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Sorry, I didn't see your reply to this until just now. I hope that you get a chance to see mine: I have to disagree that nomenclature being fractured is not the problem. Within any given field, it is true that as you go deep enough into how things work, it gets complicated and hectic. However, as we have done throughout the entire written history of humanity, we have a special set of tools to help us engage with those complications, and reduce them down to complexes of simple objects whose behavior we understand - mathematics. If we are unable to reach deeply enough within a single field, it is because the tools we teach are not up to the task. A large part of the issue is that the mathematics in common use in these disciplines, and at the elementary level, is in need of an upgrade. That upgrade is in the process of being performed (category theory), and as we learn to apply it in more and more fields, concepts and processes that seem deep, difficult, and essentially different turn out to be related in mathematically precise 'analogies'. This means that the same set of 'deep concepts', applied with different sets base objects and different operators that obey the same rules, will unfold into some of the main ideas in each discipline. Baez's Physics, Logic, Topology, Computation, a Rosetta stone is a good example of the beginnings of this, but googling 'applied category theory' or 'applied category theory course azimuth' ought to bring you some interesting extra links. More generally, what we see of as specific processes within a particular field, when viewed through the right lenses, I expect we will find are instead instantiations of much more general processes that are the same across most, if not all, fields of discipline. How will we convince everyone to use these different naming systems and toolsets? Because those people who do use them will perform better, and the logic of competition will pull the educational system and society along with them. If you disagree, I'd love to hear more about it. Nomenclature and Education are near and dear to me - I always jump and an opportunity to discuss with someone who does so in good faith. |