The Importance of Space and Time in Analogies used for Scientific Education,
by Anthony Peter Iannini, 2001 |
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Essay Overview from 05.04.2011:
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This article attempts to explain how we could teach an artificial mind about scientific concepts of space and time by analytically deconstructing the process of analogical reasoning. I posit that the STRFs (Structural, Temporal, and Relational Features) of a system must be isolated and compared to the STRFs of the system to be compared to. The illustrated figures numbers 1, 2, and 3 have been updated in 2011. It should be noted that I invented the term STRFs to highlight and clarify what aspects of systems must be isolated in order to be compared, contrasted, etc. in analogous reasoning.
Analogical reasoning encompasses a number of complex processes that compare representations of different entities for likeness or similarity. The key to understanding analogy is understanding the nature of the similarity between two representations.
Structure-mapping theories of analogy (Gentner, 1980, 1982, 1983, 1987) are successful because they capture the similarity between such things as 'pressure' and 'temperature' (Gentner, 1989) in situations such as the analogous movement of water in a tube (pressure) and the movement of heat through metal (temperature). In what follows, I will examine and suggest minor refinements to structure-mapping models of analogical reasoning in scientific educational circumstances.
In scientific educational circumstances, the educatees of scientific concepts are often presented with deep-structure analogies between known entities and entities within science's ontology that are to be explained by the educator.
For example, to explain the concept of an 'atom' to students that have no prior concept of an atom, the following example is unhelpful, "A hydrogen atom is like a helium atom".However, if the students have a concept of the 'solar system', use of analogical reasoning could prove highly useful, as in the following statement "An atom is like the solar system".
It is my hypothesis that in scientific education, analogy is often a useful tool for expressing the essential spatial, temporal, and relational features (STRFs) of an entity that is within the ontology of science but is outside the ontology of everyday perception.
For example, what an atom is like in terms of its STRFs can not be known through everyday observation of atoms. Rather, the STRFs of atoms must be represented in terms of an atom's analogous STRFs with more tractable objects.
The difficulty in making analogies that are useful in teaching scientific concepts is that the analogies must be made across domains rather than within domains of knowledge. A within-domain analogy, such as "a hydrogen atom is analogous to a helium atom" is hardly useful in teaching the concept of an atom.
Therefore, a classroom of students that has just learned the STRFs of the solar system will be able to represent, through analogy, STRFs essential to a scientific understanding of atoms.
However, STRFs must be, for analogy to be successful, categorized in such a way as to be found similar in each of the relevant entities to be compared. For example, one of the relational features between the parts of the entity 'solar system' could be categorized at 'orbital'.
Also, the same 'orbital' categorization could be made for the entity 'atom' because it has at least on part that stands in relation to another part in the entity that is categorized as an 'orbital' relation. As Mark Turner has commented, "Analogies exist because of the way we categorize" (1988, p. 3).
It is my goal to outline a cognitive and computational model of how analogy works in these type of educational situations based upon STRFs. Therefore, I will provide potential suggestions for the educator's (i) aquisition of knowledge of entites and (ii) deployment of analogical processes between sets of known entities.
Learning a scientific ontology through the use of analogy can be limited to situations of the following form: The STRFs of some base object B, which are stored in memory of an educator as categorized descriptions of B, are to be conveyed to some educatee that has no prior knowledge of the STRFs of B.
However, the educatee may have knowledge of the STRFs of some target object T, as categorized descriptions of T, where T is analogous to B in terms of B's STRFs that have been categorized. The STRFs of T then (as categorized), must either be stored in the memory of the educatee or the STRFs of T must be perceptually available in the educatee's immediate environment. I will suggest a way in which a computational model could provide visual representations of entities that are analogical to the base entity.
Explanation of STRFs: Before considering a paradigmatic case of analogy, it is necessary to first expand upon the constituent parts of the STRFs of some object.
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As shown in Fig. 1, I will use a simple two-body solar system as an example for this explanation. The spatial features of an object are spatial representations of the object in three-dimensional space (x,y,z coordinate space) at a given moment in time.
The spatial features include information about the shape(s) volume(s), and mass(es) of the object(s) and possibly the distance between the constituent parts of the object if there are such. Objects can be spatially represented in a hierarchy using 'part-whole' relations (Darden & Rada, 1988) such as ([SOLAR SYSTEM] has-part: SUN, PLANET) and categorical descriptions of spatial features like ([SUN] has-vol: 1000), ([PLANET]has-vol: 50), ([SUN]has-shape: SPHERE), ([SUN] has-shape: SPHERE). |
The mass of a given object could be represented by a simple value, as in ([SUN]has-mass: 20000). Distances could be measures of the distance between surfaces of parts relative to the highest entity in the current hierarchy such as (in [SOLAR SYSTEM] distance-between [SUN] and [PLANET]: 100). All of these could be represented in and x,y,z coordinate space. A number of relative properties could be derived computationally based solely on spatial information such as (if {[ENTITY1] has-vol [x] and [ENTITY2] has-vol [y] and [x] > [y]} then [ENTITY1] is 'bigger than' [ENTITY2]).
The temporal feature of an object is the spatial representation of the entity through time, which is a finite set of representations of some entity as it changes in time. If there is no perceptible change in an entity at the current level of analysis, for example, there will be no relevant temporal feature. However, the concept of many entities, such as the solar system, require the temporal feature. The temporal feature is a representation of the movement of parts and a categorization of the relations of the parts.
For example the relational temporal categorization of (in [SOLAR SYSTEM] movement-between [SUN] and [PLANET] is-type: ORBITAL) could be determined from two criteria: (i) distance (which is a spatial property) between two objects never reaches zero, and (ii) the 'orbiting' object passes through sequentially (in two possible ways) through all four quadrants of coordinate space, where the orbited object is the origin.
Other categories of temporal relations could be STATIONARY, MOVE PAST, WAVE, and other categorizations that would allow for analogical reasoning to be made. The relational feature of an object is the interaction of the parts of the object at a moment in time. Relational features include notions of cause and effect, force, resistance, etc.
For example, (in [SOLAR SYSTEM] relation-between [SUN] and [PLANET] is-type: GRAVITY OR SPACE-TIME CURVATURE). The specific categorization of the relational type GRAVITY could be given a hierarchy itself, where gravity is a sub-type of ATTRACTIVE FORCE. Thinking of GRAVITY as SPACE-TIME curvature only may also help teach the concept to a mind. Other sub-types of ATTRACTIVE FORCE could be WEAK NUCLEAR, STRONG NUCLEAR, MAGNETIC, etc. Mechanisms of STRFs in Computer Models: Because I wish to provide a plausible account of how STRFs of objects can be used in educational analogy, I will provide a few possibilities as to the acquisition and storage of STRFs.
Three-dimensional spatial information about an object could be gained from extraction of information from environmental scenes using algorithms developed by Marr (1982) or using pre-programmed (or innately specified) combinatorial 'geons' (Biederman, 1995) that can be described mathematically. Storage capacity for the complex ontology required of analogy could be made tractable because STRFs are the most basic features of systems that need be known in order to have understanding required for analogical reasoning with the relavant bases and targets.
Any system (human or computer) that is capable of educating others about scientific ontologies using analogy would have to come equipped with a rich ontology to utilize. In such cases, the system making the analogy for the purpose of educating others must have STRF knowledge of both B (the base object) and T (the target object) and have some way of knowing or finding out that T is within the ontology of the audience. I claim that this process has the following stages:
[1]. Represent some base object B
[2]. Extract the STRFs of B
[3]. Search a database for STRFs analogous to the STRFs of B
[4]. If (3) is successful, represent the target object T
Step (1) is the process of being able to represent an object in its entirety, with all of its 'secondary' qualities that are relatively unimportant to its STRFs. However, it could be imagined that some systems could be programmed such that the only information about objects they have is the STRFs information and complications of the move from step (1) to step (2) would be avoided.
Step (3) is the step by which hypothesizing must be done through a process of comparing very close matches to at least one (and possibly more) of the categories to which STRFs have been assigned (such as ORBITAL temporal features, etc).
For the current example, which will utilize the STRFs, I will examine the following situation: The concept of a CELL is to be expressed to educatees in two ways. First, the educator must convey the STRFs of an individual CELL and then the educator must convey the STRFs of how a CELL relates to the (human) BODY. Then, the educator must search a database for the most similar STRFs that are within the educatee's ontology. I will leave out a detailed explanation of this last step and suggest how categories used to classify STRFs can be used.
The cell: Basic spatial properties: ([CELL] has-part: NUCLEUS, MEMBRANE), ([CELL] has-shape: SPHERE), ([CELL] has-vol: 1), ([CELL] has-mass: 1), ([NUCLEUS] has-part: DNA), ([NUCLEUS] has-shape: HOLLOW-SPHERE), ([NUCLEUS] has-vol: .05), ([NUCLEUS] has-mass: .05), ([DNA] has-shape: CYLINDER), ([DNA] has-vol: .03), ([DNA] has-mass: .02), ([MEMBRANE] has-shape: HOLLOW-SPHERE), ([MEMBRANE] has-vol: 1), ([MEMBRANE] has-mass .3). Basic temporal properties: (in [CELL] movement-between [NUCLEUS] and [MEMBRANE] is-type: STATIONARY).
Basic relational properties: (in [CELL] relation-between [NUCLEUS] and [MEMBRANE] is-type: NONE). With this knowledge alone, the educator can represent the basic structure of a cell as a spherical object with a membrane and a nucleus that contains DNA. Further information about the functional properties of the parts could certainly be included but were left out as this is an analysis of the STRFs alone and the power of just these properties.
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As shown in Fig. 2. the graphical representation of the cell based on the STRFs would be the three-dimensional, spherical representation of the structure. Now, this captures the most important features of the cell in terms of its existence in space and time. The next step is to get STRFs about the BODY. This will be relatively easy because the CELL has already been explained in detail.
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The Body: Basic spatial properties: ([BODY] has-composite: [CELL]), ([BODY] has-shape: CYLINDER), ([BODY] has-vol: 1000). For clarification, some entity has a part 'has-part' if the part does not compose the entire entity that is one level up from it in the hierarchy.
However, if the BODY is composed completely (for the current purposes) from the object of type CELL, then it can be said to be a composite part, as opposed to a simple part like a head, arm, leg, etc.
With the simple knowledge that the body has a shape and a volume, the cells can then be represented as 'filling' the volme of the body. Although this is a rather crude way to represent the relationship, it is enough to convey the basic features of the compositional relationship so as to be able to search for a target entity that has similar features. So, the body, in this example, would be represented as in Fig. 3.The challenge the transfer the STRFs of the base to some target STRFs, where the STRFs of the target are available to the ontology of the educatees is the next step. |
Search for STRFs in Potential Targets: Any composite relationship would be a potential candidate for the target. The constraints on which composite could be constraints upon the objects that could be used as composites in the immediate perceptual environment of the educatees.
For humans, the potential range of objects that could be used to convey the STRFs of the BODY as it is composed of CELL is quite extensive. A successful search would require that there be categorical matches between some aspects of the STRFs.
I will not present a possible ontological search. However, based on the preceeding discussion, it is apparent what categories must be assigned to STRFs in order for the CELL as a composite of BODY relationship to be conveyed in a way that utilizes analogical reasoning and conveys essential features of the base.
References:
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Biederman, I. (1995). "Visual Object Recognition," in Kosslyn & Osherson (eds.) An invitation to cognitive science, Vol. 2: Visual Cognition. 2nd ed. Cambridge, Mass: MIT Press.
Gentner, D. (1980). The Structure of Analogical Models in Science (BBN Tech. Rep. 4451). Cambridge, MA: Bolt, Beranek, & Newman.
Gentner, D. (1982). Are Scientific Analogies Metaphors? In D. Miall (ed.), Metaphor: Problems and Perspectives. Brighton: Harvester Press.
Gentner, D. (1983). "Structure-mapping: A theoretical framework for analogy," in Cognitive Science, 7: 155-170.
Gentner, D. (1987). "Analogical inference and analalogical access," in A. Prieditis (ed.), Analogica: Proceedings of the First Workshop in Analogical Reasoning. London: Pitman.
Gentner, D. (1989). "The Mechanisms of Analogical Learning," in Vosniadou & Ortony (eds.) Similariy and Analogical Reasoning. Cambridge: Cambridge UP.
Marr, D. (1982). Vision. San Francisco: W.H. Freeman
Turner, M. (1988). "Categories and Analogies," in Helman, D. (ed.), Analogical Reasoning: Perspectives of Artificial Intelligence, Cognitive Science, and Philosophy.
