← Interactive Math Narratives

Psychronometrics

Kaz Maslanka, 1983 — an interactive mathematical poem.

The Flammarion engraving: a traveller pushes his head through the boundary of the sky
The Flammarion engraving, 1888 — a traveller reaches the edge of the sky and pushes his head through it. Colored by Kaz Maslanka, 2026.

There is therefore no time of the philosophers;
there remains only a psychological time different from the time of the physicist.

Albert Einstein · Paris, 6 April 1922

It seems almost everyone agrees that time goes by faster as we get older. I first noticed it when I was about eight, remembering that when I was four the summers and winters lasted forever. I was not excited by the notion that I would be in school until I was eighteen. Yet when I turned eighteen, it seemed hardly any time had passed at all.

It is my belief that we judge increments of time in relation to how long we have existed. A forty year old experiences twenty years much as a twenty year old experiences ten, or a ten year old experiences five — each of them reflecting on half a life. One year to a sixty year old is one sixtieth of that life; one year to a ten year old is one tenth. And one tenth of your life is a far bigger piece of time than one sixtieth.

I was excited when this idea struck me in 1983, though I am not surprised to learn that it was probably first introduced in 1877 by Paul Janet. What Janet could not have seen — Einstein’s concepts were not yet introduced — is that this perceptual time shift can be metaphorically mapped onto time dilation as it is used in the Special Theory of Relativity. There are other psychological factors that affect the plasticity of time, but time dilation is the one I want to follow in this poetic expression.

Time dilation

If you have studied a little of Einstein’s Special Theory of Relativity, you may remember that the speed of light is constant in any frame of reference. That epiphanic concept is the inspiration for the theory.

To illustrate time dilation, imagine a space ship capable of traveling close to the speed of light, instructed to send a radio signal — which travels at the speed of light — to earth every second of its voyage. On the launch pad, the signals arrive every second, as expected. But as the ship accelerates toward the speed of light, they begin to spread apart: two seconds, three, four, five, ten, fifteen, forty-five. The closer the ship comes to the speed of light, the longer the duration between signals. Traveling extremely close to it, they might arrive a year apart, or further.

Einstein’s time dilation. The time measured on earth equals the time measured aboard the ship, divided by the square root of one minus v squared over c squared. The prime on the ship’s Δt is what distinguishes the two.
Einstein’s time dilation. The time measured on earth equals the time measured aboard the ship, divided by the square root of one minus v squared over c squared. The prime on the ship’s Δt is what distinguishes the two.

Let me reiterate that the people on the ship have been watching their own clock and sending their signal every second. What the people back on earth experience is time slowing down aboard the ship. In Einstein’s theory, this is called time dilation.

Psychological time dilation

Now, the interesting thing to me is that this is the same feeling I have when I look back at time in my life. The past seems to have slowed, almost as if I have been traveling in a space ship accelerating through some sort of psychological space, where I am experiencing a psychological time dilation.

Physical time can be viewed as an analog of psychological duration in our mind, for we use the harmonic motion of objects traveling in physical space as our standard for it. The International System of Units defines one second as the time it takes a Cesium-133 atom at the ground state to oscillate exactly 9,192,631,770 times. Physical time changes little to none. Psychological time changes incessantly.

Using this idea of increments of time based on our past experience, I have written this computer program to map our psychological time dilation onto Einstein’s equation for his special theory.

This computer poem expresses a metaphor that raises questions about the nature of time.

What this piece is

The aesthetics of the piece lie in the beauty of analyzing and thinking about the nature of time — how it is defined, and how it is perceived. Psychronometrics is difficult to categorize, for there are many facets to this aesthetic expression. It is an interactive computer artwork, originally created on a Radio Shack Color Computer in 1983, and it was unusual at the time in using an equation from physics as a vehicle for poetic metaphor. It also points to the spiritual nature of the human experience, in how time plays a role in where we come from and where we are going.

The Radio Shack Color Computer that Psychronometrics was written on in 1983. Thirty-two columns, sixteen rows, capitals only.
The Radio Shack Color Computer that Psychronometrics was written on in 1983. Thirty-two columns, sixteen rows, capitals only.

How to use it

The next page will ask you for the names and birthdates of two people. I suggest starting with one of your parents, or your child, and then yourself. The further apart the two ages, the more drastic — and the more interesting — the result.

On the left side of the screen, enter the two names and birthdates. Below them are buttons that set the frame of reference between the people you have chosen. Start by pressing Today, and see how fast time is moving for your parent relative to you. The results appear at the upper right. Below them, you can see how fast a space ship would need to travel for the two of you to experience the same physical time dilation you already experience psychologically. Experiment with the buttons and the slider on the left to change the results on the right. The graph at the lower right shows that experience as a percentage of the speed of light.

Enter the program

You will be asked for two names and two birthdates. Use one of your parents, or your child, and then yourself. The further apart the two ages, the more drastic the result.