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Ranking mechanisms - ideas/comments?

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Ranking mechanisms - ideas/comments?

Welcome back!

As this time of year is back, the Google Summer of Code 2008 has just started. This year I will be working on improving last year's work. Therefore, I would like to start this discussion and hope to get feedback from you on what to improve, what are your thoughts/general opinions about both ranking meters (entries ranking and users ranking), or what additional features you would like to have.

Entries ranking system.
I have checked discussion from last year, and it seems that you mentioned two additional features: include meter for entry ranking in list of owned objects and include two modes: browsing and ranking to prevent bias. The latter feature was proposed by Wkbj79:
I would like to propose a compromise to this issue of whether we see ratings or not. It would be nice if we had a "browse mode" in which users can see ratings but cannot rate entries, and a "rate mode" in which the ratings are hidden and users can rate entries.
Do you have any additional ideas?

Users ranking system.
As you probably know, one of meters for objects that you see in encyclopedia shows user ranking. I know that some of you were disappointed with the quality of ranking that is produced (or with that users were classified to "medium" confidence instead of "high" etc.). Therefore, I would like to improve this feature. As you might remember, current algorithm uses HITS method to calculate the rankings. You can obtain more details after clicking on the meters. To evaluate this method, I have prepared a list of top-600 users found by HITS. It is available at http://www.mathcs.emory.edu/~pjurczy/users.htm. I think that the biggest problem is with decoding score value to meaningful text label (do not focus on score value so much, as this score is HITS value, rather focus on position in ranking that users have). I have looked at the list and observed that the current decoding thresholds that decode values to text labels can be too strict. Therefore, in the ranking I am also proposing new thresholds. Also, what do you think about the ranking? Is the order of users corresponding to your feelings about the community?

The last point I would like to rise is overall evaluation of the ranking systems. Do you have any ideas for evaluation of usefulness? One method we can use now for users ranking is just to take the current ranking of users with points and check the correlation of this ranking with the HITS ranking I am calculating - any additional ideas? Do you think we should run an evaluation survey? If yes, what kind of questions you would ask there?

Thanks a lot for all input!
Pawel


Pawel, I shouldn't have even mentioned it a couple of weeks ago. Now vindictive rating is back with a vengeance. Looking at Primefan's entries, they're all rated 1 across the board: 1 on correctness even when no corrections were ever filed, 1 on clarity even when he explains the concept in a way a child could understand, 1 on language even when there are no misspellings or grammatical errors, and 1 on pedagogy even when, like I said, a child. What is it about that placid old man that inspires such hatred? On the positive side, Wkbj79 is now rated more accurately. I regard Wkbj and Primefan as role models for clarity and humility (as opposed to "ha ha I'm so advanced you can't understand what I'm saying").

But why am I worrying about this? Don't I have real problems to worry about, like mortgage and credit card payments, the dwindling job market plus the rising price of gas?

Maybe the board should permit ratings only by registered users.

If that doesn't end the drive-by shootings, then the next step might be to record the ID of the peer reviewer along with their rating.

Jon Awbrey

The prejudice isn't against a specific author: it's against entries which use actual numbers, regardless of the authors. Compare two entries by CWoo:

http://planetmath.org/encyclopedia/ChangeOfBases.html uses numbers like 2 and -4/9. It's rated 2.29... even after I rated it 5 across the board.

http://planetmath.org/encyclopedia/GeneralizationOfAUniformity.html doesn't use any actual numbers, but it's rating shows up as a full 5.0 even though I set all the buttons to 1.

The moral of the story: if you want high ratings on PlanetMath, for god's sake, don't mention any actual numbers!!!

The evidence for your assertion is a bit anecdotal, don't you think? On another note, what exactly did you find fault with in the object GeneralizationOfAUniformity? All the relevant definitions are properly linked, definitions are clearly made, and the object is world-editable, so if you find the quality of the entry to be lacking, you can fix it.

The rating of all 1s was just a test. Since it showed up as all 5s regardless means my opinion doesn't matter, so whatever.

Maybe it will still seem anecdotal to you, but consider that almost all of Primefan's entryes are about actual numbers and use actual numbers, and very few obfuscations. That's what led compositefan to think the prejudice was against primefan in particlar.

CyclotomicQ says that

"The rating of all 1s was just a test. Since it showed up as all 5s regardless means my opinion doesn't matter, so whatever."

I've just witnessed the exact opposite. A rating of all 5s shown up as all 1s. But I wouldn't be so quick to assume there is some sort of malicious intent. Maybe something is broken. After all, this website seems to have at least one glitch a month and no one assumes malice, if, for example, all the images are sized absurdly, or every entry looks like nothing in normal mode but shows up just fine in page images, etc.

Pawel's table (http://www.mathcs.emory.edu/~pjurczy/users.htm) shows an unprecedented gap between Primefan's rank and the second highest rank. Primefan is a valued contributor, but his incredibly high rank is clearly not accurate. It seems that some users have abused the rating system to make a personal statement against abstract mathematics. The encyclopedia is not a political forum -- deliberately distorted ratings of any sort damage the credibility of the entire site, and undermine the efforts of all the contributors.

#1? Really? Even I have to disagree with that. #2 or #3 I would be OK with, but #1 seems too high to me. Pahio has three years more seniority on this site than me.

But that's not what this website reflects right now. I wish I could say I don't care about ratings, but being given all those little red bars is discouraging. I have to find strength in PM's slogan: "Math for the people, by the people." I take "math" to mean actual numbers and "people" to mean average folks.

The stand is against concrete math, regardless of the author. Otherwise, how do you explain CyclotomicQ's observation of two entries by the same author, that the one with numeric characters 2 - 9 can't be rated good?

You can't draw that conclusion based on a couple entries. That's complete lunacy. I guarantee you could find dozens of objects in which "numbers" explicitly appear that are highly rated, and plenty where they do not that are not so highly rated. That's just absurd.

Most mathematicians don't interpret "math" in the same way as you do. Mathematical skill and knowledge are cumulative; for most students, it takes many years to become comfortable with the core concepts and more years still to achieve a deep knowledge of some (usually) narrow branch of mathematics. It follows that mathematicians are likely to interpret "math by the people" as "math by the people who have devoted many years to the study of math". Also most of mathematics simply is very abstract and cannot be explained in an easily understood manner to people who have not invested the time to learn the requisite concepts, language and symbolism. If this were not the case, then everyone would be a mathematician.

Well said.

When I first saw the following entry, it had been rated by five users. The cumulative rating was "very high" despite the fact that the entry is incoherent and contains grammatical and mathematical errors. If you believe that this entry deserves a high rating, please explain why.

<<This is a commentary on the entry:>>

proof that there are infinitely many primes using the Mersenne primes

<<The title is misleading, Mersenne primes play no significant role in the proof.>>

Like Euclid's classic proof, this is also a proof by contradiction which starts out from the assumption that there is a largest prime number. But instead of building a primorial or a factorial, a Mersenne number is computed instead.

<<In the last sentence of the preceding paragraph the "but" is ungrammatical at the head of the sentence, and "instead" appears once too often.>>

\begin{proof}
Assume that the odd prime $p$ is the largest prime number. Then $2^p - 1$ is composite, not a Mersenne prime.

<<Presumably because 2^n-1 > n for n > 2. The name dropping is a distraction -- a cue to anticipate something that never arrives.>>

So what is the integer factorization of $2^p - 1$? By Fermat's little theorem we have $2^{p - 1} \equiv 1 \mod p$, doubling that we get $2^p \equiv 2 \mod p$, therefore $2^p - 1 \mod p$.

<<This seems to be a vestige of some other approach that was not removed when its context disappeared. The final clause lacks a verb.>>

Since $2^p - 1$ is composite, it must have at least two prime factors.

If $q$ is a factor of $2^p - 1$ (that is, $2^p - 1 \equiv 0 \mod q$) then, since $2^{q - 1} - 1 \equiv 0 \mod q$, assigning $d = \gcd(p, q - 1)$, we have $2^d - 1 \equiv 0 \mod q$. Then $d$ can not be 1 (for 2 - 1 is congruent to 0 modulo $q$). Therefore $d = p$ and $q - 1$ is multiple of $p$, and thus we derive that $q = np + 1$.

<<Here q must be prime, though the author doesn't say as much. That being the case, this is where Fermat's little theorem should be invoked. The properties of d are the least obvious portion of the proof, but they are simply stated without comment. The parenthesized remark is false. Setting aside these minor flaws, the proof is now complete since q is a prime greater than the greatest prime p. However the entry continues on for another half page of pointless confusion. The finale is provided by examples of primes that are not the largest prime.>>

Regardless of whether or not your rating was a test, if you want people to take your opinion about some conspiracy against entries with arabic numerals seriously, you should at the very least be able to provide some indicaiton as to why you felt that CWoo's entry warranted such a low rating. It's vastly more polished and comprehensible than the entry mentioned by ratboy; do you know why 2^d-1 is congruent to 0 modulo q in the proof given in the aforementioned entry, because, as ratboy notes, that is the least obvious portion of the proof, and it is asserted without justification. Is that "math for the people" in your estimation?

Now the correction gets filed! Gee, the timing is suspicious. Had it been filed earlier, like, the next day after the entry was created, or the day after the paragraph was added, it would be very easy to assume a genuine desire for the correctness of the entire site. But now it just looks, like, a secret weapon that was held in reserve for just the right moment to strike with maximum effect, to encourage PrimeFan to tear down everything he's built and leave like a dog chastised for scratching the furniture. I learned interesting things about numbers and 2- and 3-dimensional figures in here, but now that's a very distant memory, thanks to ratings.

The problem is that ratings bring out all the worst male insincts of competitiveness. As long as the ratings are given by the same writers of the content, they will be distorted. The anti-concretes threw the first punch, with all 1s ratings and keeping quiet on the corrections for the few choice examples. That doesn't excuse the anti-abstracts overcompensating. Instead of rushing to respond the artificially low ratings with artificially high ones, they would've needed to instead create gradually rising ratings, but for that they needed the cooperation of PrimeFan to create much shorter entries and gradually lengthen them to justify the gradually rising ratings. Now the system is enforcing the bias, with entries using concrete numbers doomed to a permanent low rating and abstract entries guaranteed a permanent high rating. But even without the system enforcing the bias, ratings won't have any good effects. If women ran this site, we wouldn't be having this problem!

i 2nd that e-motion ...

Jon Awbrey

I subscribe it too.

As a PM user, the rating system had no effects on the way I read (and use) entries.

As a PM writer, the rating system had little effect on the improvement of my own entries. Not because I don't want to change my entries (they are in fact world-editable), but sometimes I simply don't know what really needs to be done. Filling corrections and suggestions is much more useful and welcome in my opinion.

They were a good experiment though, like yark pointed.

I wonder what the secret-weapon corrections are for safe prime, Cunningham chain, theorem on Collatz sequences starting with Mersenne numbers, proof that 3 is the only prime perfect totient number, etc. Why are those rated so low? Do they actually have a mistake of logic or computation, or is the strongest criticism a misplaced comma or an E after an I? For all we know, you could have consulted with primefan to make sure proof that there are infinitely many primes using the Mersenne primes had that many flaws that you would one day melodramatically point out. That would set him up for an even more melodramatic event: the delivery of an altruistic-sounding speech that would make all of us ashamed of ourselves.

No, the secret weapon is the sudden reversal of ratings. Let them think that the entries dealing with actual numbers and actual geometrical constructions were being rated fairly, and then WHAM! sudden change, the enemies reveal their strategy in their scramble to deal with the nasty surprise.

> As a PM user, the rating system had no effects on the way I read (and use) entries.

That's you, but what about someone who winds up here on PM after following a link from a reputable resource, like the OEIS? Say they look at EulerPhifunction, or KolakoskiSequence, or ArmstrongNumber, or MultiplicativeEncoding. They might wonder what the red bar means and find out that it means that the entry they're looking at is essentially worthless. So they click the back arrow to go back to the OEIS and follow a link to a more reliable resource, like Mathworld or Wikipedia (yeah, ouch!). Granted, garbled entries desperate for a rerender, like ValueOfTheRiemannZetaFunctionAtS2, won't make a good impression either.

> They were a good experiment though, like yark pointed.

In that case, I'm waiting for the hidden camera to be revealed and where do I sign on the talent release form.

> As long as the ratings are given by the same writers of the content, they will be distorted.

If you don't believe the conspiracy theories, believe that it's hard for writers to be objective about their own stuff.

Agreed!

"If women ran this site, we wouldn't be having this problem!"

Hah! I take some Umbridge at that!

http://harrypotter.wikia.com/wiki/Dolores_Umbridge

Jon Awbrey

CompositeFan, I filed the correction after reading ratboy's description of the object because it needed filing and I personally had never read the article; if I had, and if I had caught the error, I would have filed it immediately. With all due respect, while you can say what you will about the site as a whole, please don't insinuate that I am part of some absurd conspiracy with the objective of discouraging PrimeFan from contributing further content to the site; I'm not, and I am offended by the accusation.

Keenan

Just a point of nomenclature.

The term "spam" has a technical and even a legal definition, the essence of which involves mass, unsolicited, message distribution (MUMD) It is best not to extend the use of the term too far, less its import become that of vacuous pejorative.

Jon B)

I have to agree. Although the term spam is quite wide (and even is still becoming wider), maybe it is a bit too careless to use it here. I should have used something like abusing ranking system.

Pawel

I think the term of art is more like "fudge".

Jon Awbrey

Earlier Jon Awbrey identified the rhetoric of antagonism which now has gotten to the point of including violent war imagery. The previous rhetoric was of victimization and persecution, and before that of mildly annoyed puzzlement (such as we get when Amazon or Netflix makes some ridiculous suggestion based on what we've browsed). The earliest, largely forgotten rhetoric, was the rhetoric of good intentions. Supposedly ratings were to impart the content a stamp of a good reputation assuring correctness for the entire site. How far we've come. Knodel speaks of "empty shell casings" and Pawel speaks of "weapons."

Nancy Smith

"Most mathematicians don't interpret "math" in the same way as you do. Mathematical skill and knowledge are cumulative; for most students, it takes many years to become comfortable with the core concepts and more years still to achieve a deep knowledge of some (usually) narrow branch of mathematics. It follows that mathematicians are likely to interpret "math by the people" as "math by the people who have devoted many years to the study of math". Also most of mathematics simply is very abstract and cannot be explained in an easily understood manner to people who have not invested the time to learn the requisite concepts, language and symbolism. If this were not the case, then everyone would be a mathematician."

For the most part I have to agree with a lot of this. But it's still no excuse to fail to mention the application for concepts that otherwise appear to be useless philosophical fantasies. How hard is it to write something like "This has applications in electrical engineering" or "This would have real-world applications if membrane string theory is proven true"?

I suppose mentioning such things is up to the writer of the entry, and not all mathematicians care about real-world applications; if a reader considers a mathematical topic to be a "useless philosophical [fantasy]," then he or she probably shouldn't worry about any applications of said fantasy. The theory of schemes is probably considered by many to be rather esoteric, but would mentioning that it has deep applications to the cleaning of urinals enhance someone's appreciation for it who already views it as nonsense? What's the point? This is a mathematics website; if someone wants to point out that a certain idea has been fruitfully applied in theoretical physics or computer engineering, let them, but they are by no means obligated to do so. If you find that someone has left something out of this nature and you truly take issue with his or her omission, why not file an addendum and make your case?

There is one positive side to the system-enforced vindictive ranking mechanism. It could force some mathematicians deal with their deep fear and hatred of numbers. Numerophobia is a serious psychological condition that afflicts quite a few professional mathematicians, rendering them as afraid of numbers as some people are of rats or clowns or heights. But even this positive effect might not be so significant because the best treatment for a professional mathematician's numerophobia remains an offer to be a highly-paid expert witness on a trial.

The negative effects of the ranking mechanism have all been discussed already: it punishes collaboration, it punishes the giving of examples and diagrams, it punishes populism and it discourages the immediate issuance of corrections.

> but would mentioning that it has deep applications to the cleaning of urinals enhance someone's appreciation for it who already views it as nonsense?

I can just imagine Euler, hard at work on the Basel problem, worrying "Gee, I hope this doesn't have any disgusting-sounding applications!"

The building blocks of number theory don't just have applications outside of mathematics (e.g., the gcd function applied to optics and quantum physics) but also to other branches of mathematics. But things like category theory and schemes I'd be surprised to hear that they have applications even in neighboring branches of mathematics. Those things probably exist only in the minds of their inventors for the pure sake of making themselves appear smart and look down their noses at others.

Your assessment of scheme and category theory is rather narrow and indicative of ignorance, not to mention insulting to the brilliant individuals that pioneered these subjects, i.e., Alexander Grothendieck and Saunders Mac Lane, to name a couple. Category theory has done much to unify seemingly disparate mathematical concepts and constructs and articulate them in a common language; scheme theory was developed as a means of doing algebraic geometry over more general rings than just algebraically-closed fields, and it has been immensely successful, and most assuredly has applications to other areas of mathematics. Don't dismiss something as vanity and egotism just because you personally don't consider it important. Mathematicians do math because they love it, not because they feel doing so makes them in some way superior to non-mathematicians. This idea of a conflict between concrete and abstract mathematics on this site is patently ridiculous and has been greatly blown out of proportion with grotesquely melodramatic war analogies and nonsense about a phobia of numbers. First and foremost, I think the term "concrete" is being confounded with the term "elementary." The theory of elliptic curves is without question abstract, and not exactly elementary by most standards, but elliptic curve cryptography is an unmistakably concrete application of these abstract ideas. If I have the misfortune of reading one more outrageous claim of an abstractist conspiracy against concretists, I may just vomit long exact sequences in homology. I apologize if what I've said offends anyone; it's merely one individual's opinion, and no one is obliged to agree with any of it. I'd also like to thank Jon Awbrey for the consistently humorous quips and comments.

For your consideration, I want to suggest
another very simple system that I've been
talking about with Ray. This is not a
ranking system per se, but I think it would
help accomplish the main thing a ranking
system should accomplish, which is: helping
people find items they want to find.

The system is -- instead of voting on the
global worth of an article, vote on which
section of the site the article belongs
in. (We'll need some agreed-upon sections
for this to work.) An article might get
kicked from section to section based on
such votes, but it will never be deleted
or "stigmatized" with a negative evaluation.

This system might be *combined* with a
more localized rating system *within each
area*. However, I don't know that we
*need* such a system.

Right now, I get the sense that people are
down-evaluating articles simply based on
their personal preferences. That has
nothing to do with the true objective
quality of the article in question (if
there even is such a thing!). It has
everything to do with defining the article's
audience. Categorization without ranking
would take care of that!

I don't understand about this proposal is this voting
about the area to which an article belongs. Rather,
I suggest that this be done just as with the current
classification by subject. In cases where an entry
is improperly classified or, at any rate, someone
believes that it is improperly classified, that cold
be handled by filing corrections.

"Those things probably exist only in the minds of their inventors for the pure sake of making themselves appear smart and look down their noses at others."

Excuse me, but I must say that this is a very sad commentary.

I guess if you knew nothing of number theory you would think the same about number theorists too..

The two particular areas you mentioned, category theory and scheme theory, were (are) areas where plenty of mathematicians have worked for decades and were founded by people whose mathematical work (even outside this particular areas) is highly respected (Grothendieck, Saunders Mac Lane and Eilenberg).

It almost seems you don't believe that, in a global point of view, the standards followed by the mathematical community concerning their work (i.e. peer reviewing, etc, etc) are correct and have decided threw history what concepts and approaches are more useful in mathematics.

Please, do not judge an area of mathematics were a vast community of (respected) people have worked, just because you do not understand it.

P.S. - I particularly don't know anything about schemes or even algebraic geometry in general too..

P.P.S. - I have nothing against number theory, applied mathematics, "concrete" mathematics (whatever that is) or elementary mathematics and I will refuse to participate if the discussion keeps going to those levels.

Perhaps it refers to the categories discussed in the PlanetMath Community Guidelines draft: http://planetmath.org/?op=getobj&from=collab&id=112

What Joe and I have been discussing is a proposed "mathematical
audience classification" which I am developing. This system is
meant to supplement the current system, which classifies by
subject area, by adding a classification by intended audience
and type of material. For instance, this classification system
would distinguish between well-known mainstream mathematics and
new research, as well as material intended for beginners from
material intended for experts.

I think this would provide a wonder technological resolution to
the issues which are now so troublesome. As it stands, our
encyclopaedia section is now a heterogenous mixture of all sorts
of standard material, non-standard material, introductory
material, current research, etc. Given that there is no easy
way to tell what is what except by reading it, this situation is
confusing and is leading to a lot of the strife we have seen
for much of the history of this project. One solution is to do
like Wikipedia, decreeing that only material which is standard
and notable, as evidenced by its inclusion in textbooks and
curricula, be allowed and that some body enforce this by deleting
anything else. While this would solve the problem, I consider this
solution as suboptimal and as severely compromising the values of
PlanetMath. Rather, I propose that by classifying the material
as described above we could do something quite similar in effect
to the suboptimal solution without the drawbacks. Namely, once
the classification is in place, we could add other views to the
encyclopaedia, like our current views by popularity and subject
area, but based upon this new classification, so that, for example,
the partisans of elitist abstract math can read an encyclopaedia
which only has the sort of content of which they approve and the
partisans of concrete garbage can read a version conducive to their
tastes rather than conspiring against each other and turning the
forum into a battlefield. Not only would the rest of us benefit
by being spared this bickering, but it would make it easier for us
to find material. For instance, it having been a while since I
studied basic analysis, when looking for material on integrals, I
am interested in advanced material and would like to skip past the
introductory expositions to get to results for which I am looking.
However, a student encountering calculus for the first time would
want to take the opposite course and steer clear of the advanced
material. Having material classified by audience as well as
subject would benefit both of us equally.

That's funny! I had to click the link before I got it. Point taken.

> and the
partisans of concrete garbage can read a version conducive to their
tastes

Brilliant! In fact, "concrete garbage" is the first category that needs to be created, and the easiest to populate. All the software would have to do is look for the characters "3", "4", "5", "6", "7", "8" or "9" in the TeX source and dump the corresponding entries into the concrete garbage category. Necessary numbers, like equation numbers can be created with the use of a TeX macro, so that valuable entries have no flags of garbage in their source. Those partisans can then wallow in their own garbage, and we can concentrate on mathematics that actually benefits society.

rspuzio wrote
> and the partisans of concrete garbage can read a version conducive to their tastes

This is obviously prejudiced, and this prejudice comes from a high-ranking person on this site. Good thing Pythagoras and Ramanujan are long dead. Imagine the scorn we'd heap on them today! 6 is the sum of its divisors? Garbage! 1729 is the sum of two cubes in two different ways? More garbage!

CyclotomicQ wrote
> In fact, "concrete garbage" is the first category that needs to be created, and the easiest to populate. All the software would have to do is look for the characters "3", "4", "5", "6", "7", "8" or "9" in the TeX source and dump the corresponding entries into the concrete garbage category.

Now, CyclotomicQ is not even half as high up as rspuzio, yet his suggestion sounds frighteningly likely to become a reality. That would be far more stigmatizing that a bunch of little red bars.

Besides, don't we already have categories? What are the AMS MSCs, chopped liver?

> rspuzio wrote
> > and the partisans of concrete garbage can read a version
> > conducive to their tastes
>
> This is obviously prejudiced, and this prejudice comes from
> a high-ranking person on this site.

To make the point clear, allow me to provide the full context of
the message which was (mis)quoted:

"Namely, once the classification is in place, we could add other
views to the encyclopaedia, like our current views by popularity
and subject area, but based upon this new classification, so that,
for example, the partisans of elitist abstract math can read an
encyclopaedia which only has the sort of content of which they
approve and the partisans of concrete garbage can read a version
conducive to their tastes rather than conspiring against each other
and turning the forum into a battlefield. Not only would the rest of
us benefit by being spared this bickering, but it would make it
easier for us to find material."

Placing the quote back in its original context, it is clear that
this is not meant as a being partial to either side because, right
before the portion which was quoted, I say "partisans of elitist
abstract math". My point in using the derogatory terms "elitist"
and "garbage" here was to label the two sides by the names they use
to identify each other. The opinion I was expressing is NEITHER
for nor against any type of math but AGAINST the bickering and
fighting I have been seeing here.

For the record, I am in favor of having all sorts of math here,
both abstract and concrete, both elementary and advanced, both
mainstream and offbeat. My only point is that, in order to
support different types of math on the same website, better
guidance is needed so that people can find what they want. As a
matter of fact, I happen to be in favor of keeping entries like
the ones on integer sequences.

> Besides, don't we already have categories?

The categories we have only classify by subject, but say
nothing about whether the entry is written at an advanced
or an introductory level, is abstract or concrete, etc.

> What are the AMS MSCs, chopped liver

Liverwurst alone, with no beer, would make for a
boring Oktoberfest ;)

Sometimes mathematical writers obfuscate on purpose and sometimes they obfuscate accidentally.

Kudos to Algeboy on a recent instance where he recognized the possibility for obfuscation: in regards to logarithm tables, he could've just said "logs are bijections, duh." But instead he chose to leave out the "duh" and explain: "You just read the table differently." and then he gave an example. So often examples can help clear up confusion. At the very least they show a willingness by the author to take responsibility for mistakes they make.

Maybe not every extreme abstraction is a deliberate obfuscation. I do wonder sometimes.

By the way, unary operators can always be mapped to binary operators by the deployment of the corresponding reverse identity element, but only when the trundle intersects the frame at a perpendicular trajectory with the help of a sheaf. Am I right or wrong on this? Can anyone tell?

Do you have an example of a professional mathematician purposefully obfuscating a concept in a piece of mathematical writing? I personally doubt it. Keep in mind that mathematical literature can be extremely narrow in scope and is often meant for a similarly narrow audience. There is quite a distinction between poor exposition, intent to confuse, and a lack of comprehension upon the part of the reader.

Oh, sure they do --- mathematicains are just people after all,
and are as prone as anyone else to obfuscate and fall victim
to fads as anyone else. For an account of obfuscation by
professional mathematicians with examples, see W. V. Quine's
essay "Mathematosis" in his book "Quiddities: An Intermittently
Philosophical Dictionary".

knodeltheory wrote:
"Sometimes mathematical writers obfuscate on purpose and sometimes they obfuscate accidentally".

For a book-length rant on this topic, see _Mathematics Made Difficult: A Handbook for the Perplexed_ by Carl E. Linderholm, World Publishing, 1971.

My example is Thomas' 1959 calculus book. Thomas, the head MIT's math department, was obviously well respected. Many colleges, mine included, bought an unedited book, rushed into publication by publisher deadlines, on reputation only.

The book was a failure. It was filled with incomplete and confusing proofs, among other 'accidental' obfuscations. Future editions filled the missing steps, child's play for Thomas' thinking, but required foundations for beginners.

Luckily, for me, I did not give up on calculus.

What I mean about "voting about the area
to which an article belongs" is that
the categorization of an article need
not be handled by that article's author.

This provides a different form of peer-based
moderation of content from that used in
correction system. By taking this aspect of
control away from the author and giving it to
the community at large, this proposal has
something in common with the rating system
(which it aims to replace or supplement).

After all, the community at large would be
better able to evaluate the usefulness of
the article than the author.

In this case, I see that your proposal is different from mine.
My proposal is to add categories which, like the current
categories, are handled by the author, but which supplement
the current classification system by describing, not only what
branch of mathematics is being discussed, but also such things
as whether the material presented is standard, maninstream
mathematics or and alternative approach (and, if so, which one),
whether the material is well-known or obscure or currently
being researched, what sort of background is assumed of the
reader. Since these are exactly the sort of things which an
author should be clear about before writing an exposition, I
think it makes sense that the author be the one to handle this
classification --- presumably, it should be a matter of entering
information which one already knows in a standardized format.
In fact, the very act of having authors do this could by itself
improve entry quality --- for instance, if somebody has not
thought about what knowledge is assumed on the part of the
intended reader, trying to classify the result as elementary or
advanced may lead the author to think the matter through and
make sure that the background material assumed is consistent.

> By the way, unary operators can always be mapped to binary
> operators by the deployment of the corresponding reverse identity > element, but only when the trundle intersects the frame at a
> perpendicular trajectory with the help of a sheaf. Am I right or
> wrong on this? Can anyone tell?

Call me crazy, but I think I actually understood that! Actually, just the first clause. After "but only when" I don't have a clue what is being said.

Like, take the unary minus operator. It can be mapped to the binary times operator. The multiplicative identity element is 1, so its reverse is -1, and that is the second operand for binary times. Or the unary bitwise negation operator, it can be mapped to the binary XOR operator. The "XORive" identity element is 0000, and the reverse of that is the Mersenne number FFFF. In fact, I think this makes sense for all the C++ unary operators except sizeof, pointer, typeof, delete, but those are kinda machine-specific or something.

What trundles, frames, sheafs, have to do with all this I have no idea whatsoever.

> What trundles, frames, sheafs, have to do with all this I have no
> idea whatsoever.

I think that someone is trying to pull your leg ;) The statement
you were trying to figure out was meant as a parody of obfuscated
mathematics, not intended seriously as a mathematical statement.
The reason that you didn't understand beyond the first clause, is
that there was nothing there to understand --- it was a spoof of
mathematical writing style from then on! Trundles, frames, and
sheaves have nothing to do with anything, they are just terms
thrown in to sound like mathematical jargon.

I'm not in a place to make such highly technical statements, but to me it seems as if the problem here is abstractions. One would not walk into a physicists study, look at his notes, and then tell him "This isn't in plain english, and isn't science until a common person can understand it"

Abstracting any field further is a necessary step for development, I think it would be unreasonable to ask any scientific mind to stop at some point because it's "too" abstract. Any sort of statement of developed theory would take pages for the simplest notion. Try expressing the notion of a derivative using only ZFC set theory axioms.. You would have to construct the real number system from scratch, develop notions of distance (and thus metric spaces), limit points, close points, interior points, functions, and many other things EVERY SINGLE TIME you wanted to say "derivative." These sorts of abstractions are important for cognitive economy and are unavoidable if progress is your goal.

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