johnhw.github.io/umap_primes/index.md.html

This is the first million integers, represented as binary vectors indicating their prime factors, and laid out using the UMAP dimensionality reduction algorithm by Leland McInnes. Each integer is represented in a high-dimensional space, and gets squished down to 2D so that numbers with similar prime factorisations are closer together than those with dissimilar factorisations.

# What do numbers look like?  ## A view of a million integers This is the first million integers, represented as binary vectors indicating their prime factors, and laid out using the [UMAP dimensionality reduction algorithm](https://github.com/lmcinnes/umap) by Leland McInnes. Each integer is represented in a high-dimensional space, and gets squished down to 2D so that numbers with similar prime factorisations are closer together than those with dissimilar factorisations. A very pretty structure

related reading

• Understanding UMAP – Topos Institutetopos.institute
• What Is a UMAP — and Why Do Scientists Love It?alleninstitute.org
• [1802.03426] UMAP: Uniform Manifold Approximation and Projection for Dimension Reductionarxiv.org
• Visualizing Algorithmsbost.ocks.org
• How to Use t-SNE Effectivelydistill.pub
• Functions are Vectorsthenumb.at
• Self-organizing map - Wikipediaen.wikipedia.org
• AlignedUMAP for Time Varying Data — umap 0.5.8 documentationumap-learn.readthedocs.io
• Dimensionality reduction in neural data analysisxcorr.net
• A short survey on almost orthogonal vectors in a few specific large dimensionsarxiv.org
• Tim Gowers - Two culturesdpmms.cam.ac.uk
• unit-distance-remarks.pdfcdn.openai.com