The Tesseract

File:8-cell-simple.gif

Look at this.

Now tell me that your mind has been blown (or at least that you are curious to know what the heck that is).

That my friends is a Tesseract, a 4 dimensional square…. or a cube… I don’t even know. Basically, the Tesseract is to the cube what the cube is to the square, one level up.

You can make a Tesseract very simply by using the same logic you apply to a square to get a cube

In Mathematics, dimensions are a collection of vectors (signifying direction). And no, the 4th dimension isn’t time (in Maths at least). Stop watching NOVA. A 4 dimensional vector is simply, if represented by a collection of points would be

(34, 2, 9, 4)

The “thing” has 4 coordinates. So this “thing” or point, exists in a plane which has an x, y, z, and w axles. Knowing that, here is how to make a Tesseract.

File:Dimension levels.svgCool stuff right?

This idea of Vector Space is heavily used in Physics but relax, it has very practical applications as well.

Information retrieval includes a wide range of sciences such as Data mining and NLP(Natural language processing). It’s basically the reason you can use Google or search an article here on wordpress.

Before we can even start dealing with documents or Webpages or any sort of written text to be compared or sorted for your info needs, we compute the similarity between those texts. This is where the idea of vector space really shines.

Basically if you have a collection of books/documents/webpages, you can represent each document as a vector of all the unique terms that appear in that document. Each word that appears is a dimension. If you think of it that way, even this blog post could be composed of some 1000 dimensions (if it had 1000 unique words in it).

Thankfully, we use computers to do all that kind of stuff but it’s still very cool to imagine the level of abstraction mathematicians are capable of.

Kudos to the human brain 😀

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