I feel that you are redefining terms. Writing down mathematical equations (or defining other mathematical structures that are not equations, e.g., automata), describing natural phenomena, and proving some properties of these, i.e., deriving some mathematical conjectures/theorems, -- that’s exactly what physicists do, and they call it “doing physics” or “doing science” rather than “doing mathematics”.
I mean “natural” as opposed to “man made”. i.e. something like “occurs in nature without being built by something or someone else”. So in that sense, DNNs are obviously not natural in the way that the laws of physics are.
I wonder how would you draw the boundary between “man-made” and “non-man-made”, the boundary that would have a bearing on such a fundamental qualitative distinction of phenomena as the amenability to mathematical description.
According to Fields et al.’s theory of semantics and observation (“quantum theory […] is increasingly viewed as a theory of the process of observation itself”), which is also consistent with predictive processing and Seth’s controlled hallucination theory which is a descendant of predictive processing, any observer’s phenomenology is what makes mathematical sense by construction. Also, here Wolfram calls approximately the same thing “coherence”.
Of course, there are infinite phenomena both in “nature” and “among man-made things” the mathematical description of which would not fit our brains yet, but this also means that we cannot spot these phenomena. We can extend the capacity of our brains (e.g., through cyborgisation, or mind upload), as well as equip ourselves with more powerful theories that allow us to compress reality more efficiently and thus spot patterns that were not spottable before, but this automatically means that these patterns become mathematically describable.
This, of course, implies that we ought to make our minds stronger (through technical means or developing science) precisely to timely spot the phenomena that are about to “catch us”. This is the central point of Deutsch’s “The Beginning of Infinity”.
Anyway, there is no point in arguing this point fiercely because I’m kind of on “your side” here, arguing that your worry that developing theories of DL might be doomed is unjustified. I’d just call these theories scientific rather than mathematical :)
I feel that you are redefining terms. Writing down mathematical equations (or defining other mathematical structures that are not equations, e.g., automata), describing natural phenomena, and proving some properties of these, i.e., deriving some mathematical conjectures/theorems, -- that’s exactly what physicists do, and they call it “doing physics” or “doing science” rather than “doing mathematics”.
I wonder how would you draw the boundary between “man-made” and “non-man-made”, the boundary that would have a bearing on such a fundamental qualitative distinction of phenomena as the amenability to mathematical description.
According to Fields et al.’s theory of semantics and observation (“quantum theory […] is increasingly viewed as a theory of the process of observation itself”), which is also consistent with predictive processing and Seth’s controlled hallucination theory which is a descendant of predictive processing, any observer’s phenomenology is what makes mathematical sense by construction. Also, here Wolfram calls approximately the same thing “coherence”.
Of course, there are infinite phenomena both in “nature” and “among man-made things” the mathematical description of which would not fit our brains yet, but this also means that we cannot spot these phenomena. We can extend the capacity of our brains (e.g., through cyborgisation, or mind upload), as well as equip ourselves with more powerful theories that allow us to compress reality more efficiently and thus spot patterns that were not spottable before, but this automatically means that these patterns become mathematically describable.
This, of course, implies that we ought to make our minds stronger (through technical means or developing science) precisely to timely spot the phenomena that are about to “catch us”. This is the central point of Deutsch’s “The Beginning of Infinity”.
Anyway, there is no point in arguing this point fiercely because I’m kind of on “your side” here, arguing that your worry that developing theories of DL might be doomed is unjustified. I’d just call these theories scientific rather than mathematical :)