Wittgenstein's rod is a problem in geometry discussed by 20th-century philosopher Ludwig Wittgenstein.
Wittgenstein's rod is a problem in geometry discussed by 20th-century philosopher Ludwig Wittgenstein.
A ray is drawn with its origin A on a circle, through an external point S and a point B is chosen at some constant distance from the starting end of the ray; what figure does B describe when all the initial points on the circle are considered? The answer depends on three parameters: the radius of the circle, the distance from the center to S, and the length of the segment AB. The shape described by B can be seen as a 'figure-eight' which in some cases degenerates to a single lobe looking like an inverted cardioid.
If B remains on the same side of S with respect to the center of the circle, instead of a ray one can consider just a segment or the rod AB.
Wittgenstein sketched a mechanism and wrote:
While the point A describes a circle, B describes a figure eight. Now we write this down as a proposition of kinematics.
When I work the mechanism its movement proves the proposition to me; as would a construction on paper.
The proposition corresponds e.g. to a picture of the mechanism with the paths of the points A and B drawn in. Thus it is in a certain respect a picture of that movement. It holds fast what the proof shows me. Or – what it persuades me of.
This text has been included among the notes selected for publication in Remarks on the Foundations of Mathematics and the editors have dated in the as spring of 1944. [1]
Wittgenstein's rod is a generalization of Hoeckens linkage.
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Remarks on the Foundations of Mathematics is a book of Ludwig Wittgenstein's notes on the philosophy of mathematics. It has been translated from German to English by G.E.M. Anscombe, edited by G.H. von Wright and Rush Rhees, and published first in 1956. The text has been produced from passages in various sources by selection and editing. The notes have been written during the years 1937–1944 and a few passages are incorporated in the Philosophical Investigations which were composed later. When the book appeared it received many negative reviews mostly from working logicians and mathematicians, among them Michael Dummett, Paul Bernays, and Georg Kreisel. Today Remarks on the Foundations of Mathematics is read mostly by philosophers sympathetic to Wittgenstein and they tend to adopt a more positive stance.
