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Link to exact code version used here: hard-to-vary/htv.py at ab8be8

Link to exact code version used in #5523, #5541, #5544, #5551:
hard-to-vary/htv.py at ab8be8

If the user already judges that both explanations have infinitely many working variations, do they really need the program to tell them that they're equally hard to vary? That seems unlikely—the result already follows from the inputs.

That said, if you think it's important for the program itself to represent this case explicitly, I can extend it to handle infinite families of variations as I suggested in #5598. I see that as a small extension to the implementation rather than a problem with the underlying HTV procedure.

Okay, so you're thinking of an edge case where two competing explanations genuinely both have infinitely many working variations.

For example, one explanation says some amount X of grass cures the disease, another says some amount Y of wheat cures it, and neither explanation constrains what X or Y should be. Both can just keep being varied indefinitely.

If that's the kind of case you have in mind, then yes, I agree it's an interesting edge case. If these were the only two competing explanations, my current program would have an awkward time representing the fact that both have infinitely many variations. But also, in this example they're genuinely both extremely easy to vary, so ranking them equally doesn't seem obviously wrong to me.

I don't think we need to get into comparing different sizes of infinity here. If a third explanation had only a finite number of working variations, it would clearly be harder to vary than either of the infinite ones.

As for the implementation, one simple extension would be to let the user indicate that a submitted variation represents an infinite family of working variations, rather than requiring them to enumerate individual examples. Something like a checkbox for "this can be varied indefinitely." That would let the program represent this edge case without changing the basic idea.

I'm not sure it's clear what you mean by this.

Are you saying the process I've outlined doesn't work for a factual matter like the Pop-Tarts question? If so, I've explained in #5586 and #5562 how facts and new knowledge change the problem situation and what explanations and variations we accept.

If, on the other hand, you're saying that this process does work, but that not all of it should be called HTV, then I think that's the same point you were making in #5585, which I'm fine with.

Ok so let’s put ourselves in the shoes of someone who genuinely thinks different decimal numbers lead to different variants for both competing explanations, and that, as a result, there are infinitely many variants for each. Walk me through how that person would use your program?

In short, the question is: how can we use the program when we genuinely think both explanations have infinitely many variants?

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.

The program can't accept my judgment that these are genuine variations and then independently override that judgment because it “knows” they're actually irrelevant. Doing that would require the program itself to understand what is doing explanatory work. That's precisely the part I'm outsourcing to the user.

Fair enough.

As of 2026-09-02, I’ve removed that part from the blog post.

Revision 12 says:

Isn’t the assignment of positive scores, of positive reasons to prefer one theory over another, a kind of justificationism? Deutsch criticizes justificationism throughout The Beginning of Infinity, but isn’t an endorsement of a theory as ‘good’ a kind of justification?

I should know better since I recently wrote about how justifying a preference for a theory is fine (as opposed to justifying the claim that a theory is true).

It sounds like you’re agreeing, in which case this shouldn’t be marked as a criticism.

I don't see why HTV failing to distinguish two good explanations before we have the knowledge that distinguishes them means it's unrelated to truth.

Because it doesn’t help us form a preference in a factual matter like the Pop-Tart question. HTV is not involved.

HTV could still be part of the process, but DD’s claim was that all rationality boils down to HTV.

I'm not defending DD's claim. My claim is that HTV can be implemented.

One would reject some explanations for reasons unrelated to HTV. It’s not that one would override a specific HTV result – one wouldn’t even get to that result because one would first make other choices leading to different inputs.

I think this is fair. You can treat new knowledge and criticism as changing the problem situation within which HTV operates, or more narrowly as filtering which explanations still work before applying HTV. I think those are functionally equivalent; if you want to call the latter preference formation outside HTV, I'm fine with that.

I think this is the same basic point as #5577.

How does this show that HTV is unrelated to finding truth?

You say:

But guess 1 and 2 are plausible and I see no reason to prefer one over the other.

That's exactly how I see it. Before looking up the historical evidence, both seem like good explanations given what we know. So HTV giving us no preference between them seems like the right result at that point.

Once we acquire new knowledge that distinguishes them, the problem situation changes, as I explained in #5562.

I don't see why HTV failing to distinguish two good explanations before we have the knowledge that distinguishes them means it's unrelated to truth.

So I don't see acquiring new knowledge as something that sits outside the process and simply overrides the HTV result.

One would reject some explanations for reasons unrelated to HTV. It’s not that one would override a specific HTV result – one wouldn’t even get to that result because one would first make other choices leading to different inputs.

If I gather new info and the problem situation changes to where I already know Pop-Tarts aren’t tart but sweet (eg because I taste test them), then I simply won’t include that guess in the inputs to the program, and I won’t bother varying that guess.

HTV could still be part of the process, but DD’s claim was that all rationality boils down to HTV.

I don't think test results need some separate formal mechanism for being “fed back” into HTV.

This is the same point I made in #5562. A test result is new knowledge, and new knowledge changes the problem situation and therefore what counts as a working explanation.

It does. Preference formation is the point of the program.

I don't think preference formation requires the program to always select exactly one variant.

If several variants are equally hard to vary given everything I currently know, then “equally hard to vary” is itself the result of the comparison. I don't currently have a rational reason from HTV to prefer one over the others.

I don't think the program should invent a preference when the current problem situation doesn't give us one. The variants can remain competing possibilities until we learn something that differentiates them.

Fair, I didn't mean to imply that #5531 says different people getting different results is itself a problem. I was explaining why I think disagreement about what counts as a variation is okay, even when that disagreement leads to different results.

The user can correct this by rerunning the program with the corrected inputs. I think the UX can be improved by adding add/edit/delete functionality, as discussed in #5559 and #5560, but the basic functionality of the MVP still holds.

Being hard to vary also doesn't guarantee that an explanation is true.

Agreed, but I’m not asking for a guarantee. I’m basically saying preference formation using HTV should help us find truth. The Pop-Tart example seems to be a case where HTV is unrelated to finding truth.

Addressed that with #5577

@jadelmourad be sure to submit separate criticisms separately. You benefit because it means I need to address each criticism individually, not in ‘bulk’. (See #5546, keyword ‘bulk’.)

I don't think those are genuine variations, so I wouldn't input them when running the program. But someone else might genuinely think they are.

The program can't decide which of us is right without itself understanding the explanation and the problem situation—in other words, without being a general intelligence. That's the point I just made in #5572, and more generally in #5553 and #5557.

At the current stage, without AGI, I think any work that requires that kind of understanding and creative judgment necessarily has to be outsourced to the user. The program then operates on the judgments the user supplies.