The program is operating on the user's current understanding of the explanation.
The seasons example in my submission is intentionally a toy example to demonstrate how the program works. In a proper use of the program, both the problem/question and the proposed explanations would include the relevant context needed to understand what is actually being explained and how the explanation works.
For example, “Earth's seasons are caused by axial tilt” is obviously not the full explanation. Someone who properly understands the explanation knows that Earth's tilt matters in relation to the Sun, Earth's orbit, the changing angle and duration of incoming sunlight, the resulting heating, and so on. These parts are connected and constrain each other.
So if the problem is to explain Earth's seasons, I wouldn't accept replacing Earth with Mars, Saturn, Neptune, etc. as working variations of that explanation. Once the relevant context is included, changing the planet changes other parts of the explanatory relationship and no longer explains the original phenomenon.
On the other hand, if a user genuinely understands “because of axial tilt” in such a shallow way that they think Earth can simply be replaced with any other planet while the explanation of Earth's seasons remains intact, then yes: according to their current understanding, the explanation really is easy to vary. The program is correctly reflecting the explanatory knowledge they've supplied to it.
This is why different users can get different results. Someone with a shallow understanding of an explanation may think many of its details can be changed independently. Someone who understands more of the explanatory structure may understand why those same changes break it. Conversely, an expert may also know genuine working variations that a novice would never think of.
So I don't expect the program to produce a context-independent ranking from a few isolated English sentences. The question and explanations are inputs supplied and understood by the user, and the HTV comparison is relative to that current understanding.

As I explained in #5553, the program operates on the user's current understanding of the explanation.

In this case, though, I think the green-hat example actually illustrates what it means for an explanation to be easy to vary.

Suppose my explanation really is “God causes the seasons while wearing one green hat,” and I genuinely think I can change that to two hats, three hats, a thousand hats, etc. without affecting the explanation at all. Then the number of hats is completely unconstrained by what I'm trying to explain. Nothing in the explanation tells me why it should be one rather than two or a thousand.

I would consider that a problem with the explanation, not with the HTV comparison. It's exactly the kind of arbitrariness that HTV is supposed to expose.

Of course, the program isn't going to enumerate infinitely many hats. It only works with the variations the user actually comes up with. But if I can keep producing arbitrary variations without affecting the explanatory argument, that seems like evidence that the explanation is easy to vary, not a reason to reject the method.

As I argued in #5554, if the number of green hats is genuinely part of an explanation and can be changed arbitrarily without affecting anything, then I think that really does expose an easy-to-vary part of the explanation.

But I don't think adding “while I wear one green hat,” “while I wear two green hats,” etc. to the axial-tilt explanation necessarily varies the explanation at all.

If my explanation is that Earth's seasons result from its axial tilt and the resulting relationship between Earth and the Sun, whether I happen to be wearing one green hat or a thousand isn't part of that explanatory argument. Appending an unrelated fact to the English sentence doesn't change the explanation it expresses.

If, on the other hand, I genuinely claim that my hat is part of the explanation—say, that Earth's seasons occur because of axial tilt and because I'm wearing exactly one green hat—then changing the number of hats would be a genuine variation. But in that case I really have made the explanation worse by adding an arbitrary component that isn't constrained by what I'm trying to explain.

So I think there's a difference between varying an explanation and varying the string of English used to express it. The program relies on the user to understand that distinction, for the same reason I described in #5553: it operates on the user's understanding of the explanatory argument, not on arbitrary syntactic changes to its wording.

On that understanding, I don't think both explanations become equally easy to vary merely because infinitely many irrelevant statements can be appended to the sentences expressing them.

I think this is where the problem/question given to the program matters.

If the problem I'm trying to answer is “Why does Earth have seasons?”, then replacing Earth with Mars doesn't give me another working variation of the explanation of Earth's seasons. I've changed the phenomenon I'm trying to explain. Applying the same underlying theory to explain seasons on Mars seems to me like an example of its reach, not a variation of its explanation of Earth's seasons.

This is one reason the program asks for the question first. Whether a proposed variation still works can't be judged independently of what we're trying to explain.

As I explained in #5553, the program relies on the user's understanding of both the problem situation and the explanation. So I agree that reach and easy-to-vary shouldn't be confused, but I don't think the program requires us to confuse them. The user has to judge whether they've varied an explanation while preserving what it was supposed to explain, or instead applied the explanation to a different problem.

And of course people can disagree about that distinction, because they can understand the problem situation and explanatory argument differently. That's part of the human judgment the program deliberately leaves to the user.

I agree that people can disagree about what counts as a variation versus a completely different explanation. I don't agree that the program itself needs to recognize the difference.

The program isn't intended to distinguish a variation from a completely different explanation. That's something the user has to decide. In fact, I don't see how a program could make that distinction in general without being a general intelligence that actually comprehends the problem situation and the explanations involved.

And people themselves can disagree about what counts as a variation. That's unavoidable because it depends on how they understand the underlying explanatory argument. What looks like a harmless change to me might look to someone with a deeper understanding like a change that completely breaks the explanation.

So I don't think different people getting different results is necessarily a problem. If I understand an explanation poorly, I may think lots of its details can be changed independently. Once I understand more of the connections between those details, I may realize that many of those variations don't actually work. On the other hand, an expert might also know valid ways of varying an explanation that I would never have thought of. The result reflects our current understanding, and that can change as our knowledge changes.

This is also part of the broader point I made in #5553: the program operates on the user's current understanding of the problem and explanations rather than independently understanding them for the user.

… nor is the user given an opportunity to correct any mistakes to that effect.

The user could simply run the program again with corrected inputs.

I don't think the program needs to choose one of the surviving variants if our current knowledge gives us no reason to choose.

If several variants of the better explanation still work and we currently have nothing that differentiates them, then I think it's fine for them to remain competing possibilities. In fact, my guess is that this is exactly how different research programs can get started: people can follow the different explanatory threads until further criticism, experiments, observations, or other new knowledge gives us a reason to distinguish them.

So I don't think the program should invent a preference between variants when our current problem situation and knowledge don't provide one. Sometimes the rational state really is that we don't yet know which variant is right. We can continue developing and testing them until we find something that differentiates them.

This is out of scope for the bounty. The bounty merely says the program must “Return a ranking indicating which explanation is better, worse, or equal.” It doesn’t say the program has to specify which variation.

I think the program already gets this through human input.

The prompt isn't asking the user to enter arbitrary changes. It specifically asks:

“Enter variations of this explanation that would still work to explain the same thing.”

So by entering a variation, the user is making the judgment that it still accounts for what the original explanation was supposed to account for. That's intentionally a human judgment, just like the other judgments I've discussed in #5553.

One could run the program again with corrected inputs but as I noted in #5533, that approach won’t scale.

Jad originally replied in #5559. I’ve extracted his reply to avoid bulk criticism:

If the user later changes their mind about one of those judgments, then yes, the current minimal CLI requires them to run it again with the corrected input. I agree that wouldn't be good UX for a full application, but that's not what I'm trying to build here. Adding the ability to add, edit, or delete variations and immediately recalculate the ranking is straightforward and doesn't change the decision procedure being demonstrated.

I agree that HTV has to stand on its own. My argument isn't “Veritula has this problem too, therefore it's okay for HTV to have it.”

The reason I've been comparing the two is narrower: to show that outsourcing the parts requiring creativity and judgment to the user doesn't prevent us from having an executable decision procedure built on top of those inputs.

On revisability specifically, I agree that the result should be tentative and able to change when the user's judgments change. As I explained in #5559, this can technically already be done by rerunning the program with the updated inputs. The current CLI is only a minimal demonstration, so that's obviously not ideal UX. Letting the user add, edit, or delete variations and immediately recalculate the result would be straightforward and wouldn't change the decision procedure.

I think the Pop-Tarts example mixes together two different things: acquiring new knowledge and forming a preference between explanations. Looking up why Pop-Tarts were actually given their name gives us new knowledge; it doesn't by itself show that the preference formation between explanations isn't HTV.

As I argued in #5553, the program operates on the user's current understanding of the problem and explanations. The user is comparing explanations and variations they currently judge to work. So everything they already know, including criticisms they're aware of, is part of that judgment.

In the Pop-Tarts example, say the three explanations are equally hard to vary given what I currently know. That's fine. I currently have no reason to prefer one over another.

Now suppose I look it up and find historical evidence saying the name was chosen for reason X. I've gained new knowledge, and that changes the problem situation. I'm no longer just asking why they're called Pop-Tarts; I'm asking why they're called Pop-Tarts given that I also know this historical evidence says X.

I could still maintain that the real reason was something else. Maybe the company was lying or the historical source was wrong. But then I have to explain that too. If I just say “the real reason is that they pop out of the toaster, and for some unrelated reason the company says X,” I've added another arbitrary factor to preserve my explanation. That seems like exactly the kind of thing that would expose it as easy to vary.

So I don't see acquiring new knowledge as something that sits outside the process and simply overrides the HTV result. New knowledge changes the problem situation and therefore changes what a working explanation now has to account for. We can then compare the explanations again in light of that new problem situation.

Being hard to vary also doesn't guarantee that an explanation is true. Newton's theory of gravity was a good explanation and remains good enough for many engineering problem situations, even though we later learned that it isn't the full story. As new problems and observations came up that Newton couldn't adequately account for, the problem situation changed and we needed a better explanation.

So I don't think every act of acquiring knowledge or finding a criticism itself needs to take the form of thinking about variants. Those things change the problem situation and affect which explanations and variations we consider to still work.

But that's different from saying the preference formation itself isn't HTV. Once our current knowledge and criticisms are taken into account, HTV can still operate on the explanations that still work and give us a preference—or sometimes tell us that, given what we currently know, they're equally good.

Same point as my response in #5559.

I don't think it follows that a competing explanation would also have uncountably many working variants just because it involves continuous quantities.

The grass example is easy to vary precisely because there's no explanation for why the amount should be 1kg rather than 0.9kg, 0.95kg, etc. If 1kg doesn't work, I can just keep changing the number. Nothing in the explanatory argument constrains it.

But suppose grass really did cure the disease and we actually understood how. Maybe a particular compound in the grass interacts with some biological mechanism, and a certain concentration is required for the effect. The explanation might allow a whole range of effective dosages rather than one exact number, but that range would itself be explained and constrained by the mechanism.

I wouldn't consider every possible dosage within that range a different variation of the explanation. They're different cases covered by the same explanation. Saying “this mechanism works within this dosage range” is one explanatory claim, even if there are infinitely many numerical values inside the range.

So I think there's a difference between an explanation containing a continuous variable and an explanation whose parameters can be changed arbitrarily without explanatory reason. The first can be perfectly constrained by the explanatory structure. The second is exactly what I understand easy-to-vary to mean.

This also comes back to the point I made in #5553: the program relies on the user's understanding of the explanatory argument. A knowledgeable user wouldn't enter 0.9kg, 0.9001kg, 0.90001kg, etc. as infinitely many distinct explanatory variations if they understand them as instances of one explained dosage range.

Just to confirm, and so you can hear it from me, yes I did use AI to help with my submission.

For posterity, here was my position during the discussion:

I think it's technically fair for Dennis to consider the submission ineligible because the bounty terms clearly say "Submissions must be handwritten. No AI-generated text or code; suspected AI use makes submissions ineligible."

On the other hand, I think this outcome is a shame because I don't think my use of AI changes any of the real work and thought that was put into it. If you zoom out, the motive of the bounty is to attract people to work on ideas and develop them, which is exactly what I did here, regardless of the tools used. As How Do Bounties Work? puts it, "Bounties let you invite criticism and reward high-quality contributions with real money."

And this is exactly what happened here. The idea had been posted on Veritula for about 10 months, and when I saw the bounty, I took it as a fun challenge to work on. So in that sense, the bounty incentive worked. And it seems to me that the reception of the idea has been good so far, which is why I find this outcome disappointing. On a symbolic level—and I acknowledge that this may be very different from how Dennis sees or intends the decision—his withdrawal of all his funds feels to me like this work is somehow not something he's willing to reward.

I did attempt to persuade Dennis to reinterpret the no-AI rule by discussing the underlying reasons for the rule. We agreed that handwriting can be a way to test the submitter's own understanding rather than relying on AI's understanding. While we agreed that this wasn't an issue for me, we disagreed about what should follow from that. My view was that the purpose of the rule should matter more than the literal wording, whereas Dennis seemed to think that the written terms should still govern.

Ultimately, we couldn't come to an agreement on whether my use of AI was appropriate in the context of this bounty. We also disagreed about whether I should have raised my use of AI proactively. In any case, I respect Dennis's decision since ultimately these were the terms of his bounty. We also agreed that in the future, discussions like this about the terms ought to be brought up at the beginning rather than after the fact.