Notations are cognitive systems that can be analyzed through their components: Brains (psychological functions; neurological regions), bodies (distinctive behaviors; physiological capacities), and material forms (sets of visually appreciated, manually engaged elements) (Malafouris, Reference Malafouris2013). Viewing notations through this lens reveals two main types: Semasiography and visible language. Their unique material predecessors and developmental histories potentially bear on Morin's ideographic puzzle.
Language is not central to semasiographic notations (music, numbers). In fact, adding language destroys the visual concision needed to bring large volumes of graphically represented information together for simultaneous viewing. These notations also involve a significant implicit component, knowledge the user must master to make proper sense of them.
Semasiographic notations can be rendered into language but do not express language: 
can be put into words, but the result is not music. Musical notations encode information about pitch, duration, and emphasis in a way that informs the motor manipulations needed to produce sounds with an instrument, including the human voice. The implicit component involves knowing how specific notations inform particular movements and acquiring proficiency in their production; the latter in particular involves distinctive neurological reorganizations (Gaser & Schlaug, Reference Gaser and Schlaug2003).
Numbers are more complex. Operational signs (+–×÷) are mechanical instructions that work equally well with written numerals (knowledge-based calculation) and abacus beads (calculation that is more manipulation based). As for the numbers they manipulate, Western numerals (0–9) descend from Mesopotamian and Egyptian notations (Chrisomalis, Reference Chrisomalis2010) that meant particular quantities by instantiating them: They meant quantity by being quantity (Overmann, Reference Overmann2022). For example, the sign for five had five elements: Mesopotamian ; Egyptian . Notations share this representational mode with their precursor technologies: Fingers , tally marks , tokens/pebbles , and cuneiform/hieroglyph numerals all mean quantity by instantiating it, without any need to encode language. Repetition also deemphasizes the need for iconic variation.
As number systems elaborate, their representations become more concise. Conventions for large values (10; 60; or 100) are added, and instantiate notations become conventions whose value is learned, rather than depending on element countability: 7 is concise but not explicit in its value; and instantiate value explicitly but are not concise (Overmann, Reference Overmann2023). Concision is critical to numbers: It enables them to be brought together at volumes and with a semantic succinctness that can reveal their relations and patterns. Like musical notations, operations and numerals can be spoken, but the result is ephemeral, memory dependent, and loses significant manipulability, accuracy, and complexity.
Granted, the implicit component of music and numbers is largely acquired and experienced through language. However, a substantial motor component is also involved, consistent with manipulating objects – both physical and conceptual – and differing significantly from neural activity associated with processing language (Amalric & Dehaene, Reference Amalric and Dehaene2018; Grotheer, Ambrus, & Kovács, Reference Grotheer, Ambrus and Kovács2016; Johansson, Reference Johansson2008; Perfetti & Tan, Reference Perfetti and Tan2013; Vandervert, Reference Vandervert2017).
In contrast, language is central to visible language. So-called glottographic scripts express particular languages with fidelity. For modern scripts like the one used here, the graphic elements are contrastive and recombinable in ways that suggest the cooption of a key language function: The ability to combinatorially recombine conceptual and phonetic units. Concision is deemphasized; signs instead become more visually complex by incorporating techniques (determinatives; phonography) for specifying the intended morphemes, syllables, or sounds. The implicit component involves knowing the language being expressed and acquiring the suite of behavioral and neurological reorganizations that recognize written characters, associate them with the meanings and sounds of language, and coordinate and guide productive movements (Dehaene & Cohen, Reference Dehaene and Cohen2007; Nakamura et al., Reference Nakamura, Kuo, Pegado, Cohen, Tzeng and Dehaene2012; Roux et al., Reference Roux, Dufor, Giussani, Wamain, Draper, Longcamp and Démonet2009).
Early writing did not express language with fidelity. In Mesopotamia, it was so poor in this regard that scholars still debate the language associated with it. Early writing consisted of pictures and conventions with approximate meanings. Pictures are ambiguous in what they mean: Resemblance suggests a range of related semantic meanings, and as Morin notes, pictures may acquire cultural meanings independent of what they resemble. This ambiguity can motivate the inclusion of techniques for specifying particular words.
The process by which early writing becomes script is complex and includes morphological change in the written form. Considered across cultural spans of time – from early writing to, say, a thousand or so years later – this morphological change is consistent with the neurological reorganizations that constitute literacy (Overmann, Reference Overmann2016): As characters became recognized topologically – through combinations of their structural features and spatial relations – they no longer needed to maintain their original forms; this freed the set of characters to converge on features and contrasts that maximized discriminability and individualization. This in turn facilitated their recombination in ways that borrowed or mimicked the combinatorial faculty of language, and over time, sets of characters shrank (e.g., syllabaries and alphabets; Chinese is exceptional in this regard). Along the way, the neurological reorganizations needed to read and write the characters became paramount: Without them, scripts were no longer meaningful.
Like script, sign language transforms over time from emergent gestures to a complex state involving combinatorial recombination (Senghas & Coppola, Reference Senghas and Coppola2001). Handwritten or signed, visible language involves a significant motor component like semasiographic notations do. Yet neither script nor sign has a similar material prehistory: There are no direct material precursors, no counterparts to the stalagmites, flutes, tallies, and tokens/pebbles used in prehistoric music and counting. Visually perceived forms (seals; reliefs; art) undoubtedly influenced the ideography used in visible language, but they did not constitute a prehistory of material engagements like those in music and numbers.
These material prehistories suggest there are two distinctive notational types (which, granted, interact and overlap at multiple levels in highly complex ways). In semasiography, notations follow from and concentrate a lengthy material sequence and act as precise instructions for manipulating physical or conceptual objects. In visible language, notations lack direct material precursors, initially emphasize the use of iconography to convey meanings, and can become increasingly expressive by recombining their elements like language does. Given these differences, extracting and blending iconicity, expressiveness, and concision, as Morin proposes, may well remain a challenge.
Notations are cognitive systems that can be analyzed through their components: Brains (psychological functions; neurological regions), bodies (distinctive behaviors; physiological capacities), and material forms (sets of visually appreciated, manually engaged elements) (Malafouris, Reference Malafouris2013). Viewing notations through this lens reveals two main types: Semasiography and visible language. Their unique material predecessors and developmental histories potentially bear on Morin's ideographic puzzle.
Language is not central to semasiographic notations (music, numbers). In fact, adding language destroys the visual concision needed to bring large volumes of graphically represented information together for simultaneous viewing. These notations also involve a significant implicit component, knowledge the user must master to make proper sense of them.
Semasiographic notations can be rendered into language but do not express language:
can be put into words, but the result is not music. Musical notations encode information about pitch, duration, and emphasis in a way that informs the motor manipulations needed to produce sounds with an instrument, including the human voice. The implicit component involves knowing how specific notations inform particular movements and acquiring proficiency in their production; the latter in particular involves distinctive neurological reorganizations (Gaser & Schlaug, Reference Gaser and Schlaug2003).
Numbers are more complex. Operational signs (+–×÷) are mechanical instructions that work equally well with written numerals (knowledge-based calculation) and abacus beads (calculation that is more manipulation based). As for the numbers they manipulate, Western numerals (0–9) descend from Mesopotamian and Egyptian notations (Chrisomalis, Reference Chrisomalis2010) that meant particular quantities by instantiating them: They meant quantity by being quantity (Overmann, Reference Overmann2022). For example, the sign for five had five elements: Mesopotamian
; Egyptian 
. Notations share this representational mode with their precursor technologies: Fingers 
, tally marks 
, tokens/pebbles 
, and cuneiform/hieroglyph numerals all mean quantity by instantiating it, without any need to encode language. Repetition also deemphasizes the need for iconic variation.
As number systems elaborate, their representations become more concise. Conventions for large values (10; 60; or 100) are added, and instantiate notations become conventions whose value is learned, rather than depending on element countability: 7 is concise but not explicit in its value;
and 
instantiate value explicitly but are not concise (Overmann, Reference Overmann2023). Concision is critical to numbers: It enables them to be brought together at volumes and with a semantic succinctness that can reveal their relations and patterns. Like musical notations, operations and numerals can be spoken, but the result is ephemeral, memory dependent, and loses significant manipulability, accuracy, and complexity.
Granted, the implicit component of music and numbers is largely acquired and experienced through language. However, a substantial motor component is also involved, consistent with manipulating objects – both physical and conceptual – and differing significantly from neural activity associated with processing language (Amalric & Dehaene, Reference Amalric and Dehaene2018; Grotheer, Ambrus, & Kovács, Reference Grotheer, Ambrus and Kovács2016; Johansson, Reference Johansson2008; Perfetti & Tan, Reference Perfetti and Tan2013; Vandervert, Reference Vandervert2017).
In contrast, language is central to visible language. So-called glottographic scripts express particular languages with fidelity. For modern scripts like the one used here, the graphic elements are contrastive and recombinable in ways that suggest the cooption of a key language function: The ability to combinatorially recombine conceptual and phonetic units. Concision is deemphasized; signs instead become more visually complex by incorporating techniques (determinatives; phonography) for specifying the intended morphemes, syllables, or sounds. The implicit component involves knowing the language being expressed and acquiring the suite of behavioral and neurological reorganizations that recognize written characters, associate them with the meanings and sounds of language, and coordinate and guide productive movements (Dehaene & Cohen, Reference Dehaene and Cohen2007; Nakamura et al., Reference Nakamura, Kuo, Pegado, Cohen, Tzeng and Dehaene2012; Roux et al., Reference Roux, Dufor, Giussani, Wamain, Draper, Longcamp and Démonet2009).
Early writing did not express language with fidelity. In Mesopotamia, it was so poor in this regard that scholars still debate the language associated with it. Early writing consisted of pictures and conventions with approximate meanings. Pictures are ambiguous in what they mean: Resemblance suggests a range of related semantic meanings, and as Morin notes, pictures may acquire cultural meanings independent of what they resemble. This ambiguity can motivate the inclusion of techniques for specifying particular words.
The process by which early writing becomes script is complex and includes morphological change in the written form. Considered across cultural spans of time – from early writing to, say, a thousand or so years later – this morphological change is consistent with the neurological reorganizations that constitute literacy (Overmann, Reference Overmann2016): As characters became recognized topologically – through combinations of their structural features and spatial relations – they no longer needed to maintain their original forms; this freed the set of characters to converge on features and contrasts that maximized discriminability and individualization. This in turn facilitated their recombination in ways that borrowed or mimicked the combinatorial faculty of language, and over time, sets of characters shrank (e.g., syllabaries and alphabets; Chinese is exceptional in this regard). Along the way, the neurological reorganizations needed to read and write the characters became paramount: Without them, scripts were no longer meaningful.
Like script, sign language transforms over time from emergent gestures to a complex state involving combinatorial recombination (Senghas & Coppola, Reference Senghas and Coppola2001). Handwritten or signed, visible language involves a significant motor component like semasiographic notations do. Yet neither script nor sign has a similar material prehistory: There are no direct material precursors, no counterparts to the stalagmites, flutes, tallies, and tokens/pebbles used in prehistoric music and counting. Visually perceived forms (seals; reliefs; art) undoubtedly influenced the ideography used in visible language, but they did not constitute a prehistory of material engagements like those in music and numbers.
These material prehistories suggest there are two distinctive notational types (which, granted, interact and overlap at multiple levels in highly complex ways). In semasiography, notations follow from and concentrate a lengthy material sequence and act as precise instructions for manipulating physical or conceptual objects. In visible language, notations lack direct material precursors, initially emphasize the use of iconography to convey meanings, and can become increasingly expressive by recombining their elements like language does. Given these differences, extracting and blending iconicity, expressiveness, and concision, as Morin proposes, may well remain a challenge.
Competing interest
None.