"almost certainly" I would go so far as to say certainly. Simply by bisecting the interval, we can achieve any arbitrarily small precision,!
Professor Mazur does an expert job of giving the behind-the-scenes wrangling of conceptual philosophy which gave rise to applied science. What is the
difference between time and motion exactly? If that question seems too
abstract, this book proves the opposite.
Most college graduates
assume that Zeno's paradoxes of motion were solved by calculus with its
continuous functions. Mazur puts the calculus at the heart of the book,
from Descartes and Cavalieri to Galileo, Newton and last but not least
Mazur's favorite: Gabrielle-Emilie de Breteuil.
In fact, upon
investigation, one finds many top scientists still studying and learning
from the anomalies in infinite measurement. Regarding relativity Mazur
states the wonder of absolute motion is that it "conspires with our
measuring instruments to prevent any possibility of detection."
As
Mazur points out "we don't measure with infinitesmial instruments" and
so the perceptual illusion of time continuity remains despite the
reliance of science on discrete symbols. With attempts at a unification
of quantum mechanics and relativity Zeno's paradoxes reemerge with
full-force in the "Calabi-Yau manifold." Mazur writes that the original
concept of dimension still holds but now means measuring more by
abstract reason than by sight.
Although each scientist featured
by Mazur appears to have increasingly solved the paradox of motion in
the end I think Zeno will be avenged and science will return to right
back where it started. There seems to be a deadlocked struggle between
discreteness (particle) and continuity (wave) in science and Mazur
argues that indeed Nature "makes jumps" despite seeming continuous. But
Mazur admits we are left with "splitting operations that can take place
only in the mind."
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