# TIAS

## 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.

### 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.

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.

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.

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.)

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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.

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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.

# ALON

## 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

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

# MATH

#### {(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.