tag:blogger.com,1999:blog-11295132.post3914585316859674717..comments2024-02-24T01:46:31.188-08:00Comments on A Neighborhood of Infinity: Counting Targets using the Euler Characteristic, Part 1sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-11295132.post-3042641576892788632010-01-11T14:05:25.066-08:002010-01-11T14:05:25.066-08:00Writing clearly is tough! Because of Conal's a...Writing clearly is tough! Because of Conal's advice I explicitly searched for vague pronoun referents and thought I had eliminated them.<br /><br />Anyway, I think special_property_2 is cool so keep at it!sigfpehttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-15774447106206378932010-01-11T11:48:13.884-08:002010-01-11T11:48:13.884-08:00Ah, that clears things up.
> Am I guilty of wh...Ah, that clears things up.<br /><br />> Am I guilty of what Conal Elliot now calls "vague pronoun referent"? <br /><br />Well, yes. I was confused as I thought "this" in the second sentence referred to the previous property. Now knowing what you actually meant, the sentence reads differently (when reading out loud, there seems to be an emphasis on "this property").Shin no Noirhttps://www.blogger.com/profile/08974372500960094990noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-32654613551396347972010-01-11T10:32:58.592-08:002010-01-11T10:32:58.592-08:00Am I guilty of what Conal Elliot now calls "v...Am I guilty of what Conal Elliot now calls "vague pronoun referent"? The 'this' refers to the following property, not the one on the line before.<br /><br />A count function would be completely invariant under scaling.<br /><br />gsum isn't completely invariant. But it *does* have the alternative transformation property I describe.<br /><br />To make this absolutely unambiguous, compare<br /><br />gsum test1<br /><br />with<br /><br />gsum (2 `scale` test1).<br /><br />The return value of gsum changes by a factor of 2^2.sigfpehttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-4707697826999979842010-01-11T05:35:08.658-08:002010-01-11T05:35:08.658-08:00Sigfpe, is the following part correct?
> So we...Sigfpe, is the following part correct?<br /><br />> So we'd also like this property:<br />> count (n `scale` f ) = count f<br />> It's easy to see that that gsum actually has this property for n > 0:<br />> gsum (n `scale` f ) = n^2 * gsum f<br /><br />As I understand, you want count to remain invariant under scaling, but the function gsum <b>does not</b> have this property?Shin no Noirhttps://www.blogger.com/profile/08974372500960094990noreply@blogger.com