Tao of Measurement
One idea that I hope to get
across in this book is that many of the realities we measure are continuous,
while our measurements our discrete. This
fact has been a problem for people who try to explain the number line as an
infinite set of points with no area. This
is actually nonsense because if you have a group of points, all of which
have no area, adding infinity to the mix doesn’t somehow create area out
of a group of arealess points. A
more logical view is that points have area, and dimension, and that the
amount of area or dimension is determined by the unit of measurement that is
specified when the measurement is made.
Here are some additional thoughts
on this topic:
I think one thing I want to make
clear in the section on time is that clocks, which were invented in the 13th
century, impose a completely arbitrary unit of measurement on what is
essentially a continuum. It really comes back to Zeno’s paradox – you
can’t get to continuity by adding the incoherent concept of infinity to a
group of discrete points. Also, the idea of a point in time is really
nonsense since every moment of time, no matter how small, has some duration.
I believe that points have area and the concept of an arealess point is a
The way out of Zeno’s paradox
is to require that every measurement have a unit of measurement specified,
whether it’s an inch, mile, kilometer, millimeter, or whatever. Granted
there can be fractions of an inch, but you can’t allow the unit of
measurement to get ever smaller and smaller, because that generates the
infinite regress. What is really going on in Zeno’s paradox is that the
unit of measurement is being shifted to something smaller each time a new
measurement is made.
I think that calendars make more
sense than clocks because they are at least tied to the rotation of the
earth and the cycles of day and night. Even so the days of the week are
pretty arbitrary. The days just come one after the other and there really is
nothing in nature corresponding to the week. I admit it would be chaos to
try to operate without the week, but it is a purely manmade invention.
There is nothing intrinsic to the day that makes a certain day a
Saturday – it simply falls into the seventh day of the never-ending
succession of seven-day weeks. We
could just as easily number the days 1 through 365, beginning with January 1
and ending with December 31. I
admit it would be hard to live without the weekend, but we could simply
designate days 6 and 7, 13 and 14, 20 and 21, etc. as “weekends.” Then
Day One would correspond to our Monday.
I am not advocating this system,
or suggesting that we do away with our “weeks.”
The point is simply to illustrate that the concept of a week is a
purely manmade idea that is imposed on reality – it is not somehow in the
nature of things that there are seven day weeks. The concept of the day
makes more sense, since it corresponds to the rising and setting of the sun,
and goes until the sun rises again. Of
course, our clocks have the day beginning one second after midnight, when
most people are either asleep or trying to catch up on their work.
I think my fundamental challenge
in the book is to show that time
and reality are both continuous in nature, and the discrete entities that
man has created to try to reign in this flowing continuum are partly bogus.
My fundamental thesis is that the infinitely discrete does not equal the
continuum. Maybe units have to be discrete but there should be a more
correct way to represent continuity than just a bunch of discrete segments.
I don’t think that anyone has yet captured the essence of continuity,
which is flow.
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