Not a working memory of four, it's really two plus two.

Tl, dr: It's easier to remember four things if you've got two on one side of your visual field and two on the other. Three or four on one side can cause overload errors.

Working memory for other senses hasn't been explored yet on this level.

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will it be easier to remember phone numbers etc. if I use this method?

That's an interesting question-- if you try testing it (I'm not sure how it would apply to phone numbers), please post.

I wonder if access to different compartments of visual memory explains certain things about the use of positional gestures in conversation, and of positions in signing space by sign-language users.

There's probably a better word for what I'm calling "positional gestures". I mean, for instance, the "on the one hand / on the other hand" gestures using one's actual hands; or gestures to locate various nouns in space as one is speaking.

ASL uses position both to indicate actual position in real space (e.g. sign "you" by pointing to the listener; sign "that person" by pointing to them) and to indicate different objects or places in an abstract space.

So if you can actually keep track of more things if some of them are to the left and some are to the right, using a balanced gestural space would logically help keep the two partitions of working memory balanced.

I see a direct causal relationship.

Recall Piaget's sensorimotor model of intellectual development. This impressed me greatly in highschool because it stuck me as absurdly obviously true, but yet I had never heard it before. For example, you can't remember the word for scissors (this happens to me all the time) and so you pretend you are cutting paper with your index and middle fingers. This physical motion is literally a 'handle' for the concept 'scissors'. I believe that concepts are very frequently (if not always) tied to physical motions and physical space, and I believe (I believe Piaget) these concepts cannot be grasped until the physical development is there. The greatest piece of personal evidence for this is that I did not understand the concept of a variable until midway through my 17th year. Until then, abstract algebra was just a frustrating symbol manipulation. Once I understood what a variable meant, there was a new dimension there that wasn't there before. And it felt very much that this understanding just physically grew one day. I had tried very hard a few months before to understand, and wasn't able to make progress. In contrast, understanding the principle of induction was the result of continuous mental exercise over several years -- that understanding felt like the development of a muscle rather than the sudden emergence of one.

Back to positional gestures in conversation, I don't believe it's a coincidence and I often listen carefully to the words mathematicians use to gain insight into how something is "physically" understood. A function "lives" "in" a space -- for example. These aren't just sloppy anthromorophisms (though I do consider them sloppy), but the proper way a human being needs to handle them as objects in order to understand them.

Finally, when I think about it, I'm not at all surprised that we have two working memories, one on either side. This is because the brain has modeled remembering objects as "holding this in one hand" and "holding this in that hand" and maybe room for one more thing in each hand as well. (I realize this is speculation but I don't personally need an experiment to bear it out, since it just feels right enough. However, I'm ever open to information to the contrary.) I wonder if we could train our memory to work better by imagining objects dangling from our fingers. This would take some physical practice, in order to make the sense of each finger quite distinct. I wonder now about the working memory of pianists. It's certainly true that my fingers remember one of my login IDs, where my brain doesn't.

This sounds like it's probably useful! Will hopefully remember to try it sometime.

Hmm, I wonder if this is related to why balanced compositions in art appear more pleasant? If so, that implies a bunch of things abut generality of the balance concept, stretching from the enjoyment of art to the efficiently of remembering things probably means it generalizes to a whole bunch of other things. Potentially easy to test to - just have a bunch of people look at balanced and imbalanced compositions with one eye closed and compare their reported enjoyment to a control group!