Interesting that the folks who wrote a proof based on the 4Chan user's post listed him as a first author. In all of my experience, Mathematics truly seems to be the field with the highest integrity.
> Mathematics truly seems to be the field with the highest integrity.
Mathematician here. I'd like to think we have high (not sure about highest) integrity. But I should also point out that the custom in the field is to list authors alphabetically by family name, and the paper in question (https://oeis.org/A180632/a180632.pdf) does not break with custom if you view "anonymous" as "family name"...
Once talking with my wife, biologist, I, mathematician, said something like, "I never get first author because my name is so late in the alphabet", and she stared at me like I had just sprouted a second head. Confusion and shock.
That's when she had to sit me down and explain that first author is super mega important in her field, not just who is literally listed first.
> the custom in the field is to list authors alphabetically by family name
This is only true in some fields of mathematics; many areas of mathematics do not follow this rule. (Also mathematician, and none of the papers I've been involved with have done the alphabetical thing.)
I'm a mathematician and some years ago wrote a joint paper with some philosophers, I suggested the paper but we all did comparable amounts of work on it: they insisted that my name was first (which was non alphabetically), it made me really quite uncomfortable as I imagined that others would assume that I was some kind of arrogant arse who had insisted on precedence.
It’s because it’s the hardest field to bullshit. Everything is black and white and you can’t just make up fake data.
On the converse, psychology and economics seem to have the most problems in terms of reproducibility and fraud. This is because they are the easiest to falsify, and their results are interpreted according to less precise epistemology.
There’s no ‘Austrian school’ vs ‘Chicago school’ in maths (to my knowledge).
Also, the general public isn’t interested in pure maths, so there are less incentives to fake data so you can get a nice press release, or so you can publish your new book, or so that the government bureaucrat will subsidise your ‘research.’
I’ve heard it’s own version of pontoons though. In particular, that it’s becoming so dense that enough people aren’t revalidating the proofs. There’s been examples on HN of published proofs that existed for years and years before someone pointed out they’re wrong. To a non-mathematician this sounds like it’s own version of the replication problem.
I've mentioned this before on here, but mathematics papers don't use the usual rules for author ordering. By convention, more or less the entire field has agreed that authors shall be listed alphabetically. So, Max Zorn probably got listed last on every single multi-author paper he published, while Odd Aalen[0] has probably been listed first on every paper he's published.
To prove that I'm not just making this up out of my ass, here[1] is a statement from the American Mathematical Society that talks about it. I'll quote the meat of it here:
> In most areas of mathematics, joint research is a sharing of ideas and skills
that cannot be attributed to the individuals separately. The roles of
researchers are seldom differentiated (in the way they are in laboratory
sciences, for example). Determining which person contributed which ideas is
often meaningless because the ideas grow from complex discussions among all
partners. Naming a "senior" researcher may indicate the relative status of the
participants, but its purpose is not to indicate the relative merit of the
contributions. Joint work in mathematics almost always involves a small number
of researchers contributing equally to a research project.
> For this reason, mathematicians traditionally list authors on joint papers in
alphabetical order. An analysis of journal articles with at least one U.S. based
author shows that nearly half were jointly authored. Of these, more than 75%
listed the authors in alphabetical order. In pure mathematics, nearly all joint
papers (over 90%) list authors alphabetically.
Exceptions do exist, as alluded to by the "over 90%" number mentioned in the AMS statement. But, many of those are caused by transliteration artifacts (e.g. Author1 and Author2 are in alphabetical order in the language the paper was originally published in, but the English transliterated versions of their names are not).
This is all true, but it's also reasonably common to make an exception in special circumstances, particularly where one of the authors made the key discovery, and move that author's name to the front.
For example, the recent papers on aperiodic monotiles have Dave Smith as the first author, even though his name doesn't come first alphabetically.
(I can also think of another recent example, which modesty forbids me to detail.)
In the case at hand, we did deliberately intend anon to be the lead author. (I was one of the ‘coauthors’ who helped to write it up.)
Fun fact. Max Zorn was at Indiana University when I was a grad student there in the '80s. He hated to be known for Zorn's Lemma instead of the other work he did. He thought that was just a fairly trivial observation.
This is kind of interesting to look back on. I checked the group really quick and they shut down the program trying to find a better solution to the n=6 problem in March of this year. The most upvoted post was also a bit optimistic in thinking this problem might be solved in a few weeks. I don't know much about it but I am assuming it has not been solved yet.
It's an action packed short story about math truths. Super good.
> A truly wonderful story in which two math grad students discover that the things we consider to be "truths" in number theory are actually part of a dynamical system, subject to change over time and in competition with alternative "truths" that are equally valid at other "locations" in the number system.
I mean the title of Permutation City is more relevant. :)
But the one I linked to is an action / adventure story about discovering new something in math. So content wise, it's more relevant. And I just liked it and want people to read it.
all I have to add, and this may be of interest to nobody but me, I remember this discussion back in the day. Not because of the number of permutations of orderings to watch, but because I was intrigued that people had different reasons for preferring different orderings for the shows. Just struck me as strangely beautiful.
This has (or had) real world implications. Back when phone answering machines were a thing, and you could dial a pin number to your own to have it play back messages... well, I remember an article in 2600 (I think) that explained that there was a superpermutation that gives up the goods. It would take up to 3 or 4 minutes to dial in, but eventually you could start hearing the messages.
There was some mention of news reporters doing this to the phone numbers of local politicians, but that must have been speculative or outright bullshit (even then there would have been an applicable law against using such an exploit).
I wonder if the problem would be simpler if the superpermutation would be treated as a repeating (circular) sequence. I.e., what is the shortest sequence (having length n) such that if the episodes where shown in an endless repetition of that sequence, viewers could start at any episode and watch the next n + k episodes to catch all permutations. This would remove both ends of the superpermutation being a special case, so to speak.
The article doesn't do a good job of explaining the constraint.
The sequence being generated is called a superpermutation [0].
From the Wikipedia article:
"""
...a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring.
"""
In other words, construct a big long string made up of the N symbols where every permutation of the N symbols appears in it. Since there's the possibility of overlaps, you can do better than the naive method of just pasting all N! permutations together.
Note that this sounds very similar to a De Brujn sequence [1] but is different since a De Bruijn sequence ask for every possible sequence of N symbols (of length M, say), not every possible permutation. So a De Bruijn sequence would have 000, 001, 002, ... 200, 201, ... , 222 in it whereas a superpermutation would exclude (or at least not count) some of those sequences as they're not permutations (012, 021, 102, 120, 201, 210).
Is a superpermuation just a more efficient annotation or is it more helpful in solving an optimization problem? They talk about the travelling salesman problem in the article but they don't exactly explain if knowing the superpermutation helps solve it faster.
> If a television series has just three episodes, there are six possible orders in which to view them: 123, 132, 213, 231, 312 and 321. You could string these six sequences together to give a list of 18 episodes that includes every ordering, but there’s a much more efficient way to do it: 123121321.
And with 7 substrings of length 3, it's provably minimal, since making every 3-substring a permutation of 123 forces every element after the first 2. Assuming without loss of generality that it starts with 1 2, it is forced to start with
1 2 3 1 2 3
but there already repeats the same permutation. So one substring must be wasted (in the article this is phrased as having to traverse one higher cost edge in the corresponding graph).
that ...,1,2,1,.. in the middle bothers me, nobody wants to watch three in a row that does not include all three, i'd rather have a duplicate triplet, or at least include the case as another potential bound, or classes of orderings where perhaps some numbers of elements have these defects while others don't.
You can interleave the orderings. If there are two episodes (1 and 2), we only have to watch three episodes in a row: 121. Then, we've watched all permutations -- 12 and 21.
The "14!" solution (where we watch 14x14! episodes) means there is no interleaving -- we just watch each permutation in turn. In our 2-episode example, we'd have to watch one extra episode (for a total of 2x2! = 4), e.g. in the order 1221.
The question is what's the shortest sequence that contains every permutation as a substring. If each episode after the 14th got you a new permutation, you would need 13+14!, but that's not possible. For example with 3 episodes, you could begin 12312, then any episode you choose from that position does not contribute a permutation. I think the shortest sequence goes 123121321.
I think they mean if say there were episodes a, b and c the orders to watch would be abc, bac, cba, acb, cab, bca. Now if you watched abcba you'd experience both orders abc and cba but only watch 5 episodes in a row instead of 6. So what is the minimum number of episodes to watch in a row to experience all six different orders?
Readit News
Mathematician here. I'd like to think we have high (not sure about highest) integrity. But I should also point out that the custom in the field is to list authors alphabetically by family name, and the paper in question (https://oeis.org/A180632/a180632.pdf) does not break with custom if you view "anonymous" as "family name"...
That's when she had to sit me down and explain that first author is super mega important in her field, not just who is literally listed first.
This is only true in some fields of mathematics; many areas of mathematics do not follow this rule. (Also mathematician, and none of the papers I've been involved with have done the alphabetical thing.)
Deleted Comment
On the converse, psychology and economics seem to have the most problems in terms of reproducibility and fraud. This is because they are the easiest to falsify, and their results are interpreted according to less precise epistemology.
There’s no ‘Austrian school’ vs ‘Chicago school’ in maths (to my knowledge).
Also, the general public isn’t interested in pure maths, so there are less incentives to fake data so you can get a nice press release, or so you can publish your new book, or so that the government bureaucrat will subsidise your ‘research.’
If you think that psychology and economics have problems with reproducibility and fraud, you haven't seen the social sciences!
After all, Mathematics is not a natural science and hereby consensus must be reached.
see Brouwer–Hilbert controversy ?
To prove that I'm not just making this up out of my ass, here[1] is a statement from the American Mathematical Society that talks about it. I'll quote the meat of it here:
> In most areas of mathematics, joint research is a sharing of ideas and skills that cannot be attributed to the individuals separately. The roles of researchers are seldom differentiated (in the way they are in laboratory sciences, for example). Determining which person contributed which ideas is often meaningless because the ideas grow from complex discussions among all partners. Naming a "senior" researcher may indicate the relative status of the participants, but its purpose is not to indicate the relative merit of the contributions. Joint work in mathematics almost always involves a small number of researchers contributing equally to a research project.
> For this reason, mathematicians traditionally list authors on joint papers in alphabetical order. An analysis of journal articles with at least one U.S. based author shows that nearly half were jointly authored. Of these, more than 75% listed the authors in alphabetical order. In pure mathematics, nearly all joint papers (over 90%) list authors alphabetically.
Exceptions do exist, as alluded to by the "over 90%" number mentioned in the AMS statement. But, many of those are caused by transliteration artifacts (e.g. Author1 and Author2 are in alphabetical order in the language the paper was originally published in, but the English transliterated versions of their names are not).
See this Math Overflow post for all the gory details: https://mathoverflow.net/questions/19987/math-paper-authors-...
---
[0]: https://en.wikipedia.org/wiki/Odd_Aalen
[1]: http://www.ams.org/profession/leaders/CultureStatement04.pdf
For example, the recent papers on aperiodic monotiles have Dave Smith as the first author, even though his name doesn't come first alphabetically.
(I can also think of another recent example, which modesty forbids me to detail.)
In the case at hand, we did deliberately intend anon to be the lead author. (I was one of the ‘coauthors’ who helped to write it up.)
It may actually be professional golf, famous for players imposing penalties on themselves.
I said professional golf, not your father-in-law's scorecard.
Deleted Comment
It's an action packed short story about math truths. Super good.
https://www.amazon.com/exec/obidos/tg/detail/-/1857985737But the one I linked to is an action / adventure story about discovering new something in math. So content wise, it's more relevant. And I just liked it and want people to read it.
There was some mention of news reporters doing this to the phone numbers of local politicians, but that must have been speculative or outright bullshit (even then there would have been an applicable law against using such an exploit).
(Cue comments about the Endless Eight.)
The sequence being generated is called a superpermutation [0].
From the Wikipedia article:
""" ...a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. """
In other words, construct a big long string made up of the N symbols where every permutation of the N symbols appears in it. Since there's the possibility of overlaps, you can do better than the naive method of just pasting all N! permutations together.
Note that this sounds very similar to a De Brujn sequence [1] but is different since a De Bruijn sequence ask for every possible sequence of N symbols (of length M, say), not every possible permutation. So a De Bruijn sequence would have 000, 001, 002, ... 200, 201, ... , 222 in it whereas a superpermutation would exclude (or at least not count) some of those sequences as they're not permutations (012, 021, 102, 120, 201, 210).
[0] https://en.wikipedia.org/wiki/Superpermutation
[1] https://en.wikipedia.org/wiki/De_Bruijn_sequence
EDIT: links (de bruijn)
The "14!" solution (where we watch 14x14! episodes) means there is no interleaving -- we just watch each permutation in turn. In our 2-episode example, we'd have to watch one extra episode (for a total of 2x2! = 4), e.g. in the order 1221.
1 2 3
you have seen all the series episodes in one order. If you watch the episode sequence
1 2 3 1
you have now seen the series in two orders by watching a sequence of 4 episodes.
but you can skip an episode, and hit all permutations with > 1, 2, 1