Manhattan distance, also known as city block distance, is the number of units one must traverse to get from point X to point Y along a grid-like path. Each step involves a change in value across exactly one dimension. In machine learning, Manhattan distance is often preferred over higher values of $p$ for high-dimensionality data due to simpler computation and relative robustness against the curse of high dimensionality. More formally, let $x_i$ be the value of point X across the $i$-th dimension, and let $y_i$ be the value of point Y across the $i$-th dimension. In $n$ dimensions, the Manhattan distance between points X and Y is: $d(X,Y) = \sum_{i=1}^n|x_i - y_i|$. This metric is an instantiation of the Minkowski distance formula where $p=1$.