For example, the current model of the beginning of the universe, most of the rules of physics go out the window as everything we know as laws when evaluated end up with division by zero. It's infinite in size and infinite in density, something that we've got no way of understanding mathematically.
As an example: "Where does the fire go, after you blow it out? The question is irritating, because fire is a side-effect of quantum interactions, while the wind that blew it off, absorbs and vaporizes this energy into measurable quanta and is comparable to what black holes do.
The rate at which vapors of flames excess from this reaction, is dependant of composition of the matter and it's catalyzation rate. The flame contains many atoms with electrons in highly excited states and keeps decaying into lower energy levels, causing the excess energy to swing in the frequencies/wavelengths or just colors/spectra of the burning material. You can learn more about that in [2].
Why this seemingly unrelated example of "fire and flames" is simply explained as an „autocatalytic set“ [3].
Adding that matter is both particle AND wave dependant on the observation is very simple to understand, when you know that we live in a two dimensional space and that energy outside of our space exists as a wave function.
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[1] http://en.wikipedia.org/wiki/Big_Rip
[2] http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/qua...