The three amigos: Time, change and boundaries - Part 1
Time and Change
Introduction
At about twelve years of age, I tried my hand at defining ‘time’. The event marked the first time I realized that, perhaps, my grasp of reality was not as solid as I had thought. While there have been many such humbling moments since then, the OG question of time, ‘what is it really?’, has always held a special place in my heart.
Of course, since the dawn of humanity, many others have asked the same question of time. And unsurprisingly, we’ve come up with several different answers for the same – with the specifics often depending on what the responder does for a living. So, if you ask a physicist, you might hear technical details about the inextricable link between space and time (‘the fabric of space time’ would be undoubtedly mentioned).
Or perhaps, a physicist might mention entropy and how time is the direction in which entropy of a closed system increases. On the other hand, ask a psychologist or neuroscientist, and they might define time as the subjective and perceptual experience of duration and order of events. To some psychologists, time is a construct of the brain – which often gives the feeling of time ‘flying’ when busy and ‘dragging’ when bored. Finally, while many of us may not have given it formal thought, we do have an intuitive understanding of it. For most of us, the concept of ‘time’ is a practical tool – something that helps us organize our days, separate ‘now’ from the past and future, and understand cause and effect.
It’s a curious fact that even after all these years, and for such an important concept as time, there is no one single definition that everyone agrees on*. But it is equally enlightening to realize that there is indeed a central theme that runs through all these definitions – the presence of change. In each of the definitions of time considered, time was a way to measure change – it was just that the type of change being measured was different in different definitions. So, for our physicists, time (along with space) is used to track changes in the co-ordinates of ‘things’ in the space-time continuum; alternatively, it is the direction in which ‘things’ (aka systems) change and become increasingly disordered (entropy). For the psychologist, the perception of time is tracking the changes in our environment and internal states. And for most of us, time helps us track the changes in our activities and environment.
That time and change seem so intricately related seems obvious when one thinks about it. In fact, the idea has been around for a long time, with personalities such as Aristotle defining time as “the number of change with respect to before and after”. Since then, contemporary scientists, such as Carlo Rovelli and Lee Smolin have explored the idea even further. While such investigations have been very enlightening for me, I always felt that there was something missing in the discussion. While a lot of definitions deal with the type of change being measured, fewer explore the notion of “what exactly is being changed?”
The question is important because if time is a concept that allows us to measure change of ‘things’; then how boundaries change is intricately linked to time as well. Namely, time ought to be tied to how easy is it for a boundary or system to either (a) become something else, or (b) get destroyed. Considering all of reality is interaction between boundaries, it seems like a better understanding of how boundaries change will help us understand reality (and time) better itself.
This article explores this very concept in greater detail. Our exploration will focus on the specific attributes of a boundary (aka ‘things’) that impact their rate of change and, thus, their propensity to become other things (incl. other boundaries or no boundary at all).
Quick boundary recap
Wait…I thought we were talking about time & change, where did ‘boundaries’ come from?
Previous readers shouldn’t be surprised that it all comes back to boundaries. This fundamental concept of reality is explored in much greater detail here. For newer readers, the following summary, though intense, ought to suffice.
1. Our reality is made up of a multitude of ‘things’
2. All ‘things’ or ‘systems’ or ‘objects’ will primarily be defined by
- their ‘distinguishing mechanism’. I.e., a mechanism that allows for a thing to be separate from its environment. Without such a mechanism, there would be no way to tell an object apart from its environment
- A collection of sub-objects interacting in specific ways.
3. We use the term ‘boundary’ to interchangeably refer to either the distinguishing mechanism or the collection of sub-objects within the said mechanism
NOTE: Each sub-object, too, is a ‘boundary’ – one defined by its own distinguishing mechanism and sub-sub-objects (…ad infinitum). It’s recursion of distinguishing mechanisms all the way down to the fundamental building blocks of our universe
Time constants
We make the case that how a boundary experiences time & how it experiences change are intricately linked. Therefore, to understand more about the passage of time for a boundary, it is critical to understand the passage of change for different boundaries. But there’s no easy, one size-fits-all answer since boundaries can vary tremendously in size (from really small to really big) and type (physical, biological or abstract).
This type of a situation, where different sizes and types of boundaries are being compared, forces us to choose relative units of measurement versus any specific ones. We do something similar in stock-markets: your return on capital will always be in terms of percentages of capital invested and not the dollar figure. Comparing investment returns as a relative percentage allows us to compare numerous different sizes and types of investment strategies,
There’s a very useful concept called time constant, often denoted as τ (tau), that deals with how systems respond to changes. It represents the time required for a system to undergo a specific percentage change—commonly about 63.2%—toward its final value after a disturbance. While this isn’t quite what we want, as there’s not necessarily a ‘final stage’ we’re after, it will have to do. We will pretend that the ‘final state’ of any boundary is the point at which it will basically become another boundary altogether or be destroyed (as in decaying systems).
It seems important to mention that our altered τ is more of an abstract concept versus an actual number. This is because it is quite subjective and difficult for anyone to clearly say that an original boundary has changed sufficiently to become an altogether different boundary (although it is easier, not necessarily easy, to determine when a boundary is destroyed).
The reason we’ll still use the abstract notion of τ is because it is useful in helping us give directionally correct statements. Specifically, this abstract τ is perfectly suited to help us make predictions about the speed of change for different boundaries – i.e., which boundaries change faster (thereby becoming different boundaries faster or experiencing a faster flow of time) and which ones change slower (thereby keeping their ‘essence’ intact for longer durations and experiencing the flow of time much more slowly).
Now that we have decided on a way of measuring a change of boundaries (τ), let’s explore the next piece of the puzzle. What all can change a boundary’s τ? The question is a bit tricky because, as mentioned before, boundaries come in all shapes, sizes and types. Is all hope lost?
I think not. From the work on boundaries in general, there are some universal truths about all boundaries – related to the way they are defined. Recall from the recap that any boundary will have two basic components:
- A distinguishing mechanism
- A collection of sub-boundaries (that interact in specific ways)
The above is true for all sizes, from an atomic nucleus (1. probability fields of charges; 2. sub-atomic particles) to a galaxy (1. density of matter; 2. Astronomical bodies such as stars, planets etc.). The above is also true for all types of boundaries, from biological boundaries such as a plant cell (1. Cell wall & cell membrane; 2. Nucleus, chloroplasts etc.) to abstract boundaries such as religion (1. Religious text/rituals; 2. believers).
Therefore, a good starting point to understand a boundary’s τ would be to understand the relationship between change and the two components of a boundary definition. This is exactly what we do in the next part.
Part 2 will deal with understanding a few key characteristics that have a big impact on how boundaries can change into boundaries (or get destroyed).
Finally in Part 3, we make some concluding statements about different possible categorizations of generalized half-lives. Including trying to predict systems that generally experience the extremes of time – either the fastest changing or slowest changing boundaries.
* Some readers might object, “Actually, the widely accepted definition of a second is duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.” But they’d be talking about a particular measurement unit, not the overall concept itself. Just as an inch or a meter are ways to measure the conceptual idea of ‘distance’, measurement units such as seconds or years are ways to measure the conceptual idea of ‘time’. The difference is (perhaps) subtle, but an important one. Especially so because, presumably, concepts don’t originate from units of measurement; rather, it is the other way round.