For creating objects in a virtual world, geometry1 plays a major role. It is a study dealing with shapes, distances, sizes, positions, etc. However, one aspect that perplexes me is the dimension2, an important concept of geometry. How many dimensions does our real-world have? We often say that we live in a three-dimensional world. What does it mean? The response is that we can perceive an object's length, breadth, and height. Is time a dimension? If length, breadth, and height are the concepts of spatial dimensions, duration is a concept of the temporal dimension. These concepts arise from applying the “difference” operation of two points on any one of the chosen dimensions. A point, therefore, looks like an important concept. We consider a point to have zero dimension, a line to have one dimension, a square to have two dimensions, and a cube has three dimensions.

Some define dimension as the minimum number of coordinates required to specify a point in a mathematical space. Others consider dimension as a direction. If an object is in 0-dimension, it cannot move in any direction, if it is in one-dimension, it can move in one direction, left or right. If it is in two dimensions, it can move in two directions: left or right, forward or backward and if it is in three dimensions, it can additionally move up or down. But the trouble comes, when we talk about the temporal dimension, objects can only move ahead in time. There are several arguments that we may be able to move backward in time if we have some sort of time-travel machine. I guess that's the main reason some of us have difficulty considering time as the fourth dimension. However, in a simulated world, this is not a problem, the creator can move back and forth in time. Thus, for the creator, there is indeed a beginning, the time at which they started the simulation. If the creator has recorded every change, going back to the first point is not difficult. What happens when the simulation creator wishes to go back to the past? What happens to the objects in the simulation? Do they continue to exist? Or does the creator create another simulation with the recorded history to replay the past? What does it mean to modify the past in the simulation? The time in the creator's world is racing ahead. However, how do the objects in the simulation perceive the reversal of time? Or do they even perceive it?

Keeping aside the temporal dimension, what does it mean to explore and visualize dimensions3,4 higher than three? What do four5 or five dimensions look like in a simulated world? Is it possible to even visualize them? Some compare the situation of humans (or other living organisms) to that of the persons in the flatland6. Those in the flatland may not be able to comprehend what we as humans can perceive in three-dimensional space. But, what if we project these higher-dimensional objects into three-dimensional space7,8,9, one slice at a time? Will we be able to obtain a mental image of the higher-dimension objects10,11?

References

  1. Geometry
  2. Dimension
  3. Exploring other dimensions - Alex Rosenthal and George Zaidan
  4. If higher dimensions exist, they aren't what you think | Exploring Worlds Beyond Our Own
  5. Making a 4D Game - 4D Explorer
  6. Flatland
  7. A Beginner's Guide to the Fourth Dimension
  8. A Journey into the 4th Dimension - Perspective [Part 1]
  9. Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 2]
  10. The things you'll find in higher dimensions
  11. Perfect Shapes in Higher Dimensions - Numberphile