Graphs for Real, Complex, Quaternions, and Hypercomplex Numbers

Transcript

carafes for real complex quaternion and hyper complex numbers the real number graph has one vertex labeled with a 1 and one edge labeled with a 1 because 1 times 1 is 1 start at the vertex 1 multiplied by 1 and you return it to that vertex labeled 1 here is the graph for complex numbers the real number 1 with its loop is already there now we have a new vertex the imaginary number I in blue the blue edges are directional one times I goes out to I but the return follows a different path I times minus I gets back to one it would have helped to understand complex numbers to have seen this graph I had to reshoot this image because I forgot the loop on the imaginary number I real numbers help imaginaries stay in place there are two under ection 'el edges in loops using only real numbers and two directional edges using only imaginary numbers the quaternions continue the theme started with the complex numbers the real number 1 with its loop is already there there are now three imaginary vertices with directional edges connecting them all real numbers provide loops for all vertices there are four under ection --all edges in sidled loops and twelve directional edges the imaginary numbers are vectors you can point to them they flip directions in mirrors a scalar isn't like that which is why I represent it as time in an animation you cannot point at time time marches on everywhere building a quaternion graph out of clay in pipe cleaners requires much work all those double directional edges it would be much simpler to use only one pipe cleaner per edge this is the graph for Hyper complex numbers 10 under ection alleges in all hyper complex numbers are totally obscure quaternions play only a few bit parts having to do with 3d rotations real and complex numbers on the other hand are central to mathematical physics this looks like a huge accounting issue to me I can spot the real numbers in all these graphs I can spot 3 complex numbers in the quaternion graph the simplicity of the hyper complex numbers suggests they should play a significant role in describing how nature works in space-time I have reason to believe that hyper complex numbers are the accounting system used for mass the involved in the universal attractive force of gravity justifying that claim requires more math that is outside the scope of graph theory the combination of quaternions and hyper complex numbers should be sufficient to cover any conceivable pattern of events in space-time no matter the source which is the job of physics I believe nature keeps double books more than one rule for multiplying patterns of events together that will be a difficult idea to sell to physicists oh well I have these graphs on my bookshelves and this YouTube video has a consolation prize thank you very much