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Ever since Newton, determinism - i.e. the concept that the prior state of a system determines the next state of the system - has become an integral part of science, in particular of physics. This is particularly because Newton invented a mathematization of the concept of change: the calculus; in doing so he did much more.
Applying this new form of mathematics to study changes of physical phenomenon, Newton discovered that the concept of motion follows very strict mathematical laws; this essentially was the discovery of the laws of physics. The laws of physics have since then always come to us in the form of differential equations (or generalizations thereof).
To make a long story short, differential equations - or any abstractions thereof or of descriptive functions where the input and outputs reside in the same space - are the prototypical mathematical implementation (or 'mathematization') of the concept of determinism.
My question is, is anyone familiar with other forms of determinism which can definitively not be reduced to or be shown to be equivalent to differential equations in any sense, not even in principle?
Applying this new form of mathematics to study changes of physical phenomenon, Newton discovered that the concept of motion follows very strict mathematical laws; this essentially was the discovery of the laws of physics. The laws of physics have since then always come to us in the form of differential equations (or generalizations thereof).
To make a long story short, differential equations - or any abstractions thereof or of descriptive functions where the input and outputs reside in the same space - are the prototypical mathematical implementation (or 'mathematization') of the concept of determinism.
My question is, is anyone familiar with other forms of determinism which can definitively not be reduced to or be shown to be equivalent to differential equations in any sense, not even in principle?