🚀 go-pugleaf

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.


--
"Somewhere else the tea's getting cold." -- The Doctor