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I'm not sure there is such a difference between mathematics and an "algorithm". Time can be factored out of a process. A process can be represented as a sequenc
by ssdfsdf 13y ago
I'm not sure there is such a difference between mathematics and an "algorithm". Time can be factored out of a process. A process can be represented as a sequence of objects. Take a function taking some arguments, one can describe this function in it's entirety by describing each sequence of objects generated by each possible input. Then if one wants to recreate the operation of the function one simply looks up the appropriate sequence of objects. A function then becomes a mathematical object in the abstract. In the same way some mathematical object can be described as the result of some process. Take the definition of the natural numbers, an object 0 is defined and a successor to this object to the next object is defined. This operation defined recursively sets up the whole natural numbers. The description of the natural numbers is the result of the evaluation of this function recursively applied, or the infinite application of this function. Since the study of mathematics is the study of these abstract objects and these objects encapsulate those objects which we can produce in the physical world through some process, mathematics by definition is a study of programming. Whether the mathematics explored by mainstream mathematics is the same mathematics explored by the code monkey is perhaps relevant. But the duality exists. In essence a study of physical reality is the study of those mathematical objects which can be constructed by the processes extant in that reality. So analysis of anything is mathematics, it just may not be the kind of mathematics we usually associate with the word.
- boomlinde 13y ago> I'm not sure there is such a difference between mathematics and an "algorithm" Well, then we fundamentally disagree. An algorithm isn't math. Arguing about an algorithm mathematically, or even analyzing it at all as an algorithm might be related to mathematics, but the algorithm itself isn't.
- ssdfsdf 13y agoI have an MSc in mathematics and a strong interest in this area. I would be happy if you were to show me that I am wrong
- pavelrub 13y agoIf a process can be represented as such and such, and then this in turn can be represented as something else, and then eventually after this possibly-long chain of transformations we reach something mathematical, then it is that something which is mathematical, and not what we started with. This is like saying: "There isn't such a difference between neurology and physics. A brain can be viewed as a collection of cells, which in turn can be viewed as a collection of organic molecules, which in turn can be viewed as a collection of particles, and physics studies particles. So neurology = physics. Q.E.D" But what is missing here is the realization that it is exactly our decision not to view the brain as a collection of particles which gives neurology it's meaning. The decision to view something as something else is not trivial. When you choose to view X as Y, it is no longer X you are talking about. You wrote: "...it just may not be the kind of mathematics we usually associate with the word." But it is precisely what we "usually associate with the word" which gives meaning to words. If in this "usual" meaning it is wrong to say that mathematics is the study of algorithms, then mathematics isn't the study of algorithms. When we want to create new precise definitions to old words, what we are trying to do is to formulate a description that fits as best as possible our everyday use of this word. If we ended up with a definition of math that says "the analysis of everything is math", the only logical conclusion is that we did a pretty bad job.