Iterative Relativization

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I appear to have completed some task systematically and in a rational and reproducible manner upon presenting the original vector summation examples in Excellence, Decency and Badness and by refining their interpretation in The 9 x 9 Grid. Specifically, the task seems to be of relativizing anecdotes into a mathematically defined framework of Sinns. None of the interpretations appear to be such that any random selection of slots would have facilitated an interpretation of equal or greater persuasiveness. This implies that I have found something real that has not been not found before.

My approach is lacking some features. As far as we are concerned of automatized decision making the most important missing feature seems to be that of evaluating patterns that belong to the same slot. For this purpose I propose that the act of relativizing patterns to a grid is iterated as many times as is necessary for producing a hierarchy of patterns that is sufficiently precise. The level of precision required depends on the task at hand.

Suppose the task were to figure out whether caloric theory is better than modern thermodynamics and that we do not presuppose information about which one is better. On a first-level interpretation both of these should be identified as intellectual patterns. On a second iteration caloric theory should be deemed an OPPRESSIVE pattern because its explanatory power is weaker than that of modern thermodynamics. Explanatory power would be measured by explicating the types of phenomena these theories explain in a way that is consistent with experiential data. To my knowledge, there is no extant procedure for entering such experiential data into an automated decision making algorithm. However, there seems to be nothing that would disallow the existence of such a procedure in theory. At least the hopes of finding such a procedure seem greater than the hopes of finding a deterministic or positivistic way of measuring relevance as that concept is understood in the context of the Problem of Induction.

This iterative relativization I am proposing means that whenever a Markover operator assigns two patterns to the same slot the program asks for another relativization. The process could be like this:

  1. Caloric theory and modern thermodynamics are both deemed primarily INTELLECTUAL patterns on grounds of being intended as such by those who have devised and relied on them.
  2. Of these intellectual patterns, caloric theory is determined as secondarily OPPRESSIVE because the best objective justification for its use would rely on someone's personal authority since the other option, modern thermodynamics, is intellectually more justified and as such also secondarily INTELLECTUAL.
  3. We could continue to identify tertiary slots but this isn't needed in order to complete this hierarchical evaluation of caloric theory and modern thermodynamics. By default, there appear to be no circumstances in which the number of iterations would need to be greater than the number of patterns that are to be evaluated. However, in case of inconsistent evaluations (eg. A > B is inconsistent with (B > C and C > A) but the program has to ask because the answer can be A = B or A < B) the program might issue a warning and, if the warning is ignored, ask for new hierarchy assignments as many times as there are conflicting patterns. Note that there are probably several ways to complete this task so that not all of them require the same amount of clicks.

The advantage of this iterative relativization is a practical one. The other option I can think of would be to use decimal numbers for the X and Y coordinates of patterns. While this works neatly in theory, in practice it would be at least painstaking, difficult and slow for a Markover user to click on the exact right spot on the grid. It is faster and more systematic that the operator clicks twice or more instead. This way the operator doesn't need to go back and revise his earlier evaluations. Finding all of them manually would be inconvenient and prone to error. If there were some way to specify identities of patterns in Markover (the simplest one would be string matching but this would mean the program can't tell a metal can that contains food from the verb can) the operator also wouldn't need to re-evaluate each specific instance of a pattern. However, re-evaluating each instance has the advantage of reducing possibility of error as the operator really has to consider for each individual case whether they are consistent with the interpretation he finds correct.

The iterative relativization process can be iterated as many times as two patterns remain in the same slot so that the user has not explicated that having them in the same slot is his intention. Ie. if the user placed caloric theory and modern thermodynamics in the same slot the program would ask for iteration of relativization but if the user still placed them in the same slot the program would stop asking for another iteration.

Iterative relativization does not seem to work for assigning hierarchies for patterns whose moral difference is not absolute but relative. The moral difference between caloric theory and modern thermodynamics is quantitative in the rather plausible context that modern thermodynamics is absolutely better than caloric theory. But iterative relativization could not be used to rank classical mechanics and quantum mechanics because they are essentially differenteven though they belong to the same quadrant – but they are not absolutely better or worse in relation to each other.

If classical mechanics and quantum mechanics were to be evaluated by way of iterative relativization they would first have to be split into smaller components such as "classical mechanics for bodies of tangible size" or "quantum mechanics for bodies of extremely small size" or "quantum mechanics as an explanation of laser" and so on. This process could be called analytical iterative relativization because the object of relativization is analyzed, ie. split into smaller pieces, until seemingly absolute moral differences between the separate pieces are found as opposed to the initial moral differences that are blatantly relative. In practice, after such a relativization a computer should be able to determine whether quantum mechanics or classical mechanics is more appropriate for performing some given task that involves physics.

In order to actually split a pattern into smaller pieces the operator might have to write his own description of the pattern if the initial description is not detailed enough. Or the operator might need to refer to some other written document in which this more detailed description is explicated by analyzing also that document in Markover.

Iterative relativization has not yet been implemented in Markover but this should be done as soon as possible. The advantage is that it is easier to judge comparative (ie. similar) patterns according to face value. Ie. the human operator is not required to have a preconceived absolute notion of how things are in order to analyze the text correctly and without excessive difficulty.

Suppose an operator who is unknowledgeable about scientific physics and is analyzing a text that first portrays caloric theory as good (as it explains the heat engine) but then, surprisingly, portrays modern thermodynamics as better (because it explains why cannons can be heated repeatedly by boring them). Without iterative relativization the operator would apparently have to be knowledgeable enough to deem caloric theory flawed before having read all of the text. Since he isn't he'd have to go back and modify his earlier interpretations upon learning that modern thermodynamics is better. But because of iterative relativization he doesn't need to do this. Instead, when the operator designates modern thermodynamics as intellectual Markover would then ask him to compare modern thermodynamics with other defined intellectual patterns. This "another round" would be of secondary relativizations, the next round of tertiary evaluations and so on until the pattern of modern thermodynamics has been explicitly deemed as equal with or inferior or superior to all other intellectual patterns. This way there is no need to "go backwards" in the process when new information is found.

By default, an intellectual pattern should be deemed equal with any intellectual pattern that does not contradict it. In case two intellectual patterns contradict each other they should be split into smaller pieces until they no longer do so. A hierarchy should be assigned only in case it is deemed impossible to resolve the contradiction this way. We can deviate from this but only under explicit criteria. An example of such a criterion might be prior usage: it might be reasonable to add a heuristic evaluation function that evaluates frequently used patterns as more important than rarely used ones.

There we go, automated scholastics ! This way we could produce a machine that has a view on what is the currently accepted scientific truth. Such a machine could conduct peer-review, leaving experts free to utilize their skills in another way than that of evaluating the work of their colleagues.

See Also