Psychon. Should Russians Fear Chinese Colonization? Psychol. The next trial started 500 ms after the response to the target was made or after the feedback. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Sci. 31, 733764. (Colchester) 63, 942954. Bull. Thus, any positive and negative effects of such mapping would have been collapsed into one average for each condition. An example of nondimensionalization in the branch of the qualitative analysis of differential equations can be found at section 1.2 of J.D. 2:15. doi: 10.3389/fpsyg.2011.00015. Lakoff, G. (1987). In Experiment 1 we found that number magnitude directed spatial attention, whereas no such effect was observed in Experiment 2. Figure 2. For trials that were preceded by numbers in abstract contexts, there was no significant interaction between magnitude and vertical position in the reaction times, F < 1, or in the error rates, F(1, 63) = 1.65, MSE = 0.001, 2 = 0.025, p > 0.20. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The results of Experiment 4 basically replicated those of Experiment 3 and showed similar effects for horizontal and vertical spatial orientation. None of the participants guessed the purpose of the experiment correctly. Processing time shifts affects the execution of motor responses. Magnitude judgments were followed by identification of a letter p or q which appeared at the top or bottom of the screen (as in the study by Meier and Robinson, 2004). Is this typical? Manuscript submitted for publication. They also assume that yes responses are coded as +. A main effect of vertical position showed that participants responded faster to letters at the bottom than at the top, F(1, 63) = 8.24, MSE = 1672.8 2 = 0.12, p < 0.01. With this assumption differences in depth of processing might explain the differences between abstract and concrete context. I am sure that at least one of them will make himself available to help you advance your investigation. Although both tasks should be affected by manipulations of spatial attention, they may still differ in how they are affected by unrelated tasks. The Body in the Mind: The Bodily Basis of Reason and Imagination. This interaction indicated that the interaction effect between magnitude and horizontal position was different between the two types of contexts. In mathematics the term "number" is usually taken to mean an abstract number. Learn. Simmons, W. K., Hamann, S. B., Harenski, C. L., Hu, X. P., and Barsalou, L. W. (2008). ISBN 0-486-20430-8. What is "Rosencrantz and Guildenstern" in _The Marvelous Mrs. Maisel_ season 3 episode 5? Johnson, M. (1987). 15, 243247. I am not completely convinced that the old concept of abstract number is the same as that of a dimensionless quantity, but certainly the concept of concrete number corresponds to that of a dimensional quantity. Psychol. Keywords: numbers, quantity, context, grounded cognition, abstract concept, Citation: Pecher D and Boot I (2011) Numbers in space: differences between concrete and abstract situations. Figure 3. Thus, even though the exact number is presented in an analog form processing benefits from a symbolic representation. Psychophysiological evidence that the SNARC effect has its functional locus in a response selection stage. Thus, at present there is no agreement yet as to whether the SNARC effect indicates a spatial representation of numbers. Mean reaction times and error rates are presented in Figure 1. Acta Psychol. Unfortunately, the effect on spatial attention is not obtained very consistently (Galfano et al., 2006; Ristic et al., 2006; Lindemann et al., 2008; Zanolie and Pecher, 2011). Sci. Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses. Borghi, A. M., Flumini, A., Cimatti, F., Marocco, D., and Scorolli, C. (2011). In that case, our results would be consistent with findings that spatial attention induced by number magnitude is weak and depends on the relevance and depth of number processing in the task (Galfano et al., 2006; Ristic et al., 2006; Lindemann et al., 2008; Zanolie and Pecher, 2011). Mem. Participants respond faster with the left hand to low numbers than to high number, and faster with the right hand to high numbers than to low numbers (see Gevers et al., 2010 for similar effects with verbal responses) even when magnitude is irrelevant to the task, as in parity judgment. Error bars represent standard error of the mean difference for adjacent bars. A denominate number is a type of concrete number with a unit of measure attached with it. Gen. 122, 372396. Overall, participants responded faster to letters at the left than at the right, F(1, 30) = 10.62, MSE = 5406.9, 2 = 0.26, p < 0.01. When more meaningful processing is required, however, as with numbers in a more concrete context, representations involve sensorymotor simulations, including metaphorical mappings. Spatial congruency effects might be explained by two opposing mechanisms (Estes et al., 2008). Di Luca, S., Lefvre, N., and Pesenti, M. (2010). Perceiving numbers causes spatial shifts of attention. (2003) found that participants were faster to detect a target at the left when it was preceded by a low digit (one or two) and faster to detect a target at the right when preceded by a high digit (eight or nine). The results are displayed in Figure 1. Therefore, the interaction between magnitude and spatial position on target identification is better explained by differences in spatial attention for low and high magnitudes. In the letter identification task such alignment effects will not play a role because the p or q response does not have an obvious polarity. Cognition 108, 263270. Time and Eternity in Augustine Sci. Several researchers have proposed that abstract concepts are grounded in sensorymotor simulations by metaphorical mappings between abstract concept and concrete, spatial domains (Lakoff and Johnson, 1980, 1999; Lakoff, 1987; Gibbs, 1994, 2005). How do I politely refuse/cut-off a person who needs me only when they want something? A possible explanation is that numbers in concrete situations have a mainly vertical orientation, whereas numbers in abstract situations have a mainly horizontal orientation. For trials that were preceded by numbers in concrete contexts, the interaction effect between magnitude and vertical position approached significance, F(1, 63) = 3.60, MSE = 2349.9, 2 = 0.054, p = 0.062. Reaction times and error rates for the letter identification task in Experiment 3. Psychol. Front. The other block had the same procedure as in Experiment 2 except that each magnitude number was preceded by a referent number. Psychol. Brain Res. Joh. Manipulating objects and telling words: a study on concrete and abstract words acquisition. Incorrect responses (4.4% in the sentence condition and 5.0% in the number condition) and remaining outliers (3.8% in the sentence condition and 7.0% in the number condition) were removed. Front. Asking for help, clarification, or responding to other answers. Jan-David Hardtke (2019). Denominate numbers are further classified as either simple, meaning a single unit is given, or compound, meaning multiple units are given. New York, NY: Basic Books. Whenever in mathematical modeling we feel the presence of dimensional physical quantities in a determined model is making its analysis harder, in the light of Buckingham $\pi$ theorem we might try to remove them through a technique known as nondimensionalization. Zanolie, K., Van Dantzig, S., Boot, I., Wijnen, J., Schubert, T. W., Giessner, S., and Pecher, D. (2011). Participants were instructed to press the middle button (labeled sentence1/number1) after they processed the referent (sentence or number) and to use it as a comparison for the next stimulus. Percept. As in Experiment 1, participants made relative magnitude judgments. (2008; see also Simmons et al., 2008) have proposed a similar mechanism for language processing. Because number meaning can vary between very concrete and very abstract, depending on the context, the representation of numbers provides an interesting case for grounded theories of cognition (Glenberg, 1997; Barsalou, 1999; Lakoff and Nez, 2000). In the reaction times we obtained a significant interaction between magnitude and vertical position, F(1, 31) = 4.75, MSE = 732.6, 2 = 0.13, p < 0.05. An alternative explanation is that numbers in concrete contexts activate spatial representations more strongly than numbers in abstract contexts, irrespective of the spatial orientation. The roles of body and mind in abstract thought. Next we investigated if the magnitude-position congruency effect could be replicated with quantities in an abstract context of just other numbers. A concrete number or numerus numeratus is a number associated with the things being counted, in contrast to an abstract number or numerus numerans which is a number as a single entity. First, some researchers have argued that abstract concepts are grounded in sensorymotor processing by metaphorical mappings (Lakoff and Johnson, 1980, 1999; Lakoff, 1987; Gibbs, 1994, 2005). Geometry terminology: concrete vs. continuous polygons? In the error rates we also obtained an interaction effect between position and magnitude, F(1, 31) = 5.06, MSE = 0.000, 2 = 0.14, p < 0.05. Ito, Y., and Hatta, T. (2004). Proctor and Cho (2006), but see Pecher et al., 2010 assume that in spatial dimensions, above and right are coded as +. Mem. None of the participants guessed the purpose of the experiment correctly. It is possible that experienced number users can rely on a similar set of associative links between numbers in simple number tasks. Why the sunny side is up: association between affect and vertical position. Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., and verguts, T. (2010). Then, 200 ms after the response, the letter p or q (28 pt Garamond) was presented at the top or bottom of the screen which had to be identified as quickly and accurately as possible by pressing the corresponding button. Sci. Meier, B. P., and Robinson, M. D. (2004). This attention shift should facilitate identification of targets in the congruent position compared to targets in the incongruent position. The systematic way in which vertical but not horizontal terms are used for magnitude suggests that magnitude is represented in terms of verticality (Lakoff and Johnson, 1980). In the 16th century textbooks began to make the distinction. It only takes a minute to sign up. Uno modo id quod numeratur actu, vel quod est numerabile, ut puta cum dicimus decem homines aut decem equos; qui dicitur numerus 'numeratus', quia est numerus applicatus rebus numeratis. We presented numbers in concrete (seven shoes in a shoe shop) or abstract (29 7) contexts and asked participants to make relative magnitude judgments. (2006). Sell, A. J., and Kaschak, M. P. (2011). Exp. Response mapping was varied between subjects. On the perceptual-motor and image-schematic infrastructure of language, in Grounding Cognition: The Role of Perception and Action in Memory, Language, and Thinking, eds D. Pecher, and R. A. Zwaan (Cambridge: Cambridge University Press), 246281. It should be noted that we did not use quantities that explicitly referred to vertical positions (e.g., we did not use items like the tree was 6 meters tall). Nicholls, M. E. R., Loftus, A. M., and Gevers, W. (2008). Numbers and space: associations and dissociations. No words were used that referred to vertical position or movement. (and in Medieval Scholasticism), 3. Dover. Proctor, R. W., and Cho, Y. S. (2006). Reynvoet, B., and Brysbaert, M. (1999). 132, 416442. Murray (2011). Whats up with god? For example, it would be a little to have in a shoe shop but a lot to bring on a weekend to Paris (at least for sensible people). A search for "concrete number" gives 54 results in this forum, but I do not have the impression that its use has a philosophical background. Pecher, D., Van Dantzig, S., Boot, I., Zanolie, K., and Huber, D. E. (2010). Participants decided whether the magnitude was relatively few or many(the Dutch words weinigand veel were used, which do not refer to height and can be used for both mass and count nouns). 58, 162170. Dove, G. (2011). 66, 651664. The mean reaction times and error rates are displayed in Figure 2. For example, in natural language people often use spatial terms when they talk about time (e.g., the meeting has been moved forward), which suggests that representations for space and time are partially overlapping (see also Walsh, 2003). Past personal studies of mine of the mathematical foundations of dimensional analysis lead me to believe that the following answers are plausible ones. Kranjec, A., and Chatterjee, A. How to prove that both people know the same dictionary word? Cogn. 27, 767780. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. How visual imagery interferes with vision. Assignment of sentences to experimental and filler trials was counterbalanced across participants, as was the order of sentence and number blocks. Neurosci. Therefore, the polarity principle predicts that yes responses will be faster when they are aligned with stimuli or response sides that are also + (i.e., above or right). Psychol. 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Reduction to a lower denomination is accomplished by multiplying by the number of lower units contained in each higher unit. Cognit. Brain Sci. Stronger evidence for a spatial representation of numbers is provided by studies that show effects of number magnitude on spatial attention (Fischer et al., 2003; Nicholls et al., 2008; Salillas et al., 2008). The letter identification task has been used in numerous studies that investigated effects on spatial attention (e.g., Meier and Robinson, 2004; Meier et al., 2007; Estes et al., 2008; Van Dantzig, 2009). In the present study we investigated the mental representation of number magnitude. The best answers are voted up and rise to the top, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, IMO, the text is a little bit misleading. The materials and procedure were the same as in Experiment 3 with two exceptions. 13, 862868. Each combination of letter identity and letter position was used equally often in each condition and block. Similarly, a division is used to reduce to a higher denomination, and remainders can be applied to the next highest unit to form compound denominant numbers. Responses to letters were faster in the many than in the few condition, F(1, 31) = 4.58, MSE = 1478.7, 2 = 0.13, p < 0.05, and responses were faster to letters at the top than the bottom of the screen, F(1, 31) = 5.38, MSE = 3421, 2 = 0.15, p < 0.05. Counterbalancing was the same as in Experiment 1, and in addition odd and even numbers were also counterbalanced across letter position. History of Mathematics. (2008). J. Exp. To prevent participants simply comparing the two quantities from referent and magnitude sentence without considering the situation half of the referent sentences were replaced by fillers that had the same quantity in a different context (e.g., 80 people attended the business meeting). Thus, any effect on vertical attention was due to the representation of the concept magnitude rather than to the literal orientation of actions or objects mentioned in the sentence. Abstract numbers have no grounding in sensorymotor processing whereas numbers in concrete contexts can be simulated by sensorymotor processing. Polarity correspondence: a general principle for performance of speeded binary classification tasks. Keus, I. M., Jenks, K. M., and Schwarz, W. (2005). Dehaene, S., Bossini, S., and Giraux, P. (1993). Reaction times and error rates for the letter identification task in Experiments 1 (Concrete Context) and 2 (Abstract Context). 36, 10471056. Four different response mappings were used, such that participants used two fingers of each hand to respond, and used one hand for each task so that the two fingers of the same hand were used to make the two responses in one task. Second, simulation of perceptual experiences with objects might occupy the same resources as those needed to identify the visual stimulus. J. Pers. rev2022.8.1.42699. MathJax reference. In our study, the target stimulus was time-locked to the magnitude decision and thus varied with decision speed. Rev. Bull. This marginal interaction indicated that the interaction effect between magnitude and vertical position was different between numbers in the two types of contexts. The results of Experiment 3 are consistent with those of Experiments 1 and 2. 122, 221233. Ristic, J., Wright, A., and Kingstone, A. Language and simulation in conceptual processing, in Symbols, Embodiment, and Meaning, eds M. De Vega, A. M. Glenberg, and A. C. Graesser (Oxford: Oxford University Press), 245283.