# Calculus is a System of Reasoning ### Commentary This is an incredibly deep point. It applies not only to calculus but mathematics as a whole. We have some objective phenomena that exist is the world. We try and capture the fundamental, obvious components of that - we call these axioms. We then develop a set of legal transformations, which follow clearly from the axioms. We are allowed to apply these transformations in any way we see fit, as long as we are abiding by the rules of logic. It is in this way that we can build up complicated chains of reasoning. We have found rules/transformations that are so general, they can be applied in any situation. That is part of the beauty of calculus, it's generality. Now, this also relates to information and constraints. We have found that our physical world operates under certain constraints. These constraints are linked nicely to calculus in that calculus can capture and model them very nicely. This relates to [Mathematical Structure, Patterns, Constraints, Information and Logic](Mathematical%20Structure,%20Patterns,%20Constraints,%20Information%20and%20Logic.md) ### Excerpt > Calculus, like other forms of mathematics, is much more than a language; it's also an incredibly powerful **system of reasoning**. It lets us transform one equation into another by performing various symbolic operations on them, operations subject to certain rules. Those rules are deeply rooted in logic, so even though it may seem like we're just shuffling symbols around, we're actually constructing long chains of **logical inference**. The symbol shunting is useful shorthand, a convenient way to build arguments too intricate to hold in our heads. --- Date: 20210815 Links to: [Calculus MOC](Calculus%20MOC) [Infinite-Powers](Infinite-Powers.md) [Mathematics MOC](Mathematics%20MOC.md) Tags: #review References: * Infinite Powers, Strogatz, pg. xii