Our Perspective of Time
Time is an illusion
- Albert Einstein
A few years ago, I experienced an intense couple weeks in Peru volunteering in various communities. With folks throughout North America who also had gone through the cancer experience like me, we helped in hospitals, clinics, and cancer centres. By the end of the program, it felt like I had been there for several months and my friends who I had just met felt like they had been in my life for much longer then 2 weeks. There was also the sensation that each week had gone by so quickly.
Our subjective perception of time is affected by a complex interplay of cognitive and perceptual processes and events. This phenomenon is underscored by the principles of Einstein's theory of relativity, which emphasizes the variability of time perception in relation to the velocity of moving objects. Given that all humans are in constant motion, this theory can be extrapolated to understand how our mind adjusts our temporal perception based on unique experiential contexts, thus significantly altering our sense of the duration of events.
My time in Peru was a densely packed couple weeks, filled with emotionally charged interactions, novel experiences, and a plethora of memorable moments, which sharply contrasted with the monotony of my everyday life. This gives rise to a temporal paradox: retrospectively, the commencement of this enriching interval seems markedly distant, yet the entire duration felt as though it elapsed in a mere instant.
To demystify this paradox, I employed a mathematical framework. In our habitual life, the human brain normalizes, grows accustomed to a certain frequency of ‘events' (e) occurring within a given temporal span (t). These 'events' encompass a broad spectrum of unique experiences.
For example, if you were to think of events in your daily life, it might be something unique that happened on your commute to work such as seeing a horrible accident. Or picking up your daughter from school but this time her friend shows up. Perhaps in that week’s grocery shopping you see the blueberries that are from Peru which catches your eye and reminds you of your recent trip there. We can define a personal 'events/time' ratio, e/t, as the quotient of these events over the temporal duration. This ratio, symbolic of our individual experiences, is inherently variable over the course of our lives. When there is a sudden surge in 'events,' our ratio adjusts accordingly, leading to a perceptual expansion or contraction of time. A sudden increase in 'events' alters this ratio to (e + n)/t, where 'n' denotes the additional experiences.
For illustrative purposes, let's assign e a value of 10 and t a value of 7. Over the course of a week, 10 unique events on average stand out, establishing a baseline ratio of 1.43. In other words, the subject has grown accustomed to an event over time ratio eot of 10/7, or 1.43 (Fig 1a). This value will be used for the baseline for this example. It's worth noting that our unconscious interpretation of an 'event' is subjective; what constitutes an 'event' for one person may not for another. Everyone’s baseline is different.
Consider a week now filled with an uncommonly high number of experiences, something most can relate to. In my case, let’s go back to Peru. The concept of an 'event' may vary from person to person as previously stated, yet imagine a scenario in which 'e', representing these events, surges to 25 in the span of a single week. I learned new things, visited in places, we shared our deep experiences. By the end of that week, brimming with novel encounters and profound interactions, the new ratio climbs to 25/7, or 3.57. (Fig 1b).
This heightened ratio, surpassing our accustomed threshold, prompts our brain to 'expand' time, effectively accommodating the excess events within our usual temporal framework, thereby extending a week to an equivalent sensation of 17.5 days (Fig 1c). When our events/time ratio is higher than what we have become accustomed to, our wonderful brain expands time to match what we are used to. In other words, our
brain adjusts the time that has normally gone by for 25 events to match the eot we are used to. When someone has a very busy day, they might tell someone that they had a long day. But the length of the day has not changed. It’s their subconscious mind’s interpretation of the day. Their event/time ratio increased for that day. An increase in this ratio simulates an increase in time in the mind.
Consider when e is smaller than usual. Perhaps a week where not much happened compared to our usual week where the eot we are used to is 1.43. In this case for example let’s give e a value of 3. Our ratio, 3/7 is now 0.43 (Fig 1e); below the ratio we are used to. So again, our brain naturally adjusts. In this case, our week has shrunk to 2.1 days (Fig 1f). Isn’t it true that when you don’t really do much, that by end of the week, it feels much shorter than usual? Now again to mention how relative this is, if someone else is used to e as 3 during a week, their week does not feel shorter than they are used to. This is another perspective of Einstein’s theory of relativity—that time passes depends on the frame of reference. In these examples, people’s frame of reference is a combination of events e over a certain time t.
This time frame can be much more than a week. Many years ago, I spent 3 months in Tsfat, Israel, in a program with a group of people I had just met. It was a completely different environment with constant new experiences. By the end of the 3 months, I felt as if the start of the program was long ago, much longer than 3 months. Therefore, my events/time ratio, eot, was a much higher than my baseline. Again, my brain expanded time to match what I was used to. For everyone I met for the first time at the start of the 3-month program, and was with them through the whole duration, there is a feeling I had known them for decades. Many of us are still in touch. In experiences such as this, three months filled with meeting new people and novel events, there is another phenomenon that one often experiences. A sensation often arises that though 3 months had passed, it felt as if it had gone by very quickly. This leads to a dichotomy in the brain; time has gone by very quickly, but the start feels so long ago.
How can this be explained? In a way there is also a reverse effect of the experience. Let’s go back to considering the example of e (events) of 10 happening over t (time) of 7 days giving the ratio of 1.43 (Fig 1a). That is what the subject is used to. Let’s also say again that e becomes 25 now over the same timespan t. As explained, our brain unconsciously adjusts t to match our usual ratio of what we are used to, our sense of time is extended. But our brain must still address the fact that e = 25 occurred in t = 7. Our brain senses the 25 ‘events’ packed into a timespan when we are accustomed to 10 events. Fitting the events in less space than what is normal between them creates a sense that they went by very quickly. The space between events, s, has shrunk. Our wonderfully talented brain can juggle both phenomena at the same time (Fig 1d).
There is another variable at play to consider, the intensity of the moment. When I was told that I had brain cancer with a very poor prognosis, there was a sensation that the moment before I was given this news, was in the far distant past. When the intensity (i) of an event increase, it is added to the variable e. We need to adjust our equation to (e + i) / t. In that moment, the brain adjusted t to match the events/time ratio, now recognized as (events + intensity) / time. The effect of the news of the tumour resulted in a new event/time ratio. The event and intensity of that moment, hearing the diagnosis, say resulted in the numerator increasing to say 1000. And so, with the normal eot ratio of 1.43, the amount of time was unconsciously adjusted to around 700 days. My life changed drastically, in that moment, as it might have after approximately 2 years. Perhaps that is why we see some people who have gone through a very traumatic event, looking older. In my case I just looked goofy with half a head of hair after 4 weeks of radiation.
In another example that can be relatable, imagine an intense relationship. Perhaps one over a short period of time. I was dating someone years ago over 6 months, yet we met only 13 times as we both had very busy schedules. We can say e = 13 and t = 6. Here t is defined as months, not days. In this case, each time we met, it was so intense, i in the ratio increased significantly. As described before, to match the baseline ratio the sense of time had to expand. Though we met only 13 times in 6 months, it felt as if we had been dating for many years and had met up much more often. This can explain the many incidences where a couple meets and gets married very shortly thereafter. The intense experiences may have been equivalent to knowing each other for many years.
Our subjective perception of time is affected by a complex interplay of cognitive and perceptual processes and events. This phenomenon is underscored by the principles of Einstein's theory of relativity, which emphasizes the variability of time perception in relation to the velocity of moving objects. Given that all humans are in constant motion, this theory can be extrapolated to understand how our mind adjusts our temporal perception based on unique experiential contexts, thus significantly altering our sense of the duration of events.
My time in Peru was a densely packed couple weeks, filled with emotionally charged interactions, novel experiences, and a plethora of memorable moments, which sharply contrasted with the monotony of my everyday life. This gives rise to a temporal paradox: retrospectively, the commencement of this enriching interval seems markedly distant, yet the entire duration felt as though it elapsed in a mere instant.
To demystify this paradox, I employed a mathematical framework. In our habitual life, the human brain normalizes, grows accustomed to a certain frequency of ‘events' (e) occurring within a given temporal span (t). These 'events' encompass a broad spectrum of unique experiences.
For example, if you were to think of events in your daily life, it might be something unique that happened on your commute to work such as seeing a horrible accident. Or picking up your daughter from school but this time her friend shows up. Perhaps in that week’s grocery shopping you see the blueberries that are from Peru which catches your eye and reminds you of your recent trip there. We can define a personal 'events/time' ratio, e/t, as the quotient of these events over the temporal duration. This ratio, symbolic of our individual experiences, is inherently variable over the course of our lives. When there is a sudden surge in 'events,' our ratio adjusts accordingly, leading to a perceptual expansion or contraction of time. A sudden increase in 'events' alters this ratio to (e + n)/t, where 'n' denotes the additional experiences.
For illustrative purposes, let's assign e a value of 10 and t a value of 7. Over the course of a week, 10 unique events on average stand out, establishing a baseline ratio of 1.43. In other words, the subject has grown accustomed to an event over time ratio eot of 10/7, or 1.43 (Fig 1a). This value will be used for the baseline for this example. It's worth noting that our unconscious interpretation of an 'event' is subjective; what constitutes an 'event' for one person may not for another. Everyone’s baseline is different.
Consider a week now filled with an uncommonly high number of experiences, something most can relate to. In my case, let’s go back to Peru. The concept of an 'event' may vary from person to person as previously stated, yet imagine a scenario in which 'e', representing these events, surges to 25 in the span of a single week. I learned new things, visited in places, we shared our deep experiences. By the end of that week, brimming with novel encounters and profound interactions, the new ratio climbs to 25/7, or 3.57. (Fig 1b).
This heightened ratio, surpassing our accustomed threshold, prompts our brain to 'expand' time, effectively accommodating the excess events within our usual temporal framework, thereby extending a week to an equivalent sensation of 17.5 days (Fig 1c). When our events/time ratio is higher than what we have become accustomed to, our wonderful brain expands time to match what we are used to. In other words, our
brain adjusts the time that has normally gone by for 25 events to match the eot we are used to. When someone has a very busy day, they might tell someone that they had a long day. But the length of the day has not changed. It’s their subconscious mind’s interpretation of the day. Their event/time ratio increased for that day. An increase in this ratio simulates an increase in time in the mind.
Consider when e is smaller than usual. Perhaps a week where not much happened compared to our usual week where the eot we are used to is 1.43. In this case for example let’s give e a value of 3. Our ratio, 3/7 is now 0.43 (Fig 1e); below the ratio we are used to. So again, our brain naturally adjusts. In this case, our week has shrunk to 2.1 days (Fig 1f). Isn’t it true that when you don’t really do much, that by end of the week, it feels much shorter than usual? Now again to mention how relative this is, if someone else is used to e as 3 during a week, their week does not feel shorter than they are used to. This is another perspective of Einstein’s theory of relativity—that time passes depends on the frame of reference. In these examples, people’s frame of reference is a combination of events e over a certain time t.
This time frame can be much more than a week. Many years ago, I spent 3 months in Tsfat, Israel, in a program with a group of people I had just met. It was a completely different environment with constant new experiences. By the end of the 3 months, I felt as if the start of the program was long ago, much longer than 3 months. Therefore, my events/time ratio, eot, was a much higher than my baseline. Again, my brain expanded time to match what I was used to. For everyone I met for the first time at the start of the 3-month program, and was with them through the whole duration, there is a feeling I had known them for decades. Many of us are still in touch. In experiences such as this, three months filled with meeting new people and novel events, there is another phenomenon that one often experiences. A sensation often arises that though 3 months had passed, it felt as if it had gone by very quickly. This leads to a dichotomy in the brain; time has gone by very quickly, but the start feels so long ago.
How can this be explained? In a way there is also a reverse effect of the experience. Let’s go back to considering the example of e (events) of 10 happening over t (time) of 7 days giving the ratio of 1.43 (Fig 1a). That is what the subject is used to. Let’s also say again that e becomes 25 now over the same timespan t. As explained, our brain unconsciously adjusts t to match our usual ratio of what we are used to, our sense of time is extended. But our brain must still address the fact that e = 25 occurred in t = 7. Our brain senses the 25 ‘events’ packed into a timespan when we are accustomed to 10 events. Fitting the events in less space than what is normal between them creates a sense that they went by very quickly. The space between events, s, has shrunk. Our wonderfully talented brain can juggle both phenomena at the same time (Fig 1d).
There is another variable at play to consider, the intensity of the moment. When I was told that I had brain cancer with a very poor prognosis, there was a sensation that the moment before I was given this news, was in the far distant past. When the intensity (i) of an event increase, it is added to the variable e. We need to adjust our equation to (e + i) / t. In that moment, the brain adjusted t to match the events/time ratio, now recognized as (events + intensity) / time. The effect of the news of the tumour resulted in a new event/time ratio. The event and intensity of that moment, hearing the diagnosis, say resulted in the numerator increasing to say 1000. And so, with the normal eot ratio of 1.43, the amount of time was unconsciously adjusted to around 700 days. My life changed drastically, in that moment, as it might have after approximately 2 years. Perhaps that is why we see some people who have gone through a very traumatic event, looking older. In my case I just looked goofy with half a head of hair after 4 weeks of radiation.
In another example that can be relatable, imagine an intense relationship. Perhaps one over a short period of time. I was dating someone years ago over 6 months, yet we met only 13 times as we both had very busy schedules. We can say e = 13 and t = 6. Here t is defined as months, not days. In this case, each time we met, it was so intense, i in the ratio increased significantly. As described before, to match the baseline ratio the sense of time had to expand. Though we met only 13 times in 6 months, it felt as if we had been dating for many years and had met up much more often. This can explain the many incidences where a couple meets and gets married very shortly thereafter. The intense experiences may have been equivalent to knowing each other for many years.
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Of course, as days pass in our lives, we experience many events, big and small, long and short, sometimes very intense, sometimes not. Life can be overwhelming and sometimes it’s good to stop and give yourself what some have described as non-time. This is disconnected quiet time, and this time of emptiness can help clear the mind. One way to do this is through meditation. In that trip in Peru, we took a break and visited Machu Picchu. I had a moment where I sat calmly, closed my eyes, and took deep slow breathes envisioning I was taking in the wisdom of the Incas into my soul.
The act of meditation can involve limiting movement and thoughts to deep breathing and not letting the mind wander. Another way to look at is to decrease the events and intensity in your mind. If we meditate, theoretically, if we are a master and can completely clear our thoughts entirely (which is very hard to do) and remain motionless, e approaches zero. During quality meditation where e decreases, t also has to decrease. Some say that during intense meditation, time appears to cease to exist. Perhaps, from our personal perspective, time really has stopped, and some say that meditation can slow down the aging process. Perhaps this is one of the reasons. Of course, it is impossible to completely stop time. The denominator can never be zero which goes for the events/time ratio. The only instance where t=0 is when a person passes away. At this point the person’s events/time ratio is undefined. |
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It’s very good for the brain to always be changing its eot, to experience and learn new things. To meet others with different histories and views and to share our wisdom. To have intense unique moments over various segments in time where we pack in so much energy and other moments to just relax and enjoy being in the present moment, leverages the brains inherent neuroplasticity. Our brain is meant to learn new things and needs to both exercise and rest, to live a long, enjoyable, and healthy life.
Butterfield, 2024
Butterfield, 2024
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Our subjective perception of time is affected by a complex interplay of cognitive and perceptual processes and events Images created by AI
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Various calculations to describe the phenomenon discussed.
Definitions:
Event count (e)
Additional events (n)
Time span (t)
Level of intensity (i)
Space between events (s)
Event/time ratio (eot)
Calculating what we are normally accustomed to (can be different for
every individual).
This is one example:
Figure 1a
e1 = 10 # events or
experiences, in this case, 10 events
t1 = 7 # time, in this case 7
days
eot = e1/t1 # events over time
eot = 1.43 # the event/time ratio we are used to
Scenario 1:
We have a week where we experience much more events than normal:
Figure 1b
n = 15
e2 = e1 + n
e2 = 25 # events have gone from
10 to 25
t1 = 7 # in that span of 7 days
eot = e2/t1
eot = 3.57 # a new event/time ratio
But our mind adjust the events/time ratio to match what we are used to
for that amount of events which results in a sensation of expanded time (17.5
days in this case) – a feeling that much more time has gone by than in reality.
Figure 1c
t2 = e2*t1/e1 # adjusting time
t2 = 17.5 # our sense of time
is now 17.5 days
eot = e2/t2
eot = 1.43 # our mind adjusts to the e/t ratio
we are used to
Our mind is also affected in another way with the sudden increase in
events over the course of the week. Each event has decreased time in between
them and a sense of them going by more quickly than normal is the result. Below
is shown for the normal weeks we are used to where eot
= 1.43, the space between events is the inverse as shown below. During the same
span of time t1 when were are suddenly experiences a
higher number of events e2, the average perceived space between events has
decreased resulting in a feeling they are passing by more quickly.
Figure 1d
s1 = t1/e1 #average perceived
space between events
s1 = 0.7
s2 = t1/e2
s2 = 0.28
Scenario 2:
We have a week where we experience less events
than normal.
Figure 1e
n = -7
e3 = e1 + n
e3 = 3
t1 = 7 # in that span of 7 days
eot = e3/t1
eot = 0.43
Our mind adjust the events/time ratio to match what we are used to for
that amount of events which results in a sensation of expanded time (2.1 days
in this case) – a feeling that much less time has gone by than in reality.
Figure 1f
t3 = e3*t1/e1 # ajusting time as before
t3 = 2.1 # our sense of time is
now 2.1 days
eot = e3/t3
eot = 1.43 # our mind adjusts to the e/t ratio
we are used to
Scenario 3:
Here, at the moment I was diagnosed with brain cancer, the intensity of
the event rose dramatically. To signify this, I adjust i
to 1000.
e1 = 10 # events / experiences
t1 = 7 # time
i = 1000 #intensity
eot = e1/t1 # event/time ratio
e4 = e1 + i
# add intensity to events
t4 = e4*t1/e1
t4 = 700 # my sense of time was
700 days (~ 2 years)
eot = e4/t4
eot = 1.43