anthony@utcsstat.UUCP (Anthony Ayiomamitis) (08/21/85)
>> The usual method of writing numbers (e.g. 10, .007) carries no information >> about accuracy. .007 could be accurate to one, two or three decimal places. > > This is getting rather off the point, but some of you might like >this. During one of my interviews for college, I was asked a typical >stupid interview question: "What's the area of a table 3 meters wide by 4 >meters long?" I poked around with various counter-probes like, "Do you >mean the area of just the top surface, or the top and bottom combined?" and >then came up with the obvious answer; 12 meters^2. > If someone tells me that something measures 3 by 4, I cannot tell whether they really mean 3 by 4, or 3.00 by 4.00, or 3.000 by 4.0, etc. However, the implicit assumption is that these dimensions are exact and, hence, a "reasonable" reply would be 12 square meters. Of course, if this question was asked on a written exam in the form of "3 by 4", then an answer of 1*10^1 square meters is indeed perhaps more appropriate. > Anyway, it turns out the "correct" answer is 1 * 10^1 meters^2; >since the initial data only had 1 digit of accuracy, that's all the final >answer can have. >-- >Roy Smith <allegra!phri!roy> >System Administrator, Public Health Research Institute >455 First Avenue, New York, NY 10016 -- {allegra,ihnp4,linus,decvax}!utzoo!utcsstat!anthony {ihnp4|decvax|utzoo|utcsrgv}!utcs!utzoo!utcsstat!anthony
trt@rti-sel.UUCP (Tom Truscott) (08/27/85)
> >... "What's the area of a table 3 meters wide by 4 > >meters long?" I poked around with various counter-probes like, "Do you > >mean the area of just the top surface, or the top and bottom combined?" and > >then came up with the obvious answer; 12 meters^2. I cannot see what is wrong with the 'obvious answer', and I cannot recall reading in any textbook the justifications used for the answer '1x10^1 m^2'. Even if we assume inexact measurements '12 m^2' is the best integral estimate. Perhaps I could be enlightened. If I tell you that a right triangle has sides of length 3 and 4 and ask you for the length of the hypotenuse are you going to answer '5' or are you going to worry about errors in measurement? If I ask you 'What is 6+7' are you going to answer 1x10^1?? If I ask you for 'the area of a table' are you going to chide me for asking a meaningless question? Are you going to assume I meant the area of an imaginary plane which has a good fit with the approximate surface of the table? Are you going to assume I meant the area of an idealized table which is flat and rectangular, and then assume I used a ruler accurate only to a half meter?? If that is the answer, then I am wrong and proud of it. Tom Truscott
inc@fluke.UUCP (Gary Benson) (08/29/85)
>>... "What's the area of a table 3 meters wide by 4 >> meters long?" I poked around with various counter-probes like, "Do you >> mean the area of just the top surface, or the top and bottom combined?" and >> then came up with the obvious answer; 12 meters^2. > I cannot see what is wrong with the 'obvious answer', > and I cannot recall reading in any textbook the justifications > used for the answer '1x10^1 m^2'. Even if we assume > inexact measurements '12 m^2' is the best integral estimate. > Perhaps I could be enlightened. > > If I tell you that a right triangle has sides of length 3 and 4 > and ask you for the length of the hypotenuse are you going > to answer '5' or are you going to worry about errors in measurement? > If I ask you 'What is 6+7' are you going to answer 1x10^1?? > > If I ask you for 'the area of a table' are you going to > ... assume I meant the area of an imaginary plane which has a good fit > with the approximate surface of the table? Are you going to assume I meant > the area of an idealized table which is flat and rectangular, and then > assume I used a ruler accurate only to a half meter?? If that is the answer, > then I am wrong and proud of it. > > Tom Truscott Right On! It always surprises me to see how applying a little common sense can make mathematical concepts more clear |-) Thanks for a breath of fresh air, Tom. It seems so droll and esoteric to insist that the table exists in some realm of thought unaffected by first rules. Your examples were all to the point, and nicely refute the eggheads' stubborn stance. It's those who argue the obverse who give science it's reputation for stogginess and indirection. Just sign me -- Wrong And Proud Of It, Too -- Gary Benson * John Fluke Mfg. Co. * PO Box C9090 * Everett WA * 98206 MS/232-E = = {allegra} {uw-beaver} !fluke!inc = = (206)356-5367 _-_-_-_-_-_-_-_-ascii is our god and unix is his profit-_-_-_-_-_-_-_-_-_-_-_
carl@aoa.UUCP (Carl Witthoft) (09/05/85)
In article <681@tpvax.fluke.UUCP> inc@fluke.UUCP (Gary Benson) writes: >> If I tell you that a right triangle has sides of length 3 and 4 >> and ask you for the length of the hypotenuse are you going >> to answer '5' or are you going to worry about errors in measurement? >> If I ask you 'What is 6+7' are you going to answer 1x10^1?? >> then I am wrong and proud of it. >> Tom Truscott > >Thanks for a breath of fresh air, Tom. It seems so droll and esoteric to >insist that the table exists in some realm of thought unaffected by first >rules. Your examples were all to the point, and nicely refute the eggheads' >stubborn stance. It's those who argue the obverse who give science it's reputation for stogginess and indirection. x x Before this stuff goes off any further, let me point out two things: 1) There's a big difference between the mathematical 3 and the scientific measurement 3 . Thus the stuff about triangles is irrelevant. 2) There's more to life than sig figs. While it is roughly true that a properly reported measurement of 3m by 4m does imply an error of +/-.5m on each measurement, it is NOT true that the result of any computation is allowed only *one sig fig*. The allowed error depends on the precision,i.e. percent uncertainty, of the inputs and on the computation done. It should be clear that the percent errors in "s=1m" and "s=8m" are different. Darwin's Dad (Carl Witthoft) ...!{decvax,linus,ima,ihnp4}!bbncca!aoa!carl @ Adaptive Optics Assoc., 54 Cambridgepark Dr. Cambridge, MA 02140 617-864-0201 " Buffet-Crampon R-13 , VanDoren B-45, and VanDoren Fortes ."
ark@alice.UucP (Andrew Koenig) (09/06/85)
Sounds like the name of a manicure shop to me.