Chapter 5 · Forgetting Is Not Erasure

A phone number from twenty years ago does not come to mind now. Yet let someone tell it to you once, and it revives incomparably faster than the first time you memorized it. If that number had been cleanly erased from long-term memory, reviving it should be as slow as memorizing from scratch. But it is not. This fast revival is explained only by taking it as not erased but merely dimmed in the path to reach it. This is why we must look again at the nature of forgetting.

A Dimmed Path, a Remaining Representation

In the previous chapter we said two forces hang on a single representation: retrieval strength, the degree of reaching now, and storage strength, which sets how slowly retrieval strength falls and how fast it recovers. Seen through these two forces, forgetting is not the representation being erased from long-term memory but the retrieval strength toward that representation falling. The representation, and the storage strength that supports it, both remain; only the present activation that spreads from a cue to the representation has weakened, so you cannot reach it right now.

Then why does that activation weaken? Not because the representation or its connections have been cut. In Chapter 3 we said that when several representations hang on one cue, the activation splits into several branches when that cue lights up. As time passes, we keep hooking new things to the same cue. Then when that cue lights up, the activation splits ever more finely, and the share returning to the old representation shrinks. Retrieval strength falling is just this—the cue's activation being divided among competitors, the share reaching the old representation thinning. It is not cut but crowded out, and so, rather than time itself erasing the memory, the competition piled up during that time veils the path. Where this competition comes from and what else it breeds we look at separately later.

So what is forgotten soon revives at a small fragment of a cue or a brief relearning. The path was merely blocked while the destination stayed in place, so the path need only be reopened. The old number coming alive at a single hint, a long-unridden bicycle ridden again within a few turns of the pedals—these are all this. To say one has "forgotten" something usually means not "it has vanished" but "the path to reach it has dimmed now." Future revival parts because the invisible storage strength differs, and so we define forgetting solely as the fall of retrieval strength.

When You Recall Once, Both Forces Move Together

When you successfully recall something, that one retrieval pulls both forces up together. Retrieval strength rising is the exact reverse of the fall seen earlier. Ride once through the path from cue to representation, and that path thickens. But the total activation a cue puts out is fixed, so as one path thickens and its share grows, the share going to competitors hooked on the same cue shrinks. Retrieval is just this—taking back the share that had been thinning to competitors—and so it restores the very share that forgetting had been gnawing away (retrieval strength rises). And that representation lodges deeper (storage strength rises). Yet the magnitudes of these two rises do not move independently; they interlock crosswise. How much one rises is set by the current value of the other. This crossed interlocking is the key that unlocks nearly everything about learning.

One direction of the interlocking is this: how much retrieval strength rises in one go is set by the representation's storage strength. The more deeply lodged a representation, the higher it revives on one recall and the more slowly it falls thereafter. Even what seems wholly forgotten—retrieval strength fallen nearly to zero—recovers high at once from a single relearning if only its storage strength is high. The old phone number coming alive far faster at a single hint than at first memorizing is exactly this: retrieval strength was at the floor, but storage strength remained high, so one retrieval lifted retrieval strength greatly in proportion to that storage strength. This is where relearning being faster than first learning comes from.

The other direction of the interlocking matters more: how much storage strength rises in one go is set, inversely, by the retrieval strength at the moment of retrieval. If at the moment of recall it was already coming easily—that is, if retrieval strength was high—storage strength rises almost not at all. The more a retrieval is one barely hauled up after retrieval strength has fallen low, the more it grows storage strength. What comes easily does not lodge deep; what is recalled with effort lodges deep. This is the kernel of the learning principle called desirable difficulty, and here one thing needs to be made clear. This inverse relation is less a precisely measured formula than a qualitative principle this model sets to organize various learning phenomena. The direction—that a retrieval hauled up with effort in proportion to how far it had fallen grows storage strength more—is confirmed again and again, but no exact constant of proportionality is assigned to the magnitude of that rise.

The Asymmetry of Learning

Combine the two directions and the asymmetry of learning shows itself. Retrieval strength and storage strength grow under different conditions. Retrieval strength rises straightaway if you recall once more now, but storage strength rises greatly only in a hard retrieval after retrieval strength has fallen enough. This divergence diagnoses one common study habit precisely.

That habit is the massed cramming of reading or recalling the same material over and over without pause. Here you are retrieving again from a state where retrieval strength is already high. Each retrieval comes easily, so performance in the moment is good and there is a feeling of "doing well." But retrieval when retrieval strength is high grows storage strength almost not at all. It has merely raised retrieval strength a little more, while storage strength—the thing that actually lasts—stays put. Conversely, if after a good while, once retrieval strength has fallen, you recall again with effort, performance in that moment is taxing and slow, but storage strength rises greatly. It feels harder at the moment of learning, but because storage strength rises along with it, more remains.

With this, the nature of the false gauge seen in the Opening becomes clear. The "feeling of ease" we take as a measure of learning reflects retrieval strength, while what actually remains as learning is storage strength. Because the two grow crosswise, the very moment retrieval strength is high and it feels easy may be the moment storage strength is barely growing. Following the feeling of doing well to raise only retrieval strength by cramming, and avoiding the stumbling hard retrieval, comes from here. The feeling systematically obstructs learning.

From this asymmetry the main stem of learning methods flows. Covering the material and recalling with effort; placing time between trials to deliberately let retrieval strength fall—these all come from the same root. All of them raise storage strength by inducing a hard retrieval where retrieval strength has fallen. Laying these techniques out properly we put off, but they all derive from this interlocking.

Yet one thing is still empty. Whether the hard retrieval that grows storage strength or the learning that binds several representations anew, that work all takes place in working memory. And working memory is narrow and volatile. How does that computation of recalling and binding actually run in the narrow working memory, and what does that narrowness make possible and what does it block? Having built the two forces of long-term memory, we now return to the working memory where those forces operate.