Wittgenstein's rod
Template:Short description Script error: No such module "Distinguish".
Wittgenstein's rod is a problem in geometry discussed by 20th-century philosopher Ludwig Wittgenstein.
Description
A ray is drawn with its origin Template:Mvar on a circle, through an external point Template:Mvar and a point Template:Mvar is chosen at some constant distance from the starting end of the ray; what figure does Template:Mvar 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 Template:Mvar, and the length of the segment Template:Mvar. The shape described by Template:Mvar can be seen as a 'figure-eight' which in some cases degenerates to a single lobe looking like an inverted cardioid.
If Template:Mvar remains on the same side of Template:Mvar with respect to the center of the circle, instead of a ray one can consider just a segment or the rod Template:Mvar.
Wittgenstein sketched a mechanism and wrote:
<templatestyles src="Template:Blockquote/styles.css" />
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.
Script error: No such module "Check for unknown parameters".
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]
Related mechanism
Wittgenstein's rod is a generalization of Hoeckens linkage.
Animations
Script error: No such module "Multiple image".
See also
- Oscillating cylinder steam engine — a steam engine using a Wittgenstein's rod scribing a figure-of-eight shape (it does not make use of the curve scribed)
References
- ↑ Wittgenstein L., Remarks on the Foundations of Mathematics, edited by G. H. von Wright and Rush Rhees, Oxford: Blackwell 1998, Template:ISBN, sect V, §72, p.434