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I work in IT and I have observed many people who cannot remember their iPhone passwords or computer passwords off the top of their head. However, if presented with a keyboard or a phone with a functioning keypad, they can instantly remember exactly what their password or passcode is.

I'm curious to know what this kind of memory is called. Since it's somewhat related to visuals, but not necessarily (you don't need to look at your keyboard to type out your password.)

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    $\begingroup$ I came back from a week-long holiday about a year ago, and tried to pay for my airport parking and go home, only to discover that the debit card PIN I'd been using for the past 12 years had completely vanished from my existence. My memory of it had gone and my muscle memory was no longer working. I couldn't explain why this was and, after resorting to a credit card that I only happened to have on me (with its PIN; don't do this!) due to exceptionally unlikely circumstances, finally got home and spent the next few days re-learning my debit PIN. A wholly bizarre experience. $\endgroup$ – Lightness Races with Monica May 29 '15 at 17:48
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Short answer
Motor memory

Background
A striking personal example of your account pictured in the question was my experience where I had to type in my PIN at the bank counter on a keypad. It turned out I entered it incorrectly several times in a row, despite the fact that I had used that PIN a zillion times on ATM machines. Luckily, the bank employee had seen this phenomenon many times before, and she explained to me that the standard computer keypads have a different numerical layout than ATM machines. So to type in my PIN correctly I had to do it under visual guidance - an awkward experience. It showed quite strikingly that I had been entering my bank PIN using motor memory.

Much of our motor behavior is learned - think of learning to walk, cycle or ice skate. To achieve motor learning, the central nervous system is believed to use internal models that predict the mechanical dynamics necessary to execute a task. In theory, the internal model is an association from a desired trajectory for the hand to a pattern of muscle movements. This map is basically unique for the objects that we have learned to interact with. Because we routinely use our hands to interact with a remarkably diverse variety of mechanical systems, the ability to learn and recall internal memories is thought to be a fundamental property of the motor system (Shadmehr & Brashers-Krug, 1997).

Reference
Shadmehr & Brashers-Krug, J Neurosci (1997); 17(1): 409-19

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