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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

728.0. "You CAN'T get a hole in one . . ." by PFLOYD::ROTHBERG () Wed Jul 08 1987 04:39

                I was  reading a book the other night by Allister
                Crowley called "The  Book  of  Thoth".    In this
                book, it states that  by using math, it is proved
                that a golf ball can  not  be  hit.  How is that?
                (Looks like some physics might be  involved  here
                too).
T.RTitleUserPersonal
Name		DateLines
728.1KIRK::KOLKERConan the LibrarianWed Jul 08 1987 11:559
    re .0
    
    Perhaps he is restating a paradox of Zeno.  For the golf club to
    hit the ball it has to arc half the angular distance to the ball.
    Then half the remaining distance, and half the remaining distance
    and so on. Therefore the club never gets to the ball.
    
    Zeno didn't know from limits.
728.2you can hit a ball, but hole-in-one becomes impossibleVIDEO::OSMANtype video::user$7:[osman]eric.sixThu Jul 09 1987 19:0636
He might also be referring to Heisenberg's uncertainty principle, which
states that the product of what we know about a piece of mass's momentum
and mass has an upperbound on accuracy.

(because data such as location, mass, momentum etc. are actually probability
functions, not absolute numbers, so when we say "the golf ball is here",
we're fudging.  More accurately, we should say "with probability 99.999%,
the golf ball is between here and 1.000001 inches away from here")

The example I once saw involved attempting to drop a pingpong ball on
another pingpong ball glued to a table.  The object is to accurately
design a smooth ball and accurately drop it from a vertical position
such that the number of times it bounces off the fixed ball before
bouncing away is maximized.

The Heisenberg uncertainty principle applied to the mass of the ball says
that no matter how accurately we measure, we'll never guarantee that
the ball will bounce more than FIVE times before missing.

In other words, due to the accumulated errors on each bounce, the accuracy
with which we'd have to aim the first bounce in order to guarantee more
than five bounces is more accuracty than the Heisenberg Uncertainty Principle
allows us to "know" the location, velocity, smoothness of a pingpong ball.

So, applying this to a hole-in-one, I see no problem with managing to HIT
the ball.  However, even in no air, smooth ball, a hole sufficiently small
or sufficiently far away from ball would be impossible to GUARANTEE a
hole-in-one for, again because to do so would mean being more precise about
the stroke speed, force, mass of ball etc., than Heisenberg allows us to
know.

I guess it's analagous to asking "How many times must I flip a fair coin
to guarantee that the ratio of heads to tails differs from the expected
1.00 by no more than X % ?"

/Eric