I would quickly start believing someone was smart if they repeatedly drew conclusions that looked wrong, but which I would later discover are correct. I would believe they were smarter than me if, as a rule, whenever they and I are presented with a problem, they reach important milestones in the solution or dissolution of the problem quicker than I can, even without prior knowledge of the problem.
Concrete example: xkcd #356 includes a simple but difficult physics problem. After a long time (tens of minutes) beating my head against it, letting it stew (for months, at least), and beating my head against it again (tens of minutes), I’d gotten as far as getting a wrong answer and the first part of a method. Using nothing but a verbal description of the problem statement from me, my dad pulled out the same method, noting the problem with that method which I had missed finding my wrong answer, within five minutes or so. While driving.
(I’ve made no progress past that insight—rot13: juvpu vf gung lbh pna (gel gb) fbyir sbe gur pheerag svryq sebz n “fbhepr” be “fvax” bs pheerag, naq gura chg n fbhepr-fvax cnve vagb gur argjbex naq nqq Buz’f-ynj ibygntrf gb trg gur erfvfgnapr—since the last time I beat my head against that problem, by the way.)
The canonical method is to nggnpu n pheerag qevire gb rirel abqr.
Jevgr qbja gur Xvepubss’f ynj ynj rirel abqr va grezf bs gur vawrpgrq
pheerag, gur ibygntr ng gung ybpngvba, naq gur ibygntr ng rnpu nqwnprag
cbvag. Erjevgr gur nqwnprag ibygntrf va grezf bs genafyngvba bcrengbef,
gura qb n (frzv-qvfpergr) Sbhevre genafsbez (gur qbznva vf vagrtref,
pbqbznva obhaqrq serdhrapvrf, fb vg’f gur bccbfvgr bs n Sbhevre frevrf),
chg va gur pbaqvgvbaf sbe n havg zntavghqr fbhepr naq fvax, naq vaireg
vg, juvpu jvyy tvir lbh gur ibygntrf rireljurer. Gur qvssreraprf va
ibygntrf orgjrra gur fbhepr naq fvax vf gur erfvfgnapr, orpnhfr gurer vf
havg pheerag sybjvat npebff gurz.
I’m not wnoise, but yeah, you probably wouldn’t want to read the (now great-)great-grandparent. Put it this way: the first 5 words are ‘The canonical method is to.’ (I read it anyway ’cuz I’m spoiler resistant. I don’t think my math/EE aptitude is enough to carry out the method wnoise gives.)
I know little about it, but if I knew how to compute equivalent resistances beyond the basics of resistors in parallel and in series, I’d fbyir n ohapu bs rire-ynetre svavgr tevqf, fbeg bhg gur trareny rkcerffvba sbe na A-ol-Z tevq jvgu gur gnetrg abqrf nyjnlf ng gur pragre, naq gura gnxr gur yvzvg nf A naq Z tb gb vasvavgl.
You can try Xvepubss’f pvephvg ynjf, but at the moment I’m thinking of nffhzvat gung nyy pheeragf sybj njnl sebz zl fbhepr naq qrgrezvavat ybjre naq hccre yvzvgf ba gur pheeragf V arrq onfrq ba gubfr vardhnyvgvrf.
The problem doesn’t say anything about sources, so I’m not sure what I’m supposed to assume for voltage or current. Can you recommend a good instructional primer? I need something more that Wikipedia’s infodump presentation.
I’m using the term as a metaphor from fluid dynamics—n fbhepr vf n abqr va juvpu pheerag vf vawrpgrq jvgubhg rkcyvpvgyl gnxvat vg bhg naljurer ryfr—orpnhfr gur flfgrz vf vasvavgr, pheerag nqqrq ng n abqr pna sybj bhg gb vasvavgl gb rssrpgviryl pbzcyrgr gur pvephvg, naq orpnhfr gur rdhngvbaf ner flzzrgevp, gur svany fbyhgvba sbe gur pheerag (sebz juvpu Buz’f ynj sbe ibygntr naq ntnva sbe rssrpgvir erfvfgnapr) pna or gubhtug bs nf gur fhz bs n cbfvgvir fbhepr ng bar raqcbvag naq n artngvir fbhepr (n fvax) ng gur bgure.
I don’t know how this compares to wnoise’s canonical method—it might be that this is a less effective path to the solution.
I would quickly start believing someone was smart if they repeatedly drew conclusions that looked wrong, but which I would later discover are correct. I would believe they were smarter than me if, as a rule, whenever they and I are presented with a problem, they reach important milestones in the solution or dissolution of the problem quicker than I can, even without prior knowledge of the problem.
Concrete example: xkcd #356 includes a simple but difficult physics problem. After a long time (tens of minutes) beating my head against it, letting it stew (for months, at least), and beating my head against it again (tens of minutes), I’d gotten as far as getting a wrong answer and the first part of a method. Using nothing but a verbal description of the problem statement from me, my dad pulled out the same method, noting the problem with that method which I had missed finding my wrong answer, within five minutes or so. While driving.
(I’ve made no progress past that insight—rot13: juvpu vf gung lbh pna (gel gb) fbyir sbe gur pheerag svryq sebz n “fbhepr” be “fvax” bs pheerag, naq gura chg n fbhepr-fvax cnve vagb gur argjbex naq nqq Buz’f-ynj ibygntrf gb trg gur erfvfgnapr—since the last time I beat my head against that problem, by the way.)
Bah. I was hoping your dad gave the actual answer. That’s as far as I got too. :)
He suggested fbyivat n frevrf grez-ol-grez zvtug or arprffnel but I didn’t know precisely what he meant or how to do it.
The canonical method is to nggnpu n pheerag qevire gb rirel abqr. Jevgr qbja gur Xvepubss’f ynj ynj rirel abqr va grezf bs gur vawrpgrq pheerag, gur ibygntr ng gung ybpngvba, naq gur ibygntr ng rnpu nqwnprag cbvag. Erjevgr gur nqwnprag ibygntrf va grezf bs genafyngvba bcrengbef, gura qb n (frzv-qvfpergr) Sbhevre genafsbez (gur qbznva vf vagrtref, pbqbznva obhaqrq serdhrapvrf, fb vg’f gur bccbfvgr bs n Sbhevre frevrf), chg va gur pbaqvgvbaf sbe n havg zntavghqr fbhepr naq fvax, naq vaireg vg, juvpu jvyy tvir lbh gur ibygntrf rireljurer. Gur qvssreraprf va ibygntrf orgjrra gur fbhepr naq fvax vf gur erfvfgnapr, orpnhfr gurer vf havg pheerag sybjvat npebff gurz.
Buggrit. Build a grid of resistors a few meters square and pull out the multimeter.
That works fairly well, as things converge quickly.
Wait, so if I want to solve it myself, I shouldn’t read the text in the great-grandparent of this comment?
Well, yes, that’s why I rot13d it. I’ll unrot13 the beginning which will provide a clear warning.
I’m not wnoise, but yeah, you probably wouldn’t want to read the (now great-)great-grandparent. Put it this way: the first 5 words are ‘The canonical method is to.’ (I read it anyway ’cuz I’m spoiler resistant. I don’t think my math/EE aptitude is enough to carry out the method wnoise gives.)
Thanks!
I know little about it, but if I knew how to compute equivalent resistances beyond the basics of resistors in parallel and in series, I’d fbyir n ohapu bs rire-ynetre svavgr tevqf, fbeg bhg gur trareny rkcerffvba sbe na A-ol-Z tevq jvgu gur gnetrg abqrf nyjnlf ng gur pragre, naq gura gnxr gur yvzvg nf A naq Z tb gb vasvavgl.
You can try Xvepubss’f pvephvg ynjf, but at the moment I’m thinking of nffhzvat gung nyy pheeragf sybj njnl sebz zl fbhepr naq qrgrezvavat ybjre naq hccre yvzvgf ba gur pheeragf V arrq onfrq ba gubfr vardhnyvgvrf.
At this rate I’m going to be proficient at reading rot13 within a week!
I’m intentionally not reading anything in rot13 and always using the electronic translator, with hopes that I will not become proficient.
The problem doesn’t say anything about sources, so I’m not sure what I’m supposed to assume for voltage or current. Can you recommend a good instructional primer? I need something more that Wikipedia’s infodump presentation.
I’m using the term as a metaphor from fluid dynamics—n fbhepr vf n abqr va juvpu pheerag vf vawrpgrq jvgubhg rkcyvpvgyl gnxvat vg bhg naljurer ryfr—orpnhfr gur flfgrz vf vasvavgr, pheerag nqqrq ng n abqr pna sybj bhg gb vasvavgl gb rssrpgviryl pbzcyrgr gur pvephvg, naq orpnhfr gur rdhngvbaf ner flzzrgevp, gur svany fbyhgvba sbe gur pheerag (sebz juvpu Buz’f ynj sbe ibygntr naq ntnva sbe rssrpgvir erfvfgnapr) pna or gubhtug bs nf gur fhz bs n cbfvgvir fbhepr ng bar raqcbvag naq n artngvir fbhepr (n fvax) ng gur bgure.
I don’t know how this compares to wnoise’s canonical method—it might be that this is a less effective path to the solution.
That is definitely part of the method.
I can see why my idea is incompatible with your approach.