Thank you for sharing SDG. I haven't heard it mentioned in many years. The simplification power it provides is beautiful! [1]
I'm elated over having delighted and filled you with music. Your kind words have made me beam from ear to ear as well :-)
I think the intuitive power of these other formulations comes from the spatial/geometric imagery that these disciplines naturally provide. Another aspect is the conversion of unwieldy processes into simpler objects. Like nonstandard analysis replacing the limit process with the infinitesimal object.
The paradigm of replacing large processes with things that can be intuited might not be very profound if as programmers we bring up first class functions. A function is just an object anyhow! True but the human mind seems to be less efficient at composing functions than composing objects. So though it's all interchangable, we seem to work better when we are given mentally ergonomic foundations.
Back to what you said in your previous posts, the ease of manipulation in these alternative theories, it probably lends a bit from this exchange of complicated processes for simpler things.
I'm elated over having delighted and filled you with music. Your kind words have made me beam from ear to ear as well :-)
I think the intuitive power of these other formulations comes from the spatial/geometric imagery that these disciplines naturally provide. Another aspect is the conversion of unwieldy processes into simpler objects. Like nonstandard analysis replacing the limit process with the infinitesimal object.
The paradigm of replacing large processes with things that can be intuited might not be very profound if as programmers we bring up first class functions. A function is just an object anyhow! True but the human mind seems to be less efficient at composing functions than composing objects. So though it's all interchangable, we seem to work better when we are given mentally ergonomic foundations. Back to what you said in your previous posts, the ease of manipulation in these alternative theories, it probably lends a bit from this exchange of complicated processes for simpler things.
[1] https://en.wikipedia.org/wiki/Synthetic_differential_geometr...