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In the latest newsletter of The Batch by Andrew Ng, he wrote that:

All of this leads me to think that we need an equivalent term for muscle memory in the intellectual domain. As knowledge work has come to play a larger economic role relative to physical labor, the ability to learn intellectual tasks has become much more important than it was when psychologists formed the idea of muscle memory around 150 years ago. This new term would help people understand that practice is as crucial to developing intellectual skills as muscular ones.

How about intellect memory? It’s not an elegant phrase, but it acknowledges this under-appreciated reality of learning.

I thought that kind of memory is just what we usually mean by memory. If I am not wrong, what Ng said is deliberate practice and in the Deliberate Practice part of The ABCs of How We Learn: 26 Scientifically Proven Approaches, How They Work, and When to Use Them two phrases are used: outsized memories and prodigious memories.

One source of evidence that expertise depends on practice and not innate ability comes from the fact that experts rarely show outsized performance on tasks unrelated to their expertise. For instance, chess grand masters can remember the placement of pieces on a game board extremely well, unless those pieces have been placed at random (Chase & Simon, 1973). They have outsized memories only for game boards that are likely to occur in a chess game, not a generally superior spatial memory. Abacus masters—-people who win abacus competitions --have prodigious memories for numbers (Hatano & Osawa, 1983). Hearing a new number every 2.5 seconds, they can compute the following in their heads and in real time without an actual abacus

The aforementioned book can be treated as a popular book rather than a primary source book, so it may not contain the terminology. I wonder if anyone has recalled that kind of memory and can tell me its name? In my own opinion, it would just be memory or more specifically long-term memory. Am I right?

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    $\begingroup$ Possible duplicate of: Is there a specific term for the notion of storing "algorithms" in human memory? $\endgroup$
    – Arnon Weinberg
    Sep 24, 2022 at 3:04
  • $\begingroup$ @ArnonWeinberg If I am not wrong, rocedual memory results in both motor and cognitive skills(as depicted in this answer), but in this question the emphasis is placed on cognitive skills or the distinction between procedural memory behind motor and cognitive skills. $\endgroup$
    – Lzn
    Sep 24, 2022 at 3:26
  • $\begingroup$ Is "cognitive skills" a suitable term then? $\endgroup$
    – Arnon Weinberg
    Sep 24, 2022 at 3:33
  • $\begingroup$ @ArnonWeinberg Skill doesn't seem like a memory? Maybe long-term cognitive memory? $\endgroup$
    – Lzn
    Sep 24, 2022 at 3:36
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    $\begingroup$ @Lnz All changes in connections in the brain are a form of memory. "Muscle memory" itself isn't actually memory of muscles but changes in brain connections that indirectly or directly control muscles. $\endgroup$
    – Bryan Krause
    Sep 24, 2022 at 3:41

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From above comments sounds like you're already familiar with some necessary background knowledge, this answer is to further address your concern of the possibility of further classification of procedural memory into motor and cognitive subtypes. Actually from WP source of procedural memory the answer is affirmative:

It took time for the idea of multiple memory systems to become firmly established. In 1962, the severely impaired amnesic patient H. M. was reported to be capable of day-to-day improvement in a hand–eye coordination skill, despite having no memory for the practice sessions (Milner, 1962). Nevertheless, subsequent discussions of memory in general and amnesia in particular tended to set aside motor skill learning and to focus on the unitary nature of the rest of memory. Amnesia was considered to impair memory globally, with the recognition that an exception should be made for motor skills.[16]

Also it's worth mentioning memory could serve as both a static object imagery and a dynamic tool, not as conventionally thought only as some static images to recall:

Memory is treated as an object in recall or recognition; it can be inspected and described to others. In this case, the focus is on the past. However, memory (from the past) can be used as a tool to perceive and interpret present events... when used as a tool, the use of a memory is unconscious because the focus is not on the past, but on the present that is being aided by the past memory. Memory can serve as a tool even when one is unable to recall or recognize the influence of the past memory. This distinction between the two functions of memory set the stage for understanding the role of unconscious (or implicit) memory.[8]

Thus in a sense the phenomenal present is not just an instant on a real time line but a kind of implicitly remembered occasion of experience as a process.

Finally inspired by the contemporary widely accepted embodied cognitivism thesis of cognitive sciences, sensorimotor systems are seen as fundamentally integrated with cognitive processing:

Many features of cognition are embodied in that they are deeply dependent upon characteristics of the physical body of an agent, such that the agent's beyond-the-brain body plays a significant causal role, or a physically constitutive role, in that agent's cognitive processing. This thesis points out the core idea that an agent's body plays a significant role in shaping different features of cognition, such as perception, attention, memory, reasoning—among others. Likewise, these features of cognition depend on the kind of body an agent has.

This conceptual reframing of cognition as an activity influenced by the body has had significant implications. For instance, the view of cognition inherited by most contemporary cognitive neuroscience is internalist in nature. An agent's behavior along with his capacity to maintain (accurate) representations of the surrounding environment were considered as the product of "powerful brains that can maintain the world models and devise plans".[11] From this perspective, cognizing was conceived as something that an isolated brain did. In contrast, accepting the role the body plays during cognitive processes allows us to account for a more encompassing view of cognition. This shift in perspective within neuroscience suggests that successful behavior in real-world scenarios demands the integration of several sensorimotor and cognitive (as well as affective) capacities of an agent. Thus, cognition emerges in the relationship between an agent and the affordances provided by the environment rather than in the brain alone... previously were thought to be highly abstract, now appear to be leaning towards an embodied approach for their explanation.[12] Wilson also describes at least five main (abstract) categories that combine both sensory and motor skills (or sensorimotor functions). The first three are working memory, episodic memory, and implicit memory; the fourth is mental imagery, and finally, the fifth concerns reasoning and problem—solving.

One researcher goes even further, positing that the multiple opportunities provided by human hands shape people's concepts of the mind.[24] One example is that people often conceive cognitive processes in manual terms, such as 'grasping an idea'.

So even the so-called "muscle memory" mentioned by OP is a necessary contributing and potentially critical factor for any conceived "cognitive memory" while actually both are under the same hood of procedural memory utilized by our thought.

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