Article 1
New Time Measurement Tool
Current Tools
Today there are mainly three tools used to visualize time:
• Within a day – clock face;
• For intervals between a week and a year – calendar;
• For intervals of arbitrary value – timeline.
Despite the fact that these tools give very different representations of time, it is the logic of nesting that brings them together:
• A day, on a week scale, is reflected as a single cell;
• A week, on a month scale, - as a row of 7 cells;
• A month, on a year scale, - as one of 12 cells.
But the very logic of nesting is entirely borrowed from spatial geometry. This is most obvious in a calendar.
Calendar Limitation
Time on a calendar is represented as a table and carries a distorted perception of time. For example, a row of 7 cells representing a week is more related to the perception of area. Even more counterintuitive is the rectangular reflection of a whole year.
Despite the fact that the calendar contains such a serious contradiction, it is very widespread. The reason for this is the prevalence of the medium itself. Initially, the use of tables was defined by the format of paper, and then by the digital screen as the successor. So even today it is the medium that continues to "format" the perception of time.
To illustrate this, we can simply "google" time.
As a result, we get all kinds of clocks, but not calendars. This means that clocks are closer to our intuitive perception of time. And yet, time and clocks are not the same thing. So, obviously, the image of time is mostly determined by the tools themselves.
If we go back to the calendar, when examined closely, it's easy to see that it's a sliced timeline, designed to fit on paper or a screen.
It can therefore be concluded that the tools closest to the perception of time are the clock and the timeline, while the calendar is the most practical, because of the widespread of the mediums themselves.
Time Perception Properties
However much we strive to exclude from the description of the world patterns, that are consciously or unconsciously built on empirical knowledge, this is likely to be impossible with respect to time.
At best, we can identify the properties of time perception rather than time as such.
The nativeness of clocks and timelines lies in the fact that their geometry reflects important properties of our perception, specifically:
• Irreversibility;
• Continuance;
• Cyclicity.
However, neither the clock nor the timeline reflects all of these properties simultaneously:
• The Clock gives a representation of Irreversibility and Cyclicity, but is limited in its representation of Continuance.
• The Timeline gives a representation of Irreversibility and Continuance, but is limited in its representation of Cyclicity.
The shared limitation of these tools is dimensionality. On this basis, it can be assumed that the Clock and the Timeline are two projections of another object, which reflects all of the listed properties.
Temporal Geometry
To find this object, it is necessary to assign geometric correspondences to the properties of time perception.
Spatial geometry uses 3 orthogonal axes to describe object properties such as length, width and height. To apply a similar approach, lets represent Continuance and Cyclicity as two orthogonal axes, and Irreversibility as the essence of these axes.
Accordingly, let us position the Clock and the Timeline as two orthogonal projections. Since this construct is designed to describe time, we introduce a process with a duration of 12 hours. The result will be a Tape-like surface.
This surface reflects Irreversibility and Continuance, but does not fully reflect Cyclicity. We see some repetition, but without a return to the initial point. The reason lies in the inequivalence of axes: Cyclicity, contains Continuance, and Continuance does not necessarily contain Cyclicity.
To solve this problem, the Timeline may be represented as a closed curve instead of a segment.
The result is a surface that reflects Irreversibility, Continuance and Cyclicity. This is a Special Solution, which operates within a limited duration.
Temporal Axis
To remove the limitation, assume that the axes themselves move along a circle with an infinite radius, i.e., on a straight line, which we denote as the Temporal Axis.
The result is a surface that reflects Irreversibility, Continuance and Cyclicity. This is a General Solution that works in unlimited duration.
In summary, combining the Clock and the Timeline gives us two Solutions:
• Special Solution, within a limited duration;
• General Solution, with no limitation of duration.
The way the axes are defined, and the solutions they provide is denoted as Temporal Geometry.
Special Solution
The Special Solution can be defined as a as a linked pair of Clocks:
• The Observer's Clock;
• And the Time Clock.
Or as a system of two linked pairs of points:
• The first pair describes the coordinates and the time dimension;
• The second pair describes the position of the Observer in the time dimension and the observation.
The first point in the Time Clock is the Zero Coordinate. This point contains a certain time dimension, which can be unfolded into a circle.
The second point is a projection of the first point in the unfolded dimension. This point determines the exact position of the Observer within the given dimension.
The last point is the projection of the Observer's point of view or the observation itself.
To summarize, then:
• The Time Clock determines the time dimensionality and the exact position in this dimension;
• The Observer's Clock determines the events that occur in this dimension.
The dimension of time, which is collapsed at the Zero Coordinate can be arbitrary, but in practice we will use standards such as second, minute, hour and so on.
Initial State
The Initial State is determined as the only state where the pairs of points coincide. This is the exact moment when the Observer captures the very fact of his initial observation.
To illustrate the Special Solution, let's run a certain process. Both clock hands (linked pairs of points) move synchronously and complete a full cycle simultaneously. This Tape is a visualization of one process that lasted 12 hours.
If the Observer tracks only his own Clock, the Tape is represented by a single edge, denoted as the Signature. The intersection between the Signature and the Zero Coordinate represents an event.
Now let's set the Observer's Clock to 12 cycles, which is equivalent to replacing the hour hand with the minute hand. In this case, 1 Time Clock cycle equals 12 Observer's Clock cycles. The Tape configuration has changed and the Signature now contains 12 loops.
The cycles do not have to be identical. For example, let's set 4 processes of 1, 2, 3 and 6 hours. The result is a Tape with 4 unequal segments or a Signature with 4 various loops.
Torus
To better understand what a pair of clocks represents, let's increase the number of cycles on the Observer's Clock.
It becomes obvious that the Signature describes a surface that can be generalized as a closed Torus.
As a result, the closed Torus is the searched object of Clock face and Timeline unification. The peculiarity of a closed Torus is that it has a special point where its surface self-intersects. We have already examined this point - it is the Zero Coordinate in which the time dimension is collapsed.
There are two more categories of Tori: open and self-intersecting. An open Torus has a Zero Line instead of the Zero Coordinate. A self-intersecting has two Zero Coordinates.
The surface of any Torus contains all possible Signatures, and it can be unwrapped on a plane where they represent straight lines.
General Solution
Now consider the General Solution when the Zero Coordinate is not static, but shifts along a circle of infinite radius, i.e., along a straight line. Such a line we previously denoted as the Temporal Axis.
Let’s limit the Temporal Axis to a duration of 24 hours and set a 12-hour process. Since the General Solution implies a shift, the Signature intersects the Axis twice, i.e. defines 2 events or 2 cycles.
Next, let's set the 6-hours process. The Signature intersects the Axis four times.
A 1-hour process. The Signature intersects the Axis 24 times.
A 24-hour process. The Signature intersects the Axis 1 time.
Quick Summary
At this stage of the research it was found that Temporal Geometry solves any problem of modern time visualization tools, but also:
• Always gives the same Image of Time, instead of multiple for each tool individually;
• Does not require the logic of nesting one Image into another;
• Based on the geometrical interpretation of our perception of time.
The new unified Image of Time can also be used as a medium of information.
In principle, recording information in Temporal Geometry can be conceptualized as recording data on a Tape, which is then wrapped uniquely in time. In this case, the very geometric configuration of the Tape carries information, even if all data is removed from the Tape itself.
Basically, if Spatial Geometry allows one to describe objects in space, then Temporal Geometry allows one to literally see in time.
For a more detailed comparison of geometries please see Article 2.
For a more detailed comparison of geometries please see Article 2.
"
Reva Artiom ©2023