Conception Precedes Comprehension
Lee Emmerich jamison
Go to: http://aimath.org/E8/
Here is described in the sort of unrevealing lay terms we can at least begin to grasp difficult ideas in the results of a pioneering study of very abstract multidimensional spaces in mathematics.
This is important because one must have an idea what one is looking at before one can really SEE it.
Several among the ancient Greeks proposed that the Earth revolved around the sun. At the time this idea was rejected because of the concept of the dome of the sky, that is, the notion that the stars were actually on the surface of a sphere. If the Earth revolved around the sun, they reasoned, the circle it described in space would be so huge that there would be a detectable parallax effect in the measure of the most distant planet (then known to be Neptune) as it progressed against the background of the sphere of the heavens. Because there was no parallax detectable to the human eye with the instruments available then the sphere of the sky would have had to have been unimaginably huge.
With more modern instruments in the last century we have, in fact, been able to detect the parallax of more than fifty stars. Gallileo, though, had long since shown that the Earth orbited the sun. In so doing he obliterated the dome of the sky.
That dome drew a fence around what it was possible for us to know. The solidity of the concept prevented us from seeing stars as suns. The dome had to be conceptually destroyed before we could comprehend suns like our own sun in numbers beyond comprehension.
That is how concepts work. We muddle along with vague interpretations of phenomena so that our conceptual space is not dominated by the blank spaces of vertiginous perception, but those interpretations are just placeholders for real comprehension. Then an idea comes along that makes sense of what we see, that allows us to know something in more than one dimension. Replacing the dome of the sky with myriad suns literally expanded the scope of human consciousness.
The description of the E8 structure is a step forward in the description of mathematical spaces. We live in a mathematical space. The better science understands the logic of such spaces the better chance we have of comprehending the space in which we live. The concept must exist before we can truly see what we see.