A Formal Statement of The Problem
The problem as stated above requires some assumptions to be made. The following fuller statement of the problem attempts to make most of those assumptions explicit.
- Consider a thin and infinitely stretchable rubber rope held taut along an -axis with a starting-point marked at and a target-point marked at, .
- At time the rope starts to stretch uniformly and smoothly in such a way that the starting-point remains stationary at while the target-point moves away from the starting-point with constant speed .
- A small ant leaves the starting-point at time and walks steadily and smoothly along the rope towards the target-point at a constant speed relative to the point on the rope where the ant is at each moment.
- Will the ant reach the target-point?
Read more about this topic: Ant On A Rubber Rope
Famous quotes containing the words formal, statement and/or problem:
“Then the justice,
In fair round belly with good capon lined,
With eyes severe and beard of formal cut,
Full of wise saws and modern instances;
And so he plays his part.”
—William Shakespeare (1564–1616)
“If we do take statements to be the primary bearers of truth, there seems to be a very simple answer to the question, what is it for them to be true: for a statement to be true is for things to be as they are stated to be.”
—J.L. (John Langshaw)
“The government is huge, stupid, greedy and makes nosy, officious and dangerous intrusions into the smallest corners of life—this much we can stand. But the real problem is that government is boring. We could cure or mitigate the other ills Washington visits on us if we could only bring ourselves to pay attention to Washington itself. But we cannot.”
—P.J. (Patrick Jake)