Think Differently(ltlprints.com)
ltlprints.com
Think Differently
http://www.ltlprints.com/blog/think-differently/
11 comments
Nope: http://www.snopes.com/college/exam/barometer.asp
This story maintains its value whether fact or fiction.
I think there's a degree of deception involved when you try to pin stories like these to actual people. If you leave out the last line, yes, the story has value. But the fabricated link makes one more likely to dismiss the story as junk.
Сказка ложь да в ней намек
Добрым молодцам урок.
Tale of sense, if not of truth!
Food for thought to honest youth.
As italians say, "se non è vero, è ben trovato". ("Even if it is not true, it is well conceived")
I had a similar experience as an undergraduate, except that I didn't get the marks: I was taking a course on differential equations, and one of the final exam questions was to demonstrate that a solution existed to a given system.
I gave a very elegant non-constructive proof which showed that a solution existed without giving any hint of what the solution was -- but the instructor expected students to provide a solution. I ended up deciding that it wasn't worth the effort of formally appealing the grade, but I still think that I should have gotten the marks -- it wasn't my fault that the exam didn't ask the question the instructor intended to ask.
I gave a very elegant non-constructive proof which showed that a solution existed without giving any hint of what the solution was -- but the instructor expected students to provide a solution. I ended up deciding that it wasn't worth the effort of formally appealing the grade, but I still think that I should have gotten the marks -- it wasn't my fault that the exam didn't ask the question the instructor intended to ask.
I had a similar experience when taking functions of a complex variable, where a midterm problem asked you to show that a solution existed and several students (not me, alas) found a non-constructive proof that worked without actually finding a solution. Unlike in your case, though, the professor gave all of them full credit.
I had good math professors. Too bad I wasn't a good math student.
I had good math professors. Too bad I wasn't a good math student.
it wasn't worth the effort of formally appealing the grade
If the question actually asked to demonstrate that a solution existed, any professor worth her salt will give you credit for doing that if you point it out to her. It's quite possible you weren't given full marks because your exam was one of hundreds that needed to be graded that week.
If the question actually asked to demonstrate that a solution existed, any professor worth her salt will give you credit for doing that if you point it out to her. It's quite possible you weren't given full marks because your exam was one of hundreds that needed to be graded that week.
Not only is this older than the web, but the fact that it's a bunch of made-up bullshit undermines its point.
Whenever someone exhorts you to "think outside the box", they usually, for your convenience, point out exactly where "outside the box" is located. Isn't it funny how nonconformists all dress the same...
- http://www.overcomingbias.com/2007/10/outside-the-box.html
- http://www.overcomingbias.com/2007/10/outside-the-box.html
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It is funny how we are being taught other people's truth as opposed to digging for our own. And then magically when you get to college or the working field they want you to come up with answers to real problems. Well "I don't remember being taught how to think for myself, but let me Google the answer".
Does anyone else remember this from the pilot episode of "Head of the Class"?
Here is how I would do the puzzle about barometer:
PV = nRT; n = m/M
PV = mRT/M; V = m/(rho)
p*m/(rho) = mRT/M
p/(rho) = RT/M
(rho) = pM/RT
p + (dp) = p + (rho)g(dh)
(dp) = (rho)g(dh)
(dp) = pMg(dh)/RT
(dp)/p = Mg(dh)/RT
integrate 0 to p (dp)/p = integrate h to 0 [Mg(dh)/RT]
ln(p) = -Mgh/RT + c
take h = 0 at bottom of building, then
ln(p_at_h=0) = c => read c from barometer to get constant
now, at height h we will read p_at_h=height from barometer, then:
ln(p_at_h=height) = -Mgh/RT + ln(p_at_h=0)
Mgh/RT = -ln(p_at_h=height) + ln(p_at_h=0)
Mgh = -RTln(p_at_h=height) + RTln(p_at_h=0)
-----------------------------------------------------------------------------
| height = -RTln(p_at_h=height)/Mg + RTln(p_at_h=0)/Mg =
| = RT/Mg(ln(p_at_h=0) - ln(p_at_h=height)) =
| = RT/Mg(ln(p_at_h=0/p_at_h=height))
-----------------------------------------------------------------------------
p in Pascals
g = 9.81
R = 8.31
T = temperature in absolute units
M = 28.97
I hope i did it right ;)
PV = nRT; n = m/M
PV = mRT/M; V = m/(rho)
p*m/(rho) = mRT/M
p/(rho) = RT/M
(rho) = pM/RT
p + (dp) = p + (rho)g(dh)
(dp) = (rho)g(dh)
(dp) = pMg(dh)/RT
(dp)/p = Mg(dh)/RT
integrate 0 to p (dp)/p = integrate h to 0 [Mg(dh)/RT]
ln(p) = -Mgh/RT + c
take h = 0 at bottom of building, then
ln(p_at_h=0) = c => read c from barometer to get constant
now, at height h we will read p_at_h=height from barometer, then:
ln(p_at_h=height) = -Mgh/RT + ln(p_at_h=0)
Mgh/RT = -ln(p_at_h=height) + ln(p_at_h=0)
Mgh = -RTln(p_at_h=height) + RTln(p_at_h=0)
-----------------------------------------------------------------------------
| height = -RTln(p_at_h=height)/Mg + RTln(p_at_h=0)/Mg =
| = RT/Mg(ln(p_at_h=0) - ln(p_at_h=height)) =
| = RT/Mg(ln(p_at_h=0/p_at_h=height))
-----------------------------------------------------------------------------
p in Pascals
g = 9.81
R = 8.31
T = temperature in absolute units
M = 28.97
I hope i did it right ;)
What is the conventional way to do it?
just guessing: record pressure at bottom of building, record at top, whip out a table and find the height. I think this is how they used to determine the elevation of mountains.
" I think this is how they used to determine the elevation of mountains."
And also by years and years of meticulous surveying,
The Great Arc by John Keay tells the story of how the height of the world's tallest peak was measured.
Hint: You start from zero and work your way up :-)
And also by years and years of meticulous surveying,
The Great Arc by John Keay tells the story of how the height of the world's tallest peak was measured.
Hint: You start from zero and work your way up :-)
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nice story.
this story rocks and if you disagree you're probably a tedious person.