tag:blogger.com,1999:blog-9818962.post745612896056156366..comments2024-03-20T13:10:11.477+05:30Comments on nanopolitan: N-dimensional Spheres in N-dimensional BoxesAbihttp://www.blogger.com/profile/06790560045313883673noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-9818962.post-143464132143005712011-12-05T19:51:18.968+05:302011-12-05T19:51:18.968+05:30@Ankur and @Digbijoy:
At least for the point Abi ...@Ankur and @Digbijoy:<br /><br />At least for the point Abi highlighted here, offhand, I think that it should be a simple exercise to supply a kind of a "visualization"---an abstract visualization, to be sure, but still, a visualization. Give it a try, and see how the logic Hayes presents might become much directly graspable.<br /><br />(If you would like to have a hint about this possible "visualization" idea, drop me a line, though, frankly, I don't think that a hint is all that necessary. ... BTW, I haven't actually tried working out Hayes' cases using it, but, guess, it should work out OK.)<br /><br />--Ajit<br />[E&OE]Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9818962.post-64967096279839939542011-12-05T12:32:13.976+05:302011-12-05T12:32:13.976+05:30@Digbijoy In fact, that is why they are useful! Th...@Digbijoy In fact, that is why they are useful! They allow us to address things that we are not equipped to or accustomed to imagine. And that is where the next challenges lie.Ankur Kulkarnihttps://www.blogger.com/profile/16411971742511540520noreply@blogger.comtag:blogger.com,1999:blog-9818962.post-12667616615338263082011-12-05T04:59:29.664+05:302011-12-05T04:59:29.664+05:30I never understand anything beyond 3 dimensions, n...I never understand anything beyond 3 dimensions, no matter how beautiful or elegant their description is mathematically ! Unless we can imagine or visualize, abstract things like n-dimensional space are of little 'use' to science or technology. But they are fun to work on mathematically, I agree.Digbijoy Nathhttps://www.blogger.com/profile/00676969785957849229noreply@blogger.com