Paul Lowrance wrote:
Stephen A. Lawrence wrote:
>
>
> Charles M. Brown wrote:
>> Feynman's ratchet used one sprung pawl on a ratchet wheel. The spring
>> biases the pawl towards the ratchet wheel so mechanical pressure on
>> the gentle slope of the ratchet wheel drives the wheel the wrong way
>> where it can rest against the sharp or even overhanging slope. If the
>> pawl is then lifted by Brownian motion and the ratchet wheel moves a
>> little the wrong way when the pawl is high, possible 50% of the time,
>> than the wheel will rotate the wrong way. If the ratchet wheel moves a
>> little the right way when the pawl is high, possible 50% of the time,
>> then the pawl will return to a low part of the gentle slope near the
>> sharp slope.
>> If there are many pawls on one ratchet wheel than they do not have to
>> be biased by springs because the probability is high, and increases
>> exponentially with the number of pawls, that at least one pawl of a
>> similar position group will be in position to block counter rotation
>> of the ratchet wheel. This type of system should behave like a larger
>> scale mechanically rectified ratchet wheel at thermal power levels.
>>
>> I don't think Feynman tried hard enough to break the Second Law.
>> Fabricating a device that fails with inadequate design doesn't prove
>> that a better design won't work.
>
> Indeed, you can't prove a theorem with examples, no matter how many
> examples you have; using an example can only serve to disprove it (if
> the example happens to violate it).
>
> One of my big flops in school was thermo -- I dropped the course at the
> point where the textbook presented a "proof" of something or other which
> I simply could not follow. As far as I could see the proof didn't prove
> anything -- and when I asked about it during the next lecture, well,
> that's when I found out the professor was /deaf/. There I was, sitting
> in the hall, in a front row seat, with the prof struggling to hear my
> question -- he walked over to stand right in front of my chair with his
> hand cupped around his ear and had me repeat it, really loud, for about
> the fourth time -- with 200 other students sitting in stunned silence in
> back of me. Finally the prof went back up to the board and answered the
> wrong question 'cause he never had managed to hear what I was asking.
>
> And so I filled out a drop slip and sold the textbook and never did
> really learn the subject, beyond Feynman's brief treatment in his
> physics lectures.
>
>
>> Classical treatment of Feynman's ratchet:
>>
>> http://www.eleceng.adelaide.edu.au/Groups/parrondo/ratchet.html
>>
>> Aloha,
>>
>> Charlie
>>
>
>
Was the teacher just playing with you so he did not have to answer your
question regarding proof?
No, I don't think so -- he was a shaky old geezer and really was
apparently almost stone deaf. I don't know why he didn't use a hearing aid.
I was the first student in that class that term to ask a question during
a lecture, so I was the one who got to make the big discovery. (Or
maybe everybody else already knew, which is why there were never any
questions...)
In any case the fact that I didn't understand the proof doesn't "prove"
the theorem was false -- it just shows I didn't understand it ...
However, with 20/20 hindsight I think it's very likely the /textbook/
was wrong, and the proof may very well have been broken, whether or not
the theorem was correct. I was a callow youth and hadn't yet learned
that most textbooks are crawling with errors.
My favorite tale of a text with errors took place in analysis class. We
were struggling with a professor's book notes rather than a real
textbook (professors love to torture their students with drafts of their
nascent textbooks). We were working through the "book" one chapter at a
time, and each week, in recitation section, the TA's would hand out a
thin sheaf of pages containing the /corrections/ to that week's chapter.
Well, one week we all filed into the room, and there was this big
stack of papers sitting on the TA's desk, and when they start handing
out the corrections, they're handing us each a stack of paper a half
inch thick. And then they asked us all to _hand_ _in_ the original
version of chapter for that week -- they wanted it back; they were
replacing it, in its entirety! It seems the prof had "proved" a false
lemma at the very start of the chapter, and used it throughout the
chapter to prove everything else.
Not surprisingly, the replacement chapter was rather longer than the
original; assuming something that's false tends to make all your proofs
quite a bit shorter.
As it happens that particular (rather wretched) book never made it into
print, and we could all have saved a lot of pain by using some standard
text instead.
