Random Walk

Enumerating many attempts to make wiki hosting easier. Reflecting on the many dead ends in this years-long random walk over possible solutions feels discouraging. Why is this so difficult?

We want to plot a timeseries where the data points shows up as they happen. We'll model this a random walk always from the same starting point. mdn mdn

In absence of any energy input, the system progressed essentially via a Random Walk, taking an expected time of Θ(n2) to advance n steps.

FRANK, Michael P., 2005. Introduction to Reversible Computing: motivation, progress, and challenges. In: Proceedings of the 2nd conference on Computing frontiers. Ischia Italy: ACM. 4 May 2005. p. 385–390. ISBN 978-1-59593-019-4. DOI 10.1145/1062261.1062324. [Accessed 18 March 2024].

For the examples Bennett studied, even if the random walk is biased in the forwards direction by a small energy input, to achieve a linear rate of progress, the performance is still very low—Bennett [4] gave the biological example of DNA polymerization, which (under normal conditions, such as during cell division) proceeds at a rate on the order of only 1,000 nucleotides per second, with a dissipation of ~40kBT per step.

[…] So the question becomes, can we engineer reversible systems that have lower energy coefficients than DNA? It turns out that we already have.