![]() ![]() Here, have a coordinate system chart~ /rHJiaV5pPm- Freya Holmér NovemWhat does a 4D object look like? Different 3D softwares, for instance, are using different conventions over which axis is “up”. Overall, there is a lot of confusion even with the “standard” X, Y and Z axes. These terms have not been wildly adopted in the scientific literature. Charles Howard Hinton refers to a positive and negative change along the W axis as ana and kata, which stands for “ up toward” and “ down from“, respectively. In case you are interested, different authors have given different names. Within this tutorial, we will refer to it generrically as hyperspace, or fourth dimension. Generally speaking, there is no agreement on what the fourth dimension should be called. And this requires the introduction of new terms that can correctly represent directions in the hyperspace. When working with four spatial dimensions, it is important to be able to orient ourselves. Geographical maps, for instance, are 2D because every location can be addressed using two points (either latitude and longitude in a Cartesian reference frame, or angle and distance in a Polar reference frame). What makes a space -dimensional, is the fact that every point it contains needs at least independent numbers to be uniquely defined. Integral to the definition of dimension is, in fact, the idea of coordinate. And a four-dimensional geometrical space is nothing more than a space in which every point needs at least four coordinates to be uniquely identified. A four-dimensional vector ( ), for instance, is nothing more than a collection of four numbers. And while these objects might not make sense in the physical sense, they can still be incredibly valuable to model complex phenomena.Ī four-dimensional object is, after all, any entity which has four independent variables. The same principles that govern one-, two- and three-dimensional objects can in fact be formalised and extended into an arbitrary number of dimensions. But while this is true for the space we live in, it does not mean that higher dimensions cannot be imagined, mathematically and geometrically speaking. ![]() Or at least, there is no evidence it does. In case it was not sufficiently clear, this legendary fourth dimension does not really exist. Neither “FEZ” nor “Monument Valley” appear on that list, since they do not feature actual 4D geometries, but only play on the concept of perspective. In case you are interested, Wikipedia keeps a (non-comprehensive) list of 4D games: List of four-dimensional games. There is nothing “made up” in those games: everything works as it should, mathematically and geometrically speaking. What makes both “Miegakure” and “4D Toys” so important in this conversation, is that they both simulate how four-dimensional objects would behave in a 3D world. Similarly to “FEZ”, “Monument Valley” plays on the idea of perspective: if two platforms appear next to each other, the player is able to cross them even if they are far apart in the 3D space. “ Monument Valley” is another brilliant example of that, and a technical achievement both in terms of gameplay and art direction. The counter-intuitiveness of its puzzles is a close example of what would be possible for us humans, if we had access to the fourth dimension. “FEZ” is technically a 2D game, set in a 3D world. One of the first games to do so and to reach the mainstream audience is “ FEZ“. Over the past ten years, there have been some steps forward in the representation of the fourth dimension in games. Our bodies and brains have evolved in a three-dimensional space, and adding an extra dimension brings a new level of counter-intuitive behaviours. And there are good reasons why that is the case. Regardless of your media of choice, the fourth dimension is very rarely integrated in a scientifically accurate fashion. An artistic interpretation of a tesseract (“Interstellar”, 2014, Paramount Pictures) ![]()
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