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Pi and the collapse of peer review
- photon-torpedo 9y agoMy favorite wrong value for pi is 355/113, as it is surprisingly accurate for its simplicity.
- montecarl 9y agoIt requires remembering 6 digits and it is just a little bit more accurate than directly remembering 6 digits of pi. Here is a long article on other pi approximations: http://mathworld.wolfram.com/PiApproximations.html http://mathworld.wolfram.com/PiApproximations.html It turns out that 355/113 does a great job compared to most of the expressions given there! But none seem to be better than just remembering 3.14159.
- radarsat1 9y agoWe should be taught in high school to remember 314-159, it's actually easier to remember than 3-point-14159.
- posterboy 9y agoit's the same row of numerals, where's the difference?
- gpawl 9y agoIn what situation is it useful to know 355/113? It's approximation so it won't be used in any closed-form solution, so it's going to be converted to decimal or some other unit, which will either be a laborious manual calculation or require a calculator, which will have a more-precise value of pi stored in its memory.
- SAI_Peregrinus 9y agoMy favorite isn't an approximation, it's Euler's formula for calculating pi: pi/4 = arctan(1/2) + arctan(1/3). Use the Taylor series expansion for arctan(x): sum for n=0 to infinity of ((-1)^n)(x^(2n+1))/(2n+1). ie x^1/1 + x^3/3 - x^5/5 + x^7/7 - ... Not hard to memorize either part. Slow to calculate, but the accuracy is only limited by how far you expand the Taylor series.
- photon-torpedo 9y ago> It requires remembering 6 digits If you remember it with denominator first, then it's 113-355, which is relatively easy to remember. :) > and it is just a little bit more accurate than directly remembering 6 digits of pi. It's accurate up to one digit more than that, which is why I called it surprisingly accurate. But I agree that there is hardly a practical purpose to such numerology.
- Someone 9y agoIt's not numerology, it's number theory. We can directly compute these fractions, and they are in some well-defined way 'best'. To find a better approximation to pi as a rational you will need a denominator of 16604 (52163/16604) See https://en.m.wikipedia.org/wiki/Continued_fraction#Best_rational_approximations https://en.m.wikipedia.org/wiki/Continued_fraction#Best_rati... for an intro to the theory. Reason for that large jump is the 292 in the continued fraction of pi.
- adrianratnapala 9y ago3.14159 is in no way "more direct" than 355/113. Decimal notation is just a concsise way of writing down expressions for certain numbers. Fractions are another.
- lgas 9y agoThey aren't equivalent though -- for example if I memorize "3.14159" then I can increase my precision by just memorizing as many more digits as I want. The memorization I've already done isn't "wasted". With the fraction version I can't / it is.
- BurningFrog 9y agoDepending on how your math brain is organized, it can mean just remembering two numbers. Of course, the real reason to prefer 355/113 is that it's cool.
- emmelaich 9y agoAnd 22/7 should be pi day, not 3/14
- aetherson 9y agoAre there 22 months in your year or 14? (That is: It seems weird to express one date as month-last and the other as month-first.)
- gpawl 9y agoParent poster was rejecting the month-first version.
- aetherson 9y agoThen why didn't he write it as 14/3? Anyhow, I thought he was more narrowly saying that 22/7 is closer to the true value of pi than 3.14 is.
- nl 9y agoBecause 3.14 is the approximation of Pi. And yes, that is the reasoning.
- vacri 9y agomonth-first or month-last doesn't matter, until you add more time periods. YY/MM/DD and DD/MM/YY are both fine, but MM/DD/YY is braindead. Month-first gains the edge, though, when you add time-of-day, since no-one does ss/mm/hh
- jkingsbery 9y agoThat's known as "Pi Approximation Day" - http://www.qwantz.com/index.php?comic=955 http://www.qwantz.com/index.php?comic=955
- milesvp 9y agoActually PI day should be 6/28. It makes a lot of important formulas simpler... makes me sad we still teach PI, when TAU is mostly superior :P
- Herodotus38 9y agoMine is: "Sir I bear a rhyme excelling, in mystic force and magic spelling...." That's all I can remember clearly without looking it up online. "Something something elucidate... " What I always remember gives 12 digits. First heard it from my favorite math teacher.
- sgt101 9y agoIt used to be "if you have to pay, then it's not worth publishing in it", but plos requires $1500 so that rules out of the window.
- mixedmath 9y agoI think it should be called "Pi and the rise of pay-for publication" or perhaps "Predatory journals and miscomputing pi". If a predatory 'journal' is more interested in taking submissions' money than presenting science, then the thought of peer review doesn't enter into the picture. The journals that are mentioned are present on Beal's list of predatory journals [1], and so are even widely acknowledged to be crap journals. [1]: http://beallslist.weebly.com/ http://beallslist.weebly.com/
- Flott 9y agoThank you for the list. It is way longer then I expected. It's also interesting to take a look at the criteria used for the creation of the list.
- joe_the_user 9y agoWell, The thing about "the collapse of peer review" (or the rise of predatory journals) is that it involves something like the collapse of the "scientific community". For a device like peer review to work, you need to have a pool of individuals who are trustworthy - who care more about the truth more than they care about one or another sources of immediate benefit. The institution of tenure is intended to facilitate this - the ideal is a professor receives tenure and then can pursue their ideals rather than constantly looking over their shoulder wondering if they are going to survive. Of course, tenure is subject to abuse and tenure isn't the only way to get a pool of people who are significantly interested in "what is true" rather than "will this benefit me". But elimination of tenure and the reworking of the university on a "neo-liberal" basis of pay-for-immediate-performance does seems to be gradually destroying the community part of the scientific community (if a given authority just wants money, why shouldn't any of their peer reviews be up for the highest bid or why should they endorse predatory journal or etc). That's not as much of a problem with technical fields where it's known that truth can be nearly mechanically verified (math is approaching that level but sociology seems unlikely to get there soon, for example). We may get to a point where our society has immense technical know-how but has abandoned science as such. Goes along with "post-truth" I suppose.
- dvfjsdhgfv 9y agoI'm sorry, I didn't follow that development - what is the relationship between the abolishment of tenure and neo-liberalism?
- currymj 9y agoi think a shift from tenured chairs to lots of low-paid, precarious adjuncts can be identified with a broader rise of neoliberal, corporate attitudes in the university. that and evaluating professors solely based on how much money they bring in, or on supposedly objective citation metrics. bringing "market forces" where they hadn't been previously.
- tshadley 9y agohttps://en.wikipedia.org/wiki/Predatory_open_access_publishing https://en.wikipedia.org/wiki/Predatory_open_access_publishi... It looks like the best place to verify reputable open access journals is through the Directory of Open Access Journals: https://doaj.org/oainfo https://doaj.org/oainfo. I don't see any of the journals mentioned in the article listed.
- coldcode 9y agoReading his little paper, I was amazed at how many formula there are for calculating pi. Math is fun.
- Recursing 9y agoYou can find many more on Wikipedia https://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80#Formulae_yielding_.CF.80 https://en.wikipedia.org/wiki/List_of_formulae_involving_%CF...
- jaclaz 9y agoAs a side note: > and by the third century Chinese mathematician Liu Hui and the fifth century Indian mathematician Aryabhata, both of whom found pi to at least four digit accuracy. Zu Chongzhi should also be mentioned: https://en.wikipedia.org/wiki/Zu_Chongzhi https://en.wikipedia.org/wiki/Zu_Chongzhi The simple fraction 355/113, or Milü: https://en.wikipedia.org/wiki/Milü https://en.wikipedia.org/wiki/Milü which is very easy to rememember (the first three odd numbers repeated twice) and gives in its simplicity an excellent approximation. On Windows Calc: 355/113-pi=2,6676418906242231236893288649633e-7
- jwilk 9y agoThe article links to 11 papers, but they have only two authors: one claming π = 17 – 8√3, and another one claming π = (14 – √2)/4.