A fun little exercise in dissolving a problem. Relatively quick, but it can wake you up on a slow day.
http://www.memedroid.com/share-meme/337837/8000
Gur pbeerpg (naq fgnoyr) nafjre vf mreb creprag, juvpu vf pbeerpg, orpnhfr mreb creprag vf abg ninvynoyr nf na nafjre :C
Me too. My thought processes went like this:
gurer ner sbhe nafjref tvira, fb vg zhfg or “gjragl-svir cre prag”;
ab, jnvg, “gjragl-svir cre prag” bpphef gjvpr, fb gur cebonovyvgl bs cvpxvat gung jbhyq or svsgl cre prag;
ab, jnvg, “svsgl cre prag” bayl bpphef bapr, fb gur cebonovyvgl bs cvpxvat gung jbhyq or gjragl-svir cre prag;
bxnl, guvf vf fbzr cnenqbk bs frys-ersreragvnyvgl yvxr “Gur sbyybjvat fragrapr vf snyfr. Gur cerivbhf fragrapr vf gehr.” Fb V thrff gur pbeerpg nafjre vf “shpx lbh!”;
jnvg... “shpx lbh!” vfa'g nzbat gur nafjref tvira, fb gur cebonovyvgl bs cvpxvat gung jbhyq or mreb cre prag;
naq vaqrrq, “mreb cre prag” vfa'g nzbat gur nafjref tvira rvgure, fb gur cebonovyvgl bs cvpxvat gung jbhyq or mreb cre prag, gbb, fb gung'f gur evtug nafjre.
Ner lbh ernyyl mreb creprag fher gung'f pbeerpg? Pbhyq lbh fcraq rgreavgl tvivat nafjref jvgu gur fnzr zrgn-pbagenqvpgbel pbasvqrapr naq abg or evtug rira bapr?
Gur crepragntrf ner pyrneyl tvira gb jvguva gjb fvtavsvpnag svtherf, fb vs gur cebonovyvgl vf yrff guna mreb cbvag svir creprag, “mreb creprag” vf fgvyy n pbeerpg nafjre. :-C
Are you really 0% sure you're right? Could you spend eternity giving meta-answers of a similar certainty and not be correct even once?
Well done! Unfortunately, you are going to Rationalist Hell for gerngvat mreb nf n cebonovyvgl.
Assuming that (A) is correct, it's true that the probability of picking it at random is (A) 25%. The same works for (D) (but not if both (A) and (D) are correct). There are no other possible (non-empty) sets of correct answers that are fixed under interpretation of the question.
(Additionally, all mixed states of knowledge that assign probability p to (A) being correct and 1-p to (D) are also fixed under interpretation of the question.)
My answer was that you are inferring information that the question doesn't actually provide. Look at it closely and try to locate what the question even is.
Jr pnaabg evtugyl pnyy guvf na rkrepvfr va "Qvffbyivat gur Dhrfgvba" orpnhfr nf vg fgnaqf vg vf zreryl n dhrfgvba gb or nafjrerq. Gur nafjre vf mreb. Guvf qbrfa'g unccra gb or bar bs gur bcgvbaf. Ohg zhygvcyr pubvpr dhrfgvbaf jurer gur pbeerpg nafjre qbrf abg unccra gb or cerfrag va gur pubvprf tvira nera'g fbzrguvat qrrc naq zlfgrevbhf gb or qvffbyirq. Gurl whfg zrna gung gur crefba znxvat gur dhrfgvba unf znqr na reebe (qryvorengryl be bgurejvfr).
Abj, vs renfrq gur qvtvg "fvk" sebz gur guveq bs gur bcgvbaf tvira jr jbhyq or yrsg jvgu n dhrfgvba jbegul bs 'qvffbyivat'.
I double learned something after posting this! Zl nafjre unq orra gung gur dhrfgvba vf jebat, orpnhfr gur nafjref tvira ner gur nafjref gb n qvssrerag dhrfgvba, abg gb guvf bar. Fcrpvsvpnyyl, zl oenva qrsnhygrq gb ernqvat guvf nf: "Vs lbh pubbfr na nafjre gb n zhygvcyr-pubvpr dhrfgvba ng enaqbz, jung vf gur punapr lbh'yy trg gur pbeerpg nafjre vs gurer ner sbhe bcgvbaf naq bar vf pbeerpg", juvpu V nffhzr vf jung zbfg crbcyr qb.
Frireny bgure crbcyr cbfgrq ng gur pbeerpg nafjre vfa'g tvira, ohg vagrecergrq gur dhrfgvba nf n yrtvgvzngr dhrfgvba.
Ybbxvat ng vg ntnva, obgu nafjref ner onfvpnyyl fnlvat gur fnzr guvat (gur dhrfgvba nfxrq naq gur nafjre-bcgvbaf tvira qb abg zngpu va n fbyinoyr jnl), whfg nccebnpuvat vg sebz qvssrerag fvqrf. As they say - "One man's modus ponens..."
What is meant by "dissolving a question"?
I find this is more of a koan than a "real question". (Example of koan: What is the sound of one hand clapping?) Since I have no idea what the answer would refer to even if all the alternatives were 100%...
Suppose n=1,2,3,4 is the number of correct answers in the set S = {A, B, C, D}. Then it is easy to see that for any of these values of n, no n element(s) of S can be found such that n/4 is equal to the percentage displayed on these elements. So the question is undefined/insoluble/weird/paradoxical/etc.
Still, this other post would have been more relevant than that IMO, so I still think the title of this post isn't terribly appropriate.
It struck me as dissolving because gelvat gb nafjre gur dhrfgvba yrnqf gb pbashfvba, naq bayl hcba rknzvavat bar'f nffhzcgvbaf naq erzbivat gurz qbrf bar ernyvmr gur dhrfgvba vgfrys vf jebat. It sounds like people agree that this is a poor post title though, do you have any suggestions that would be clearer?
gelvat gb nafjre gur dhrfgvba yrnqf gb pbashfvba, naq bayl hcba rknzvavat bar'f nffhzcgvbaf naq erzbivat gurz qbrf bar ernyvmr gur dhrfgvba vgfrys vf jebat
That reminds me of the puzzle where you have to touch all of the nine dots on a 3x3 square array with at most four line segments and without ever taking the pencil off the page, which znal crbcyr pna'g qb orpnhfr gurl qba'g ernyvmr gurl'er nyybjrq gb yrnir gur fdhner qryvzvgrq ol gur bhgre qbgf.
It sounds like people agree that this is a poor post title though, do you have any suggestions that would be clearer?
I can't think of anything decent (except trivial stuff like “Interesting self-referential question on Memedroid”) at the moment.
Maybe it's time for hints and simplifications...
What happens if D) is 30%?
What happens if the only choices are A) 50% and B) 50%?
This equation not properly being answered and other languages are really throwing me off. This comment is the only comment i thought was common to my senses.
My answer remains the same - http://lesswrong.com/lw/gzn/exercise_in_dissolving/8mbp
(Specifically, gur dhrfgvba vf jebat, orpnhfr gur nafjref tvira ner gur nafjref gb n qvssrerag dhrfgvba, abg gb guvf bar. Gung dhrfgvba orvat: "Vs lbh pubbfr na nafjre gb n zhygvcyr-pubvpr dhrfgvba ng enaqbz, jung vf gur punapr lbh'yy trg gur pbeerpg nafjre vs gurer ner sbhe bcgvbaf naq bar vf pbeerpg". Gur cnegvphyne dhrfgvba va gur cvpgher vfa'g rira n pburerag dhrfgvba.)
A variant of this question was discussed on Mathematics Stack Exchange. The top answer has a good explanation of the nature of this question – “vg'f n zhygvcyr-pubvpr inevnag […] bs gur pynffvpny yvne cnenqbk” (un-ROT13).
Just in case anyone else has been copying and pasting lots of posts in rot13.com, the Firefox addon Leet Key lets you read rot13 more easily via the context menu.
Va Zngyno/Bpgnir: vs (enaq < .6) qvfc("P") ryfr qvfc("N") raqvs
V nz gelvat gb znkvzvmr zl cebonovyvgl bs n pbeerpg nafjre, evtug? Naq V'z nyybjrq gb vagrecerg gung "lbh" nf frpbaq-crefba fvathyne engure guna cyheny?
Gnobb "or pbeerpg". (Nyfb gnobb "nafjre": qbrf vf zrna pubbfvat n ahzore, pubbfvat bar bs gur sbhe vgrzf, be pubbfvat nal rzcgl be aba-rzcgl fhofrg bs gur sbhe vgrzf?)
Nsgre gnobbvat, lbh trg fbzrguvat yvxr: Jung vf gur ahzore A jvgu gur cebcregl gung gur frg {gjragl svir, svsgl, fvkgl, gjragl svir} pbagnvaf rknpgyl A creprag bs gur ahzore A? Gura ernyvmr gung lbh qba'g unir gb nffhzr gung gurer vf rknpgyl bar A yvxr guvf, be gung rira nal fhpu A rkvfgf. Gura ernyvmr gur qvssrerapr orgjrra fnlvat "A qbrf abg rkvfg" naq fnlvat "A vf rdhny gb mreb".
Vf "pbeerpg" gvrq gb n fvatyr cnegvphyne pubvpr nf va Nnl,Orr,Prr, be Qrr? Be vf vg gvrq gb n fvatyr inyhr, gjragl svir creprag be svsgl creprag be fvkgl creprag? Be vf vg gvrq gb zhygvcyr inyhrf be pubvprf sbe fbzr nepnar ernfba?
Njxjneq ynpx bs ahzoref nobir qhr gb vanovyvgl gb rssrpgviryl ebg13.
Strange loops FTW! Anyway, the tricky part is defining what "correct" means in this case. Oh, and here is my answer.
Gur pbeerpg (naq fgnoyr) nafjre vf mreb creprag, juvpu vf pbeerpg, orpnhfr mreb creprag vf abg ninvynoyr nf na nafjre :C
I came up with this answer, too. Also, this post really made my morning.
A fun little exercise in dissolving a problem. Relatively quick, but it can wake you up on a slow day.
http://www.memedroid.com/share-meme/337837/8000