Yes, I think this is a very interesting feature of your formalism. These “love” and “hate” are “abstract counters”, their relationship with subjective feelings is complicated.
But this might be the correct way to capture this “ethicophysics” (it is a frequent situation in modern physics that there is some tension between naive intuition and the correct theory (starting with relativistic space-time and such)).
Let″s interact, try to work together a bit, think together, this might be quite fruitful :-) Perhaps, I’ll actually earn a co-authorship, we’ll see :-)
This monotonicity (non-decrease in accumulated love and hate) is interesting (it resembles motifs from Scott topology used in denotational semantics).
And this decomposition into positive and negative components which evolve monotonically does resemble motifs in some of my math scribblings...
So, about the decomposition into positive and negative components which evolve monotonically:
So, basically, if one considers real numbers, one can define a strange non-Hausdorff topology on them, so that continuous transformations are monotocally non-decreasing functions, “continuous on the left”, and the open sets being open rays pointing upward. There is also a dual space with open sets being open rays pointing downward (I am thinking in terms of a vertical real line, with positive numbers above, and negative numbers below). They have quasi-metrics as distances, ReLU(y-x) and ReLU(x-y), so that going along one direction accumulates a usual distance on the meter, but going in the opposite direction accumulates zero (like a toll bridge charging toll only in one direction).
One of the most interesting mathematical structures in this sense comes from interval numbers, but there is a bit of twist to those interval numbers, one might want to even allow “partially contradictory interval numbers”, and then the math becomes more straightforward. It’s probably the best to share a few pages I scribbled on this 10 years ago: https://anhinga.github.io/brandeis-mirror/PartiallyInconsistentIntervalNumbers.pdf
(Eventually this ended up as a part of Section 4 of this “sandwich paper” (where Section 4 is the “math filling” of the sandwich): https://arxiv.org/abs/1512.04639)
I think when Dana Scott was first doing this kind of “asymmetric topology” in late 1960-s/early 1970-s, in some of his constructions he did focus on the bases which were like rational numbers, and then it’s really similar in spirit...
(And when I started to work with his formalism in mid-1980-s and early 1990-s, I also focused on those bases, because it was easier to think that way, it was less abstract that way...)
Yes, I think this is a very interesting feature of your formalism. These “love” and “hate” are “abstract counters”, their relationship with subjective feelings is complicated.
But this might be the correct way to capture this “ethicophysics” (it is a frequent situation in modern physics that there is some tension between naive intuition and the correct theory (starting with relativistic space-time and such)).
Let″s interact, try to work together a bit, think together, this might be quite fruitful :-) Perhaps, I’ll actually earn a co-authorship, we’ll see :-)
So, about the decomposition into positive and negative components which evolve monotonically:
So, basically, if one considers real numbers, one can define a strange non-Hausdorff topology on them, so that continuous transformations are monotocally non-decreasing functions, “continuous on the left”, and the open sets being open rays pointing upward. There is also a dual space with open sets being open rays pointing downward (I am thinking in terms of a vertical real line, with positive numbers above, and negative numbers below). They have quasi-metrics as distances, ReLU(y-x) and ReLU(x-y), so that going along one direction accumulates a usual distance on the meter, but going in the opposite direction accumulates zero (like a toll bridge charging toll only in one direction).
One of the most interesting mathematical structures in this sense comes from interval numbers, but there is a bit of twist to those interval numbers, one might want to even allow “partially contradictory interval numbers”, and then the math becomes more straightforward. It’s probably the best to share a few pages I scribbled on this 10 years ago: https://anhinga.github.io/brandeis-mirror/PartiallyInconsistentIntervalNumbers.pdf
(Eventually this ended up as a part of Section 4 of this “sandwich paper” (where Section 4 is the “math filling” of the sandwich): https://arxiv.org/abs/1512.04639)
I love this! It’s basically Dedekind cuts, right?
It is related in spirit, yes...
I think when Dana Scott was first doing this kind of “asymmetric topology” in late 1960-s/early 1970-s, in some of his constructions he did focus on the bases which were like rational numbers, and then it’s really similar in spirit...
(And when I started to work with his formalism in mid-1980-s and early 1990-s, I also focused on those bases, because it was easier to think that way, it was less abstract that way...)