I will explore the following essay topics through the prism of a mathematical universe, the premise being that our universe in its entirety, down to the Planck level, is a mathematical simulation, and thus fundamentally the Laws of Nature are mathematical structures operating at the Planck scale. In essence, I will argue that while physics summaries the laws of nature, and successfully applies them, the mathematics used by physics is not the same as the mathematics as used by nature, and that nature, as a mathematical science, deserves its own distinct category alongside physics, chemistry, biology … We must also conjecture that any self-learning self-programming AI will eventually adopt the mathematics of nature.
The laws of nature deserve their own category in science alongside physics, chem
a month later
"the Laws of Nature are mathematical structures operating at the Planck scale"
You should not trust much to Planck scale. Planck system of unities is a home made system and can have not any relationship with the physical world.
What do you think about the system of unities where Planck constant=Gravitationnal constant =Lambda constant=one: it is also another absolute system and it is a home made system.
The problem of physics now is a problem of scale and nowbody pay attention to it. There is only one and a unique system of unities where we can unify all the fundamental interactions. This system is where Planck constant= Speed of light=mechanical impedance of vacuum= one. The problem of scale is resolved as we associate a 4-vector identity for every corpscule as follows:
4-vector identity=( speed of light times the inertial time, speed of the corpuscle times its inertial time)
Inertial time of the corpuscle=Energy of the corpuscle/( square of speed of light times mechanical impedanceof vacuum)
the speed of light times the inertial time translate the notion of scale: it is like a space forth dimension.
It is clear that you can apply the 4-vector identity to a pocket of waves and deduce directly the wave-corpuscle duality. It is like that you had split the wave-corpuscle duality in two dualities as corpuscle-identity duality and wave-identity duality.
You can get an approximate value of the mechanical impedance of vacuum as follows: the most commun natural radiation have a frequency of 1E14 Hz. This radiation comes from the oscillation of a dipole (electron-nuclei bounded system). The lifetime of the electron in a level is about 1E-7 second to change its energy level and emit a photon. the mechanical impedance of vacuum = Energy of the photon/(square speed of light times the lifetime of the lectron).