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<DIV><FONT size=2>As the webpage was to do with calculating sizes in =
the
universe it would be interesting to know just how many tuners there are =
to see
how good or bad the math's is in the prediction dept of astronomy
.</FONT></DIV>
<DIV>Brian</DIV>
<DIV> </DIV>
<DIV><BR> </DIV>
<BLOCKQUOTE
style="BORDER-LEFT: #000000 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: =
0px; PADDING-LEFT: 5px; PADDING-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A href="mailto:Billbrpt@AOL.COM" =
title=Billbrpt@AOL.COM>Billbrpt@AOL.COM</A>
</DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A =
href="mailto:pianotech@ptg.org"
title=pianotech@ptg.org>pianotech@ptg.org</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> 10 January, 2002 05:17 =
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: How many piano =
tuners are
there in Chicago?</DIV>
<DIV><BR></DIV><FONT face=arial,helvetica><FONT size=2>In a =
message dated
1/10/02 8:48:30 AM Central Standard Time, <A
href="mailto:jgunderson@monmouth.com">jgunderson@monmouth.com</A> =
(John
Gunderson) writes: <BR><BR><BR>
<BLOCKQUOTE
style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; =
MARGIN-RIGHT: 0px; PADDING-LEFT: 5px"
TYPE="CITE">Just in case you were wondering. <BR><BR></FONT><FONT
color=#000000 face=Arial lang=0 size=3
FAMILY="SANSSERIF"></BLOCKQUOTE><BR></FONT><FONT color=#000000 =
face=Arial
lang=0 size=2 FAMILY="SANSSERIF"><BR>Here is what I read on this =
website:
<BR><BR><<As a lecturer, Enrico Fermi used to challenge his =
classes with
problems that, at first glance, seemed impossible. One such problem =
was that
of estimating the number of piano tuners in Chicago given only the =
population
of the city. When the class returned a blank stare at their esteemed
professor, he would proceed along these lines:</FONT><FONT =
color=#000000
face=Arial lang=0 size=3 FAMILY="SANSSERIF"> =
<BR><BR></FONT><FONT
color=#000000 face=Arial lang=0 size=2 =
FAMILY="SANSSERIF">From the almanac, we
know that Chicago has a population of about 3 million =
people.</FONT><FONT
color=#000000 face=Arial lang=0 size=3 FAMILY="SANSSERIF"> =
<BR></FONT><FONT
color=#000000 face=Arial lang=0 size=2 =
FAMILY="SANSSERIF">Now, assume that an
average family contains four members so that the number of families in =
Chicago
must be about 750,000.</FONT><FONT color=#000000 face=Arial =
lang=0 size=3
FAMILY="SANSSERIF"> <BR></FONT><FONT color=#000000 face=Arial =
lang=0 size=2
FAMILY="SANSSERIF">If one in five families owns a piano, there will =
be 150,000
pianos in Chicago.</FONT><FONT color=#000000 face=Arial lang=0 =
size=3
FAMILY="SANSSERIF"> <BR></FONT><FONT color=#000000 face=Arial =
lang=0 size=2
FAMILY="SANSSERIF">If the average piano tuner</FONT><FONT =
color=#000000
face=Arial lang=0 size=3 FAMILY="SANSSERIF"> <BR></FONT><FONT =
color=#000000
face=Arial lang=0 size=2 FAMILY="SANSSERIF">serviced four =
pianos every day of
the week for five days</FONT><FONT color=#000000 face=Arial =
lang=0 size=3
FAMILY="SANSSERIF"> <BR></FONT><FONT color=#000000 face=Arial =
lang=0 size=2
FAMILY="SANSSERIF">rested on weekends, and</FONT><FONT =
color=#000000
face=Arial lang=0 size=3 FAMILY="SANSSERIF"> <BR></FONT><FONT =
color=#000000
face=Arial lang=0 size=2 FAMILY="SANSSERIF">had a two week =
vacation during the
summer,</FONT><FONT color=#000000 face=Arial lang=0 size=3 =
FAMILY="SANSSERIF">
<BR><BR></FONT><FONT color=#000000 face=Arial lang=0 size=2
FAMILY="SANSSERIF">then in one year (52 weeks) he would service =
1,500 pianos.
150,000/(4 x 5 x 50) = 150, so that there must be about 150 piano =
tuners in
Chicago.</FONT><FONT color=#000000 face=Arial lang=0 size=3
FAMILY="SANSSERIF"> <BR></FONT><FONT color=#000000 face=Arial =
lang=0 size=2
FAMILY="SANSSERIF">This method does not guarantee correct results; =
but it does
establish a first estimate which might be off by no more than a factor =
of 2 or
3--certainly well within a factor of, say, 10. >></FONT><FONT
color=#000000 face=Arial lang=0 size=3 FAMILY="SANSSERIF">
<BR><BR></FONT><FONT color=#000000 face=Arial lang=0 size=2
FAMILY="SANSSERIF">There seems to be a little problem with the math, =
here
(duh). 4 x 5 x 50 = 1000, not 150, for starters. Next, =
this idea
that a piano "tuner" would "tune" 4 pianos a day, 5 days a week would =
also
amount to 1,000 pianos, not 1,500. But this supposition would =
amount to
a rarity, not what an *average* piano technician would do. =
<BR><BR>First of
all, pianos need more than *just tuning*, as I'm sure we can all =
confirm.
I'd really question such a claim, that *anyone* really, only =
tuned 1,000
pianos every year, year after year. That would inevitably amount =
to a
*dis* service, not a good and honest way to make a living. =
Please don't
ask me to believe that there 150 of these guys running that kind of =
racket in
Chicago! <BR><BR>My off the cuff guess is there would be about 50 =
piano
technicians in Chicago. I'm not sure in this exercise if the 3 =
million
figure is just Chicago or the whole metro area that includes all the =
suburbs
or not. The PTG directory lists a total of 110 for both the =
Chicago and
Waukegan (a north suburb of Chicago) Chapters. Of course there =
may be
many people who are not PTG members. <BR><BR>But still, that list =
includes
people like Jack Greenfield and Virgil Smith whom I'm quite certain =
don't tune
20 pianos a week, 1,000 a year. Then, there are people like Alan =
Vincent
who run a company and do belly work and hardly ever tune and people =
like Kurt
Saphir who probably *sells* 1,000 pianos a year and also rarely do any =
tuning.
<BR><BR>Wouldn't an easier and more accurate way of determining this =
number be
to look in the phone book and count the names, then add maybe 10% for =
those
who don't list themselves? <BR><BR>Bill Bremmer RPT <BR>Madison, =
Wisconsin
<BR><A href="http://www.billbremmer.com/">Click here: -=w w w . b =
i l l b r e
m m e r . c o m =-</A> </FONT></FONT></BLOCKQUOTE></BODY></HTML>