Winter, B., Marghetis, T., & Matlock, T. (2015). Of magnitudes and metaphors: Explaining cognitive interactions between space, time, and number. cortex, 64, 209-224.
Of magnitudes and metaphors: Explaining cognitive interactions between space, time, and number - ScienceDirect
- 1. Introduction
- 2. Explaining space, time, and number in the brain
- 3. Asymmetry: between what, when, and why?
- 4. Magnitudes or relations?
- 5. Directions for unification
- 6. Conclusions
1. A Theory of Magnitude (ATOM) posits a domain-general magnitude system. Conceptual Metaphor Theory (CMT) maintains that cross-domain interactions are manifestations of asymmetric mappings that use representations of space to structure the domains of number and time.
2. ATOM and CMT are complementary: magnitudes and metaphors are both needed to understand our neural and cognitive web of space, time and number.
|position||behavioral cross-domain interactions emerge from a shared reliance on the same neural resources||understand abstract domains by mapping them onto our understanding of more concrete domains|
|approach||neuroimaging and relatively low level psychological tasks||behavioral studies of reasoning and language comprehension, or descriptive analyses of language and gesture|
|focus||interactions between low-level magnitudes||the role of high-level reasoning and language understanding|
|asymmetries||symmetrical mappings between domains||asymmetrical mappings cross domians|
|emphasis||evolution||experience and culture during ontogeny|
|"more"||associate “more” in one domain with “more” in another||conceptualize quantities using the metaphor MORE IS UP|
|scope||magnitude||relation between conceptual elements: magnitude, temporal order, spatial location, etc.|
2. Explaining space, time, and number in the brain
1) We experience spatial, temporal and numerical magnitudes in terms of "more than" or "less than" which can be laid out along a continuous scale of increasing or decreasing magnitude.
2) Converging evidence from imaging and clinical studies suggest that numerical, spatial, and temporal magnitudes rely on shared neural machinery that rests within parietal cortex.
3) Behavioral predictions: ① associate “more” in one domain with “more” in another (Size-Congruency Effect); ② space, time and number should influence action
4) Size-Congruency Effect:
Spatial Numerical Association of Response Codes, or SNARC effect
Spatial Temporal Association of Response Codes, or STEARC effect
→ They should be understood as one instance of a more generalized Spatial Quantity Association of Response Codes (SQUARC) effect.
These effects undeniably speak to the presence of some kind of association between space, number, and time (consistent with ATOM), but they involve interactions with spatial location, not spatial magnitude.
5) Evolution: There is evidence, therefore, that humans share an innate, domain-general magnitude system with other species, the product of shared evolutionary pressures or common descent.
1) A central claim of CMT is that these systematic linguistic metaphors are not mere stylistic devices, but instead reflect entrenched conceptual mappings across cognitive domains.
2) Mental time line~STEARC is compatible with a conceptual metaphor in which times are conceptualized as spatial locations; mental number line~SNARC is compatible with the claim in CMT that numbers are conceptualized metaphorically as locations along a path.
3) Conceptualize quantities using the metaphor MORE IS UP.
4) Support for the metaphorical understanding of number and time also comes from spontaneous co-speech gestures.
5) Proponents of CMT argue that this conceptual asymmetry is responsible for analogous asymmetries in language and behavior (cf. discussion in Casasanto & Boroditsky, 2008)
2.3 The inter-dependence and independence of domains
Even though the domains of space, time, and number are interconnected and rely on shared neural machineryd—as predicted by both CMT and ATOM—they each also involve distinct structures, properties, and neural substrates.
3. Asymmetry: between what, when, and why?
3.1 Domain asymmetry and symmetry
1) Whether particular domains are more likely to exhibit interactions than others.
2) ① ATOM: Space, time, and number all symmetrically interact with each other does not entail that all magnitudes are equal, but time and number are both more tightly connected with space than other magnitude-related domains.
② CMT: Mappings between source (space) and target (time and number) domain to explain cross-domain interactions are asymmetrical, but not necessarily focus on the mappings between one target domain and another.
③ Time and number interact perceptually, conceptually, and neurally. This Domain Symmetry is a
natural prediction of ATOM, but does not follow naturally from CMT which does not posit conceptual metaphors like TIME IS NUMBER or NUMBER IS TIME.
3.2 Directional asymmetry and symmetry
1) Whether, for a pair of domains (e.g., space and time), the strength of influence from one domain to another is equal or unequal to the strength of influence in the other direction.
2) CMT claims to be a theory of thought, not just of language, and thus seeks to explain linguistic asymmetries in terms of underlying conceptual asymmetries.
3) ATOM claims that all magnitudes are not created equal. Although the ATOM framework does not explicitly predict cross-domain asymmetries, it is in principle compatible with directional asymmetries that derive from differences in the domains themselves.
4) The strongest evidence for asymmetry is at the linguistic level, but these linguistic asymmetries might have alternative explanations that do not have to do with neural or cognitive asymmetries.
3.3 Evaluating asymmetry
4. Magnitudes or relations?
1) ATOM is about magnitudes, whereas CMT is about relations between conceptual elements.
2) Space, time and number are complex conceptual domains, replete with diverse elements: numbers that are even and odd, prime and composite; events that vary in duration and order; places that vary in location and extent.
① Time: the passage of time (i.e., future, past) , temporal relations (e.g., earlier, later) →temporal order, change and perspective; temporal duration→ magnitude.
② Space: spatial magnitude, location.
3) ATOM needs to invoke additional assumptions to explain locational effects.
4) In terms of scope, therefore, CMT is able to account for a broader range of cognitive phenomena than ATOM.
5. Directions for unification
Within cognitive neuroscience, research will draw on the strengths of both CMT and ATOM to account for the full breadth of cross-domain interactions.
5.1 Scaling up from magnitudes to metaphors
1) One possible connection between the two theories: The selective, directional, and asymmetric mappings discussed by CMT might build on biologically determined, symmetric connections between space, time and number.
2) The domain-general magnitude system posited by ATOM may favor the development of specific metaphorical mappings over others.
3) ATOM and CMT might then reflect cross-domain interactions that develop over different time-scales, with ATOM focusing on phylogeny and CMT focusing on ontogeny.
4) A generalized magnitude system(ATOM) may be the evolutionary and developmental substrate that helps scaffold more complex and culturally specified concepts(CMT).
5.2 Functional relevance of cross-domain mappings
1) CMT has traditionally argued for a multiplicity of roles across various arenas: reasoning, language comprehension, early concept acquisition and semantic change.
2) A domain-general representation of magnitude posited by ATOM could play a role in learning environmental regularities and predicting one dimension from another.
3) Cross-domain mappings do actually play a functional role in reasoning, understanding, and
1) CMT's emphasis on Directional Asymmetry between domains calls for investigating the neural mechanism that underlie these asymmetries, a topic that only a few studies have begun to address.
2) If ATOM is right, cross-domain associations may be a beneficial part of our evolutionary inheritance, functionally relevant for the coordination of action.
3) From its outset, CMT has viewed spatial mappings as foundational to more abstract reasoning and understanding.
4) ATOM and CMT highlight how the interweaving of space, time, and number in the human mind may form a fabric that supports thought, from low-level perception to the acquisition of complex concepts.