# Blog Post Ideas 1. R2 vs R, data generating processes (get some of these thoughts catalogued, or at least on paper? this seriously is an interesting question/post to dig into) 2. [Dimensionality reduction intuitions (compare methods)](Dimensionality%20reduction%20intuitions%20(compare%20methods).md) 4. Skin in the game mathematics (if you have a probability of death > 0%, your expected result is 0) 5. Kelly Criterion - time vs ensemble probability (see talk given by ole peters) 6. How does the gaussian work (cancellation process) 7. Fourier and Laplace transform intuitions (maybe even applied to generating functions) 8. How does recursion exploit repetitive structure 9. high dimensionality 10. information content of a function, of a language (JW and unsupervised conversation) 11. Geometry of hash functions 12. Geometric progressions and limiting distributions/linear transformations (Shape) 13. Random walk and recurrence in 1, 2 but not 3 dimensions (see 155 Model Thinker) 14. Relationship of linear algebra and graph structures. Viewing graphs as linear transforms (how does that compare to traditional graph algorithms?), this may not be necessary if the previous post cleared everything up. 1. See BFS implementation via linear algebra (here) 15. How graphs have trees embedded within them 16. Topological sort orders vertices on a line such that all edges go from left to right. This seems like we are trying to find an embedding. How does this relate to embeddings in the general sense? 17. Topology, transformations of space, linear separability, UMAP (manifold approximation). See great post from colah, [here](https://colah.github.io/posts/2014-03-NN-Manifolds-Topology/). Specifically, he has a line: "We want points of the same manifold to be closer than points of others, as opposed to the manifolds being separable by a hyperplane. This should correspond to inflating the space between manifolds for different categories and contracting the individual manifolds. It feels like simplification." -> This idea seems to be worth exploring with some nice visualizations. How would we "inflate space"? How does this relate to UMAP or manifold learning, based on your understanding? To KNN? 18. Covariance matrix as a transformation/data generating process (see spectral clustering notability, covariance_matrix_as_transformation notebook). 19. Blog post on randomness (random projections, evolution chance preface the blind watch maker, JL lemma, random algorithms, mcmc, probability space, etc) 20. Transformations of Spaces and coordinate systems 21. [Physics vs Machine Learning](Physics%20vs%20Machine%20Learning.md)