Search results for tag #topology
Having sat with the notion for about six months now, I think Jay's critique of the Church-Turing thesis has legs. I don't see clearly yet exactly where and how the limits of computation manifest in his own system(s), which of course they must. But I think he's correct that this thesis as it's colloquially presented (and taught to students, including me!) is misleading at best and false in a certain important sense. Apparently he is regularly called a crackpot for forwarding this critique even though it's straightforwardly demonstrated.
Waaldijk's book is more of a constructive mathematics exploration. In this it is closely related to computer science, but it's focused on traditionally mathematical notions like topological space. The latter is usually quite complicated, but Waaldijk shows that the core concept of compact space can be represented with finitely-branching trees, making these spaces amenable to computation. Since we imagine physics taking place in spaces that are topological (among other things) there's potentially an interesting bidirectional flow of ideas between computer science and physics.
Jay calls his central notion "natural trees". Waaldijk calls his central notion "natural spaces". In both cases I think the intended sense is "with minimal artifice".
Well done and thorough article on gift-wrapping stratagems evidently aimed at a population more versed in math(s) than we are. Informative and entertaining.
"When you place your gift onto the paper, rotate it so it sits diagonally in the centre of the paper. Then carefully bring the four corners of the paper into the centre, tucking in the tabs at each corner of your box under the larger flaps as you fold them in. You should be able to secure the paper with just three small pieces of tape, and if you're using stripey paper, the pattern may even match up at the joins."
https://www.bbc.com/future/article/20251212-how-maths-can-help-you-wrap-your-presents-better?utm_source=firefox-newtab-en-us
I'd like to have easy to switch paper disks on an axis. An "obvious" solution would be to cut pices of a spiral where the beginning and the end just overlap, so they only get off when turned to the direction of the axis.
But how do I cut/produce such pieces so that they remain flat when on the axis?!
#topology
Alt...
Dr. Zoidberg: You kids and your topology!