The Swelling Pin hole Conundrum

[Howard S. Rosen]

Hi Jim,

We have a problem with semantics here. I believe you misunderstood my
IMPOSSIBLE. 

> Try this howard, get one of your spare old keys and find a
> balance rail pin, or nail, that fits the hole.  Now wet the hole and set
the
> key aside for a few minutes......does the pin still fit in the hole? 

I never questioned that the hole will change when the wood is moistened.
That is not germane to my point. I think you mistakenly said in your last
post on this issue, that the cicumference is increased while the diameter
is decreased (or vice versa). I only responded with my IMPOSSIBLE statement
which was that these measurements (diameter and circumference) as we know
and use them,  are directly proportional to each other. It is impossible
for one to increase while the other decreases. 

>If not
> what happened to impossible ?

You see, Jim? You are assuming that I think it's impossible for the balance
rail hole to change. Not true  of course. However, if the hole shrinks,
then the circumference is smaller AND the diameter is smaller. If the hole
becomes larger, then the circumference is larger AND the diameter is
larger. No circle,  whether it be a piano key balance rail hole or a
rhubarb pie can have one dimension increase while the other decrease. It
has nothing to do with pianos or wood etc. Pure semantics.

>  Now let the key thoroughly dry..... does it fit the hole now?
> Is my contention, re: presented paradox, still impossible?

YES!  It is absolutely impossible for the circumference of a circle to
increase while the diameter decreases. Your example does not disprove my
point. It correctly illustrates that the piano balance rail hole does
change with changes in moisture.

>   Remember we are speaking of a living substance and not an abstract
line.

It doesn't matter. These dimensions of a circle are directly proportional
to each other.
If this living substance changes every 2 minutes it does not alter the fact
that these dimensions are directly proportional to each other.

> Cicumference relates to diameter directly but not to 'inside' diameter
> needfully.

I do not understand this statement. The diameter of a circle is the longest
distance
from one edge of the circle to the other, that cuts it in half. What are
you thinking of when you say 'inside' diameter? Please forgive this tedious
post, but let me sum up my point by saying that if the hole gets bigger,
then BOTH diameter AND circumference will get bigger, and vice versa.  

IT IS IMPOSSIBLE FOR THE CIRCUMFERENCE OF ANY CIRCLE TO BE THE INVERSE OF
ITS  DIAMETER 

Best regards, Jim

Howard S. Rosen, RPT
Boynton Beach, Florida