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Science and Technology|Why Use High Dimensions In a 3D World | Data Science Crash Course

Let's first think about vectors. A vector can be viewed as an array of numbers, where each of its element represents a quantified feature of the same object. A common use of vectors is in the representation of forces in physics, a force is decomposed to three dimensions that are orthogonal to each other, which suits our understanding of a 3-dimensional world. But if you have learnt linear algebra, then you already know that a vector can have more than 3 dimensions. In mathematics, a vector can have as many dimensions as you want. So why do we bother to create an n-dimensional vector in a 3-dimensional world? The answer is we need these dimensions to help us analyse an object from as many perspectives as we can. For example, the statue of liberty can be represented with a 3 -dimensional vector, including its height, width and length. But this is still very limited. If you want to study the years when different sculptures were created, so that you can gain a better understanding of the history of sculpture, you'll need to attach a 4th dimension to represent the year to each of the sculpture. You can even add a fifth and a sixth dimension to represent the latitude and longitude of the place where it was created, so maybe you can find some interesting patterns. Were all sculptures that depict the natural figure of humans created in Europe? Were all sculptures of animals created in Asia? By adding more dimensions, you can understand a certain object more thoroughly, and have the ability not to be confused if you have seen many of them. Since adding more dimensions gives us more information, it's not surprising that high dimensions are commonly used in data analysis in many fields, such as clinical research, financial systems, and many other areas. With the freedom of creating more dimensions, we can break the limitations of a 3d world, and avoid being bombarded by the explosion of information in a digital age. Attributions by order of appearance: By Maschen [Public domain], from Wikimedia Commons By Les Bossinas (Cortez III Service Corp.) [Public domain], via Wikimedia Commons By Daniel Schwen [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0) or Public domain], from Wikimedia Commons By Aurbina (This file was derived from  Moai Rano raraku.jpg:) [Public domain], via Wikimedia Commons By Jastrow [Public domain], from Wikimedia Commons [Public domain], via Wikimedia Commons By Alex Covarrubias [Public domain], via Wikimedia Commons