It is generally acknowledged that memories are not attached to specific locations in the brain1. A possible, though not widely accepted explanation for how they are stored is via the analogy of the hologram.

Holograms were invented in 1946 by Dennis Gabor, when he found a way to encode a 3D image in a beam of electrons (later, with the invention of the laser, a beam of light could be used instead). The way that a hologram works, and one of the things that makes it so interesting, is that all of the information needed to create the 3D image is stored in any small portion of the glass plate that the beam hits. The information is not localised, it is all distributed everywhere, in all places at once.

Part of how this works is with patterns of waves, or ‘interference patterns’. If you can get a piece of the hologram big enough to contain the pattern, you can retrieve the whole hologram from that piece. All that happens is that, the smaller the piece of hologram you have to work from, the more ‘noise’ the extrapolated whole will have. The fuzzier it will be.

Not long after holograms were invented, theories arose to suggest how memory could be working in a similar manner, and this information system could explain why we cannot locate individual memories to specific places in the brain. Karl Pribram proposes that, rather than the brain working as if it’s a literal hologram, it works holonomically - it too uses patterns of waves to store information, but many of them, overlapping2. In the brain these waves are electrical. The waves travel across a certain region of the brain, so the memory is stored where the waves are, but non-locally. After all, all objects are vibratory structures.

I liked this idea as soon as I started to read about it, because of the idea that memories are not defined things in our brains but are vibrations travelling through us. Our brains are buzzing with these vibrations, travelling back and forth in the background for our whole lives, ready to be assembled into consciousness at any point.

The holonomic brain model is not accepted by mainstream neuroscience and probably belongs more to the realm of quantum mysticism. But the analogies of multiplicity that these theories evoke are exciting, and have a resonance with the experience of memory. Like the concept of the hypertext the structure that is rhythmic and proliferating, rather than linear and finite, mirrors our contemporary world and the epistemological pluralism necessary to understand it.
1. Richard C. Mohs, "How Human Memory Works”, 8 May 2007.
HowStuffWorks.com. <https://science.howstuffworks.com/life/inside-the-mind/human-brain/human-memory.htm> [Accessed 23 February 2020]

2. Holonomic brain theory is most associated with Karl Pribram and David Bohm. David Bohm was a theoretical physicist, and he had unorthodox ideas about how the brain works, including that the conscious mind works in a way that has something to do with quantum physics. Like holography, in quantum physics things can be in more than one place, or state, at the same time (loosely speaking). Holonomic brain theory becomes one way that quantum effects in the brain might be responsible for some of these things that cannot yet be explained fully by traditional neuroscience - memory, and consciousness.