Amazing to see 'magnitude' on the front page of Hacker News! If you are interested in a direct application of this invariant beyond ecology, check out our recen

Amazing to see 'magnitude' on the front page of Hacker News! If you are interested in a direct application of this invariant beyond ecology, check out our recent pre-print in which we study the generalisation behaviour of neural networks: https://arxiv.org/abs/2305.05611 https://arxiv.org/abs/2305.05611 My personal approach to magnitude is not based on category theory but rather based on weightings of a metric space. If your metric satisfies certain properties, you can obtain a measure of the 'effective number of points' of a metric space. This is particularly relevant when looking at the metric space from different scales---zooming in gives you a lot of disconnected points, while zooming out gives you clusters. Magnitude then captures the changes in the number of points in a principled manner.