>>8614084>>8615532Take some object like a cube[show cube in hand], it has symmetries, in this case you can rotate it along x,y,z, by 90 degrees to get the same cube again. These rotations form a group where you can add to rotations to get another rotation that is a symmetry. [move cube around to show symmetry]. Some symmetries are continuous, for example if you take a ball you can rotate it in the same way, but now you can rotate it any amount in a direction and it remains a ball.
You arnt limited to just a 3D ball, there are all kinds of groups like this that describes some symmetries of some object in all kinds of dimensions. It was found out some time ago that all these groups are built up off only a handful of simple symmetries, any complex symmetry can be decomposed into a combination of these simple symmetries, we have 4 families of symmetries which are quite easy to understand, like the rotations of a spere, but for any dimension. But then we also find five exceptional cases, five groups that cant be broken down, yet are not part of these simple to understand families. We label them G2,E6, E7, E8 and F4.
Its important to note that we didnt invent them just to study them, there are a result of fairly basic assumptions of how a symmetry must act, for some reason they are the result of what we define as symmetries.
G2,E6, E7, E8 and F4 are the symmetries of very complex objects in very high dimensions, but E8 is by far the largest and most complex one living in about 250 dimensions, and what makes it even more uniue, is that its the only one of all of these which doesn't describe the symmetries of some other object, but it actually describes the symmetries of itself! [astonished le black man face to emphasize point].
