Title: Fractals are not infinite? Post by: willvarfar on February 03, 2015, 09:41:53 AM http://motherboard.vice.com/read/a-new-proof-shows-how-some-spaces-cant-always-be-divided-into-smaller-spaces is a nice popular-science article.
Title: Re: Fractals are not infinite? Post by: asimes on February 03, 2015, 03:24:18 PM I interpreted it to mean that some spaces (or in our point of view some fractals) cannot be divided up evenly no matter how you try in higher dimensions
Title: Re: Fractals are not infinite? Post by: youhn on February 03, 2015, 05:46:41 PM Yes, not generalized to fractals but space. But the piece of text is not much worth on itself. Nothing is explained, no examples. The last words are a good indication for the rest of it:
Quote So, Manolescu came up with a whole new invariant, which he calls just "beta." Using beta, he was able to show a necessary discontinuity in some spaces, e.g. where things just didn't line up. As such, these spaces were to shown to be indivisible in the most complete sense. There is always something left over. Triangulation is a tool which can be used to calculate properties of spaces (real world example are the mesher programs in FEA methods). Now these triangles need to line up perfectly, and they won't allow rectangles or other shapes. This is no law, this is just convention. Now insert the meaning of "triangulation" into words like "cutting" and "splitting", after which you can say nonsense like "There Are Spaces That Cannot Be Divided" and allow the things to get stretched out of context even further. Just get me a piece of pie in whatever shape you like and a sharp knife ... Title: Re: Fractals are not infinite? Post by: PieMan597 on February 03, 2015, 06:00:35 PM Youhn, never!
I believe that because fractals are a mathematical construct and don't exist in the physical world without added approximation (ex. you can't zoom in forever and get more detail on a mountian), so you can cut them forever. Basically, you can cut the idea of something up forever, but not the actual thing. Title: Re: Fractals are not infinite? Post by: willvarfar on February 03, 2015, 07:53:13 PM But the piece of text is not much worth on itself. Nothing is explained, no examples. There are lots of links in the article, e.g. to the main paper http://arxiv.org/abs/1303.2354 Title: Re: Fractals are not infinite? Post by: Sockratease on February 03, 2015, 10:32:21 PM ... I believe that because fractals are a mathematical construct and don't exist in the physical world without added approximation (ex. you can't zoom in forever and get more detail on a mountian), so you can cut them forever. Basically, you can cut the idea of something up forever, but not the actual thing. I was going to say that, but I say that so much I was getting tired of typing it. Glad to see somebody else who konws the distinction between a real world object and a mathematical construct! Title: Re: Fractals are not infinite? Post by: quaz0r on February 04, 2015, 02:43:29 AM I believe that because fractals are a mathematical construct and don't exist in the physical world without added approximation (ex. you can't zoom in forever and get more detail on a mountian), so you can cut them forever. Basically, you can cut the idea of something up forever, but not the actual thing. try telling that to this wildberger guy http://youtu.be/WabHm1QWVCA (http://youtu.be/WabHm1QWVCA) he actually argues that math concepts are stupid and wrong if there isnt a real-world manifestation of them somewhere ;D |