Dimensions

Today I am going to talk about the mysterious extra dimensions of space :) How Can we go about visualizing extra dimensional space? Well we can think of it as extending the plane outwards to a new level. Take for example the picture above it goes from zero dimensional ( just a dot) to four dimensional just by extending the planes out to a new 'level' so to speak.

A Tesseract orthoganally doubly rotating. Another way of visualizing these abstract geometrical entities is by using on of the most wonderful tools of the universe (that can potentially let us interact with aliens) MATHEMATICS!!!! We can do this by using such things called manifolds which are pretty much just surfaces but instead of using just a complex number to define them (a real number mixed with the imaginary number, Sqrt(-1),)we an use things called Quaternions or Octonions (Pretty much extended Complex numbers with more 'parts'). Now what these 'numbers' are, are our gateway to understanding all of the complexities of the fourth, fifth, sixth...etc dimensions that we can ever imagine. I wont go into detail... The weird things about these numbers are that they describe dimensions and our natural world to an extraordinary degree of accuracy very well but the don't act like normal numbers: for example with quaternions they break one of the fundamental rules of algebra since they are non-commutative. This means that if you took two quaternions lets call them 'A' and 'B'. A X B =/ B X A (A times B isn't equal to B times A). And what is weirder still is that their crazy cousins the Octonions are both non-commutative and Non associative which means that A X(B X C) =/ (A X B) X C which also breaks one of the most fundamental laws of algebra even more so. Therefore some of the craziest things that can describe our world in all its glorious (Maybe extra) dimensions, describe it almost perfectly. :)