Permutations and Transformations – Shadow Landscapes

The three-dimensional world – a world of shadows? A surface effect of a higher-dimensional space? Or are the shadow world and quantum dimension mutually dependent upon one another, do they exist because they form a symbiosis? Is the future just a rearrangement, a permutation of the past? How do new things enter the world? Follow me into my dimension.

In combination with the U1 Quantum Dimensions and U2 Quantum Reflections, the U3 Quantum Symmetries reveals a topological view on the standard model of elementary particle physics, with symmetry groups U1, U2 and U3.

However, first of all let us, at the first station, take a look at the permutation of information taking simple examples – based on pictures and music. The caretaker plays a xylophone that has had its bars swapped round. No wonder the music does not sound the way Bob is normally used to it sounding.

Music scores always refers to a base – in this case the arrangement of the bars on the xylophone. We have played the coordinates – i.e. the notes of the piece of music – using the wrong base. Let us transform the base, by swapping around the bars. Then we return to the standard base, namely to the xylophone as we know it, with the notes in ascending order.

We might as well, however, also do it the other way around: If we transform the base, and say that that is supposed to be the proper base, then the coordinates are wrong! Consequently, we not only have to transform the base, but also, accordingly, the coordinates.

If we play the piece of music using the notes that match the base, we hear the same piece of music again! When subjected to this sort of transformation, the music is rendered invariant – meaning that the permutations are the corresponding symmetry group.

With 13 bars, we obtain over 6 billion possible permutations of the base and coordinates. In the standard model of elementary particle physics, we will rediscover permutations as the core of all symmetry groups.