrote to me telling me that quasars were actually powered by supermassive black holes, and he never mailed back when I told him this was correct and we had known this for some time.
posted by edd at 12:20 AM on October 14, 2019 [50 favorites]
Newton used infinitesimals in his physics and his calculus — and was famously mocked for it by John Henry Cardinal Newman, who was canonized yesterday.
posted by jamjam at 12:34 AM on October 14, 2019 [5 favorites]
posted by jamjam at 12:34 AM on October 14, 2019 [5 favorites]
Was Hitler's penis cursed by a shaman? According to this local renowned history professor, "Get the hell out of my office."
posted by straight at 1:10 AM on October 14, 2019 [45 favorites]
posted by straight at 1:10 AM on October 14, 2019 [45 favorites]
My mathematician dad gave me a compass and straight edge and set me on trisecting angles as a kid.
I think it kept me quiet and out of trouble for a while.
posted by sciencegeek at 2:33 AM on October 14, 2019 [2 favorites]
I think it kept me quiet and out of trouble for a while.
posted by sciencegeek at 2:33 AM on October 14, 2019 [2 favorites]
Was Hitler's penis cursed by a shaman?
Considering this would only require one shaman to have muttered “Hitler’s dick should just fall off,” there were more than 0 shaman* in the 1930s and 40s who likely wished Hitler ill, the honest response would be “Maybe, but it is not, as far as we know, part of the historical record.”
* For a broad enough definition of shaman
posted by GenjiandProust at 2:37 AM on October 14, 2019 [10 favorites]
Considering this would only require one shaman to have muttered “Hitler’s dick should just fall off,” there were more than 0 shaman* in the 1930s and 40s who likely wished Hitler ill, the honest response would be “Maybe, but it is not, as far as we know, part of the historical record.”
* For a broad enough definition of shaman
posted by GenjiandProust at 2:37 AM on October 14, 2019 [10 favorites]
This reminds me how I miss USENET.
Ah, the days of alt.conspiracy, when cranks were (relatively) harmless gentleman amateurs like Dr. Alexander “TIME HAS INERTIA” Abian or the Secret Underground World Society guy, with novel theories of history/physics/cosmology, rather than recruiting operations for genocidal fascist meme-complexes. More Art Bell, less Alex Jones.
(Granted, the harmless cranks, in many cases, had problematic views, like the guy who wrote the world's first sacred operating system whose views were racist and reactionary, but at least they weren't organised into troll-militias.)
posted by acb at 2:44 AM on October 14, 2019 [7 favorites]
Ah, the days of alt.conspiracy, when cranks were (relatively) harmless gentleman amateurs like Dr. Alexander “TIME HAS INERTIA” Abian or the Secret Underground World Society guy, with novel theories of history/physics/cosmology, rather than recruiting operations for genocidal fascist meme-complexes. More Art Bell, less Alex Jones.
(Granted, the harmless cranks, in many cases, had problematic views, like the guy who wrote the world's first sacred operating system whose views were racist and reactionary, but at least they weren't organised into troll-militias.)
posted by acb at 2:44 AM on October 14, 2019 [7 favorites]
Also, probably needs a “psychoceramics” tag.
posted by acb at 2:47 AM on October 14, 2019 [2 favorites]
posted by acb at 2:47 AM on October 14, 2019 [2 favorites]
Definitely needs “crank” tag added, to link it with mefi’s rich archive of posts on crankery.
posted by ardgedee at 4:05 AM on October 14, 2019 [1 favorite]
posted by ardgedee at 4:05 AM on October 14, 2019 [1 favorite]
One of my favorites is origami
I like the bisect back-and-forth (forever) method of trisection. Impractical? Sure, but Is there any price too high to be able to do the impossible?
posted by klausman at 4:58 AM on October 14, 2019 [4 favorites]
I like the bisect back-and-forth (forever) method of trisection. Impractical? Sure, but Is there any price too high to be able to do the impossible?
posted by klausman at 4:58 AM on October 14, 2019 [4 favorites]
jamjam: There's another kind of squaring the circle which involves taking the circle apart into a number of disjoint pieces (no two have any points in common) and then reassembling those pieces into a square with no points left out or covered twice.
This is Tarski's circle-squaring problem.
This is Tarski's circle-squaring problem.
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area. This was proven to be possible by Miklós Laczkovich in 1990; the decomposition makes heavy use of the axiom of choice and is therefore non-constructive. Laczkovich estimated the number of pieces in his decomposition at roughly 1050. More recently, in 2017, Andrew Marks and Spencer Unger gave a completely constructive solution using Borel pieces.posted by a car full of lions at 5:47 AM on October 14, 2019 [11 favorites]
In particular, it is impossible to dissect a circle and make a square using pieces that could be cut with an idealized pair of scissors (that is, having Jordan curve boundary). The pieces used in Laczkovich's proof are non-measurable subsets.
Laczkovich actually proved the reassembly can be done using translations only; rotations are not required. ...
well how would spherical, frictionless scissors cut anything?
posted by thelonius at 5:53 AM on October 14, 2019 [7 favorites]
posted by thelonius at 5:53 AM on October 14, 2019 [7 favorites]
In the old days (let's say 20 years ago) cranks and their crank theories seemed laughable. Now they have their own Youtube channels and legions of Twitter followers, and they influence Presidents.
posted by Pararrayos at 5:55 AM on October 14, 2019 [10 favorites]
posted by Pararrayos at 5:55 AM on October 14, 2019 [10 favorites]
They have to do it as the lone outsider
I cover politics pretty regularly as a photojournalist and there are so many cranks. I can identify them before they approach me now, usually with a binder of folder full of rumpled papers. They ask for my card (after a year of calls from one I've gotten more judicious in how I hand my business card) and then hand me a packet of papers that conclusively uncovers some government malfeasance or other. I've talked to people who have "uncovered" something massive in the nuclear power industry, childcare, interstate transportation, and quite a few other areas of the American economy.
The most well-funded among them follow the campaign trail around the country and pay fees to get on various state ballots. In New Hampshire, there's a debate for them every four years called the Lesser Known Candidates Forum. Internet-fave and perpetual satirical candidate Vermin Supreme has been banned from that event because he glitter-bombed one of his fellow participants.
This cycle, the cranks seem to be most attracted to Marianne Williamson events; last cycle they were pretty evenly spread among Republican candidates' events. The most notable/sad I've seen this year (photo) was an elderly man who'd traveled from Long Island, New York, to Keene, NH, to present work he'd started in high school getting to the bottom of the JFK assassination. Williamson is good at making people feel like they're heard--from what I can tell that's one of her trademarks. At the four or five events of hers that I've covered, there've been cranks talking about and presenting their evidence about the harm of vaccines, Snowden's revelations, the JFK assassination, the Illuminati, clandestine military activity in Antarctica (something to do with a lot of flights going there), and a few other topics.
posted by msbrauer at 6:05 AM on October 14, 2019 [11 favorites]
I cover politics pretty regularly as a photojournalist and there are so many cranks. I can identify them before they approach me now, usually with a binder of folder full of rumpled papers. They ask for my card (after a year of calls from one I've gotten more judicious in how I hand my business card) and then hand me a packet of papers that conclusively uncovers some government malfeasance or other. I've talked to people who have "uncovered" something massive in the nuclear power industry, childcare, interstate transportation, and quite a few other areas of the American economy.
The most well-funded among them follow the campaign trail around the country and pay fees to get on various state ballots. In New Hampshire, there's a debate for them every four years called the Lesser Known Candidates Forum. Internet-fave and perpetual satirical candidate Vermin Supreme has been banned from that event because he glitter-bombed one of his fellow participants.
This cycle, the cranks seem to be most attracted to Marianne Williamson events; last cycle they were pretty evenly spread among Republican candidates' events. The most notable/sad I've seen this year (photo) was an elderly man who'd traveled from Long Island, New York, to Keene, NH, to present work he'd started in high school getting to the bottom of the JFK assassination. Williamson is good at making people feel like they're heard--from what I can tell that's one of her trademarks. At the four or five events of hers that I've covered, there've been cranks talking about and presenting their evidence about the harm of vaccines, Snowden's revelations, the JFK assassination, the Illuminati, clandestine military activity in Antarctica (something to do with a lot of flights going there), and a few other topics.
posted by msbrauer at 6:05 AM on October 14, 2019 [11 favorites]
Tarski's circle-squaring problem ... was proven to be possible by Miklós Laczkovich in 1990;
If you want to get some insight into this, I recommend Laczkovich's book Conjecture and Proof. I don't think I know any book that goes further with fewer prerequisites or more basic material. Like, "The pigeonhole principle? Isn't that... kind of silly? How much could you do with that, really?" "Hold my beer."
Reading it won't make you Laczkovich, but it willmake your head hurt make you feel slow and gormless probably lead you to an appreciation of the virtuosity possible in the application of elementary ideas.
posted by Wolfdog at 6:20 AM on October 14, 2019 [9 favorites]
If you want to get some insight into this, I recommend Laczkovich's book Conjecture and Proof. I don't think I know any book that goes further with fewer prerequisites or more basic material. Like, "The pigeonhole principle? Isn't that... kind of silly? How much could you do with that, really?" "Hold my beer."
Reading it won't make you Laczkovich, but it will
posted by Wolfdog at 6:20 AM on October 14, 2019 [9 favorites]
Also: I recently read a paper online which proves the twin prime conjecture. The only possible little hitch might be the line in the first paragraph beginning, "We use a nonstandard definition of prime, ..."
posted by Wolfdog at 6:25 AM on October 14, 2019 [12 favorites]
posted by Wolfdog at 6:25 AM on October 14, 2019 [12 favorites]
As they say, 2+2=5 for large values of 2.
posted by acb at 6:27 AM on October 14, 2019 [7 favorites]
posted by acb at 6:27 AM on October 14, 2019 [7 favorites]
After his many years studying mathematical cranks, Dudley realized that they fit a pattern.
1. They are male.
2. They are old, often retired.
I'd bet anything that if he'd written this in the 2010s instead of the 1990s, he'd have added "they are white."
So much of the psychology of the crank seems wrapped up in not having been told/shown that you're wrong enough early in life.
posted by explosion at 6:55 AM on October 14, 2019 [6 favorites]
1. They are male.
2. They are old, often retired.
I'd bet anything that if he'd written this in the 2010s instead of the 1990s, he'd have added "they are white."
So much of the psychology of the crank seems wrapped up in not having been told/shown that you're wrong enough early in life.
posted by explosion at 6:55 AM on October 14, 2019 [6 favorites]
If you want to get some insight into this, I recommend Laczkovich's book Conjecture and Proof. I don't think I know any book that goes further with fewer prerequisites or more basic material. Like, "The pigeonhole principle? Isn't that... kind of silly? How much could you do with that, really?" "Hold my beer."
I will second that. I attended a class that basically consisted of working as far as we got into the book taught by Elekes Gyorgy (who resembled in affect accent and dress a sort of Carpathian Mr Rogers) - it was the highlight of my undergrad math education.
posted by PMdixon at 7:27 AM on October 14, 2019 [2 favorites]
I will second that. I attended a class that basically consisted of working as far as we got into the book taught by Elekes Gyorgy (who resembled in affect accent and dress a sort of Carpathian Mr Rogers) - it was the highlight of my undergrad math education.
posted by PMdixon at 7:27 AM on October 14, 2019 [2 favorites]
ok but seriously you guys i am *this close* to figuring out perpetual motion
posted by sugar and confetti at 7:46 AM on October 14, 2019 [5 favorites]
posted by sugar and confetti at 7:46 AM on October 14, 2019 [5 favorites]
A previously on physics cranks.
I know this guy through online trivia circles. He also did music under the name Stark Effect and was responsible for Dictionaraoke.
posted by jonp72 at 8:07 AM on October 14, 2019 [2 favorites]
I know this guy through online trivia circles. He also did music under the name Stark Effect and was responsible for Dictionaraoke.
posted by jonp72 at 8:07 AM on October 14, 2019 [2 favorites]
Somebody pick up a sack of sliders and we’ll finally get this moving.
posted by Huffy Puffy at 8:17 AM on October 14, 2019
posted by Huffy Puffy at 8:17 AM on October 14, 2019
I used to love cranks and conspiracy theories. I even had my own personal "freaklit" book collection that included things like the Book or Urantia, Behold a Pale Horse, books on HAARP, the Trilateral Commission, the Bilderburg Group, and even some Alan Watts and Alister Crowley for good measure. (I never really got into mathematicians, mainly for my lack of a mathematical acumen.)
This was all 20 years ago or more. At the time I thought it was just good clean fun. But since then, conspiracy theories and fringe interests have become so weaponized and politically influential that it's no longer something to laugh at. Some of the things I've heard come out of Trump's mouth could be tied directly back to things I had read in those books, especially some of the more unsavory ones. It's definitely not funny anymore.
posted by slogger at 8:25 AM on October 14, 2019 [15 favorites]
This was all 20 years ago or more. At the time I thought it was just good clean fun. But since then, conspiracy theories and fringe interests have become so weaponized and politically influential that it's no longer something to laugh at. Some of the things I've heard come out of Trump's mouth could be tied directly back to things I had read in those books, especially some of the more unsavory ones. It's definitely not funny anymore.
posted by slogger at 8:25 AM on October 14, 2019 [15 favorites]
... a retired engineer with the sort of mechanical mindset that physicists of the 19th century made good use of. He (it's always he) sits down and rolls his eyes at General Relativity ... There is usually a woman in his life who takes care of him ...
Which Thomas Pynchon novel is this
posted by panglos at 9:00 AM on October 14, 2019 [4 favorites]
Which Thomas Pynchon novel is this
posted by panglos at 9:00 AM on October 14, 2019 [4 favorites]
Which Thomas Pynchon novel is this
Gravity's Rainbow. Duh.
posted by Your Childhood Pet Rock at 9:08 AM on October 14, 2019 [4 favorites]
Gravity's Rainbow. Duh.
posted by Your Childhood Pet Rock at 9:08 AM on October 14, 2019 [4 favorites]
Due to my work I occasionally get calls from alien conspiracy theorists or astronomy cranks. The odd thing about these interactions is how they are convinced that I am interested in hearing about them. There’s very little self-awareness.
posted by bq at 9:20 AM on October 14, 2019 [4 favorites]
posted by bq at 9:20 AM on October 14, 2019 [4 favorites]
The mathematical physicist John Baez (1961–) proposed a “crackpot index” that was intended to provide “a simple method for rating potentially revolutionary contributions to physics.” The individual begins with a score of −5. Then Baez presented a list of thirty-seven characteristics of a crackpot. Each time a criterion is met, a prescribed number of points is added to the index.
Mathematician Chris Caldwell was inspired by Baez’s list and devised a mathematical version. Some (lightly edited) examples from Caldwell’s list are:
posted by box at 9:25 AM on October 14, 2019 [8 favorites]
Mathematician Chris Caldwell was inspired by Baez’s list and devised a mathematical version. Some (lightly edited) examples from Caldwell’s list are:
1 point for each word in all capital letters;That list reminds me of somebody's tweets.
5 points for every statement that is clearly vacuous, logically inconsistent, or widely known to be false;
10 points for each such statement that is adhered to despite careful correction;
10 points for not knowing (or not using) standard mathematical notation;
10 points for expressing fear that your ideas will be stolen;
10 points for each new term you invent or use without properly defining it;
10 points for stating that your ideas are of great financial, theoretical, or spiritual value;
10 points for beginning the description of your work by saying how long you have been working on it;
10 points for each favorable comparison of yourself to established experts;
10 points for citing an impressive-sounding, but irrelevant, result;
20 points for naming something after yourself;
30 points for not knowing how or where to submit their major discovery for publication;
30 points for confusing examples or heuristics with mathematical proof;
40 points for claiming to have a “proof” of an important result but not knowing what established mathematicians have done on the problem.
posted by box at 9:25 AM on October 14, 2019 [8 favorites]
paladin: Sorry if off topic: does an infinitesimal exist?
Yes. And no.
Asking if mathematical objects "exist" is a thorny question. Does the number 2 exist? What color is it? Does it weigh anything? What about 2.1? sqrt(2)? 2.718281828459045...? sqrt(-2)? Do infinite dimensional matrices exist?
I think the idea for working mathematicians is that you can say that these things exist if you can provide some sort of consistent mechanism for working with them and adding them doesn't make the system you are using inconsistent (inconsistency is bad, because it lets you prove things that are false. For a lot of things you can't prove consistency (see Godel's First Incompleteness Theorem) but you sometimes can show that adding this or that doesn't make things any worse. For a long time it was unclear if infinitesimals could be precisely defined and if adding them to the real numbers made the system inconsistent. Now we know that they can be defined precisely and don't add inconsistency if it wasn't there already).
There are systems that have infinitesimals. If you want to use one of those systems then infinitesimals are absolutely real. If you use standard analysis then they are not real. Or perhaps "not relevant" is a better term (like elephants. Obviously elephants are real, but mathematics doesn't use them).
So, yes. And no.
posted by It's Never Lurgi at 9:32 AM on October 14, 2019 [12 favorites]
Yes. And no.
Asking if mathematical objects "exist" is a thorny question. Does the number 2 exist? What color is it? Does it weigh anything? What about 2.1? sqrt(2)? 2.718281828459045...? sqrt(-2)? Do infinite dimensional matrices exist?
I think the idea for working mathematicians is that you can say that these things exist if you can provide some sort of consistent mechanism for working with them and adding them doesn't make the system you are using inconsistent (inconsistency is bad, because it lets you prove things that are false. For a lot of things you can't prove consistency (see Godel's First Incompleteness Theorem) but you sometimes can show that adding this or that doesn't make things any worse. For a long time it was unclear if infinitesimals could be precisely defined and if adding them to the real numbers made the system inconsistent. Now we know that they can be defined precisely and don't add inconsistency if it wasn't there already).
There are systems that have infinitesimals. If you want to use one of those systems then infinitesimals are absolutely real. If you use standard analysis then they are not real. Or perhaps "not relevant" is a better term (like elephants. Obviously elephants are real, but mathematics doesn't use them).
So, yes. And no.
posted by It's Never Lurgi at 9:32 AM on October 14, 2019 [12 favorites]
I was recently looking for a hand-wavy explanation of why trisecting an angle is impossible. I think I found it.. Trisecting an angle ends up being equivalent to finding the cube root of a polynomial. But the only constructible numbers are rational numbers and square roots, so trisecting is impossible. This matches the hand-wavy explanation for why squaring the circle is impossible. It's equivalent to constructing π, but π is not constructible.
Is that about right? I haven't proved anything of course; the question of what numbers are constructible is a much larger one. But the shortcut helps my intuition.
posted by Nelson at 9:50 AM on October 14, 2019 [3 favorites]
Is that about right? I haven't proved anything of course; the question of what numbers are constructible is a much larger one. But the shortcut helps my intuition.
posted by Nelson at 9:50 AM on October 14, 2019 [3 favorites]
Nelson, I believe that's exactly right. See for example the video I linked above and its prequel by mathematician Zsuzsanna Dancso for Numberphile; she ends up explaining it in exactly that way. It's also why doubling the cube using Euclidean construction is impossible. Paper folding, unlike the compass-and-straightedge construction, allows for certain moves that are effectively equivalent to taking cube roots, and so trisecting an angle (and I assume doubling a cube) become possible. Squaring a circle is probably still impossible because π is transcendental, though I haven't thought about it much further than that.
posted by biogeo at 10:03 AM on October 14, 2019 [6 favorites]
posted by biogeo at 10:03 AM on October 14, 2019 [6 favorites]
Looking at the previously linked threads, it is worrying how normalized crankitude has become. For example, the formerly linked point-and-laugh example of Theodore J. Rout can now be recognized as the behaviour of a sovereign citizen.
Creating small safe enclaves on the internet for like-minded people may not always be a good thing.
posted by scruss at 10:51 AM on October 14, 2019 [6 favorites]
Creating small safe enclaves on the internet for like-minded people may not always be a good thing.
posted by scruss at 10:51 AM on October 14, 2019 [6 favorites]
NOW you tell us.
posted by Chrysostom at 11:57 AM on October 14, 2019 [8 favorites]
posted by Chrysostom at 11:57 AM on October 14, 2019 [8 favorites]
I used to work for a company that helped people register IP with the government. I was so tickled the day some legit alchemy came through -- "a method to transmute base metals into gold." I'll never forget that!
posted by fiercecupcake at 1:15 PM on October 14, 2019 [4 favorites]
posted by fiercecupcake at 1:15 PM on October 14, 2019 [4 favorites]
Well, don’t hold out. Tell us how!
(Or can you not, because they registered their IP?)
posted by Huffy Puffy at 1:18 PM on October 14, 2019 [1 favorite]
(Or can you not, because they registered their IP?)
posted by Huffy Puffy at 1:18 PM on October 14, 2019 [1 favorite]
Yeah, unfortunately, I did learn the secret of the philosopher's stone, that which innumerable people have pursued for centuries, but due to the NDA I signed, I guess it's gonna die with me. ;]
IIRC, it was some chemistry that even I could tell was not going to work, something along the lines of "just take X atom and add Y protons to it." We passed it around and had a good laugh.
posted by fiercecupcake at 1:39 PM on October 14, 2019 [2 favorites]
IIRC, it was some chemistry that even I could tell was not going to work, something along the lines of "just take X atom and add Y protons to it." We passed it around and had a good laugh.
posted by fiercecupcake at 1:39 PM on October 14, 2019 [2 favorites]
Obviously elephants are real
Sure, if you believe the so-called “experts”.
posted by dephlogisticated at 2:03 PM on October 14, 2019 [4 favorites]
Sure, if you believe the so-called “experts”.
posted by dephlogisticated at 2:03 PM on October 14, 2019 [4 favorites]
Regarding physics cranks, my father attracted them in droves and they wouldn't go away; if he ignored them or told them they were nuts they would assume he hadn't received their careful "proofs," didn't understand them or, worst of all, intended to claim credit for their ideas. Any of these misapprehensions would generate increasingly aggressive inquiries. So (this was pre-internet days) Dad would write each crank a note saying that the work was outside of his field but that he would be delighted to put them in touch with someone better equipped to appreciate it. Then he would forward the crank's work on to the previous crank: lather rinse repeat. Occasionally he received thank you notes from cranks who were now happily collaborating.
posted by carmicha at 2:04 PM on October 14, 2019 [59 favorites]
posted by carmicha at 2:04 PM on October 14, 2019 [59 favorites]
That is hilarious.
I've learned never to engage. I just say I'm not taking on new clients at this time, never 'I don't believe in aliens'.
posted by bq at 2:14 PM on October 14, 2019 [1 favorite]
I've learned never to engage. I just say I'm not taking on new clients at this time, never 'I don't believe in aliens'.
posted by bq at 2:14 PM on October 14, 2019 [1 favorite]
I had a math teacher in high school who, when I was acting up because I was bored in class, set me to trisecting an angle and showing her my proof. It literally frustrated me to tears. I assume she didn't tell me it was impossible so she could keep using it to distract me all year; I didn't find out it was impossible until much later on. I'm still kind-of pissed!
Yeah, I had a science teacher in 7th grade who asked us to build perpetual motion machines over our spring vacation week. My astrophysicist father was livid. His explanation of why it was impossible made sense to me, but I struggled with the idea that my science teacher would assign an impossible task.
I guess we were supposed to "discover" that perpetual motion machines were hokum, but I was afraid to show up empty-handed. So I made a terrarium, sealed it with hot glue and tried to claim it was a perpetual motion machine for watering the single succulent within. Other kids arrived with various devices powered by rubber bands. Still others submitted angry notes from their parents. It was a shitshow.
posted by carmicha at 2:17 PM on October 14, 2019 [13 favorites]
Yeah, I had a science teacher in 7th grade who asked us to build perpetual motion machines over our spring vacation week. My astrophysicist father was livid. His explanation of why it was impossible made sense to me, but I struggled with the idea that my science teacher would assign an impossible task.
I guess we were supposed to "discover" that perpetual motion machines were hokum, but I was afraid to show up empty-handed. So I made a terrarium, sealed it with hot glue and tried to claim it was a perpetual motion machine for watering the single succulent within. Other kids arrived with various devices powered by rubber bands. Still others submitted angry notes from their parents. It was a shitshow.
posted by carmicha at 2:17 PM on October 14, 2019 [13 favorites]
I remember finding the Dudley Underwood book in a library in ninth grade and loving it. This brought back happy memories.
Also, this is the second colleague of mine on the blue in a week. If you or a high school senior you know and love wants to study with the author of this piece and of Rocking the Closet, let me commend historic Dickinson College to your attention.
posted by sy at 2:30 PM on October 14, 2019 [1 favorite]
Also, this is the second colleague of mine on the blue in a week. If you or a high school senior you know and love wants to study with the author of this piece and of Rocking the Closet, let me commend historic Dickinson College to your attention.
posted by sy at 2:30 PM on October 14, 2019 [1 favorite]
It was fun arguing with creationists and Intelligent Design wingnuts on Usenet. I learned a lot of evolutionary biology that way; it helped to go back to the "It's against probability that x happened" with some decent numbers, for example, and it gave me a real feel for the scale of biological systems.
After a while, though, you've seen it all and it's time to move on. My father has a credulous streak and occasionally comes up with some nutty stuff he's either read or as a result of bumping into an enthusiast crank, and I've learned that there's no point in engaging with him, just to politely refuse to talk about it until he loses interest and forgets about it.
The latest nonsense in the UK is local councils refusing permission for 5G network towers because of 'health concerns'. These are being gleefully promoted by the likes of Russia Today and seem to be particularly effective in the sort of rural community where they could really do with the connectivity. The battle will never end...
posted by Devonian at 2:42 PM on October 14, 2019 [3 favorites]
After a while, though, you've seen it all and it's time to move on. My father has a credulous streak and occasionally comes up with some nutty stuff he's either read or as a result of bumping into an enthusiast crank, and I've learned that there's no point in engaging with him, just to politely refuse to talk about it until he loses interest and forgets about it.
The latest nonsense in the UK is local councils refusing permission for 5G network towers because of 'health concerns'. These are being gleefully promoted by the likes of Russia Today and seem to be particularly effective in the sort of rural community where they could really do with the connectivity. The battle will never end...
posted by Devonian at 2:42 PM on October 14, 2019 [3 favorites]
My favorite one of all time is a guy who is convinced that the electrons in all hydrogen atoms are actually in a metastable excited state, and that his machine can bump them down to their actual ground state, and thereby derive oodles of power from water.
Despite the clear problems (to say nothing of the hell this would play with the Schroedinger equation solutions), I liked it because his proposal is explicitly *not* perpetual motion; you are limited by the amount of fuel available. It's just that the fuel was the most abundant element in the universe and usable in any chemical form. I'm sure he's toiling away somewhere muttering about all the fools with their free energy machines.
posted by Dr.Enormous at 3:17 PM on October 14, 2019 [7 favorites]
Despite the clear problems (to say nothing of the hell this would play with the Schroedinger equation solutions), I liked it because his proposal is explicitly *not* perpetual motion; you are limited by the amount of fuel available. It's just that the fuel was the most abundant element in the universe and usable in any chemical form. I'm sure he's toiling away somewhere muttering about all the fools with their free energy machines.
posted by Dr.Enormous at 3:17 PM on October 14, 2019 [7 favorites]
As has been pointed out above, squaring a circle is only impossible in the context of a specific toolset (not just a compass and straightedge, but specific ways of using them that are considered sufficiently reliable -- no sliding and no fudging!). Change the tools and you change what is possible. I love introducing students to this idea, which prefigures so much of computer science: what you can do depends on your tools and on how you conceptualize them.
Did you know that everything you can measure with a compass and straightedge, you can measure with just a compass? Or with just matchsticks?
There's a couple of good reasons to define 0!=1. One is to consider what n! is often used to represent, which is the number of ways a set of n elements can be rearranged. Then 0! denotes the number of ways the empty set can be ordered: exactly 1 way.
One of my mantras for intro combinatorics classes is "There are no ways to do the impossible, but there's one way to do nothing."
posted by aws17576 at 4:18 PM on October 14, 2019 [10 favorites]
Did you know that everything you can measure with a compass and straightedge, you can measure with just a compass? Or with just matchsticks?
There's a couple of good reasons to define 0!=1. One is to consider what n! is often used to represent, which is the number of ways a set of n elements can be rearranged. Then 0! denotes the number of ways the empty set can be ordered: exactly 1 way.
One of my mantras for intro combinatorics classes is "There are no ways to do the impossible, but there's one way to do nothing."
posted by aws17576 at 4:18 PM on October 14, 2019 [10 favorites]
A few months back, I happened to notice a crank on one of the Stack Exchange sites that I frequent. For a crank, he was relatively sophisticated and had chosen a bit of an unusual thing to try to disprove, Tarski's Undefinability Theorem; the usual crank fodder in this neighborhood would, of course, be Gödel's Incompleteness theorems. Anyways, I realized that I've seen very few cranks on the Stack Exchange sites, and definitely none with the staying power of an Archimedes Plutonium so I decided to try to keep track of this one user to see what becomes of cranks on Stack Exchange.
As it turns out, there's a common mechanism on Stack Exchange sites where once you've amassed enough negative reputation (e.g.: via people downvoting your questions), you lose the ability to post questions. So, as near as I can figure, what happens with cranks is that they bounce around from subsite to subsite, amassing downvotes and negative reputation everywhere they go, until they can no longer find an on-topic Stack Exchange site to post to.
posted by mhum at 4:22 PM on October 14, 2019 [2 favorites]
As it turns out, there's a common mechanism on Stack Exchange sites where once you've amassed enough negative reputation (e.g.: via people downvoting your questions), you lose the ability to post questions. So, as near as I can figure, what happens with cranks is that they bounce around from subsite to subsite, amassing downvotes and negative reputation everywhere they go, until they can no longer find an on-topic Stack Exchange site to post to.
posted by mhum at 4:22 PM on October 14, 2019 [2 favorites]
I used to work for a company that helped people register IP with the government. I was so tickled the day some legit alchemy came through -- "a method to transmute base metals into gold." I'll never forget that!
I briefly thought I had figured out how to turn lead into gold—or rather, how to make lead look as if it had turned into gold by dropping it into auric nitrate (nitrite?). My excuse is that I was fifteen and I thought I might get extra credit if I could prove it to the chemistry teacher. It sounds like this is the same kind of bright idea, fiercecupcake.
posted by Countess Elena at 5:29 PM on October 14, 2019 [1 favorite]
I briefly thought I had figured out how to turn lead into gold—or rather, how to make lead look as if it had turned into gold by dropping it into auric nitrate (nitrite?). My excuse is that I was fifteen and I thought I might get extra credit if I could prove it to the chemistry teacher. It sounds like this is the same kind of bright idea, fiercecupcake.
posted by Countess Elena at 5:29 PM on October 14, 2019 [1 favorite]
If you're in the mood for crankiness, there's viXra.
posted by oonh at 6:47 PM on October 14, 2019 [2 favorites]
posted by oonh at 6:47 PM on October 14, 2019 [2 favorites]
I once had a particularly nasty fever that left me in a practically hallucinatory state. I'd suddenly and violently fall asleep and have absolutely crazy dreams... I remember awakening from one, and frantically scrambling to find pen and paper, convinced I was on to something amazing, some world changing discovery. I scrawled down an illustration and some captions, enough to help me remember the details and bring it to the world, and them immediately passed out.
Later on, when I had been feeling better for a while, I discovered a paper with very poorly rendered but excited text at the top - "PERPETUAL MOTION MACHINE!" This was the only thing I could read, there was a bunch of illegible text (which my friends jokingly called a cipher) and also a drawing of something that vaguely resembled a ferris wheel, possibly with balloons and candles involved - I honestly don't know. My friends like to joke that I was clearly on the verge of changing the world, but it was obviously delusional - and that's often what I think of when I hear some of the more crackpot theories.
This was like 20 years ago, and to this day, whenever I feel especially sick in a visible way and someone asks me what's wrong, I often tell them that I think I'm on the verge of figuring out perpetual motion.
posted by MysticMCJ at 6:57 PM on October 14, 2019 [9 favorites]
Later on, when I had been feeling better for a while, I discovered a paper with very poorly rendered but excited text at the top - "PERPETUAL MOTION MACHINE!" This was the only thing I could read, there was a bunch of illegible text (which my friends jokingly called a cipher) and also a drawing of something that vaguely resembled a ferris wheel, possibly with balloons and candles involved - I honestly don't know. My friends like to joke that I was clearly on the verge of changing the world, but it was obviously delusional - and that's often what I think of when I hear some of the more crackpot theories.
This was like 20 years ago, and to this day, whenever I feel especially sick in a visible way and someone asks me what's wrong, I often tell them that I think I'm on the verge of figuring out perpetual motion.
posted by MysticMCJ at 6:57 PM on October 14, 2019 [9 favorites]
Yeah, I had a science teacher in 7th grade who asked us to build perpetual motion machines over our spring vacation week.
Did this teacher by any chance have tenure? And was your 7th grade class full of little assholes?
posted by axiom at 9:39 PM on October 14, 2019 [2 favorites]
Did this teacher by any chance have tenure? And was your 7th grade class full of little assholes?
posted by axiom at 9:39 PM on October 14, 2019 [2 favorites]
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area. This was proven to be possible by Miklós Laczkovich in 1990; the decomposition makes heavy use of the axiom of choice and is therefore non-constructive.
Which makes it bundling bedfellows with von Neumann's theorem that you can decompose a disk into a square the size of the Sun if you also allow area-preserving affine transformations on the pieces.
posted by away for regrooving at 9:57 PM on October 14, 2019
Which makes it bundling bedfellows with von Neumann's theorem that you can decompose a disk into a square the size of the Sun if you also allow area-preserving affine transformations on the pieces.
posted by away for regrooving at 9:57 PM on October 14, 2019
Then he would forward the crank's work on to the previous crank: lather rinse repeat. Occasionally he received thank you notes from cranks who were now happily collaborating.
Oh my God, this seems like a profoundly bad idea. Brilliantly chaotic neutral to chaotic evil, yes, but the potential for some kind of Nuclear Boyscout incident just goes up exponentially when you start introducing crackpots to each other like that.
That and UFO cults.
posted by loquacious at 10:21 PM on October 14, 2019 [1 favorite]
Oh my God, this seems like a profoundly bad idea. Brilliantly chaotic neutral to chaotic evil, yes, but the potential for some kind of Nuclear Boyscout incident just goes up exponentially when you start introducing crackpots to each other like that.
That and UFO cults.
posted by loquacious at 10:21 PM on October 14, 2019 [1 favorite]
It should be rather obvious by now that the answer to all of these is 42.
posted by halfbuckaroo at 10:25 AM on October 15, 2019 [1 favorite]
posted by halfbuckaroo at 10:25 AM on October 15, 2019 [1 favorite]
Did this teacher by any chance have tenure? And was your 7th grade class full of little assholes?
Definitely the former, but I think we were pretty good kids and this class was intended for the most capable and/or serious students. Another memory from this class that annoys me now entails an incident in which this teacher banked on probability and threw a fit when it didn't turn out as expected. In an effort to model the scientific method and demonstrate that psychics were charlatans, he had us record guesses about whether a series of hidden playing cards were black or red suits. Obviously he expected us all to post ~50 percent success rates, but one kid had about 85 percent right. Instead of using this outcome as an opportunity to teach us about normal curves, discuss outliers, tie it to relatable phenomenon like rolling all identical dice in Yahtzee or flipping a coin to heads six times in a row or whatever, he just sort of... panicked, and started yammering about how predicting the future wasn't possible. Meanwhile the lucky kid just sat there, confused, and wondering if he was being accused of cheating. Cue additional outraged letters from parents with an understanding of statistics. Need I mention that many of these parents were college professors?
posted by carmicha at 12:02 PM on October 15, 2019 [3 favorites]
Definitely the former, but I think we were pretty good kids and this class was intended for the most capable and/or serious students. Another memory from this class that annoys me now entails an incident in which this teacher banked on probability and threw a fit when it didn't turn out as expected. In an effort to model the scientific method and demonstrate that psychics were charlatans, he had us record guesses about whether a series of hidden playing cards were black or red suits. Obviously he expected us all to post ~50 percent success rates, but one kid had about 85 percent right. Instead of using this outcome as an opportunity to teach us about normal curves, discuss outliers, tie it to relatable phenomenon like rolling all identical dice in Yahtzee or flipping a coin to heads six times in a row or whatever, he just sort of... panicked, and started yammering about how predicting the future wasn't possible. Meanwhile the lucky kid just sat there, confused, and wondering if he was being accused of cheating. Cue additional outraged letters from parents with an understanding of statistics. Need I mention that many of these parents were college professors?
posted by carmicha at 12:02 PM on October 15, 2019 [3 favorites]
My brother and a couple of his friends spent a summer day or two trying to trisect an angle while in junior high school. Their math teacher was around and gave them access to an empty classroom. I don't know if they knew it was impossible or just that no one had ever done it. Either way they had a fun time doing geometry instead of getting into trouble (who am I kidding, the only trouble these kids could have gotten into is if they actually managed to trisect the angle).
posted by any portmanteau in a storm at 2:21 PM on October 15, 2019 [1 favorite]
posted by any portmanteau in a storm at 2:21 PM on October 15, 2019 [1 favorite]
> I don't know if they knew it was impossible or just that no one had ever done it.
I kinda doubt either of these would discourage a teenager.
posted by ardgedee at 6:16 PM on October 15, 2019 [4 favorites]
I kinda doubt either of these would discourage a teenager.
posted by ardgedee at 6:16 PM on October 15, 2019 [4 favorites]
When I was in grade school, the kid next door said her dad was working on a perpetual motion machine. At the time, I wasn't aware that this was such a long-shot proposal.
All I know of the plan is that it involved the use of ~4 or 5 ounces (if my memory of the bottle is correct) of mercury, which was kept on a shelf in the garage. I can't tell you how many times my friend and I entertained ourselves with a bit of stolen mercury.
Between lawn darts, monkey bars set on concrete surfaces, and ready access to poisonous materials, the baby boomer cohort should have been truncated in childhood.
posted by she's not there at 9:29 PM on October 15, 2019 [1 favorite]
All I know of the plan is that it involved the use of ~4 or 5 ounces (if my memory of the bottle is correct) of mercury, which was kept on a shelf in the garage. I can't tell you how many times my friend and I entertained ourselves with a bit of stolen mercury.
Between lawn darts, monkey bars set on concrete surfaces, and ready access to poisonous materials, the baby boomer cohort should have been truncated in childhood.
posted by she's not there at 9:29 PM on October 15, 2019 [1 favorite]
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I am still honestly half-convinced it OUGHT to be possible!
posted by Eyebrows McGee at 7:32 PM on October 13, 2019 [31 favorites]