Wittgenstein's rod is a geometry problem 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 of eight' which in some cases degenerates to a single lobe looking like an inverted cardioid.
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.
- Wittgenstein L., Remarks on the Foundations of Mathematics, edited by G.H. von Wright and Rush Rhees, Oxford: Blackwell 1998, ISBN 0-631-12505-1, sect V, §72, p.434
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