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This is a very important rebuttal to the “The Mathematical Hacker” article because it shows Maths is useful but should not be taken too literally. Even Knuth us

by arocks 13y ago

This is a very important rebuttal to the “The Mathematical Hacker” article because it shows Maths is useful but should not be taken too literally. Even Knuth uses assembly language of a hypothetical machine in his Art of Computer Programming books because any discussion on optimisation is incomplete without the context of which machine we are talking about.

ska 13y ago
I really don't understand this sort of response. The right way to understand the behaviour of computations on a real machine is inherently mathematical. This is why, for example, we have an entire discipline of numerical analysis, just for starters. Programmers very commonly make elementary mistakes in computation precisely because they don't understand this, and don't approach the problems mathematically. Ignoring overflow, or pretending floats have infinite precision is antithetical to thinking about these problems mathematically. Conversely, any mathematician worth their salt will approach computation on a computer not as a black box, but as a concrete implementation. Mathematicians make lots of programming errors (some of them quite egregious and easily avoidable). Misunderstanding floating point representations or the overflow behaviour don't tend to be among them in my experience. By the way: Knuth used a hypothetical machine to avoid the quirks of a concrete one distracting from the discussion.
- arocks 13y ago
  My response can be very simply stated as the well-known adage - Profile Before Optimizing I am not completely discounting Numerical Analysis here. Mathematicians can make entire mathematical models of a machine but it will be at a certain level of abstraction. In practice there will be abstraction leaks due to some quirks of the implementation or real world dependencies. So one should not merely depend on the mathematical model.
  - ska 13y ago
    A more important and often overlooked adage - make it correct before you try to make it fast. My confusion at your (and others, not meaning to pick on this one) response is more fundamental than that. There is no way in which thinking about these things is somehow divorced from thinking about things mathematically. To me "Merely depending on a mathematical model" isn't a problem that actually happens much. Failing to think about these things, on the other hand, very much is.
  - coldtea 13y ago
    >My response can be very simply stated as the well-known adage - Profile Before Optimizing Well, profiling IS also math. If anything, it would be "optimizing" which is programming proper.

by arocks 13y ago

ska 13y ago

I really don't understand this sort of response. The right way to understand the behaviour of computations on a real machine is inherently mathematical. This is why, for example, we have an entire discipline of numerical analysis, just for starters. Programmers very commonly make elementary mistakes in computation precisely because they don't understand this, and don't approach the problems mathematically. Ignoring overflow, or pretending floats have infinite precision is antithetical to thinking about these problems mathematically. Conversely, any mathematician worth their salt will approach computation on a computer not as a black box, but as a concrete implementation. Mathematicians make lots of programming errors (some of them quite egregious and easily avoidable). Misunderstanding floating point representations or the overflow behaviour don't tend to be among them in my experience. By the way: Knuth used a hypothetical machine to avoid the quirks of a concrete one distracting from the discussion.

arocks 13y ago
My response can be very simply stated as the well-known adage - Profile Before Optimizing I am not completely discounting Numerical Analysis here. Mathematicians can make entire mathematical models of a machine but it will be at a certain level of abstraction. In practice there will be abstraction leaks due to some quirks of the implementation or real world dependencies. So one should not merely depend on the mathematical model.
- ska 13y ago
  A more important and often overlooked adage - make it correct before you try to make it fast. My confusion at your (and others, not meaning to pick on this one) response is more fundamental than that. There is no way in which thinking about these things is somehow divorced from thinking about things mathematically. To me "Merely depending on a mathematical model" isn't a problem that actually happens much. Failing to think about these things, on the other hand, very much is.
- coldtea 13y ago
  >My response can be very simply stated as the well-known adage - Profile Before Optimizing Well, profiling IS also math. If anything, it would be "optimizing" which is programming proper.