Chapter 4 · The Two Forces of a Single Representation

The number of the hotel room you are staying in and your home address both come to mind right now, equally sharply. By degree of coming-to-mind alone, the two are indistinguishable. Yet think a week ahead and their fates part. The hotel room number will vanish without a trace; the home address will still be there. That they come to mind equally now but have such different futures is because two independent forces hang together on a single representation.

The Force of Reaching Now and the Force That Lasts

One force is retrieval strength. It indicates how well you reach that representation at this moment—how fast and surely activation spreads to the representation when a cue is given, that is, how well it comes if you try to recall it now. What we sense as the "feeling of knowing," what shows in whether the answer comes straight off the tip of the tongue or stumbles, is this value. That the hotel room number and the home address come to mind equally now means their retrieval strengths are equally high now.

The other force is storage strength. It is the value that sets how deeply that representation is woven into related knowledge—and so how slowly its retrieval strength falls and how quickly it recovers when pulled up again. The home address, gone in and out of countless times and woven with all sorts of memories, is lodged deep; the hotel room number, seen once today, floats woven into nothing. Their storage strengths differ vastly. And it is exactly this difference that makes the parting a week later. The home address, high in storage strength, has its retrieval strength fall slowly and remains a week on; the hotel room number, low in storage strength, has its retrieval strength fall fast and soon becomes unreachable.

The decisive difference between the two forces is this: whether something comes to mind now is set by retrieval strength alone. However high the storage strength, if retrieval strength has fallen, it does not come to mind now; even with low storage strength, if retrieval strength is high, it comes to mind clearly now. What we see as performance and sense as a feeling is always the retrieval-strength side. Storage strength, by itself, does not show on the surface.

Why the Two Must Be Kept Apart

Saying there are two forces may sound like excess. If it comes to mind you know it, and if it does not you do not—why split it into two? The reason lies in the future. Even for two representations with equal retrieval strength now, if their storage strengths differ, the speed of forgetting and the speed of relearning ahead will part.

The two forces can have one at rock bottom while the other is high. At one extreme is the phone number of the house you lived in twenty years ago. Try to recall it now and it scarcely comes; its retrieval strength is at the floor. Yet let someone tell you the number once, and it revives with an "ah, that's it" incomparably faster than memorizing a number for the first time. Retrieval strength is at the floor, but storage strength still remains high. At the other extreme is the hotel room number you just memorized. Right now its retrieval strength is high and it is clear, but in a few days it will vanish without a trace, and once gone, not even a cue to revive it will remain. Retrieval strength is high, but storage strength is nearly none.

The point is that these two cases cannot be explained by one value alone. Of the old phone number and the just-memorized hotel number, which should we say you "know better"? By degree of coming-to-mind now, the hotel number is on top; but by degree of reviving at a single cue, the old number overwhelms it. The two yardsticks diverge because they measure two different forces. Merge them into one and you cannot hold this divergence. So we keep two forces apart on a single representation. "Well learned"—meaning slow to forget and easy to revive—and "well recalled"—meaning coming to mind right now—are different matters, and the side that remains as learning is the former.

How to Read an Invisible Force

Storage strength has one awkward property: it is never observed in itself. What we can measure and feel is retrieval strength only; it shows in whether something comes to mind now, and how fast. Storage strength shows only indirectly, through how that retrieval strength moves over time. If, under the same forgetting conditions, retrieval strength falls slowly, we know that representation has high storage strength; and if it recovers high quickly on relearning, we again know storage strength is high. Storage strength is not a quantity directly seen but a hidden variable read off from the behavior of retrieval strength.

This model assumes one more thing about storage strength: once accumulated, it does not diminish. Retrieval strength rises and falls, but storage strength is taken to only go up, never down. This is less a fact proven by observation than an axiom the model sets. We have not looked inside the head and confirmed that storage strength is eternal; rather, the behavior whereby something once deeply learned is unusually fast to revive even after lying fallow long enough to seem wholly forgotten can be cleanly explained by taking storage strength not to have vanished, and so it is set that way. Accept this axiom, and long-term memory does not erase what was once properly written. Even what feels wholly forgotten is in fact only a dimmed path to reach it; what is deeply lodged remains in place, awaiting a single cue.

Come this far and we must ask again what "forgetting" means. Is the old phone number's not coming to mind now because it has been erased from long-term memory, or because the path to reach it has merely been blocked? That it revives at a single hint suggests it has not been erased. Then what exactly is forgetting, and how do the two forces move together each time we recall something?