Probability Theory Predicts That Chunking into Groups of Three or Four Items Increases the Short-Term Memory Capacity
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Short-term memory allows individuals to recall stimuli, such as numbers or words, for several seconds to several minutes without rehearsal. Although the capacity of short-term memory is considered to be 7 ± 2 items, this can be increased through a process called chunking. For example, in Japan, 11-digit cellular phone numbers and 10-digit toll free numbers are chunked into three groups of three or four digits: 090-XXXX-XXXX and 0120-XXX-XXX, respectively. We use probability theory to predict that the most effective chunking involves groups of three or four items, such as in phone numbers. However, a 16-digit credit card number exceeds the capacity of short-term memory, even when chunked into groups of four digits, such as XXXX-XXXX-XXXX-XXXX. Based on these data, 16-digit credit card numbers should be sufficient for security purposes.Keywords:
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Memory for verbal material improves when words form familiar chunks. But how does theimprovement due to chunking come about? Two possible explanations are that the inputmight be actively recoded into chunks, each of which takes up less memory capacity thanitems not forming part of a chunk (a form of data compression), or that chunking is basedon redintegration. If chunking is achieved by redintegration, representations of chunks existonly in long-term memory and help to reconstructing degraded traces in short-termmemory. In six experiments using two-alternative forced choice recognition and immediateserial recall, we find that when chunks are small (two words) they display a patternsuggestive of redintegration, while larger chunks (three words), show a pattern consistentwith data compression. This is concurs with previous data showing that there is a costinvolved in recoding material into chunks in short-term memory. With smaller chunks thiscost seems to outweigh the benefits of recoding words into chunks. The main features ofthe serial recall data can be captured by a simple extension to the Primacy model of Pageand Norris (1998).
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This paper describes a class of number representations which are called signed-digit representations. Signed-digit representations limit carry-propagation to one position to the left during the operations of addition and subtraction in digital computers. Carry-propagation chains are eliminated by the use of redundant representations for the operands. Redundancy in the number representation allows a method of fast addition and subtraction in which each sum (or difference) digit is the function only of the digits in two adjacent digital positions of the operands. The addition time for signed-digit numbers of any length is equal to the addition time for two digits. The paper discusses the properties of signed-digit representations and arithmetic operations with signed-digit numbers: addition, subtraction, multiplication, division and roundoff. A brief discussion of logical design problems for a signed-digit adder concludes the presentation.
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Short-term verbal memory is improved when words in the input can be chunked into larger units. Miller (1956) suggested that the capacity of verbal short-term memory is determined by the number of chunks that can be stored in memory, and not by the number of items or the amount of information. But how does the improvement due to chunking come about? Is memory really determined by the number of chunks? One possibility is that chunking is a form of data compression. Chunking allows more information to be stored in the available capacity. An alternative is that chunking operates primarily by redintegration. Chunks exist only in long-term memory, and enable items in the input which correspond to chunks to be reconstructed more reliably from a degraded trace. We review the data favoring each of these views and discuss the implications of treating chunking as data compression. Contrary to Miller, we suggest that memory capacity is primarily determined by the amount of information that can be stored. However, given the limitations on the representations that can be stored in verbal short-term memory, chunking can sometimes allow the information capacity of short-term memory to be exploited more efficiently.
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Abstract Rapid serial visual presentation (RSVP) of words or pictured scenes provides evidence for a large-capacity conceptual short-term memory (CSTM) that momentarily provides rich associated material from long-term memory, permitting rapid chunking (Potter 1993; 2009; 2012). In perception of scenes as well as language comprehension, we make use of knowledge that briefly exceeds the supposed limits of working memory.
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Different methods of handling the summing process for the geometric series are shown to give results indicating widely differing significances when carried out in a machine incorporating “significant-digit” arithmetic.
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Short-term verbal memory is improved when words can be chunked into larger units. Miller (1956) suggested that the capacity of verbal short-term memory is determined by the number of chunks that can be stored in memory, rather than by the number of items or the amount of information. But how does the improvement due to chunking come about, and is memory really determined by the number of chunks? One possibility is that chunking is a form of data compression. It allows more information to be stored in the available capacity. An alternative is that chunking operates primarily by redintegration. Chunks exist only in long-term memory, and enable the corresponding items in short-term memory to be reconstructed more reliably from a degraded trace. We review the data favoring each of these views and discuss the implications of treating chunking as data compression. Contrary to Miller, we suggest that memory capacity is primarily determined both by the amount of information that can be stored but also by the underlying representational vocabulary of the memory system. Given the limitations on the representations that can be stored in verbal short-term memory, chunking can sometimes allow the information capacity of short-term memory to be exploited more efficiently. (202 words).
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Many general linguistic theories and language processing frameworks have assumed that language processing is largely a chunking procedure and that it is underpinned and constrained by our memory limitations. Despite this general consensus, the distinction between short-term memory (STM) and working memory (WM) limitations as they relate to language processing has remained elusive. To resolve this issue, we propose an integrated memory- and chunking-based metric of parsing complexity, in which STM limitations of 7±2 (Miller, 1956a) are relevant to the Momentary Chunk Number (MCN), while WM limitations of 4±1 (Cowan, 2001) are relevant to the Mean Momentary Chunk Number (MMCN). Examples of concrete calculations of our new metric are presented vis-à-vis Liu’s MDD metric and Hawkins’ IC-to-word Ratio metric. Related methodology issues are also discussed. We conclude the paper by echoing some recently repeated calls (O'Grady, 2012 & 2017; Gómez-Rodríguez et al., 2019; Wen, 2019) to include STM and WM limitations as part and parcel of the language device (LD; cf. Chomsky, 1957) in that their impacts are ubiquitous and permeating in all essential linguistic domains ranging from phonology to grammar, discourse comprehension and production. (PDF) Short-term and working memory capacity and the language device: Chunking and parsing complexity. Available from: https://www.researchgate.net/publication/340490956_Short-term_and_working_memory_capacity_and_the_language_device_Chunking_and_parsing_complexity [accessed May 31 2021].
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