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Time is a Square

Temporal reference

The fundamental time unit in TIAS is the day. The day is a simple astronomical phenomenon, existing in every culture and every era as the basic unit of time measurement. Divisions such as hours and minutes are, in contrast, random and based on cultural agreement. The fractions 1/24, 1/60, are not an inevitable result of dividing the time unit “day”.

In TIAS the black square area represents the duration of a day.

The square, Das Quadrat

From stills to film

All smaller units result as a division of the basic square into four equal square parts. Three parts are black, the fourth is white. The white square area denotes the present quarter of the day. In the first quarter of the day the white square is to the upper left, in the second quarter to the upper right, in the third to the lower right and in the fourth quarter of the day to the lower left. This system of highlighting the present period of time, continues within the smaller square divisions with ever opposing colours. Thereby the stills appear to move.

Die vier Bilder der ersten Ebene

Four pictures depicting the first level (detailed view)

A tangible image representing the respective part of the day appears four times a day.

The film now has four pictures per day.

Further divisions of a similar nature follow, resulting in the perception of movement. (see following examples). In the process, each current square is marked with the opposite color of the primary level. Thus a unique picture evolves for every time of the divided day, made up of alternating black and white squares systematically changing into each other. A mathematical fractal.

Die vier Bilder der zweiten Ebene

Four pictures of the second level, here pictured in the first square of the first level (detailed view)

The film now has 16 pictures per day.

weitere Bilder der zweiten Ebene

Four further pictures depicting the second level in the second, third and fourth quarters (detailed view)

In TIAS, each day has 8 sub levels. Thereby 65536 individual pictures are created per day, each showing one 65536th of a day as a unique graphic pattern. In existing time measurement a day has 86400 seconds, for human perception, a negligible difference, thus one second and the smallest unit in the TIAS clock appear to be of a similar length of time.


Default setting:
The day begins with the first time period after midnight.
(Timecode 1111 1111)

Beispielbild 1

Example 1:
It’s early in the morning. The third quarter of the first quarter of the day is coming to an end.
(Timecode 1344 2334)

Beispielbild 2

Example 2:
Early morning.
(Timecode 2233 4422)

Beispielbild 3

Example 3:
Shortly after midday.
(Timecode 3113 3344)

Beispielbild 4

Example 4:
Evening. The third quarter of the last quarter of the day begins.
(Timecode 4321 2344)

On the following day the procedure is repeated, however in an imaginary square on an upper level, which represents the area of four days. The second day is positioned in the upper right corner of the area, the third day in lower right, the fourth day in the lower left corner of the area. Once the divisions have run through each of the four squares, four days have elapsed. The system is thus infinitely repeatable. Although the pattern for each day is the same, the whole pattern never repeats itself. (The four day square moves to its next unique position within a sixteen day square, which in turn moves to its next unique position within a sixty-four day square and so on.)



Soon available again at App-Store and at Google Play.

The TIAS application allows for the representation of between a day (default setting) and up to a time frame of 1,048,579 days. It is also possible to depict the 1,048,576th part of a day. Each step moves into the next larger or smaller square, continually changing color.

The zoom functions as usual with two fingers. These steps are also controllable using the menu bar.
Moving two fingers away from each other, zooms into the graphic. The time representation becomes more accurate and TIAS moves faster.
In Menu: zoom.
Moving two fingers towards each other, zooms out of the graphic. The time representation encompasses a longer time period.
In Menu: extend.
Under the menu position “one day” the settings go back to the default setting of a day.


Under the TIAS icon further settings can be found for TIAS.
The TIAS-time-index shows the numerical translation of the graphic representation, together with the actual time period of the currently pictured square in the upper left area of the display.



TIAS will continue to be developed in the future.
Time can also be translated as a cube. Malevich’s “Black Square” could also have been a sculpture.
Find first illustrations and ideas to a three dimensional model at the end of this page.


A List Of Numbers

The TIME IS A SQUARE (TIAS) default setting has 8 subdivisions.



A single day, as defined by the fixed size of the basic square, is itself composed of 65536 of the smallest displayed units (compared to 86400 seconds in a day, as defined by existing time measurement).



Let’s talk about ONE day — Zoom units in summary

One day:
black basic square
1/4 of a day:
one white square division with positive/negative exchange
1/16 of a day:
one black square division
1/64 of a day:
two white square divisions
1/256 of a day:
2 black square divisions (a complete execution of this sequence takes a little longer than 5.5 minutes)
1/1024 of a day:
3 white square divisions
1/4096 of a day:
3 black square divisions
1/16.384 of a day:
4 white square divisions
1/65.536 of a day:
4 black square divisions - the smallest visible unit in a day
1/262,144 of a day:
visible in the first zoom as the smallest white unit
1/1048.576 of a day:
visible in the second zoom as the smallest black unit (a complete execution of this sequence takes a little less than a hundredth of a second)



Well, there is more than ONE day — Extended units in summary

One day:
black basic square
4 days:
first extended increment with positive/negative exchange
16 days:
second extended increment (a complete execution of this sequence takes 16 days)
64 days:
third extended increment (about two months)
256 days:
forth extended increment (about 3/4 of a year)
1024 days:
fifth extended increment (more than 2.5 years)
4096 days:
sixth extended increment (just over 11 years)
16,384 days:
seventh extended increment (nearly 45 years)
65,536 days:
eighth extended increment (about 179.5 years)
262,144 days:
ninth extended increment (over 718 years)
1048,576 days:
tenth extended increment (a complete execution of this sequence would take nearly 2873 years) * Please connect your device to the power plug and stay connected!




{(x,y)} = ({0,1} x/2, {0,1} y/2)

A single day, as defined by the fixed size of the basic square, is itself composed of 65536 of the smallest displayed units (compared to 86400 seconds in a day, as defined by existing time measurement). TIAS is based on a mathematical fractal {(x,y)} = ({0,1} x/2, {0,1} y/2) and is almost infinitely expandable into smaller or larger time periods. The patterns are always similar but never the same.




The English version for the following part CUBE is a first translation by my self only — it still needs some “time” for improvements and an exact wording. Correction by a native speaker will follow ASAP.

Thinking a few steps further, time also can be displayed as a cube. One with all edges equally long — a dice. This cube has three inherent dimensions itself. If one takes the also three dimensional space which is surrounding all of us (space-cube) and which tends to be infinite large, one can imagine a second three dimensional construction (time-cube) which tends to be infinite small within the space-cube. The proportional relations of those two in one another placed cubes explain a possible relationship of time and space quite simple.
The hypothesis of a quasi zero movement* of human beings in the time-cube, the time-cube appears as nearly infinite small in comparison to the space-cube. This relationship matches our reality, it matches what we recognise as our reality.
*(Say, 100 years is the life time of one of us, these 100 years are our movement within the time-cube. That’s why it so small.)

The relative position of the “human” time-cube within the space-cube kinda does not change. One can not exactly define where the time-cube is placed again caused by the fractal structure of the construction.
By increasing speed (of a humans movement) through the space-cube the relationship of the two, in one another placed cubes, changes. Along to the change of speed the recognition of space and time changes, too. Assuming the cubes become equal in size at a specific speed (i.e. the speed of light) one would be everywhere in time at the same time and everywhere in space in the same place. *with a twinkle in one’s eyes this is how the „Infinite Improbability Drive“ in Douglas Adams world famous novel „The Hitchhikers Guide to the Universe“ works.

Imagine: If one now hypothetically speed up with movement (in relation to the space-cube) at this state of each other fully filling and one in another fitting cubes the system it self flips. The space-cube from here on is the larger cube and embraces the time-cube. A theoretical existence in a system of this kind of the relationship of time and space might be able to move in a way freely within the time-cube but on the other hand is stuck more or less in the space-cube.
Living and dying in a space-bounded-proportionality might imply an existence is eternal in a temporal way but maybe might just dissipate when it is widely spread in space. It then could be seen as “dead”. Well, mere theory more ore less and hard to be approved.

A three dimensional system like that must be numerical configured with 8 but 4 code points. Within a cube another cube with half edge length can take place in exactly 8 positions:

1 = top, right, back
2 = top, left, back
3 = top, right, front
4 = top, left, front
5 = bottom, right, back
6 = bottom, left, back
7 = bottom, right, front
8 = bottom, left, front

(Using figures to define the 8 positions should simplify matters only. Although the verbally determination of the sub-cubes within their parent-cube does not solve the problem of definition finally. Though, finally this issue does not matter at all, because the system itself is an autarkic one where any position can be described from any other position as a reference point within the parent-cube independently and exactly at the same time. The kind of description is just to be seen as a convention of communication to enable communication itself.)

All that is a sketch only. It is built and described by my personal possibilities and knowledge only. It is a try of a graphical, two dimensional and solid, three dimensional way to display time and space in relation to each other. I am aware nor Einstein’s or Heisenberg’s, nor the recognitions and theories of the recently died Hawking or recognitions and theories of any other scientist are considered correctly or considered absolutely.

This quite simple visual concept to describe time and space, making time and space equal in a kind, understanding each of them as a congeneric multi dimensional systems itself and draw and interpret that construction maybe opens up an even wider field.
One can imagine multiple cubes of different kinds within those (already within each other placed) two cubes — time-cube and space-cube. Those additional cubes still remain to the same relation to each other and to the both already described cubes.
A multi dimensional construction based on each itself three dimensional cubes with a factional base makes it possible to expand or see the system as one of endless variations. Name it knowledge-cube, love-cube or doubt-cube, curiosity-cube, maybe cold-cube, soft-cube, loud-cube or sauer-cube.
Depending on the position and the relation of a possible, different kind of an existence and its connection with the particular base-dimensions as well as the recognition of those base-dimensions, as well as their relationship to each other and also the number of recognised base-dimensions multiple scenarios of perception of a possible reality may be contstructed.

Roll the Dice — Time Is A Cube … to be continued.

Let’s talk and discuss just for fun. Though, I'd love to learn and understand.
Contact via carrois.com
Twitter @CarroisCarrois

Copyright 2018 by Ralph du Carrois — all rights reserved.


TIAS was first presented in 2004 at the ZKM // Zentrum für Medienkunst in Karlsruhe under the project name “Quadratime”. The Artwork was part of the exhibition “Algorithmic Revolution”.

Time Is A Square is a website of:

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Ralph du Carrois & Jennifer du Carrois