Zeno Machine
In mathematics and computer science, Zeno machines (abbreviated ZM, and also called Accelerated Turing machine, ATM) are a hypothetical computational model related to Turing machines that allows a countably infinite number of algorithmic steps to be performed in finite time. These machines are ruled out in most models of computation.
More formally, a Zeno machine is a Turing machine that takes 2-n units of time to perform its n-th step; thus, the first step takes 0.5 units of time, the second takes 0.25, the third 0.125 and so on, so that after one unit of time, an infinite number of steps will have been performed.
The idea of Zeno machines was first discussed by Hermann Weyl in 1927; they are named after the ancient Greek philosopher Zeno of Elea. Zeno machines play a crucial role in some theories. The theory of the Omega Point devised by physicist Frank J. Tipler, for instance, can only be valid if Zeno machines are possible.
Read more about Zeno Machine: Zeno Machines and Computability
Famous quotes containing the word machine:
“But a man must keep an eye on his servants, if he would not have them rule him. Man is a shrewd inventor, and is ever taking the hint of a new machine from his own structure, adapting some secret of his own anatomy in iron, wood, and leather, to some required function in the work of the world. But it is found that the machine unmans the user. What he gains in making cloth, he loses in general power.”
—Ralph Waldo Emerson (1803–1882)