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Suppose I give you two different lists of numbers or maybe two different functions and I ask you to think of all the ways you might combine those two lists to get a new list of numbers or combine the two functions to get a new function. Maybe one simple way that comes to mind is to simply add them together term by term. Likewise, with the functions, you can add all the corresponding outputs. In a similar vein, you could also multiply the two lists term by term and do the same thing with the functions. But theres another kind of combination just as fundamental as both of those but a lot less commonly discussed known as a Convolution. But unlike the previous two cases, its not something thats merely inherited from an operation you can do to numbers. Its something genuinely new for the context of list of numbers or combining functions. They show up all over the place, they are ubiquitous in image processing. Its a core construct in the theory of probability, theyre used a lot in so