Following up on my last post, some measure of debate has occurred at the Dinofarm Games Forums concerning the purported inverted puzzle form. I'd like to try to perform an analytic survey of the issues at the heart of the debate that seems to be happening. For sake of brevity, I will be using "system" to refer to "interactive system" throughout. In addition, I'll be using "inverted puzzle," but please understand that I am not especially committed to this terminology. If you disagree with the use of the term, then just please bear with me. It is merely a term chosen for ease of communication, because I simply need to use one term or another.
To provide a quick recap, an inverted puzzle is a system with prescriptively negative states ("fail states") but no prescriptively positive states ("goal states"). A contest is a system with both fail states and goal states.
As far as I can tell, the central claim that seems to be being made in the debate is that for all inverted puzzles, there exists a set of victory conditions that would improve the system by its addition.
There are a lot of qualifications and details concerning this that we can explore, but let's start at the beginning.
There seem to be a couple of assumptions inherent in this claim.
(1) Some systems sometimes deliver some kind of value to some persons.
(2) There is a legitimate sense in which in some cases we can evaluate two systems and determine that one is more effective than the other at delivering this value.
I think we all agree that (1) is true, especially since with so many uses of "some" it is a very weak claim. In any case, I don't really need a stronger claim for my purposes. As for (2), there are some important notes to make. First, we are not saying that we can so evaluate any two systems. We are merely saying that there exist pairs of systems for which we can correctly evaluate which is more effective. Second, it seems that in such evaluations we would be taking the kind of value to be fixed, though of course there could potentially be situations where one system is more effective at delivering one kind of value and the other is more effective at delivering a different kind of value. Third, because of the "some people" clause in (1), I am allowing that the effectiveness of systems may depend upon which persons the value is being delivered to. We might suppose that there exist properties of the persons upon which the effectiveness depends. Fourth, it is possible that the effectiveness differs situationally. That is, for some person, system A might be more effective than system B at one time but the opposite scenario might obtain at another time. I will explore these complications later, but for now, I will take for granted that in some legitimate sense, we can, at least in some cases, sort out which systems are more effective than others.
So let's define a function for this evaluation:
(3) EFF(A, B) = the system more effective at delivering value, where the kind of value and the class of person are held fixed
I will allow that sometimes EFF(A, B) = ∅, where ∅ is the null set. This indicates that neither A nor B is more effective than the other at delivering value, or possibly, that EFF(A, B) actually returns either A or B, but that it is not possible to determine the correct answer.
Now, it seems clear that we can take an inverted puzzle and add victory conditions to it to produce a contest. So let's define a function for this as well:
(4) C(IP, VC) = the contest produced by adding victory conditions VC to inverted puzzle IP, keeping all other details of IP fixed
Another assumption now appears to be:
(5) For every inverted puzzle IP, C(IP, VC) exists for some set of victory conditions VC.
And the claim now can be formulated as follows:
(6) For every inverted puzzle S, there exists an adequate set of victory conditions VC, such that EFF(S, C(S, VC)) = C(S, VC).
Note that the claim is not that there is some optimal set of victory conditions. It is not necessary to be able to produce “the right” victory conditions for the system. What we’re saying is merely that there is at least one set of victory conditions that would improve the system in some way. The idea here appears to be that if every inverted puzzle can be improved by transmuting it into a contest, then there would appear to be no special reason why anyone should ever decline to include victory conditions in their system’s design, unless they are designing a toy. That is, there would appear to be no special reason why anyone should ever specifically design an inverted puzzle.
There are a number of ways in which (6) could be false or in which (6) might technically be true but with the force of its intended consequence undermined by the weakness of the details. I will offer some suggestions below for such scenarios, but I do not take it that this constitutes an exhaustive list of all possibilities.
I. There exist inverted puzzles for which EFF(IP, C(IP, VC)) = IP for all VC.
If this is true, then the task set before us is to determine under what circumstances an inverted puzzle cannot be improved by adding victory conditions. We might begin, as some have above, by positing theoretical systems that might fit the bill and theorize about why such systems are adequate as they are. However, it would seem quite difficult to be reasonably sure that any such systems simply cannot be improved in the way we care about by adding victory conditions.
A further complication of such systems is that it seems there might be important methods for improving such systems that do not involve merely adding victory conditions but also performing some other important transformation to the system. That is, adding victory conditions while the system is not held universally fixed besides. It seems that if this is true, then the central claim must simply be modified by using a different function:
(7) C’(ip, vc, f) = the contest produced by adding victory conditions vc to inverted puzzle ip and performing some additional important transformation f to ip
The central claim then becomes:
(8) For every inverted puzzle IP, there exists an adequate set of victory conditions VC and an adequate additional transformation F such that EFF(IP, C’(IP, VC, F)) = C’(IP, VC, F)
Note that (8) entails that even an inverted puzzle system that has in itself been optimized—that is, made into the best inverted puzzle that it can be made into—can be improved by transmuting it into a contest. The problem with this avenue is that it would then fall to those advocating for the truth of (8) to posit an adequate transformation for improving all inverted puzzles or to develop a generalized method for determining an appropriate transformation for each inverted puzzle or else to formulate a proof that such a transformation exists for all inverted puzzles. Because inverted puzzles can vary wildly (compare Tetris and Dwarf Fortress, for instance), it seems that a generally applicable transformation would be very difficult to formulate, if it even exists. A generalized method for finding an appropriate transformation would seem about as difficult to discover. It is unclear whether a proof that such transformations exist would be simple or difficult to construct.
II. For all inverted puzzles, EFF(IP, C(IP, VC)) = IP for all VC.
This is a very strong claim, and it seems to be a very difficult proposition to support. Surely this is a highly implausible scenario, and one that needs no further exploration as is. However, it becomes slightly more plausible if we stop taking for granted some general value that all interactive systems deliver:
III. For all (or some) inverted puzzles, EFF(IP, C(IP, VC)) = IP for all VC for a particular kind of value.
Until now I have supposed that we are considering a general sort of “interactive system” value that inverted puzzles and contests would both be trying to deliver. However, it would seem that puzzles, contests, and decision games theoretically might function best when they are designed to deliver different kinds of value. It seems to be a real possibility that inverted puzzles are best implemented such that they deliver some other value besides those that contests are especially good at delivering.
For any value that contests deliver well, this avenue of thought does nothing for the idea that inverted puzzles can be appropriate systems for delivering that kind of value. For instance, if we suppose that one kind of value that decision games are good at delivering is the intellectual achievement associated with the acquisition and application of objectual understanding, then if (6) is true for that kind of value, then inverted puzzles can never constitute an optimized system for delivering such value. It would always be possible to improve upon the design by transmuting it into a contest. Tetris, for instance, seems to deliver that kind of value in some measure. But (6) would entail that victory conditions would necessarily improve upon the delivery of that value.
If some other kind of value exists that inverted puzzles are good at delivering in a way that contests are not, then the task before us is to determine what that other kind of value is.
IV. For some inverted puzzles, EFF(IP, C(IP, VC)) = IP for all VC for some, but not necessarily all, persons.
The claim in (1) was worded weakly to allow for different persons to procure value from interactive systems differently. So for one person, an inverted puzzle may deliver its value most effectively, while for another person, some related contest produced by adding victory conditions delivers its value most effectively.
Surely there will be those who dispute this possibility, and of course, if they are right, then IV is an unimportant avenue of thought. Never mind that for now. For the sake of argument, let us suppose that if IV is true, then there must be some reason that one person draws value differently from another person.
If the reason is that person A has property set P while person B does not, then this simply makes our task more specific. Rather than merely determining what properties of the system make for a good inverted puzzle, we must also search for what properties of person combine with those properties to allow for the system’s value to be delivered most effectively. Practically speaking, we would be identifying what sorts of person benefit in a special way from interacting with inverted puzzles, what that special way is, and how best to design inverted puzzles to accommodate their needs.
Note that it is also theoretically possible that inverted puzzles are more effective at delivering their value under certain non-systemic circumstances, but this does not make our task much more complicated. We must simply also identify what those circumstances are, but in practice this component of the task would be hardly different from identifying what properties of inverted puzzles are desirable. We would simply be identifying the proper usage practices of well-designed inverted puzzles, and it would presumably fall to the designer to recommend or enforce such practices.
Of course, if those who dispute IV’s possibility are right, for instance, if different persons do not, in fact, procure value from systems differently, then the content of this section is moot.
V. Though (6) is technically true, the improvement made by adding victory conditions is negligible.
This claim would attempt to undermine the weight of (6)’s consequences. Rather than contests being always preferable to inverted puzzles, if the improvement made by adding victory conditions was not of a particular degree, then perhaps the difference between the effectiveness of inverted puzzles and contests would be akin to the difference between two contests that are of roughly the same effectiveness. I take it that if a person identifies one contest as being slightly better than another contest, she will not necessarily disavow any and all interest in the inferior contest. Similarly, there would seem to be little motivation for discarding inverted puzzles entirely, especially if it is not necessarily a simple matter to determine adequate victory conditions for slightly improving the system.
Of course, it is certain that those who advocate for adding victory conditions will claim that the improvement made by adding victory conditions is significant and that it is not at all an insurmountable task to identify adequate victory conditions.
VI. For some inverted puzzle IP, EFF(IP, C(IP, VC)) = ∅ for all victory conditions VC.
It is a possibility that whether an improvement is made by adding victory conditions is unclear. I will not explore this possibility, because it seems to leave very little recourse for coming to a resolution of the problem, or at least, I do not see how such recourse is available. However, in the interest of being thorough, I wanted to at least state that the possibility exists in order to allow for the prompting of others to tackle the avenue of thought where I am myself incapable.