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Science 26 January 1968:
Vol. 159. no. 3813, pp. 396 - 406
DOI: 10.1126/science.159.3813.396
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Articles

Are "Infinity Machines" Paradoxical?

Can processes involving an infinite sequence of operations or "acts" be completed in a finite time?

Adolf Grünbaum 1

1 Philosophy at the University of Pittsburgh, Pittsburgh, Pennsylvania

The mathematical physicist Hermann Weyl (2) has claimed that, unless machines can accomplish an infinite sequence of distinct operations in a finite time, the standard mathematical theory of motion is beset by one of Zeno's kinematical paradoxes. Hence I have compared the kinematics of several such "infinity machines" to the kinematics of the continuous motion of Achilles. And I have argued that, while some designs for infinity machines are indeed inconsistent, others are not impossible on purely kinematical grounds. This argument was coupled with several reasons for denying Zeno's and A. N. Whitehead's allegation of paradox against the mathematical, description of the motion of Achilles.

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Science. ISSN 0036-8075 (print), 1095-9203 (online)