Problem of Old Evidence, the Paradox of Ignorance and Shapley Values
Paradox of Ignorance
Paul Christiano presents the “paradox of ignorance” where a weaker, less informed agent appears to outperform a more powerful, more informed agent in certain situations. This seems to contradict the intuitive desideratum that more information should always lead to better performance.
The example given is of two agents, one powerful and one limited, trying to determine the truth of a universal statement ∀x:ϕ(x) for some Δ0 formula ϕ. The limited agent treats each new value of ϕ(x) as a surprise and evidence about the generalization ∀x:ϕ(x). So it can query the environment about some simple inputs x and get a reasonable view of the universal generalization.
In contrast, the more powerful agent may be able to deduce ϕ(x) directly for simple x. Because it assigns these statements prior probability 1, they don’t act as evidence at all about the universal generalization ∀x:ϕ(x). So the powerful agent must consult the environment about more complex examples and pay a higher cost to form reasonable beliefs about the generalization.
Is it really a problem?
However, I argue that the more powerful agent is actually justified in assigning less credence to the universal statement ∀x:ϕ(x). The reason is that the probability mass provided by examples x₁, …, xₙ such that ϕ(xᵢ) holds is now distributed among the universal statement ∀x:ϕ(x) and additional causes Cⱼ known to the more powerful agent that also imply ϕ(xᵢ). Consequently, ∀x:ϕ(x) becomes less “necessary” and has less relative explanatory power for the more informed agent.
An implication of this perspective is that if the weaker agent learns about the additional causes Cⱼ, it should also lower its credence in ∀x:ϕ(x).
More generally, we would like the credence assigned to propositions P (such as ∀x:ϕ(x)) to be independent of the order in which we acquire new facts (like xᵢ, ϕ(xᵢ), and causes Cⱼ).
Shapley Value
The Shapley value addresses this limitation by providing a way to average over all possible orders of learning new facts. It measures the marginal contribution of an item (like a piece of evidence) to the value of sets containing that item, considering all possible permutations of the items. By using the Shapley value, we can obtain an order-independent measure of the contribution of each new fact to our beliefs about propositions like ∀x:ϕ(x).
Further thoughts
I believe this is closely related, perhaps identical, to the ‘Problem of Old Evidence’ as considered by Abram Demski.
Suppose a new scientific hypothesis, such as general relativity, explains a well-know observation such as the perihelion precession of mercury better than any existing theory. Intuitively, this is a point in favor of the new theory. However, the probability for the well-known observation was already at 100%. How can a previously-known statement provide new support for the hypothesis, as if we are re-updating on evidence we’ve already updated on long ago? This is known as the problem of old evidence, and is usually levelled as a charge against Bayesian epistemology.
[Thanks to @Jeremy Gillen for pointing me towards this interesting Christiano paper]
The matter seems terribly complex and interesting to me.
Notions of Accuracy?
Suppose p1 is a prior which has uncertainty about ϕ(x1),ϕ(x2),... and uncertainty about ∀nϕ(xn). This is the more ignorant prior. Consider p2 some prior which has the same beliefs about the universal statement -- p1(∀nϕ(xn))=p2(∀nϕ(xn)) -- but which knows ϕ(x1) and ϕ(x2).
We observe that p1 can increase its credence in the universal statement by observing the first two instances, ϕ(x1) and ϕ(x2), while p2 cannot do this -- p2 needs to wait for further evidence. This is interpreted as a defect.
The moral is apparently that a less ignorant prior can be worse than a more ignorant one; more specifically, it can learn more slowly.
However, I think we need to be careful about the informal notion of “more ignorant” at play here. We can formalize this by imagining a numerical measure of the accuracy of a prior. We might want it to be the case that more accurate priors are always better to start with. Put more precisely: a more accurate prior should also imply a more accurate posterior after updating. Paul’s example challenges this notion, but he does not prove that no plausible notion of accuracy will have this property; he only relies on an informal notion of ignorance.
So I think the question is open: when can a notion of accuracy fail to follow the rule “more accurate priors yield more accurate posteriors”? EG, can a proper scoring rule fail to meet this criterion? This question might be pretty easy to investigate.
Conditional probabilities also change?
I think the example rests on an intuitive notion that we can construct p2 by imagining p1 but modifying it to know ϕ(x1) and ϕ(x2). However, the most obvious way to modify it so is by updating on those sentences. This fails to meet the conditions of the example, however; p2 would already have an increased probability for the universal statement.
So, in order to move the probability of ϕ(x1) and ϕ(x2) upwards to 1 without also increasing the probability of the universal, we must do some damage to the probabilistic relationship between the instances and the universal. The prior p2 doesn’t just know ϕ(x1) and ϕ(x2); it also believes the conditional probability of the universal statement given those two sentences to be lower than p1 believes them to be.
It doesn’t think it should learn from them!
This supports Alexander’s argument that there is no paradox, I think. However, I am not ultimately convinced. Perhaps I will find more time to write about the matter later.
Alexander analyzes the difference between p1 and p2 in terms of the famous “explaining away” effect. Alexander supposes that p2 has learned some “causes”:
The reason is that the probability mass provided by examples x₁, …, xₙ such that ϕ(xᵢ) holds is now distributed among the universal statement ∀x:ϕ(x) and additional causes Cⱼ known to the more powerful agent that also imply ϕ(xᵢ). Consequently, ∀x:ϕ(x) becomes less “necessary” and has less relative explanatory power for the more informed agent.
An implication of this perspective is that if the weaker agent learns about the additional causes Cⱼ, it should also lower its credence in ∀x:ϕ(x).
Postulating these causes adds something to the scenario. One possible view is that Alexander is correct so far as Alexander’s argument goes, but incorrect if there are no such Cj to consider.
However, I do not find myself endorsing Alexander’s argument even that far.
If C1 and C2 have a common form, or are correlated in some way—so there is an explanation which tells us why the first two sentences, ϕ(x1) and ϕ(x2), are true, and which does not apply to n>2 -- then I agree with Alexander’s argument.
If C1 and C2 are uncorrelated, then it starts to look like a coincidence. If I find a similarly uncorrelated C3 for ϕ(x3), C4 for ϕ(x4), and a few more, then it will feel positively unexplained. Although each explanation is individually satisfying, nowhere do I have an explanation of why all of them are turning up true.
I think the probability of the universal sentence should go up at this point.
So, what about my “conditional probabilities also change” variant of Alexander’s argument? We might intuitively think that ϕ(x1) and ϕ(x2) should be evidence for the universal generalization, but p2does not believe this—its conditional probabilities indicate otherwise.
I find this ultimately unconvincing because the point of Paul’s example, in my view, is that more accurate priors do not imply more accurate posteriors. I still want to understand what conditions can lead to this (including whether it is true for all notions of “accuracy” satisfying some reasonable assumptions EG proper scoring rules).
Another reason I find it unconvincing is because even if we accepted this answer for the paradox of ignorance, I think it is not at all convincing for the problem of old evidence.
What is the ‘problem’ in the problem of old evidence?
This doesn’t feel like it resolves that confusion for me, I think it’s still a problem with the agents he describes in that paper.
The causes Cj are just the direct computation of Φ for small values of x. If they were arguments that only had bearing on small values of x and implied nothing about larger values (e.g. an adversary selected some x to show you, but filtered for x such that Φ(x)), then it makes sense that this evidence has no bearing on∀x:Φ(x). But when there was no selection or other reason that the argument only applies to small x, then to me it feels like the existence of the evidence (even though already proven/computed) should still increase the credence of the forall.
I didn’t intend the causes Cj to equate to direct computation of \phi(x) on the x_i.
They are rather other pieces of evidence that the powerful agent has that make it believe \phi(x_i). I don’t know if that’s what you meant.
I agree seeing x_i such that \phi(x_i) should increase credence in \forall x \phi(x) even in the presence of knowledge of C_j. And the Shapely value proposal will do so.
It’s funny that this has been recently shown in a paper. I’ve been thinking a lot about this phenomenon regarding fields with little to no capacity for testable predictions like history.
I got very into history over the last few years, and found there was a significant advantage to being unknowledgeable that was not available to the knowledged, and it was exactly what this paper is talking about.
By not knowing anything, I could entertain multiple bizarre ideas without immediately thinking “but no, that doesn’t make sense because of X.” And then, each of those ideas becomes in effect its own testable prediction. If there’s something to it, as I learn more about the topic I’m going to see significantly more samples of indications it could be true and few convincing to the contrary. But if it probably isn’t accurate, I’ll see few supporting samples and likely a number of counterfactual examples.
You kind of get to throw everything at the wall and see what sticks over time.
In particular, I found that it was especially powerful at identifying clustering trends in cross-discipline emerging research in things that were testable, such as archeological finds and DNA results, all within just the past decade, which despite being relevant to the field of textual history is still largely ignored in the face of consensus built on conviction.
It reminds me a lot of science historian John Helibron’s quote, “The myth you slay today may contain a truth you need tomorrow.”
If you haven’t had the chance to slay any myths, you also haven’t preemptively killed off any truths along with it.
One of the interesting thing about AI minds (such as LLMs) is that in theory, you can turn many topics into testable science while avoiding the ‘problem of old evidence’, because you can now construct artificial minds and mold them like putty. They know what you want them to know, and so you can see what they would predict in the absence of knowledge, or you can install in them false beliefs to test out counterfactual intellectual histories, or you can expose them to real evidence in different orders to measure biases or path dependency in reasoning.
With humans, you can’t do that because they are so uncontrolled: even if someone says they didn’t know about crucial piece of evidence X, there is no way for them to prove that, and they may be honestly mistaken and have already read about X and forgotten it (but humans never really forget so X has already changed their “priors”, leading to double-counting), or there is leakage. And you can’t get people to really believe things at the drop of a hat, so you can’t make people imagine, “suppose Napoleon had won Waterloo, how do you predict history would have changed?” because no matter how you try to participate in the spirit of the exercise, you always know that Napoleon lost and you have various opinions on that contaminating your retrodictions, and even if you have never read a single book or paper on Napoleon, you are still contaminated by expressions like “his Waterloo” (‘Hm, the general in this imaginary story is going to fight at someplace called Waterloo? Bad vibes. I think he’s gonna lose.’)
But with a LLM, say, you could simply train it with all timestamped texts up to Waterloo, like all surviving newspapers, and then simply have one version generate a bunch of texts about how ‘Napoleon won Waterloo’, train the other version on these definitely-totally-real French newspaper reports about his stunning victory over the monarchist invaders, and then ask it to make forecasts about Europe.
Similarly, you can do ‘deep exploration’ of claims that human researchers struggle to take seriously. It is a common trope in stories of breakthroughs, particularly in math, that someone got stuck for a long time proving X is true and one day decides on a whim to try to instead prove X is false and does so in hours; this would never happen with LLMs, because you would simply have a search process which tries both equally. This can take an extreme form for really difficult outstanding problems: if a problem like the continuum hypothesis defies all efforts, you could spin up 1000 von Neumann AGIs which have been brainwashed into believing it is false, and then a parallel effort by 1000 brainwashed to believing it is as true as 2+2=4, and let them pursue their research agenda for subjective centuries, and then bring them together to see what important new results they find and how they tear apart the hated enemies’ work, for seeding the next iteration.
(These are the sorts of experiments which are why one might wind up running tons of ‘ancestor simulations’… There’s many more reasons to be simulating past minds than simply very fancy versions of playing The Sims. Perhaps we are now just distant LLM personae being tested about reasoning about the Singularity in one particular scenario involving deep learning counterfactuals, where DL worked, although in the real reality it was Bayesian program synthesis & search.)
A variant of what you are saying is that AI may once and for all allow us to calculate the true counterfactual Shapley value of scientific contributions.
( re: ancestor simulations
I think you are onto something here. Compare the Q hypothesis:
Yup. Who knows but we are all part of a giant leave-one-out cross-validation computing counterfactual credit assignment on human history? Schmidhuber-em will be crushed by the results.
While I agree that the potential for AI (we probably need a better term than LLMs or transformers as multimodal models with evolving architectures grow beyond those terms) in exploring less testable topics as more testable is quite high, I’m not sure the air gapping on information can be as clean as you might hope.
Does the AI generating the stories of Napoleon’s victory know about the historical reality of Waterloo? Is it using something like SynthID where the other AI might inadvertently pick up on a pattern across the stories of victories distinct from the stories preceding it?
You end up with a turtles all the way down scenario in trying to control for information leakage with the hopes of achieving a threshold that no longer has impact on the result, but given we’re probably already seriously underestimating the degree to which correlations are mapped even in today’s models I don’t have high hopes for tomorrow’s.
I think the way in which there’s most impact on fields like history is the property by which truth clusters across associated samples whereas fictions have counterfactual clusters. An AI mind that is not inhibited by specialization blindness or the rule of seven plus or minus two and better trained at correcting for analytical biases may be able to see patterns in the data, particularly cross-domain, that have eluded human academics to date (this has been my personal research interest in the area, and it does seem like there’s significant room for improvement).
And yes, we certainly could be. If you’re a fan of cosmology at all, I’ve been following Neil Turok’s CPT symmetric universe theory closely, which started with the Baryonic asymmetry problem and has tackled a number of the open cosmology questions since. That, paired with a QM interpretation like Everett’s ends up starting to look like the symmetric universe is our reference and the MWI branches are variations of its modeling around quantization uncertainties.
(I’ve found myself thinking often lately about how given our universe at cosmic scales and pre-interaction at micro scales emulates a mathematically real universe, just what kind of simulation and at what scale might be able to be run on a real computing neural network.)
Problem of Old Evidence, the Paradox of Ignorance and Shapley Values
Paradox of Ignorance
Paul Christiano presents the “paradox of ignorance” where a weaker, less informed agent appears to outperform a more powerful, more informed agent in certain situations. This seems to contradict the intuitive desideratum that more information should always lead to better performance.
The example given is of two agents, one powerful and one limited, trying to determine the truth of a universal statement ∀x:ϕ(x) for some Δ0 formula ϕ. The limited agent treats each new value of ϕ(x) as a surprise and evidence about the generalization ∀x:ϕ(x). So it can query the environment about some simple inputs x and get a reasonable view of the universal generalization.
In contrast, the more powerful agent may be able to deduce ϕ(x) directly for simple x. Because it assigns these statements prior probability 1, they don’t act as evidence at all about the universal generalization ∀x:ϕ(x). So the powerful agent must consult the environment about more complex examples and pay a higher cost to form reasonable beliefs about the generalization.
Is it really a problem?
However, I argue that the more powerful agent is actually justified in assigning less credence to the universal statement ∀x:ϕ(x). The reason is that the probability mass provided by examples x₁, …, xₙ such that ϕ(xᵢ) holds is now distributed among the universal statement ∀x:ϕ(x) and additional causes Cⱼ known to the more powerful agent that also imply ϕ(xᵢ). Consequently, ∀x:ϕ(x) becomes less “necessary” and has less relative explanatory power for the more informed agent.
An implication of this perspective is that if the weaker agent learns about the additional causes Cⱼ, it should also lower its credence in ∀x:ϕ(x).
More generally, we would like the credence assigned to propositions P (such as ∀x:ϕ(x)) to be independent of the order in which we acquire new facts (like xᵢ, ϕ(xᵢ), and causes Cⱼ).
Shapley Value
The Shapley value addresses this limitation by providing a way to average over all possible orders of learning new facts. It measures the marginal contribution of an item (like a piece of evidence) to the value of sets containing that item, considering all possible permutations of the items. By using the Shapley value, we can obtain an order-independent measure of the contribution of each new fact to our beliefs about propositions like ∀x:ϕ(x).
Further thoughts
I believe this is closely related, perhaps identical, to the ‘Problem of Old Evidence’ as considered by Abram Demski.
[Thanks to @Jeremy Gillen for pointing me towards this interesting Christiano paper]
The matter seems terribly complex and interesting to me.
Notions of Accuracy?
Suppose p1 is a prior which has uncertainty about ϕ(x1),ϕ(x2),... and uncertainty about ∀nϕ(xn). This is the more ignorant prior. Consider p2 some prior which has the same beliefs about the universal statement -- p1(∀nϕ(xn))=p2(∀nϕ(xn)) -- but which knows ϕ(x1) and ϕ(x2).
We observe that p1 can increase its credence in the universal statement by observing the first two instances, ϕ(x1) and ϕ(x2), while p2 cannot do this -- p2 needs to wait for further evidence. This is interpreted as a defect.
The moral is apparently that a less ignorant prior can be worse than a more ignorant one; more specifically, it can learn more slowly.
However, I think we need to be careful about the informal notion of “more ignorant” at play here. We can formalize this by imagining a numerical measure of the accuracy of a prior. We might want it to be the case that more accurate priors are always better to start with. Put more precisely: a more accurate prior should also imply a more accurate posterior after updating. Paul’s example challenges this notion, but he does not prove that no plausible notion of accuracy will have this property; he only relies on an informal notion of ignorance.
So I think the question is open: when can a notion of accuracy fail to follow the rule “more accurate priors yield more accurate posteriors”? EG, can a proper scoring rule fail to meet this criterion? This question might be pretty easy to investigate.
Conditional probabilities also change?
I think the example rests on an intuitive notion that we can construct p2 by imagining p1 but modifying it to know ϕ(x1) and ϕ(x2). However, the most obvious way to modify it so is by updating on those sentences. This fails to meet the conditions of the example, however; p2 would already have an increased probability for the universal statement.
So, in order to move the probability of ϕ(x1) and ϕ(x2) upwards to 1 without also increasing the probability of the universal, we must do some damage to the probabilistic relationship between the instances and the universal. The prior p2 doesn’t just know ϕ(x1) and ϕ(x2); it also believes the conditional probability of the universal statement given those two sentences to be lower than p1 believes them to be.
It doesn’t think it should learn from them!
This supports Alexander’s argument that there is no paradox, I think. However, I am not ultimately convinced. Perhaps I will find more time to write about the matter later.
(continued..)
Explanations?
Alexander analyzes the difference between p1 and p2 in terms of the famous “explaining away” effect. Alexander supposes that p2 has learned some “causes”:
Postulating these causes adds something to the scenario. One possible view is that Alexander is correct so far as Alexander’s argument goes, but incorrect if there are no such Cj to consider.
However, I do not find myself endorsing Alexander’s argument even that far.
If C1 and C2 have a common form, or are correlated in some way—so there is an explanation which tells us why the first two sentences, ϕ(x1) and ϕ(x2), are true, and which does not apply to n>2 -- then I agree with Alexander’s argument.
If C1 and C2 are uncorrelated, then it starts to look like a coincidence. If I find a similarly uncorrelated C3 for ϕ(x3), C4 for ϕ(x4), and a few more, then it will feel positively unexplained. Although each explanation is individually satisfying, nowhere do I have an explanation of why all of them are turning up true.
I think the probability of the universal sentence should go up at this point.
So, what about my “conditional probabilities also change” variant of Alexander’s argument? We might intuitively think that ϕ(x1) and ϕ(x2) should be evidence for the universal generalization, but p2 does not believe this—its conditional probabilities indicate otherwise.
I find this ultimately unconvincing because the point of Paul’s example, in my view, is that more accurate priors do not imply more accurate posteriors. I still want to understand what conditions can lead to this (including whether it is true for all notions of “accuracy” satisfying some reasonable assumptions EG proper scoring rules).
Another reason I find it unconvincing is because even if we accepted this answer for the paradox of ignorance, I think it is not at all convincing for the problem of old evidence.
What is the ‘problem’ in the problem of old evidence?
… to be further expanded later …
This doesn’t feel like it resolves that confusion for me, I think it’s still a problem with the agents he describes in that paper.
The causes Cj are just the direct computation of Φ for small values of x. If they were arguments that only had bearing on small values of x and implied nothing about larger values (e.g. an adversary selected some x to show you, but filtered for x such that Φ(x)), then it makes sense that this evidence has no bearing on∀x:Φ(x). But when there was no selection or other reason that the argument only applies to small x, then to me it feels like the existence of the evidence (even though already proven/computed) should still increase the credence of the forall.
I didn’t intend the causes Cj to equate to direct computation of \phi(x) on the x_i. They are rather other pieces of evidence that the powerful agent has that make it believe \phi(x_i). I don’t know if that’s what you meant.
I agree seeing x_i such that \phi(x_i) should increase credence in \forall x \phi(x) even in the presence of knowledge of C_j. And the Shapely value proposal will do so.
(Bad tex. On my phone)
It’s funny that this has been recently shown in a paper. I’ve been thinking a lot about this phenomenon regarding fields with little to no capacity for testable predictions like history.
I got very into history over the last few years, and found there was a significant advantage to being unknowledgeable that was not available to the knowledged, and it was exactly what this paper is talking about.
By not knowing anything, I could entertain multiple bizarre ideas without immediately thinking “but no, that doesn’t make sense because of X.” And then, each of those ideas becomes in effect its own testable prediction. If there’s something to it, as I learn more about the topic I’m going to see significantly more samples of indications it could be true and few convincing to the contrary. But if it probably isn’t accurate, I’ll see few supporting samples and likely a number of counterfactual examples.
You kind of get to throw everything at the wall and see what sticks over time.
In particular, I found that it was especially powerful at identifying clustering trends in cross-discipline emerging research in things that were testable, such as archeological finds and DNA results, all within just the past decade, which despite being relevant to the field of textual history is still largely ignored in the face of consensus built on conviction.
It reminds me a lot of science historian John Helibron’s quote, “The myth you slay today may contain a truth you need tomorrow.”
If you haven’t had the chance to slay any myths, you also haven’t preemptively killed off any truths along with it.
One of the interesting thing about AI minds (such as LLMs) is that in theory, you can turn many topics into testable science while avoiding the ‘problem of old evidence’, because you can now construct artificial minds and mold them like putty. They know what you want them to know, and so you can see what they would predict in the absence of knowledge, or you can install in them false beliefs to test out counterfactual intellectual histories, or you can expose them to real evidence in different orders to measure biases or path dependency in reasoning.
With humans, you can’t do that because they are so uncontrolled: even if someone says they didn’t know about crucial piece of evidence X, there is no way for them to prove that, and they may be honestly mistaken and have already read about X and forgotten it (but humans never really forget so X has already changed their “priors”, leading to double-counting), or there is leakage. And you can’t get people to really believe things at the drop of a hat, so you can’t make people imagine, “suppose Napoleon had won Waterloo, how do you predict history would have changed?” because no matter how you try to participate in the spirit of the exercise, you always know that Napoleon lost and you have various opinions on that contaminating your retrodictions, and even if you have never read a single book or paper on Napoleon, you are still contaminated by expressions like “his Waterloo” (‘Hm, the general in this imaginary story is going to fight at someplace called Waterloo? Bad vibes. I think he’s gonna lose.’)
But with a LLM, say, you could simply train it with all timestamped texts up to Waterloo, like all surviving newspapers, and then simply have one version generate a bunch of texts about how ‘Napoleon won Waterloo’, train the other version on these definitely-totally-real French newspaper reports about his stunning victory over the monarchist invaders, and then ask it to make forecasts about Europe.
Similarly, you can do ‘deep exploration’ of claims that human researchers struggle to take seriously. It is a common trope in stories of breakthroughs, particularly in math, that someone got stuck for a long time proving X is true and one day decides on a whim to try to instead prove X is false and does so in hours; this would never happen with LLMs, because you would simply have a search process which tries both equally. This can take an extreme form for really difficult outstanding problems: if a problem like the continuum hypothesis defies all efforts, you could spin up 1000 von Neumann AGIs which have been brainwashed into believing it is false, and then a parallel effort by 1000 brainwashed to believing it is as true as 2+2=4, and let them pursue their research agenda for subjective centuries, and then bring them together to see what important new results they find and how they tear apart the hated enemies’ work, for seeding the next iteration.
(These are the sorts of experiments which are why one might wind up running tons of ‘ancestor simulations’… There’s many more reasons to be simulating past minds than simply very fancy versions of playing The Sims. Perhaps we are now just distant LLM personae being tested about reasoning about the Singularity in one particular scenario involving deep learning counterfactuals, where DL worked, although in the real reality it was Bayesian program synthesis & search.)
Beautifully illustrated and amusingly put, sir!
A variant of what you are saying is that AI may once and for all allow us to calculate the true
counterfactualShapley value of scientific contributions.( re: ancestor simulations
I think you are onto something here. Compare the Q hypothesis:
https://twitter.com/dalcy_me/status/1780571900957339771
see also speculations about Zhuangzi hypothesis here )
Yup. Who knows but we are all part of a giant leave-one-out cross-validation computing counterfactual credit assignment on human history? Schmidhuber-em will be crushed by the results.
While I agree that the potential for AI (we probably need a better term than LLMs or transformers as multimodal models with evolving architectures grow beyond those terms) in exploring less testable topics as more testable is quite high, I’m not sure the air gapping on information can be as clean as you might hope.
Does the AI generating the stories of Napoleon’s victory know about the historical reality of Waterloo? Is it using something like SynthID where the other AI might inadvertently pick up on a pattern across the stories of victories distinct from the stories preceding it?
You end up with a turtles all the way down scenario in trying to control for information leakage with the hopes of achieving a threshold that no longer has impact on the result, but given we’re probably already seriously underestimating the degree to which correlations are mapped even in today’s models I don’t have high hopes for tomorrow’s.
I think the way in which there’s most impact on fields like history is the property by which truth clusters across associated samples whereas fictions have counterfactual clusters. An AI mind that is not inhibited by specialization blindness or the rule of seven plus or minus two and better trained at correcting for analytical biases may be able to see patterns in the data, particularly cross-domain, that have eluded human academics to date (this has been my personal research interest in the area, and it does seem like there’s significant room for improvement).
And yes, we certainly could be. If you’re a fan of cosmology at all, I’ve been following Neil Turok’s CPT symmetric universe theory closely, which started with the Baryonic asymmetry problem and has tackled a number of the open cosmology questions since. That, paired with a QM interpretation like Everett’s ends up starting to look like the symmetric universe is our reference and the MWI branches are variations of its modeling around quantization uncertainties.
(I’ve found myself thinking often lately about how given our universe at cosmic scales and pre-interaction at micro scales emulates a mathematically real universe, just what kind of simulation and at what scale might be able to be run on a real computing neural network.)
This post sounds intriguing, but is largely incomprehensible to me due to not sufficiently explaining the background theories.