Yeah, it’s definitely a spherical cow in a frictionless vacuum kind of assumption.
If you (or any reader of this comment) want an exercise to work on while you read, you could try to add a treatment of emotional dissipation; presumably it would function more or less like air resistance in traditional physics; the mechanism would be that liking or disliking someone alive that you know with perfect and pure intensity is exhausting and not particularly evolutionarily valuable. Liking or disliking a fictional or dead person with perfect and pure intensity (say, Jesus and Hitler respectively) might be quite evolutionarily valuable, though, since it would enable the youth to take seriously the accumulated wisdom of their tribe. So perhaps dissipation only holds for the people with whom the minutiae of daily contact causes us to reevaluate our models, and fails to hold for those people (historical or fictional) whom we have ample Bayesian evidence to consign to either the Good or the Evil bin.
I am trying to think about the informal meaning of op(a,b) on page 8.
Am I correct that we impose a condition that l(a,b) and h(a,b) are always non-negative? And that their derivatives can’t be below 0, so that l(a,b) and h(a,b) are monotonically non-decreasing with time?
I thought about this some more, and I think you’re right that they should be monotonically non-decreasing with time. I was hesitant to bite that particular bullet because the subjective, phenomenological experience of hate and love is, of course, not monotonically non-decreasing. But it makes the equations work much better and everything is much simpler this way.
Ultimately, if one is in a loving marriage and then undergoes an ugly divorce, one winds up sort of not-caring about the other person, but it would be a mistake to say that your brain has erased all the accumulated love and hate you racked up. It just learns that it has more interesting things to do than to dwell on the past.
So I will add this to the next draft of Ethicophysics I. Let me know if you would like to be acknowledged or added as a co-author on that draft.
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...)
Well, they would be represented in the brain by neurons, which have a natural ReLU function attached to them. I think they are always non-negative, but the derivative is unbounded, so they can saturate at 0 if someone grows totally uninterestsed in the question of whether they hate or love some particular entity.
It would be hard to carry through in the theoretical domain, as you say, but in the empirical domain it should be relatively straightforward. Just rip off the math of air resistance, make some predictions, and do a gut check of what you get out.
Yeah, it’s definitely a spherical cow in a frictionless vacuum kind of assumption.
If you (or any reader of this comment) want an exercise to work on while you read, you could try to add a treatment of emotional dissipation; presumably it would function more or less like air resistance in traditional physics; the mechanism would be that liking or disliking someone alive that you know with perfect and pure intensity is exhausting and not particularly evolutionarily valuable. Liking or disliking a fictional or dead person with perfect and pure intensity (say, Jesus and Hitler respectively) might be quite evolutionarily valuable, though, since it would enable the youth to take seriously the accumulated wisdom of their tribe. So perhaps dissipation only holds for the people with whom the minutiae of daily contact causes us to reevaluate our models, and fails to hold for those people (historical or fictional) whom we have ample Bayesian evidence to consign to either the Good or the Evil bin.
I am trying to think about the informal meaning of op(a,b) on page 8.
Am I correct that we impose a condition that l(a,b) and h(a,b) are always non-negative? And that their derivatives can’t be below 0, so that l(a,b) and h(a,b) are monotonically non-decreasing with time?
I thought about this some more, and I think you’re right that they should be monotonically non-decreasing with time. I was hesitant to bite that particular bullet because the subjective, phenomenological experience of hate and love is, of course, not monotonically non-decreasing. But it makes the equations work much better and everything is much simpler this way.
Ultimately, if one is in a loving marriage and then undergoes an ugly divorce, one winds up sort of not-caring about the other person, but it would be a mistake to say that your brain has erased all the accumulated love and hate you racked up. It just learns that it has more interesting things to do than to dwell on the past.
So I will add this to the next draft of Ethicophysics I. Let me know if you would like to be acknowledged or added as a co-author on that draft.
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...)
Well, they would be represented in the brain by neurons, which have a natural ReLU function attached to them. I think they are always non-negative, but the derivative is unbounded, so they can saturate at 0 if someone grows totally uninterestsed in the question of whether they hate or love some particular entity.
Indeed.
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...
Indeed.
That would be a pretty non-trivial work, though, since dissipative physics is not Hamiltonian, so it is likely to require different techniques.
It would be hard to carry through in the theoretical domain, as you say, but in the empirical domain it should be relatively straightforward. Just rip off the math of air resistance, make some predictions, and do a gut check of what you get out.