Turing Machines and behavioral dispositions
I've been thinking of late about the conditions required for attributing 'rule guided', and more specifically, 'inference driven' behavior to an agent, as occasioned by recent science reports such as this one, concerning maze-navigation by oil droplets.
The difficulty with applying Turing Machine interpretations to nature is that the conditions that a natural phenomena must satisfy in order to be subject to a Turing interpretation are extremely weak. Let's say we have two historical records of different sets of phenomena, with the data in each record recorded using a countably enumerable set of features. It doesn't matter what phenomena are involved. Let's label one record 'input', and the other record, 'output'. It doesn't matter which. Enumerate the features recorded in the 'input' set and enumerate the features recorded in the 'output' set. Now find a computable arithmetic function that has the set of 'input' encodings as its domain and the set of 'output' encodings as the range. A Turing Machine which computes that function figures as a Turing interpretation of the two data records.
The fact that most such interpretations are going to be about as convincing as the Bible Code begs the question of when they must be taken seriously, if ever. There are in fact two important kinds of case I can think of:
i) Computable functions which, because they are associated with measurable scalar features embedded in the input data, allow one to reliably predict the occurrence of features of interest in output data. Mathematical equations which state the scalar relationships involved are conventionally understood to specify natural laws.
ii) Universal Turing Machine architectures coupled to interfaces that associate features with number tokens in such a way that members of families of TMs which can be encoded and run on the UTM architectures can be seen as implementing useful activitites via the interface content linked to the domain and range elements of the arithmetic function being computed. Such computing architectures are what we ordinarily understand to be programmable computers.
It is significant that in both of these kinds of cases, the regularity of nature is a necessary, but not sufficient condition for the validity of the interpretation. Human utility is also necessary here; thus, we may reasonably ask whether there's ever a case where human intentionality and salience are not preconditions for a Turing Machine interpretation's applicability.
I'm strongly inclined to think that there are examples to be found in biological metabolisms, but there are significant caution flags. It's reasonable to think that, for a living organism or a living metabolism, it might in fact be possible to represent and enumerate all of the environmental types to which an organism might respond, along with all of the types of action it might conceivably instantiate, and have a computable arithmetic function that maps pairings of perception types and space-time locations to pairings of action types and space-time locations in such a way as to give the complete behavioral disposition of the organism - every circumstance the organism could possibly experience is correctly mapped to the action the organism would take under those circumstances. However, we should not make the mistake of thinking that the matters of representation and enumeration are uncomplicated. Even if one starts with the presumption that all of the agents in a given community are simple 'Turing agents' whose behavioral dispositions can be given by means of finite rule sets expressed in a common first-order language, a question arises concerning what happens when alliances, or more specifically, corporate agents begin to emerge within the Turing agent ecology, featuring behavioral plasticities born of internalized natural selection over the replicating agents which compose them. For at least some such corporate agents, it seems that the language which must be used to specify their behavioral disposition machines must quantify over predicates of the language used to characterize the basal agent population; furthermore, if the number of predicates in the base language is countably infinite, this suggests that the cardinality of potential predicates in the language used to describe corporate agents is that of the power set of the positive integers: which raises serious doubts about whether the second order language machine specifications of every possible agent in the corporate agent class could be encompassed within a common numerical encoding; hence, whether there could exist a universal Turing Machine capable of simulating any corporate agent. It should be emphasized that such conclusions in no way undermine the thesis that agent behavior is consistent with and governed by natural law; it does, however raise questions about the predictability attaching to behaviors of some complex agents in the limit, as well as the weight that must be given to second order factors and second order effects.
The difficulty with applying Turing Machine interpretations to nature is that the conditions that a natural phenomena must satisfy in order to be subject to a Turing interpretation are extremely weak. Let's say we have two historical records of different sets of phenomena, with the data in each record recorded using a countably enumerable set of features. It doesn't matter what phenomena are involved. Let's label one record 'input', and the other record, 'output'. It doesn't matter which. Enumerate the features recorded in the 'input' set and enumerate the features recorded in the 'output' set. Now find a computable arithmetic function that has the set of 'input' encodings as its domain and the set of 'output' encodings as the range. A Turing Machine which computes that function figures as a Turing interpretation of the two data records.
The fact that most such interpretations are going to be about as convincing as the Bible Code begs the question of when they must be taken seriously, if ever. There are in fact two important kinds of case I can think of:
i) Computable functions which, because they are associated with measurable scalar features embedded in the input data, allow one to reliably predict the occurrence of features of interest in output data. Mathematical equations which state the scalar relationships involved are conventionally understood to specify natural laws.
ii) Universal Turing Machine architectures coupled to interfaces that associate features with number tokens in such a way that members of families of TMs which can be encoded and run on the UTM architectures can be seen as implementing useful activitites via the interface content linked to the domain and range elements of the arithmetic function being computed. Such computing architectures are what we ordinarily understand to be programmable computers.
It is significant that in both of these kinds of cases, the regularity of nature is a necessary, but not sufficient condition for the validity of the interpretation. Human utility is also necessary here; thus, we may reasonably ask whether there's ever a case where human intentionality and salience are not preconditions for a Turing Machine interpretation's applicability.
I'm strongly inclined to think that there are examples to be found in biological metabolisms, but there are significant caution flags. It's reasonable to think that, for a living organism or a living metabolism, it might in fact be possible to represent and enumerate all of the environmental types to which an organism might respond, along with all of the types of action it might conceivably instantiate, and have a computable arithmetic function that maps pairings of perception types and space-time locations to pairings of action types and space-time locations in such a way as to give the complete behavioral disposition of the organism - every circumstance the organism could possibly experience is correctly mapped to the action the organism would take under those circumstances. However, we should not make the mistake of thinking that the matters of representation and enumeration are uncomplicated. Even if one starts with the presumption that all of the agents in a given community are simple 'Turing agents' whose behavioral dispositions can be given by means of finite rule sets expressed in a common first-order language, a question arises concerning what happens when alliances, or more specifically, corporate agents begin to emerge within the Turing agent ecology, featuring behavioral plasticities born of internalized natural selection over the replicating agents which compose them. For at least some such corporate agents, it seems that the language which must be used to specify their behavioral disposition machines must quantify over predicates of the language used to characterize the basal agent population; furthermore, if the number of predicates in the base language is countably infinite, this suggests that the cardinality of potential predicates in the language used to describe corporate agents is that of the power set of the positive integers: which raises serious doubts about whether the second order language machine specifications of every possible agent in the corporate agent class could be encompassed within a common numerical encoding; hence, whether there could exist a universal Turing Machine capable of simulating any corporate agent. It should be emphasized that such conclusions in no way undermine the thesis that agent behavior is consistent with and governed by natural law; it does, however raise questions about the predictability attaching to behaviors of some complex agents in the limit, as well as the weight that must be given to second order factors and second order effects.
posted by BenjaminRode at 9:34 PM
0 comments
