The Case of
The Missing Calendar
describes the strangely consistent forgetfulness of young children about the order of events in the past. The rich and vivid memories of children have a consistent pattern of gaps which reveals some of the purposes of children's memories. Looking closer, we see that our adult memories have similar gaps but that we use a sophisticated model of events --- the calendar --- to cover them.
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There are many models which human beings use to look at time. The "calendar model" which we used to understand "The Year 2000 problem" is only one of many. Even if we only consider "objective" dates from the calendar, sometimes we look at time as individual events (the moon landing) while sometimes we look at time as intervals (the sixties). We can also look at time in the first-person (the next six months), the second-person (her first year of college), or the third-person (the summer of 1968). We can see intervals as having a clear purpose and identity (the period between the launch of Apollo 11 from Cape Kennedy and its touchdown at Tranquility Base) or as being arbitrary (the period between the 1968 Democratic National Convention and the 1969 moon landing). We can also distinguish events by their ordering (the construction of Stonehenge preceded the construction of the Eiffel Tower) or by their context (Stonehenge was constructed during prehistory, the Eiffel Tower early in the industrial revolution). For different kinds of questions, different viewpoints are appropriate and our different viewpoints are what enable us to answer so many different kinds of questions and to solve so many different kinds of problems. And when we use the wrong viewpoint for a particular kind of question, we get answers which are either subtly or spectacularly wrong.

Fortunately, we don't usually use the wrong viewpoint and normally switch so fluidly between viewpoints that we may not even notice that we are looking at something (like the ordering of events or periods we remember) in many different ways. We generally only notice the multiplicity of viewpoints when, for some reason, we consider two models of the "same thing" at the same time. This may happen when one model "fails" in a way which another model can describe, or we need to understand how another individual's (or a computer's) model differs from our own.

Learning from Children

A common and instructive form of this juxtaposition is looking at the ways in which children see the world. For millenia, people thought that children thought about and saw the world pretty much like adults, but that they lacked skills, or knew fewer facts or thought less consistently. Only in the last century, mostly through the insights of psychologists like Jean Piaget, have we widely recognized that children often "know differently" but in completely consistent ways which are sometimes just inadequate for adult purposes. This recognition both helps us help children become adults and helps us understand the patterns which underly our own thoughts. In the latter case, this understanding of our own patterns of thought may be the key to changing patterns which no longer fit our situation.

In the same way that we learned something about models by examining computer models of time (limited to two digits) against the background of our own models of time (without those limitations), we can learn something more by looking at aspects of how children and adults each represent time. Of course, we can't look at the programs written or wired into children's brains, but we can tell something about how they think about time by asking questions. This is tricky, as it may be difficult to tell whether a difference arose from understanding the question differently or from understanding time differently. But if we're careful and thoughtful, we can reduce the problems introduced by language to learn things about both our own and children's ways of understanding time.

If we look at children's understanding of time, we see that some of the adult ways of looking at time are missing. Looking at these differences can tell us a story of how models change and grow. In particular, we can learn things by looking at how children understand and remember the ordering of events in time, the very thing which the computers of the last section did simply by comparing numeric values describing dates.

Following Order

Even few-month old infants are sensitive to ordering of events in time. This sensitivity has substantial everyday consequences for the infant, helping it prepare for the many changes outside of its control. The arrival of a parent may presage physical comfort and food or a shift to the changing table may foreshadow the itchy ordeal of a diaper change. This anecdotal evidence has been confirmed by careful and clever experiments where infants indicate surprise (by a variety of subtle cues such as widening pupils) when a familiar sequence of images A,B,C is replaced by an out-of-order sequence A,C,B.

While these experiences and experiments show that infants are sensitive to the ordering of kinds of events, they don't tell us whether they recall the order of particular events. Only when they have accquired enough language to report or confirm the details that make an event unique (in our adult recollection), can we begin to ask questions about how they understand events and how they relate to one another. But even this is tricky, as a child's memory may combine unique details from different occasions into a single event; alternatively, children's more detailed memories may distinguish events as being of different kinds in ways which adults cannot. The distinctness or uniqueness of events may be reckoned differently for children and adults. But when it is clear that the experimenter and the child are talking about the same events, a fascinating pattern appears.

As soon as children becomes old enough to answer some patient experimenter's questions, they can readily remember and describe the order of actions or events which they have observed in the recent past. But as the events being compared move further and further from the time of questioning, the answers become less reliable. Up until around the age of 5, children cannot accurately answer questions about the order of events occuring more than 60 days earlier. If, on a June day, a child with a January birthday is asked whether their birthday or Christmas was more recent, the child cannot reliabily respond with an accurate answer. From a distance, it appears, the ordering between events becomes confused.

Why should this be? One simple explanation (or non-explanation) of this error is that the child simply "forgot" the ordering of events which it once knew. The problem is that children seem to be able to remember other aspects of the events and to readily learn ordering information between kinds of events over such long periods. The systematicity of this forgetfulness suggests that something else is going on.

A different answer might be that some organ or structure of the brain, which keeps track of order, does not mature for some years into the child's life. Unfortunately, this does not explain the 60 day threshold; if we ask our child on New Year's day whether Christmas or birthday occured earlier, it will have no problem answering the question which, six months later, will stump it. A weaker version of this answer would be that the organ just "isn't very good" until later in the child's life, but this is more of a description than an explanation.

A more interesting answer comes if we realize that our adult recollection of the order of events can sometimes be just as confused as a small child's. For instance, in the spring semester of my freshman year at MIT (when I at least thought I was an adult), I remember two particularly significant events: while running down the steps to turn in a problem set (eager young student that I was), I twisted my knee and needed crutches for several weeks; and during the same semester, I found that I had done poorly on a mathematics exam for the first time in my life. Despite the fact that I remember both of these events clearly, I have no idea in which order they occured. Most people, with some effort, can probably find similar "disconnected" pairs of events, but it is difficult, because we do not naturally remember things based on what we don't know about them!

So, in some cases, our adult understanding of our adult experience shows the same sorts of phenomena which are so pervasive in the child's understanding of distant events. This realization splits the question into two parts: why do children (and sometimes adults) not recall the order of events after some time has passed? And why do children get better at it as they become adults?

Why Remember?

Why would we remember chronological order in the first place? In reformulating the question (why doesn't such remembering always happen) in this way, I am taking a tricky step of invoking purpose in my explanations. Some would say that this is so dangerous a step --- what do we know of real purposes? --- that it invalidates any subsequent steps. But I need to talk about purposes because they lie at the roots of what models are. Models ignore and emphasize according to their implicit (or occasionally explicit) purposes and we cannot discuss differences between models without bringing in arguments based on purpose.

Why remember chronological ordering? Well, we mentioned above that chronological ordering is important to prediction, which is important to survival. Even infants learn to anticipate consequences, which requires some recall of chronological ordering. But why remember it over time? Why should we remember the ordering of events for a long time after they have occured?

One important reason is that some orderings are accidental while others are significant. If I hurt my finger after getting mad at my mother, it is probably an accident; if I hurt my finger after I touch the hot stove, it is probably significant. One reason to remember orderings is that if orderings occur again and again, they are more likely to be significant and thus more likely to help predict the future. If orderings came with little tags saying "significant" or "accidental" we wouldn't need to remember them in particular, but since they don't, but are spread out through our experience like articles in a magazine (between the advertisements), it helps to remember them over time.

This explanation also explains why it might not be as useful to remember orderings of events for a long time. If a certain ordered pairs of events does not recur within some interval of time, the order is more likely to be accidental than significant. If there is any expense associated with remembering things, it may make sense to discard information about events and orderings which may not be significant. Interestingly, if it turns out that a pairing of events recurs over time, the actual details of the individual events become less significant and so we may need less detailed information about them.

This is one place where arguing with purpose gets tricky, as I can't say why remembering things should have any cost. I have made an argument from purpose, but I can't ground it in a real tradeoff between remembering everything and remembering only what you need to. Of course, I expect from basic principles that there are real expenses associated with memory, but I have neither the background nor the resources (within the context of this book and the reader's attention) to articulate that more. I'll leave that to some other book and probably some other author.

Arguing from purpose is also tricky because we only partially understand our purposes. We remember many things from our past that don't seem to be significant. Why? There are various possible answers: thinking about the significance could be difficult if some of the events were painful or traumatic; or the past events could be significant in ways which we are not conscious of; or, finally, they could have been significant at the time for reasons we have forgotten.

So one good reason for remembering past orderings is so that we can learn from our experience over time. But the value of such remembering diminishes over time and so we probably don't need to remember orderings from the distant past. If there is any real cost to remembering things, it will make sense to lose information about those events. But why, then, do adults get better at remembering chronological order?

Getting our Bearings

What happens when we adults ask ourselves whether Christmas or our birthday is more recent? In many cases, we think about the calendar and how the three dates (now, birthday, and Christmas) fit on the calendar and the "calendar" answers the question for us. Because adults understand the calendar and seasons and the broader scope of human time, we understand dates as more than just events. Because we remember events in this way, we can more readily answer questions about ordering for events long past. Indeed, as adults, we can know what we should have told the experimenter when we were children, just by knowing when we were asked the question.

As adults, we use the calendar as a model for time, and this allows us to answer questions to which we do not literally "remember" the answers. The calendar in this case is playing multiple roles: it allows us to "remember less" by telling us how events are ordered whose actual ordering we have forgotten (as in a childhood Christmas and birthday); it allows us to "remember more" by ordering events we have not actually experienced (I know that Thanksgiving in 1864 preceded Christmas in 1864); and the calendar allows us to communicate and coordinate our lives with others ("I'll meet you on the 17th of May") knowing that our calendars advance at the same pace.


We began this example by talking about different ways in which humans think about time. These different ways of thinking are usually invisible and only reveal themselves when we need to compare and contrast two models at the same time. Comparisons like these reveal something about the gaps and assumptions of each model which no single model alone could reveal. Such comparisons routinely occur when we seriously consider the way in which children see the world. We learned that children forget the ordering of events which have occured too long ago. In attempting to explain this forgetfulness, we invoked purpose to ask why remembering the order of events might be important. One important reason is that remembering the order of events may help us learn things about which orderings are significant and which are not. However, the potential significance of these memories diminishes with time, as the sequence of events it describes fails to repeat itself.

We then addressed the question of why adults recall the order of events when children do not and recognized that there are cases where adults don't recall order either. The solution for adults, it seems, is to use an external model, the calendar, to augment their own descriptions. This augmentation goes further than reviving the order of forgotten experiences and actually allows reasoning about the order of events we haven't even experienced.

The first lesson is that we learn about models when we compare models of the same "thing" whether they are dates on the calendar or events we recollect. We saw this in the Case of the Year 2000 but it is reinforced here, where we see that looking at children's understanding can illuminate our own.

The second lesson is that models not only help people understand but also help people "learn" by both highlighting certain things (the order of experienced events) and hiding certain things (the order of events experienced long ago). Forgetting, in some cases, may just be hiding details which would be confusing or misleading in the current situation. In this case, forgetfulness is a powerful tool of the mind.

Turning to adult's thinking about such questions, we learned that part of of our model of events is based on powerful social inventions such as the calendar. These constructions both repair and extend our more natural modes of understanding.

We have also learned about some of the tricky aspects of considering human models. We cannot generally look at human models with the same precision as computer models; there is no way to tell that children are just using certain characteristics (such as place, caretaker, or weather) to represent events as we could tell that computers were just using two digits to represent years. Instead, we probe human models with questions and puzzles which are peculiarly dependent on the hiding or highlighting of particular aspects of what we believe they are representing.

In the next example, we look at the powerful model of the inertial frame which has been and remains one of the foundations for our physical understanding of the universe.

Copyright (C) 1997, 1998 by Kenneth Haase
Draft, not for citation or circulation
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