Time

What is time and how is it perceived? This is of course a vast philosophical question, which I will only scratch.

1) Time, space and existence

It is customary to describe time as “the fourth dimension”. This point of view comes from the equations of mechanics and is highly misleading, because it seems to imply that time is of the same kind as space. A century ago, Henri Poincaré noted that our concept of space, both perceptually and scientifically, derives from our physical interactions with the world. That is to say, knowing where something is is knowing how to get there. Space is defined by the laws that govern movements in the physical world and the structure of these laws (Euclidean geometry). A law, some property that does not change, can only be defined with respect to something that changes. Therefore, time, defined as the source of change in the world, is a prerequisite to space. Space exists only by its persistence through the passing of time.

2) Time and change

In fact, nothing exists without the passing of time, because the essence is precisely what does not change through the flow of time. If we see someone throwing a ball, that ball is moving. Our visual sensations change, but we see a ball in movement: this is to say that there is something in the visual signals that does not change, which characterizes the ball as such. We do not see an object in the flickering white noise of a TV set.

In the TV series Bewitched, Samantha the housewife twitches her nose and everyone freezes except her. Then she twitches her nose and everyone unfreezes, without noticing that anything happened. For them, time has effectively stopped. This is to say that time is not perceived as such, but only through the changes it causes in our body. It is these changes that are perceived, not time per se (i.e., not time as in the variable in the equations of mechanics).

3) Irreversibility of time

From the fact that time is the perceived cause of changes, it follows that time has a direction, because physical processes are generally irreversible. This is also related to the theorem in information theory that states that information can only be lost, and never gained, when a process is applied to a variable. The current state of a physical system results from previous processes only, which constitutes “the past”.

A physical system in which events occur (our body) can be seen as a dynamical system, or series of processes that make the state of the system evolve. From one state s, the system changes subsequently to state s’. There is a direction to this change: s -> s’. This is the action of time on the system, and it is directed (the “arrow of time”). If the system where isolated, then time would be arbitrary. One could consider any dimension that is isomorphic to time and preserves directionality, and call it “time”, without changing the organization of changes within the system. It would make no difference for the system.

4) The unity of time

This raises the question of the perceptual unity of time: if time is perceived through changes in our body, then why do we feel that time is a single thing, when lots of different things change in our body? How is it that an auditory event and a visual event can appear to occur “at the same time”, given that they impact different receptors? Why isn’t there a different time for each process in our body? What does it mean that an event occurs “before” another one?

Imagine two independent processes that are spatially separated. From the perspective of these processes, it would make no difference if time passed at a different pace. The unity of time must come from an interaction between processes. The interaction between different processes defines a common flow of time.

Going further would probably require a discussion of consciousness and working memory, so I will leave these questions mostly unanswered for now.

5) The grain of time

How fine is our perception of time? When one listens to an auditory click played through headphones with 500 µs delay between the two ears, we do not hear two clicks. We hear a single click, lateralized towards one side. If we repeatedly play clicks at 50 Hz (every 20 ms), we do not hear a series of clicks. We hear a single continuous sound. When we listen to a pure tone at 50 Hz, the amplitude of the tone varies all the time but we do not hear this variation of amplitude. On the contrary, it feels like the tone has constant loudness.

These remarks suggest that our perception of time has a “grain” of a few tens of ms. That is, processes occurring within a few tens of ms are perceived as being caused by the same event, and the temporal occurrence of events within that time window is not perceived as time. Why?

To see how tricky this is, consider again the first example, when we listen to two clicks delayed by 500 µs between the two ears. The temporal order of the clicks can be clearly distinguished: if the click is first played in the left earphone, the sound is perceived as coming from the left, and conversely if the click is first played in the right earphone. In addition, if the delay between the two clicks is changed, then the sound is perceived as coming from a different direction (usually somewhere between the two ears), in a way that is reproducible. Such changes are perceived when the delay is changed by about 20 µs.

So from a computational point of view, time is processed with a grain of 20 µs. But phenomenologically, time appears to have a grain about a thousand times larger. Why such a difference? The perceptual grain of time does not appear to reflect the precision of neural processing, or in other words, the timescale at which states of the brain seem constant.

6) Duration

This post probably raised more questions than I could answer. I will end it with a discussion of the concept of duration. Spinoza described it as follows: “Duration is an attribute under which we conceive the existence of created things insofar as they persevere in their actuality”. This is essentially the point I have developed at the beginning of this post. In contrast with, say, color and pitch, duration is not a quality of things. Duration is about existence (the fact that a thing exists), while color or pitch is about essence (what this thing is). Properties of objects are defined by their persistence through time, but duration does not persist through time. Rather, duration quantifies how much time some properties exist. For example, it can be said that a musical note has a timbre (the instrument), a pitch and a duration. These are not three independent qualities: duration is about the pitch and timbre (for how much time they can be said to exist), but timbre is not about duration.

In summary: time is about existence, space is about essence.

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