Computer simulations are tractable mathematics

The invention of differential and integral calculus in the 1660s was a remarkable accomplishment. Indeed, much of progress in the physical sciences can be credited to the pioneering work of Newton and Leibnitz. This is because calculus enhanced the unaided human brain in the following two major ways. 

The second category of human capacity enhancement is augmentation. Augmentation is well exemplified with nuclear magnetic resonance instruments. There is no a-priori human ability to detect the resonance of nuclear magnetic moments to an external magnetic field. NMR equipment gives humans instrumental access to physical phenomena beyond our unaided capacities. 

Analogously, calculus provides access to tractable mathematics and analytical solutions previously inaccessible to the human brain. Augmentation can then be considered as a qualitative shift in abilities. With results attainable only with calculus, the foundation can be solidly laid for theories that capture and explain physical phenomena. The development of the gravitational theory, the electromagnetic theory, or the quantum mechanical theory, is now possible, resulting, in turn, in tectonic changes in the human mindset. 

Of course, with calculus analytical solutions became tractable only for linear, deterministic problems. For non-linear or probabilistic phenomena, the invention of computational mathematics has introduced an equivalently distinctive set of scientific methods. Paul Humphreys has best presented convincing arguments that computational science 

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