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One morning, I was standing on the New Jersey side of the Delaware River, looking across to Philadelphia. As I was accompanied by several grandchildren, I decided to tell a story, “Once upon a time, a long time ago, an Indian princess might have climbed into a canoe with her grandfather right here at this very spot. He might have paddled her all the way across the river to their village on the other side.”

“I’m glad I’m not that princess,” my older granddaughter offered.

“Why?” I asked, somewhat surprised.

“Because she’s dead now and I’d rather be alive.”

Without realizing it, my granddaughter had shone a spotlight on a usually neglected paradox concerning time. We accept that living in 2015 is different in many superficial ways from living in 1515…or in 2515. But we also assume that the essence, and therefore the value, of the life experience itself is always the same. As much as the content of our lives may differ one from one another, we assume that the process itself is identical. Therefore, we are not inclined to accept my granddaughter’s contention that living later is necessarily living better.

Looking at our own lives, however, it is hard to see how events that took place in the past could possibly have equal ontological weight compared with current or future events. What ex-monarch, in the process of being burned at the stake, thinks, “Oh well, I certainly had fun when I was five”? More likely, that desperate creature curses the day he was born.

The reverse is also the case. As a painful experience fades into the past, it loses at least some of its sting.

The memory of past happiness can rarely, if ever, overcome the horror of immediate pain; on the other hand, the hope of future happiness may. A mother in labor is comforted by the hope that she will soon have a baby to love and care for. An athlete may train hard all summer hoping for the thrill of victory in the fall. A saint embraces martyrdom as a small price to pay for admission to the Kingdom of Heaven.

So apparently time is not symmetrical after all. Events that took place in the past do not have as much value for us as events taking place now or in the future. Carrying this logic even further, I would propose that nothing that happened in the past can have any value whatsoever for those of us living in the present.

There are two obvious objections to this proposition. First, past events and experiences may cause or at least condition current events and experiences. Second, past events may leave memories that in turn give depth, value and intensity to our current experiences.

Consider, however, the following thought experiment: Suppose we were all just created de novo with partial ‘memories’ of a fictional past implanted. In that case there is no question of that past causing present events and our memories would be unrelated to any actual events in the past. The past would truly not exist; it is erased by time.

How would that be any different for us than if we had lived through an actual past and encoded those memories on our own? Unless we can specify and demonstrate such a difference, we have to agree that the actual past is of zero value to those of us living in the present. Further, if our own past experiences have no value for us, why would the past experiences of others?

In truth, the past exists for us only as the shadow we call memory and as the flat ground against which novelty appears.

Evaluating the future is trickier. We need at least two variables here, one measuring the intensity of the potential reward (e.g. baby, victory, heaven) and another representing its probability. If the hoped for reward is a sufficient improvement over our present circumstances and if uncertainty does not exact too great a discount, we may actually place a higher value on a future event than a present one.

My granddaughter was not willing to trade places with that Indian princess no matter how exciting her life might have been. Her life had zero value for my granddaughter. On the other hand, that princess might have gladly changed places with my granddaughter, giving up a life being lived for a life to be lived.

On another day, I was watching two of my grandsons play with blocks on the living room floor. One was building a train, the other a tower. It occurred to me that they were acting out two very different conceptions of time: serial time vs. cumulative time.

Serial time is like box cars on a train. Every car is interchangeable with every other car. Just ask any motorist stopped interminably at a rail road crossing. The train may ultimately have an engine and a caboose but that does not in any way undermine the inconvenient reality of each and every box car in between.

Likewise, a stretch of serial time may have a beginning and end but those terminals do not impact the reality of the moments of experience in between.

Cumulative time, however, is something else again. It is like the tower that my older grandson is building. The position of each newly placed block recapitulates in some way and to some extent the position of every block placed before it. It is not too much of a stretch to say that each new block in some sense ‘contains’ all previous blocks.

This building process continues, breathtakingly, until inevitably the tower collapses. It has to collapse. The tower constitutes a local increase in order in a universe that is incurably entropic. The Second Law of Thermodynamics guarantees that the tower will fall and that catastrophe becomes more and more immanent as the tower assumes a more and more ordered state.

When the tower does collapse, not only does the final block tumble to the ground but everything that went before (i.e. all prior states of order) is destroyed as well. All that is left is a scattering of blocks on the living room floor. A state of high and ever increasing order is instantaneously reduced to a state of nearly maximal disorder.

Notice that the relationship between the blocks and the structure differs in the two examples. In one case, the structure (train) is independent of any particular block. In the other case, the structure (tower) is entirely dependent on each and every block.

We imagine that time is like the box cars of the train and not like the bricks of the tower. We imagine that every unit of time is commutative with every other unit. The subtraction of one unit shortens the train but it has no impact on nature of the train itself or on any of the other box cars that make up the train.

On the other hand, if we look at the tower model, it is clear that the subtraction of just one block impacts, at least potentially, every block in the structure and threatens the very existence of the tower itself.

So is time really serial or is it cumulative? Is it independent of the events that make it up or is it an epiphenomenon of those events? Which model actually corresponds to our experience?

I propose that all time behaves cumulatively and that serial time is a special, perhaps even a degenerate, case of cumulative time. Likely, no actual span of time is ever completely serial. A de minimus amount of novelty must creep in, creating an ever so slight asymmetry.

But is that really so? Does each moment of time recapitulate all of the moments that went before it? Certainly, when we consider our own lives, it is clear that there is a certain order to events and that the relationship between a present event and a past one is very different from the relationship between a present event and a future one. Events cannot be shunted around like box cars on the Island of Sodor. The order of events (if not their content) is apparently immutable.

I’m not talking just about human experience here. Even inanimate objects undergo a sequence of modifications, each modification ‘building’ in some way on the one that went before it. At any single point in time, any object is in part at least the sum of its history (real or imagined). Therefore, when the object ceases to exist, must not its history (real or imagined) cease to exist as well?

It is popular today to consider time as a manifestation of entropy (Stephen Hawking, et al). According to this theory, the arrow of time and the arrow of entropy are the same thing. But entropy concerns actual events and structures. Therefore, entropy is cumulative. The entropy at time t is dependent on the entropy at time t – 1. If entropy (disorder) is cumulative, so order (negentropy) must be cumulative as well.

Consider the creation narrative in Genesis. God created the world in 7 days. On Day One, God merely separated darkness from light, introducing a single quantum of order. By Day 7, the world is more or less as we experience it today. But as God created, he did not start over again each day. Instead each day built on the accomplishments of the day before. The world as it is on Day 7 encompasses the world as it was on Day 6 and Day 5 and Day 4, and so on…

So, if and when the world as it is on Day 7 is destroyed, the world will not magically go back to the way it was on Day 6. Day 6 is now just an integral part of Day 7. It is not just Day 7 that will be wiped out but Day 6 and Day 5 and Day 4 and so on. Disorder cascades like blocks from a falling tower. We are left with the world as it was prior to Day 1: “The earth was without form or shape with darkness over the abyss”; blocks are scattered randomly on the living room floor.

Evolution tells exactly the same story. A species evolves over time through a seemingly endless series of genetic modifications. Each new modification builds on all the modifications that have gone before. But when the species becomes extinct, that entire sequence of modifications is wiped out in one fell swoop. Like the bumper sticker says, “Extinction is forever.”

According to virtually all contemporary cosmological theories, all islands of order in our universe will ultimately be overcome by entropy and decay. The universe as a whole will ultimately end in a Big Freeze (or perhaps a Big Crunch). In any event all prior states of order will be eliminated. Cumulative time is a universal eraser; it wipes out everything.

According to the notion of serial time, time is pre-existent and events just fill available slots. The train is logically precedent to the box cars that make it up. According to the organic theory of cumulative time, time is a function of the events that create it. Events by nature are not normally commutative and therefore time itself must be asymmetrical (cumulative).

So the paradox of time comes down to this: to the extent that you believe in the reality of events, you can’t believe in the reality of time; and to the extent that you believe in the reality of time, you can’t believe in the reality of events.

No one is more closely associated with the classical theory of time than Sir Isaac Newton. Yet even he recognized that his theory could not account for locality or duration. He invoked God to bridge the gap:

“He is Eternal and Infinite, Omnipotent and Omniscient; that is, his duration reaches from Eternity to Eternity; his presence from Infinity to Infinity… He is not Eternity and Infinity, but Eternal and Infinite; he is not Duration and Space, but he endures and is present. He endures forever, and is everywhere present; and, by existing always and everywhere, he constitutes Duration and Space.”

When I told my lame story on the banks of the Delaware, I was espousing a serial concept of time. My granddaughter exposed the fallacy of my argument advancing instead a cumulative model. So it seems that she was right and I, and most everybody else, wrong, right?

Not so fast! Accepting this conclusion leads to some strange corollaries. For example, the last person alive must then be the most favored. Likewise, the prolongation of individual life beyond all reason becomes a moral imperative. Life becomes a giant tontine and the last man standing is the big winner…just before he freezes to death.

As we have seen, the notion of cumulative time assigns 100% of the value of events to the present and the future. By definition, past events have zero value. However, our current cosmological theories predict heat death for the universe. There will be no more present or future. Everything will be past but then there will be no past either because (1) the past has zero value and (2) the past only exists in the present and only to the extent that it colors and conditions that present and (3) time itself disappears at the Big Freeze (or Crunch).

So all experience will ultimately be relegated to the past and therefore destroyed; total value = zero. All information would be destroyed (something not allowed by quantum mechanics and by contemporary cosmological theories).

I don’t think many of us would be willing to accept these logical consequences. So something must be wrong with our argument; we must be missing something. But what?

Serial or cumulative, we have assumed that events are entirely co-incident with time. What if that were not true? What if there was an aspect to events that is outside of time entirely? In fact, our considerations suggest that to be real, an event must have an a-temporal (aetemporal, eternal) aspect to it. While events certainly do occur in time, those same events must also occur outside of time, or they are doomed to be erased.

Spacetime can be thought of as a geometric construction (e.g. ‘vector equilibrium’ per Buckminster Fuller) in which events come to be and interact with one another. Time is an integral part of what lets events come to be what they are. But once that process is complete, time is no longer relevant. Ultimately, temporal events and the time that gives birth to them will vanish; we are left only with ‘the thing-itself’, the a-temporal, eternal aspect of the event.

Time is like the imaginary quantities that arise in the course of certain calculations but that necessarily cancel out into real values at the end. Indeed, Stephen Hawking has proposed that quantities of time are best expressed using imaginary numbers.

Time is but one component of multi-dimensional spacetime. But it turns out that dimensionality itself is ambiguous. For centuries we were content to view ourselves living in 3-dimensional space plus time. Einstein showed that this really amounts to a 4-dimensional spacetime. Later Kaluza-Klein theory suggested that certain phenomena are best explained by assuming a 5-dimensional spacetime.

Today, string theory and M-theory work with 10, 11 and 26 dimensional spacetimes. At the other end of the spectrum, the holographic theory of universe suggests that space might be just 2-dimensional.

Even more astounding, in many cases systems with different degrees of dimensionality have been shown to be mathematically equivalent. Clearly, spacetime is not a sub-structural.

Finally, since events occurring in time will always be retroactively destroyed (erased) by gentle entropy or cosmic catastrophe, it turns out that it is only the eternal aspect of events that ultimately matters. Time is part of a medium (or a reflection of a medium) that facilitates novelty which in turn drives the emergence of events. But that is it. Time is at best a means to an end.

So it turns out that my granddaughter was wrong after all…but for reasons that none of us expected that morning on the river bank. In the end, the value of a quantum of experience is time independent. Priority confers no special value, nor does it preclude it. Life is just what it is, regardless of when you live it, because in the end all of our experiences are eternal.