Playing with Blocks

One day, I was watching two of my grandchildren 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 models of Reality based on contrasting conceptions of time: serial time (train) vs. cumulative time (tower).

Serial time is like box cars in a train. Properly arranged, the boxcars exhibit a certain order. Depending on your model, that order either (1) remains fixed, regardless of the number of cars in the train, or (2) increases by a fixed amount (a constant) with each car added, or (3) increases arithmetically as the train grows.

In the serial model, order is relatively resilient; when disorder does (inevitably) increase, the change is gradual (over time) and local (in space). The subtraction of one car shortens the train, but only by one unit; it has no impact on the train’s ‘structure’ or identity as a train.

Cumulative time is something else entirely. It’s more like the tower that my older grandchild is building. Each newly placed block recapitulates every block before it. Block (N+1) = (Block N) + 1. Each new block ‘contains’ in some way all previous blocks. 

Block N ‘stands on the shoulders of giants’, beginning with Block One, and giants will stand on the shoulders of Block N. Block N also contains Block (N + X)…but as a potentiality rather than actuality. 

Prior to the addition of Block N, the Tower is already stressed (gravity). The addition Block N increases that stress. Here order increases geometrically with the size of the tower…as does the risk of collapse. This is a catastrophe waiting to happen. Remember the Tower of Babel.

Eventually, with the addition of Block (N + X) the structure will collapse. The ‘malfunction’ of a single block (present) eliminates the future as well as the past.

Collapse it must. The tower constitutes an island of locally increasing order in a universe that is incurably entropic. The Second Law of Thermodynamics guarantees that the tower will fall, and that catastrophe becomes more imminent as the tower assumes an ever more ordered state (aka height).

If the block last placed on the stack, (Block N + 1) malfunctions, it tumbles to the ground, but the removal of Block (N + 1) does not threaten Block N or any Block (N – X). However, with the removal of Block N = 1, all the blocks fall. In that event, everything that went before (i.e. all prior states of order) is destroyed. All that is left is scattered blocks on the living room floor, a state of 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.

Notice also the radically different ways in which order and disorder play out. In the cumulative model, each increase in order increases both the likelihood and the median impact of incipient disorder; and when disorder does come, when the tipping point is reached, it is instantaneous and catastrophic.

On the other hand, in the serial model, the likelihood and impact of a disordering event is only marginally related to the size of the train. Now consider real life…like TV, for example: I’m watching the 1,000th episode of Law & Order. Each episode is a self-contained story. However, the characters and the mise-en-scène have evolved gradually over the seasons so that the 1000th episode is fully meaningful only in the contest of the 999th episode. Likewise, the 1001st… 

So what about the time we know (and normally don’t love)? Is your experience of time serial or cumulative? Is it independent of the events that make it up, or is it an epiphenomenon of those events? Which model corresponds to your experience?

I propose that all time behaves cumulatively, and that the notion of serial time is a special, degenerate, case of cumulative time (like a series of one-block ‘towers’). No actual span of time is ever completely serial. A de minimus amount of novelty must creep in, creating an ever so slight asymmetry. Real blocks are never perfectly interchangeable (just ask identical twins). 

But does each moment of time truly recapitulate all the moments that went before it? When we consider our own lives, there is a certain order to events and 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 Isle of Sodor. 

IRL, the commutative property does not hold. In arithmetic, we say that x R y = y R x; example: x + y = y + x. Where the commutative property applies, these relations hold for all values of x and y. If the commutative property does not apply, then there are values of x and y for which the relation (R) does not reciprocate. 

Life is ‘radically non-commutative’. There are precisely NO values of x and y for which x R y is commutative. The order of events in the real world (if not their content) is apparently immutable. Counter intuitively, that means that the order of events is substructural to their content and meaning. When > What + Why!

This is true because every event is a recapitulation of whatever went before it. What + Why are subsets of When. 

I’m not talking just about human experience here. Even inanimate objects undergo a sequence of modifications, each modification building on the ones that went before it. Nature carved out the Grand Canyon over eons of time; it will not refill itself in an instant. Every ‘actual entity’ (event) is a recapitulation (and modification) of its history. 

So what happens when an entity ceases to exist? Entity (N + 1) = Entity (N) + 1. N is an ordered subset of (N + 1). So if (N + 1) is removed from the tower, the order represented by ‘N’ is removed in the process. Of course, Block N remains in place, but ‘the copy’ of N that resides in (N + 1), and was modified by (N + 1) is erased and that version of N is lost forever.

Why? If (N + 1) is removed from the tower, why can’t the tower simply revert to its status @ N? Because you can’t go home again, Tom: (N + 1) – 1 ≠ N. (N + 1)  ≠ N + 1. Per Jacques Derrida, every iteration of N, every copy, every application is differant (French with no English equivalent) from every other copy -  infinitesimally different but different nonetheless. 

Evolution tells the story. A species evolves over time through a seemingly endless series of genetic modifications. Each successful modification builds on the modifications before it. But when a species becomes extinct, the latest behavioral adaptations fail, and the entire sequence of modifications is wiped out.

It’s like the bumper sticker says, “Extinction is forever.” But as above, earlier evolutionary branches may survive. There is hope that bonobos may endure long after humans have vanished, but those bonobos are not the same bonobos that evolved into humans. Bonobos evolve too! 

According to virtually all contemporary cosmological theories, all islands of order in our universe will ultimately be overcome by entropy. The universe as a whole will ultimately end in Heath Death (Big Freeze or Big Crunch). In any event, all present and prior states of order will be erased.

‘Cumulative time’ turns out to be another name for ‘universal eraser’; it wipes out everything. Consider my grandchild’s tower. At some point, some block will malfunction. Over time, every block will malfunction. When the Base Block (N = 1) malfunctions, all vestiges of order are destroyed. The fate of the tower is sealed, from Block One.

According to the mechanical model of serial time, time is pre-existent, and events just fill available slots. The train is logically precedent to the individual box cars that make it up. According to the organic theory of cumulative time, time is a function of events as they occur. Events by nature are not normally commutative, and therefore time itself must be fundamentally asymmetric.

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.

We must be missing something. But what? What if there was an aspect of events that lies outside of time entirely? In fact, our considerations suggest that to be real, an event must have an a-temporal (eternal) aspect to it. While events certainly do occur in time, those same events must also exist outside of time, or they are doomed to be erased.

Spacetime can be thought of as a geometric construction (‘vector equilibrium’ per Buckminster Fuller) in which events come to be and come to interact with one another. Time lets events be what they are; but once that process is complete, time is no longer relevant. Time relates to becoming, not being. To be is to be beyond time.

Ultimately, temporal events and the spacetime that births them vanish; we are left only with ‘the thing itself’, the eternal aspect of the event, its ‘objective immortality’, its footprint in the sand. 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. 

So in the end, the value (trace) of a quantum of experience is time independent. Life is just what it is, regardless of when you live it because in the end all of our experiences are eternal…or they are not!

David Cowles is the founder and editor-in-chief of Aletheia Today Magazine. He lives with his family in Massachusetts where he studies and writes about philosophy, science, theology, and scripture. He can be reached at david@aletheiatoday.com.

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