tag:blogger.com,1999:blog-3679812208800765969.post5039147534361793299..comments2012-05-25T17:36:44.028-07:00Comments on monoidal: The universal spaceghttp://www.blogger.com/profile/04686862403622560424noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3679812208800765969.post-85942807613965564722010-12-24T00:01:14.275-08:002010-12-24T00:01:14.275-08:00I wrote a more formal and full definition of unive...<a href="http://hpaste.org/42527/universal_space_vector_space" rel="nofollow">I wrote a more formal and full definition of universal space in Haskell.</a>beroalhttps://www.blogger.com/profile/13229768366613602827noreply@blogger.comtag:blogger.com,1999:blog-3679812208800765969.post-72624252174527041702010-12-23T07:27:33.622-08:002010-12-23T07:27:33.622-08:00In fact you can enlarge the space. Define an objec...<em>In fact you can enlarge the space. Define an object to be either a vector with mass 0, or a pair (p,m) which is a point p with a nonzero mass m. I'll write a point as m*p.</em><br />Using another sign for a point with a mass would be less ambiguous. The formula "weighted mean of points" seems not typable then. I believe that it should be<br /><br />m0#p0 + m1#p1 = if m0+m1==0<br /> then &m1*(p1-p0)<br /> else (m0+m1)#((m1/(m0+m1))*(p1-p0) + p0)<br /><br />where m#p is a point p with a mass m. We are using only subtraction of points, as required by the rigorous definition.<br /><br />I wonder, if interpreting a vector as having 0 mass really means something. I can not imagine a limit transition "point->vector" while "mass->0".beroalhttps://www.blogger.com/profile/13229768366613602827noreply@blogger.com