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Since math is just the formalization used to describe quantitative patterns observed, you're already seeing math as purely as it will ever get. Really, it's the

Since math is just the formalization used to describe quantitative patterns observed, you're already seeing math as purely as it will ever get. Really, it's the other way around--since math is an abstraction of observation, what you observe with your senses day to day is a much more direct and fundamental reality. Math is a language, and reality is what it talks about. Similarly, people who speak English will find that the most effective visualization and perception of what they speak about is to just directly see and perceive the thing that they talk about. That's why I've never thought that there's any "Unreasonable Effectiveness of Mathematics in Describing the World". Math is derived from reality and describes it insofar as it can be observed to be given a description, and so it's unsurprising that math is effective at describing what it's designed to effectively describe. It's like saying that English is unreasonably effective at talking about things.

6ren 14y ago
The surprising bit is not that it explains the observations that it was modelled on, but that it explains further, unexpected observations that were unknown at that time. It's not that maths is so great, or even that models are great, but that we were able to model some essence of a phenomenon, beyond what we witnessed. This happens not because it's a model (you can have as many models/theories as you like), but because we selected that model, usually due to beauty/parsimony/elegance - which amounts to some version of Occam's Razor: to not make a model more complex than needed to explain the observations. (do not multiply elements unnecessarily; given different models that explain the observations, the simplest one is most likely the truest of them). http://en.wikipedia.org/wiki/Occam%27s_razor http://en.wikipedia.org/wiki/Occam%27s_razor The real puzzle (if it's a puzzle) is why Occam's Razor works so well...

6ren 14y ago

The surprising bit is not that it explains the observations that it was modelled on, but that it explains further, unexpected observations that were unknown at that time. It's not that maths is so great, or even that models are great, but that we were able to model some essence of a phenomenon, beyond what we witnessed. This happens not because it's a model (you can have as many models/theories as you like), but because we selected that model, usually due to beauty/parsimony/elegance - which amounts to some version of Occam's Razor: to not make a model more complex than needed to explain the observations. (do not multiply elements unnecessarily; given different models that explain the observations, the simplest one is most likely the truest of them). http://en.wikipedia.org/wiki/Occam%27s_razor http://en.wikipedia.org/wiki/Occam%27s_razor The real puzzle (if it's a puzzle) is why Occam's Razor works so well...