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Poll: What level of math is programming roughly analogous to?
161–165 of 165 posts
Re: Poll: What level of math is programming roughly analogous to?
#162Earlier quoted context omitted.
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 ap…
> 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.
I 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
Re: Poll: What level of math is programming roughly analogous to?
#163Earlier quoted context omitted.
Mathematics can easily be applied to anything from cooking to theoretical physics. That doesn't make any of these things math or the other way around. You can use math to solve a programming problem (perhaps to a greater extent than in cooking) and you can express many of the problems in mathematical terms, but in the end math is an abstract tool and programming is not.
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 ap…
If 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.
Re: Poll: What level of math is programming roughly analogous to?
#164Earlier quoted context omitted.
> 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.
I 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
This has nothing to do with mathematics or with your MSc, this is a a philosophical discussion about the meaning of words.
Re: Poll: What level of math is programming roughly analogous to?
#165Earlier quoted context omitted.
> 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.
I 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
Is there anything concrete you can say in response to my argument, or is this it?