| > What percentage of coders do programming on a turing tape? Is this partial evidence that turing tapes are trash? Does that question even make sense? ZFC should be more like machine code we actually use than turn tape concept which we don't. The fact that no one uses something higher level that compiles down to ZFC is disheartening. As the FOM mailing list demonstrates, it's really about goal posts here. For one camp, the goal posts are such that ZFC or many other things are equally good. ZFC by share age has the "large cardinal" advantage in that people have been grinding away at it longer. For the other camp, large-cardinal-type research agendas aren't very interesting, and the goal posts are dramatically different. I still think ZFC is trash, but I will admit my mistake in thinking other share my goal posts. > The abstractions of category theory are useless in many areas of mathematics. For example, PDEs. At the moment that is true. But I think this is more due to the human concerns than the actually Math. Until Statistics overtook it, differential equalization were the most-applied branch of mathematics, which definitely influenced the culture around it. There is also the general algebraist---analyst cultural divergence. I look forward to the day when the computer tools are so good they are used in those fields too. That should bridge the culture gap, and then we shall see what the math holds. |