Our world And three -dimensional, And on this there is no doubt. Our three dimensions are: length, width And thickness. And if we wanted to find one Fourth size? “The fourth dimension is time!”, We hear it often. But if we wanted to look for a fourth dimension other than time, what would happen? We try to understand why a fourth dimension is important in video games And how mathematics think of dimensions beyond the third. And spoiler: you will acopire that everyone can act to act in a world with more than 4 dimensions!
The three dimensions in real life: length, width and thickness (or depth)
We live in a three -dimensional world. But have you ever wondered what it means? To understand it, we start from a single dimension and try to build our world.
When we move with the car in a stretch of road without crossings we can only go back or backwards, that is, we can move in one direction. More precisely, the mathematicians would say that we move in a space of size one, one space linear. In a world to one dimension, it is enough for us A single spatial coordinate To find out where we are. Returning to the example of the car, if while we are driving, we are reported a danger to km 10, to check how far we are from the danger, just check the road signs that report the mileage and pay attention at the right time. The number 10 alone is sufficient to make us precisely identify the indicated place. A size, a single number!
We now think about the game of chess: it takes place on a square, that is, a space of Dimension two that mathematics call surface. To indicate the position of a piece, in fact, one number is not enough but a number and a letter are needed to indicate the positions on the chessboard. In the image below, for example, the Black King is in position E7 while the white king is in D4. Each piece, in short, can be moved in two possible directions, horizontal and vertical, and by combining them it can also move diagonally! The chessboard is in fact a two -dimensional world, in which Each movement can be described through two coordinates. In short, two dimensions, two numbers!
In mathematics two numbers indicating the position of an object on a plan take the name of Cartesian coordinates and are indicated in brackets: the couple (4; 3) indicates a point that is moved by 4 to the right compared to a point of reference (said origin) and 3 upwards.
We then arrive in our world: the three -dimensional one. In addition to the “plans” movements, there is also height! In three -dimensional space In fact, we can indicate the position of a point with an orderly list of three numbers. For example, let’s think about the position of a glass that is located on a table, like the one in the figure below. The table is 90 cm high, while the glass is moved 120 cm to the right and 80 cm forward compared to the corner of the table. By putting these three information together, the position of the glass will be indicated by the Terna (120; 80; 90). Three dimensions, 3 numbers!
This way of describing the positions of objects is systematically used when they must be provided Spatial indications. The idea is that each number of the Terna indicates the position in the context of one of the three dimensions, which in our reality can be described as a length, width and thickness.
It must be said, however, that in our daily life, but also in video games, we are dealing with objects that can differentiate ourselves on the basis of many more aspects than simply the position and this can help us extend the idea of dimension beyond the third.
Go beyond the third dimension: when passing from position to quantity
We remain on our example of glass, But now let’s imagine that contain water. If we resume the triad described above which contains the Spatial coordinates of the glasswe can also describe how much water contains the glass by adding a number that expresses the amount of liquid. In the event that it contains 20 cl of water – as in the image below – we can write the list (120; 80; 90; 20) which describes everything we know on the glass: position And amount of contained liquid. Similarly, the glass of the image above, the empty one, will be indicated with (120; 80; 90; 0) because it does not contain liquid. In short, we have now completely described the glass using four numbers: from the mathematical point of view we have just Added a fourth size to the description of the glass. Four numbers, four dimensions!
Time as a size: how can variables change
Now that we have learned the makeup, we can add all the dimensions we need. For example, always returning to the example of the glass, in the summer we could be interested in knowing if the contained water is fresh Or not. If we just took the water from the refrigerator his temperature It is about 4 ° C and we can summarize all the information we have on the glass by writing (120; 80; 90; 20; 4) and then reporting position, quantity liquid e temperature. Let’s now try to take one step more: that storm!
This list of numbers refers to a static description of the glass but, if we move the glass, the first 3 numbers of the list will change because they indicate, as we have seen, the location. In mathematics the quantities that can change they are called variables And when we are dealing with many variables that change independently from each other – as in our example – each of them can be seen as a different dimension: Many variables, many dimensions!
Among the many variables that can be taken in consideration it is often useful to consider the time. For example, to describe the fact that the water temperature has climbed from 4 ° C to 10 ° C in 20 minutes Then we can write that the glass went from (120; 80; 90; 20; 4; 0)that is 4th at time 0 minutes, a (120; 80; 90; 20; 10; 20), that is 10 ° at the time 20 minutes. The last two numbers of both descriptions indicate the variation of temperature and the time spent. We therefore reached 6 dimensions … in a glass of water!
When the dimensions do not include space and time
But It is possible to exclude space and time From size? Short answer: yes! It depends on what we want to describe.
Suppose the glass contains a drink and that what we are interested in describing are the nutritional values. For example, a can of a well -known drink provides 571 KJ of energy and contains 9 g of proteins, 0 g of fat e 10 g of carbohydrates, so we can describe its nutritional intake by writing: (571; 9; 0.1; 10). If we consider the same amount of water its nutritional intake will be with good approximation (0; 0; 0; 0). In this case we are using four numbers, or four dimensions of which no one concerns space or time. Whenever we choose the food based on their nutritional values we are actually thinking in four dimensions, and if we also consider the cost of the food the size become five!
The many dimensions of video games
Finally, let’s go back to the question of gamers, fans of video games. Many video games provide that the user checks a character who moves in an environment by performing actions whose outcome depends on several quality of the characterwhich can be described through numbers. For example, in combat games the characters are usually characterized byenergy and from skills (skills) As rapidity, dexterity, resistance. If the energy drops to zero, the character is defeated, while the outcome of a move will depend on the combination of the variables of the skills of the character and his opponent, as well as by position in which they are in the game. In short, for the purpose of carrying out the game, a character of a combat simulation is described by many independent variables. In our example, assuming a 3D simulation, the character would be described by seven variables (three for the plus position for four for skills) And the computer would deal with a point of a 7 -dimensional space indicated by 7 numbers. The knowledge of how these parameters can vary and how their different combinations affect the outcome of the game, is crucial for the gamers as, usually, the higher the values of the skills and the greater the probability of winning.
We can see a gamer like a professional of the multidimensional spaces: the next time you happen to play a video game on football try to count how many skills They characterize your players, you will find that your goleador in Vive in a world of a dozen size …
