All Possible Paths

Full Title or Meme

When more than one path is possible, it is sometimes necessary to consider All Possible Paths or trajectories to get a complete solution.

Mathematics

The concept of "all possible paths" is often discussed in the context of graph theory and algorithms. One of the earliest and most well-documented references to this concept can be found in the field of computer science, particularly in the study of graph algorithms.

For example, the NetworkX documentation provides a detailed explanation of generating all simple paths in a graph from a source node to a target node. This involves using a modified depth-first search algorithm to explore all possible paths without repeating nodes.

If you're interested in a more practical example, you can check out the MathWorks documentation on calculating all paths between nodes in a graph using MATLAB. This resource provides examples and explanations on how to implement these algorithms.

Physics

The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This idea originated in 1948 with Feynman.