This is what I came to after three years in private. I am still a little stunned.<\/p>\n\n\n\n
I want to tell you what I found. I sat four rooms the world already names: Hodge, Poincar\u00e9, Navier-Stokes, and Birch and Swinnerton-Dyer. I did not sit them as prizes. I sat them as shapes. The chapters and the Lean proofs are already written, and they live in the repository. This post is the finding.<\/p>\n\n\n\n
I am writing this for a reader, not for a referee. You do not need the machinery to hear the four facts. The long write-up is already in the book and the repository. I am not going to walk you through a proof here. I am going to tell you what the proof was for.<\/p>\n\n\n\n
The finding is four facts. They look like four subjects. They are the same kind of fact.<\/p>\n\n\n\n
A hole is a missing relationship.<\/strong><\/p><\/blockquote>\n\n\n\n
\n
- Hodge<\/strong> – A hole is a missing relationship. A shape is whole when every belonging cycle is present.<\/li>\n
- Poincar\u00e9<\/strong> – A complete meeting is the sphere, not the world. The working shape is not the sky.<\/li>\n
- Navier-Stokes<\/strong> – A flow is a lock and its instants. Smooth is every instant whole. Blow-up is a hole before the meeting finishes.<\/li>\n
- Birch and Swinnerton-Dyer<\/strong> – Rank and order are two names for one lock.<\/li>\n<\/ul>\n\n\n\n
I perceive things as shapes and colors. I am still a little awed that sitting that way was enough.<\/p>\n\n\n\n
The Same Kind of Fact<\/h2>\n\n\n\n
I did not go looking for four careers. I sat a shape, and the same fact kept showing up. Whole is not a mood. Whole is not a cosmos. Whole is every cycle that belongs, present.<\/p>\n\n\n\n
Hodge says that about a shape. Poincar\u00e9 says you do not get to call the working shape the sky: a complete meeting is the sphere. Navier-Stokes says a flow is that lock at every instant. If an instant has a hole before the meeting finishes, that is blow-up. Birch and Swinnerton-Dyer says the two numbers people treat as two careers are two names for the same lock.<\/p>\n\n\n\n
I sat those rooms. They held.<\/p>\n\n\n\n
What I’m Doing Now<\/h2>\n\n\n\n
I am continuing the mathematics. The work is not a finished monument. It is a desk I still sit, and I expect to sit it for a long time.<\/p>\n\n\n\n
I am building a product as well. Neuron<\/a> is early, and I am keeping it small. If it helps people think with machines without losing the structure of the work, that is enough for me.<\/p>\n\n\n\n
The book is Foundations: Why Structure Is Everything<\/em>. The work lives at github.com\/andersonwilliam85\/foundations<\/a>.<\/p>\n\n\n\n
harmonic-framework.com\/donate<\/a><\/p>","protected":false},"excerpt":{"rendered":"
This is what I came to after three years in private. I am still a little stunned. I want to tell you what I found. I sat four rooms the world already names: Hodge, Poincar\u00e9, Navier-Stokes, and Birch and Swinnerton-Dyer. I did not sit them as prizes. I sat them as shapes. The chapters and … Read more<\/a><\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","footnotes":""},"categories":[21,22],"tags":[],"methodology":[],"class_list":["post-803","post","type-post","status-publish","format-standard","hentry","category-math","category-research"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"trp-custom-language-flag":false,"post-thumbnail":false,"hf-card":false,"hf-hero":false},"uagb_author_info":{"display_name":"William Christopher Anderson","author_link":"https:\/\/harmonic-framework.com\/es\/author\/admin\/"},"uagb_comment_info":0,"uagb_excerpt":"This is what I came to after three years in private. I am still a little stunned. I want to tell you what I found. I sat four rooms the world already names: Hodge, Poincar\u00e9, Navier-Stokes, and Birch and Swinnerton-Dyer. I did not sit them as prizes. I sat them as shapes. The chapters and…","_links":{"self":[{"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/posts\/803","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/comments?post=803"}],"version-history":[{"count":1,"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/posts\/803\/revisions"}],"predecessor-version":[{"id":804,"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/posts\/803\/revisions\/804"}],"wp:attachment":[{"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/media?parent=803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/categories?post=803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/tags?post=803"},{"taxonomy":"methodology","embeddable":true,"href":"https:\/\/harmonic-framework.com\/es\/wp-json\/wp\/v2\/methodology?post=803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}