From: gisle@ifi.uio.no (Gisle Hannemyr)
Subject: Re: PV equation
Organization: gisle@ifi.uio.no
Date: Sun, 15 Nov 1992 19:17:18 GMT
Originator: gisle@gyda.ifi.uio.no

In article <goD5TB2w165w@throb.mcws.fidonet.org> hardman@throb.mcws.fidonet.org (Bill Hardman) writes:

> gisle@ifi.uio.no (Gisle Hannemyr) writes:

>> [[ The story so far: ph36@unixg.ubc.ca (Richard Nistuk) has come across
>>    a really weird equatuion in "Dianetics", and want somebody to explain
>>    it to him.  The equation is:
>> 
>>                    PV=I*D^x
>> 
>>    and we later learn that:
>>       PV = potential value of an individual or group
>>       I  = intelligence (presumably IQ)
>>       D  = the "Dynamic".  This is a number between 1 and 4
>>            indicating where the individual are within 4 "dynamics".
>>       x  = the magnitude on which the person is surviving on the
>>            dynamic, it is a number between 1 and 10
>> 
>>    Mr. Nistuk's basic question is "How do you apply the equation?",
>>    to which Mr. Hardman gives the snappy answer "Insert the known
>>    factors and use standard algebra".  This doesn't seem to satisfy
>>    Mr. Niestuk, who keeps bringing up a strange thing called "units".
>>    Now -- let's return to the discussion...]]


>> Bill:
>>> To keep it simple for you, try using units of 1 to 10 [[for x?]].
>>> The unit [[of the Dynamic]] is between 1 and 4.

>> Eh, Bill, I think you've missed something really basic somewhere
>> along the line.  The word "unit", you see, is short for "unit
>> of measurement", and is usually expressed in terms such as 
>> "seconds","kilos" "meters", "volts" or whatever.  Numbers that
>> doesn't have units, such as "1", "4" and "10" is referred to as
>> "unitless".
>> 
>> Units play a fairly significant part in standard algebra, where the
>> SI (Systeme International d'Unites) devised to keep the units used
>> in equations consistent.
>> 
>> For example, the equation for speed is
>> 
>>                      s = At
>>     where
>>            meaning            unit
>>        ---------------------------------------
>>        s = speed              1 meter/second
>>        A = accelaration       1 meter * second^-2
>>        t = time               1 second
>> 
>>      now if we want to compute the speed of an object beeing
>>      accelarated by earth's gravity (9.8 ms^-2) in vacuum
>>      in 10 seconds we get:
>> 
>>      s = 9.8 ms^-2 * 10 s = 98 ms^-1 = 98 meter/second
>> 
>> Please note that the algebra not only involved the quantities,
>> but also the units, and that the unit of the answer became
>> meter/second (meters per. second), which is a unit of measurement
>> for speed.

Bill:
> Please note that you assigned the unit.  You assigned meters, and
> seconds as the unit measures.  If you would have observed that in
> the beginning, you wouldn't need long winded explanations of the
> obvious.

No, Bill, I didn't assign the units.  When I learnt about this equation
in high school, the text book that told me how to apply the equation
also told me which units to use.

In his very first posting, Richard Nistuk pointed out that the basic
problems with the equation as it is expressed by L. Ron Hubbard, is
that in his textbook, Hubbard doesn't tell you what units to use, or
how to measure the values.  The implication is of course that Mr.
Hubbards claims about his theories being "science" must be taken with
a pinch of salt if not even simple questions like these can be
answered satisfactorily.

Sometimes selecting appropriate units is trivial.  Sometimes it isn't.
For example -- if you do physics calculations involving temperature
using degrees Celcius or Farhenheit as your unit of measurement, you
may get some strange results.  Using degrees Kelvin usually works much
better.  I would say that finding appropriate units for the PV
equation is a non-trivial matter.


> You could also substitute like units of measure and the
> equation would still work, wouldn't it?

Yes -- there are a number of alternative systems that all work.  Some
physics textbooks uses imperial units and will tell you how to apply
this speed equation using inches instead of meters.  With imperial
units, the numbers become different, but the equations still work.

Now let's try it out:
Let's to some for speed calculations for the speed of an object
accelarated in vacuum for 10 seconds on two planets with
different gravities:

                Planet A                         Planet B
            metric      imperial            metric     imperial
Gravity:  9.8 ms-^2   385.8 is^-2          4.9 ms-^2  192.9 is-^2
Time:      10 s        10   s               10 s       10   s
Speed      98 m/s     3858  i/s             49 m/s    1929  i/s

Let's compute the relative speed between the object accelarated
at planet A and B for both our metric and our imperal measurements.

          Metric:     98 ms^-1 /   49 ms^-1 = 2
          Imperial: 3858 ms^-1 / 1929 ms^-1 = 2

Note that it didn't matter which units we used -- in both cases we get
the same results -- that objects would fall twice as fast on planet A
than on B.  Because computing relative values cancels the units, this
is what you should expect.  The realtive values are unitless, and
therefore we should get the _same_ answer no matter what system was
used for the measurement and the original computation (that is -- if
the unit system and the theory behind equation make sense in the first
place).

Now, let's return to the PV equation:

	      PV=I*D^x

and compute the potential value of two persons in unit system X (since
we don't know what they are, I'll leave out their symbols).

               Person A   Person B
           I:        70        156
           D:         3          3
           x:         8          6
          PV:    459270     113724

Let's do it again, using another range of values for x.  (i.e. using a
different unit measurement for x), this new unit happens to be exactly
a tenth of the previous one, so we get (in unit system Y):

               Person A   Person B
           I:        70        156
           D:         3          3
           x:       0.8        0.6
          PV:     168.6      301.6

Now let's compute the relative PV of these two persons:

          Unit system X: 459270 / 113724 = 4.04
          Unit system Y:  168.6 /  301.6 = 0.56

Isn't this strange?  In one system, person A has a PV more than 4
times that of person B.  If I use another system, his PV computes to
56% of that of B?  Which is correct?  And why do this equation exhibit
the strange feature that we get different results depending upon the
range used for values of x?

As always, Bill, I am looking forward to your explanation.


PS:  I apologize for ascribing the term "out-gradient" to you.
     As others has pointed out -- it was Jonathon who used that
     expression.

--
Meta-disclaimer: A society that needs disclaimers has too many lawyers.
 
- gisle hannemyr  (Norsk Regnesentral)
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