{"action":"created","issue":{"url":"https://api.github.com/repos/JuliaDiff/ForwardDiff.jl/issues/66","labels_url":"https://api.github.com/repos/JuliaDiff/ForwardDiff.jl/issues/66/labels{/name}","comments_url":"https://api.github.com/repos/JuliaDiff/ForwardDiff.jl/issues/66/comments","events_url":"https://api.github.com/repos/JuliaDiff/ForwardDiff.jl/issues/66/events","html_url":"https://github.com/JuliaDiff/ForwardDiff.jl/issues/66","id":113172339,"number":66,"title":"Define ForwardDiffNumber <: Real","user":{"login":"jrevels","id":3277443,"avatar_url":"https://avatars.githubusercontent.com/u/3277443?v=3","gravatar_id":"","url":"https://api.github.com/users/jrevels","html_url":"https://github.com/jrevels","followers_url":"https://api.github.com/users/jrevels/followers","following_url":"https://api.github.com/users/jrevels/following{/other_user}","gists_url":"https://api.github.com/users/jrevels/gists{/gist_id}","starred_url":"https://api.github.com/users/jrevels/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jrevels/subscriptions","organizations_url":"https://api.github.com/users/jrevels/orgs","repos_url":"https://api.github.com/users/jrevels/repos","events_url":"https://api.github.com/users/jrevels/events{/privacy}","received_events_url":"https://api.github.com/users/jrevels/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"milestone":null,"comments":14,"created_at":"2015-10-24T17:06:17Z","updated_at":"2015-10-29T18:00:35Z","closed_at":null,"body":"See discussion [here](https://github.com/JuliaStats/Distributions.jl/pull/430/files#r42935897).\r\n\r\nDoes anybody have any practical arguments for why we *shouldn't* do this?"},"comment":{"url":"https://api.github.com/repos/JuliaDiff/ForwardDiff.jl/issues/comments/152267129","html_url":"https://github.com/JuliaDiff/ForwardDiff.jl/issues/66#issuecomment-152267129","issue_url":"https://api.github.com/repos/JuliaDiff/ForwardDiff.jl/issues/66","id":152267129,"user":{"login":"goretkin","id":581043,"avatar_url":"https://avatars.githubusercontent.com/u/581043?v=3","gravatar_id":"","url":"https://api.github.com/users/goretkin","html_url":"https://github.com/goretkin","followers_url":"https://api.github.com/users/goretkin/followers","following_url":"https://api.github.com/users/goretkin/following{/other_user}","gists_url":"https://api.github.com/users/goretkin/gists{/gist_id}","starred_url":"https://api.github.com/users/goretkin/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/goretkin/subscriptions","organizations_url":"https://api.github.com/users/goretkin/orgs","repos_url":"https://api.github.com/users/goretkin/repos","events_url":"https://api.github.com/users/goretkin/events{/privacy}","received_events_url":"https://api.github.com/users/goretkin/received_events","type":"User","site_admin":false},"created_at":"2015-10-29T18:00:35Z","updated_at":"2015-10-29T18:00:35Z","body":"(re-add deleted comment since it's quoted. I had deleted it because I panicked about not finding a reference to Dual numbers as intervals and forgetting exactly how they work.)\r\n\r\nI hope this comment doesn't distract from the main discussion, but I want to mention that you can also make Dual numbers to work as interval arithmetic (where instead of maintaining upper and lower bounds, the non-epsilon part is the center of the interval, and the epsilon part is the radius). I think it is nifty that the same algebraic properties gives you both an \"Interval Number\" and a \"Forward Diff\" number of order 1. I don't know if a hyperdual number behaves in any other interesting ways, but I just wanted to point out that Dual numbers do more than strictly AD in the space of practical numerics outside the realm.\r\n\r\nWhat that's an argument for, I'm not totally sure. But this same discussion probably would happen again regarding Interval arithmetic. Except that AD/differentiation is used a ton ton more than interval arithmetic."}}