In my economics lectures, I sometimes ask whether students are familiar with various concepts from science, particularly physics. The response is more often than not blank stares, due perhaps to the fact that science is, like, hard, and students would sooner forget it than dig deep into the recesses of memory. But in addition to the difficulties of science itself, it is difficult to imagine how the principles of a field as concrete as physics might be applied to a field as squishy as economics. An illuminating example is that of light cones.
In physics, a light cone represents the path that a flash of light will follow, unhindered, in response to some initial event, such as the striking of a match. Imagine being able to slow time down to a hyper-glacial pace, striking a match, and then observing the light of the tiny flame emanating in all directions, slowly illuminating everything around it. If you could take a three-dimensional snapshot at each subsequent second…each millisecond…each nanosecond…centered at the flame, and then view the entire collection of snapshots, you would observe a series of concentric spheres of increasing radius. As time moves forward, the sphere of light encompasses an ever-greater volume of physical space.
Unfortunately, when we think about the universe in terms of physical space and time simultaneously, what we call space-time, the human mind limits our ability to adequately conceptualize dynamic changes, such as the expansion of the match-flame’s light (it’s hyperspace, man). To keep things simple, we can reduce the dimensions of physical space from three to two, giving us a plane of physical space rather than the three-dimensional space that we observe in real life. We are effectively flattening physical space – think of the square that results from a flattened box. In addition to the two dimensions of space, we add a third dimension, time, measured along an axis perpendicular to the plane.
With this modification of space-time, the light from our match now expands in a two-dimensional circle, rather than a three-dimensional sphere, and as it moves forward along the axis of time, it creates a cone.
But we are not confined to considering only the emanation of light that resulted from the striking of the match – we can also use this concept of light cones to think about what information and events caused the striking of the match. If space is measured both forward and backward in time…if the circle of light is allowed to both expand and contract, we end up with a pair of symmetric light cones – the Einstein-Minkowski representation of space-time.
With this model of space-time in mind, we can start to think about the confluence of factors that lead up to any singular moment of time in our lives, and from that point, we can explore the realm of possibilities, both past and future.
Let us leave our light cones for a moment, and turn to economics.
In the field of economics, we spend a great deal of time studying how individuals make decisions, particularly when confronted with a scarcity of resources.
Think for a moment about all of the decisions you make in a single day. The very second your alarm clock sounds, and you snap (or drift) from the perceived space-time of the dream-state to the space-time of consciousness, the decision-making gears in your brain are set in motion. Will you turn the alarm off and get out of bed, embarking on your daily rituals of preparation? Or will you hit the ‘snooze’ button? What would you gain or lose in either case? Turning off the alarm and foregoing additional sleep would allow you to start the day off ‘right’, ready and raring to go. Hitting snooze, on the other hand, would allow you a few more precious moments of sleep.
But what is the scarce resource in this case? It is time itself, perhaps the only resource that is universal to man and all living creatures. As Diogenes Laertius records in Book V of his Lives and Opinions of Eminent Philosophers, a favorite expression of the Peripatetic philosopher Theophrastus was “that time was the most valuable thing that a man could spend.”
Our decisions at any point in time are based on a multitude of factors. We analyze the information we know (or…suspect we know) about our present circumstances, both material and abstract. We then weigh that information against our personal preferences, thinking about the consequences of any decision, both personal and social. All of these inputs are taken in or recalled by our brain, the numbers are crunched, and a decision is made.
\With this model of decision-making in mind, we can construct a synthesis of these theoretical concepts, both physical and economic.
LIGHT CONES AS LIFE CONES
As we move forward through time, we are constantly making decisions. Are we ignoring the past as we progress? No! We survey all of the past events and experiences that have led us up to a particular choice-moment in space-time, relying heavily on the lessons and accumulation of information gleaned from our past experiences to make optimal choices moving forward. Economists refer to this backward-looking approach as adaptive expectations.
In making any decision, we rely not only on past information, but also on what we can reasonably expect to follow from whatever choice is selected; we can’t truly predict the future, but we can at least define some limited realm of future possibilities, forming what economists describe as rational expectations. Weighing our options, we project forward all of the possible paths that might result from our decision based on past experience. Thus, in any singular moment in our personal niches of space-time, we are both backward- and forward-looking.
And so, with eyes to the past and the future, cognizant of our present state of being, we progress through space-time. There exists a finite number of possible paths that could converge on a particular moment, and from that singular moment, there extends a finite number of possible paths forward. Any events that might transpire that lead not to that moment, or follow not from that moment, are beyond the realm of the possible for the individual experiencing that moment. And so individual travelers we are, drifting through the realms of the possible and the unpossible.
But we are not alone! As we move forward through life, our paths cross with those around us, perhaps for only a single moment, or…perhaps for many moments.
I board a bus, and for the better part of an hour, I share a series of consecutive moments with the driver and the other passengers. Our paths have crossed, converged, and remain intertwined for the duration of my trip. When I reach my stop, I disembark, and our paths diverge – I proceed into my own future of possibilities, and the driver and passengers into theirs, never to cross again…or will we?
Having once crossed paths, we have established a realm of shared possibilities. That shared realm might itself be finite, existing for period of time that will come to an end once our paths reach a point of critical divergence.
A man I have seen before on the bus wearing worn clothes, now wearing a hospital bracelet. What unfortunate incident sent him to the hospital? Will this alter his future path? Is it possible that this will be the last time our paths cross? Our paths having converged, will we now, individually, wander into our separate realms of possibilities?
Or the girl I see each day in the dining hall, dining alone. What series of events have led to these solitary suppers? Will she always break bread for one? Or will some day she dine with a companion?
There is nothing that guarantees that our paths will remain intertwined. But neither is there anything that will prohibit our paths from crossing again in the future. At every moment in time, our decisions will alter our unique future realms of what’s possible. Maybe I will never see the man on the bus again. Maybe his future is bleak. Or maybe it is beautiful. I may never know.
Sometimes, however, we might encounter another person, and the resulting collision realigns our individual paths such that there is a future realm of shared possibilities. It does not necessarily mean that we will be attached at the hip for all eternity, but certainly our lives will be lived in a common space across time. Perhaps two people will fall in love, choosing to join their lives, two flashes of light in the universe, growing and fading in tandem, binary stars revolving around a common center of gravity. But still, nothing is guaranteed. A lifetime together is possible, but there still exists for each of them a separate future realm of possibilities. And like two stars, they could slowly drift apart over time into far-flung corners of the universe, never to cross paths again.
This is how I see people, wherever I go – fellow cone-headed travelers in space-time. Every mind I encounter is a universe unto itself, with a rich history and future distinct from my own, perhaps but for a single shared moment. It is a beautiful thing.