# recap

We have introduced a number of unfamiliar concepts so it is worth having a recap. Please excuse a certain amount of unavoidable vagueness and hand waving in the outline of the overall vision.

In the maths section we explained how we define a number system using rotational numbers.

In the sequence section we derive a hierarchy of dimensions from this number system: 1,1,3,6,30,30,210,…

A generating function calculates multi-dimensional numbers based in its neighbours.

We are investigating types of generating functions with complexity gradients. We have previously shown how we look at dimensions with complexity gradients as time dimensions, so our generating functions exhibit a hierarchy of time dimensions.

We have chosen generating functions such that the smallest set of dimensions containing time dimensions is 6, with 3 space and 3 time dimensions.

Recap of the terminology in 6-dimensions: We have 3 time dimensions, tx,ty,tz. (Each point in the diagram above represents a 3-dimensional space with dimensions x,y,z.)

The distance to the origin is called generation g.

g = tx + ty + tz

The number of spaces at generation g forms a triangle. Marked in red is the dominant timeline.

Far away from the origin, at a large value for g, the spaces of generation g are a large plane, and there are many parallel timelines.

We are investigating the generating functions where the higher hierarchies become more and more similar, this way we could choose use the 6-dimensional set as an approximation. In effect we treat the 5 groups of 6 dimensions in the 30-dimensional level as identical, as well as all the hierarchy levels above that.

At each level of hierarchy, we have m-dimensions of numbers and each of these numbers if also m-dimensional. As an example, in our 6-dimensional level of hierarchy each point has 6 coordinates, say (x,y,z,tx,ty,tz). The value at that point, V(z,y,z,tx,ty,tz) is also 6-dimensional, i.e. a 6-dimensional vector.

We are looking for stable sets of patterns in these sets, where stable means persistent along the time dimensions. We call such a pattern a ‘particle’.  This short blog post argues that the concept of a real, physical particle is not a fundamental entity. Instead, the foundation is entirely mathematical.

Even through their boundaries are fuzzy, different particle types can have different sizes. Since they are made up of vectors spinning in the time dimensions, they also have a phase.

As such they combine properties from wave and particle concepts. They are countable by positive integers, you can’t have fractions of these patterns, and they have a size and phase.

We can hypothesise that a generating function exists that creates stable patterns, that correspond to the particle types of our standard model.

In 6 dimensions we are looking for particles that correspond to photons, electrons, gluons and up and down quarks. For the other particles of the standard model we need 30 dimensions. The next level of 210-dimensions and higher levels might harbour more, as yet undiscovered, particles.

The most vital concept to appreciate is multiple time dimensions and how a fully deterministic world would appear to observers inside it.

This section describes how observers experience time in a world with multiple time dimensions.

Here is a blog post that illustrates some of the effects by simulating bouncing balls in 2 time dimensions.

If we had a mathematical universe based on a generating function that created the above particle types, we can make some predictions of how such a universe would appear to observers living inside it.

We will list some of them in the next section.