We are going to prototype a new universe.
- There is an empty 3D (R3) space.
- The universe changes it’s states abruptly only from takt to takt.
- State changes occur in intervals (takts).
- Time in the universe can only be experienced by changes of it’s state.
- The universe can be occupied by entities only.
- The universe starts with one simple punctiform Ur-entity.
- Whenever a new Ur-entity is created in the universe, a new takt (interval) occurs.
- There are no changes in the universe between the takts.
- All entities can only change their individual state with the next takt (interval).
- The state of an entity is represented by it’s individual relation to other entities.
Each change of state of the universe is a change of state of its entiities from takt to takt..
This is the alternative way to the big bang to get the universe startet. It started with one single punctiform entity. Time does not flow continously. Time is only experiencable by changes in the universe. Changes take place only in certain intervals, I call takt (german). Time exist only in quantums.
You cannot observe any changes in the universe between two takts. The minimum changes which can take place is between two takts. No finer time grain is possible.
Mathematics
Please solve following math problem. Punctiform entities exist in a three dimensional relationship to each other. Time can be experienced only from takt to takt.
Properties of all Entities
- All Entities can change their Position by one unit of length from takt to takt.
- Every entity starts in a arbitrary position which is defined in a relativ position to the others, if any.
- All entities can define their new relativ postion for the next takt.
Every Entities Urge
- Changes in postion must be made from takt to takt.
- Every entity wants to close in to all other entities.
- Every entity calculates the optimum of the next position to follow the urge to unite with others.
- The distances of others are used for weighting the position changes to approach the others.
- Every entity nears faster to near entites than to those farer away.
- Position changes can be made only in units of length. This leads to space quantums.
The Genesis
- The very first entity is created at an arbitrary position which has no relation to nothing.
- It must not calculate any new position because there is no relation yet to anything.
Next takt of time
- A new entity is created with any new takt.
- The position of any new entity is arbitrarily defined in relation to the other existent entities.
- Space is starting to exist.
- Every single entity calculates its new position for the next takt which should be the optimum to approach all.
- This new position comes immediately to existence with the new takt. There is no movement. There are only jumps.
- The new takt is defined by the creation of a new entity.
Formula
Please develop a formula reflecting the requirements above. It should be capable to calculate the new positions for every entity from the view of this entity.
The formula should be capable of calculating the positions of any number of entities. I understand that the effort gets increasingly bigger as bigger the number of entites is. The universe is huge.
IT
I guess that the problem can be solved only by a software iterating the number of entities with each takt.
The software itself should not limit the number of entities considered. The power of the computer in use should be the limiting factor which forces to select a proper maximal number of takts.
The software should have a graphical interface to show all entities and all their changes in positions to get an animation of movements.
A zooming function will be required to show the movements on the screen if the number of entities gets larger.
The very beginning of the universe is of special interest anyway. I assume that from a certain number of entities on, all animated movements look like a straight line.
I would be happy if anyone can provide me with above functionality.
