🚀 go-pugleaf

In article <3kkvt7$h5j@utdallas.edu>,  <son3776@utdallas.edu> wrote:
>Thomas S. Zemanian (ts_zemanian@pnl.gov) wrote:
>
>> Allow me to suggest that there really can be no consensus on this issue at
>> this point.  "Son" from UT/Dallas is in too deeply now to back down and
>> still save face, although it's rapidly becoming clear to me that he is
>> mistaken.  I'll try one last attempt, and if this fails to settle the issue
>> I recommend we all let this drop.
>
>> If we are to distinguish whether pi be a physical or a mathematical
>> constant (or both, as some have recently suggested), we must have some way
>> to distinguish the two.  I feel that a physical constant would be one which
>> is determined by a measurement, whereas a mathematical constant should drop
>> out of a mathematical argument.  This is the gist of the
>> circles-on-curved-surfaces arguments that have been batted back and forth.
>
>> Now, we can calculate the value of pi, in theory, to arbitrary precision. 
>> The precision of a physical measurement, by constructing a huge circle, is
>> maximized by making as large a circle as possible and measuring the
>> circumference and radius as accurately as possible.  However, given a
>> finite universe (I hope we can agree on that, but if not, how about a
>> finite region of space accessible to us to build a circle within...) and a
>> limit due to quantum uncertainty in how well we can measure the
>> circumference and diameter of that circle, we see that we can never measure
>> pi as precisely as we can calculate it.  How, then, can pi _possibly_ be a
>> physical constant?
>
>> It's just a number.
>
>The fact that we can't measure it to total accuracy does not exclude it 
>from being a physical constant.
>
>Elementary charge is a physical constant with a computational value of 
>1.60e-19C and a *best* (1986) value of 1.60217738e-19C with an 
>uncertainty of .30 parts per million.  Even though we still haven't 
>measured this to an exact accuracy, we still consider it to be a physical 
>constant . . . so saying that we can't measure pi to a certain degree of 
>accuracy does not mean that pi is not a physical constant.

Take a deep breath, now: pi can be calculated to any arbitrary
precision desired. So far this has been done to some milion decimal
places. That's because it is a mathematical constant.

Electrical charge can only be determined by experiment. That's because
it's physical constant.

Got it?

-- 


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