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I love the way that math reveals ultimate truths. We consider math to be some abstract thing that we're applying to help explain reality. Instead, it often ap

by crusso 14y ago

I love the way that math reveals ultimate truths. We consider math to be some abstract thing that we're applying to help explain reality. Instead, it often appears that the abstraction is somehow the True Reality(tm), and our reality is really just an imperfect view of Math(tm). We view math about like we view electromagnetic waves with our eyes. We see effects of it and reflections and complex interactions of only small parts of the em spectrum. It's interesting to wonder if we could develop a way to "see math" in its pure form. (Sorry, Friday afternoon speculation... not currently taking any drugs.)

sheeps 14y ago
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_...
kjhughes 14y ago
Math is but a medium for modeling. Any model can have predictive power. The challenge is in determining which surprising aspects of the model have faithful correspondence to the domain and which are nonessential artifacts of the modeling medium.
- jblow 14y ago
  No. The surprising thing is that the models generate predictions far beyond the domains they were designed for (and far beyond the original knowledge of the people making the models), and that the predictions are so mindbogglingly accurate that there seems to be Something Else going on. See the Unreasonable Effectiveness of Mathematics link below.
  - kjhughes 14y ago
    No? Surprising thing: Math's not the only modeling medium that can be Unreasonably Effective. Unreasonable Effectiveness of Mathematics: Know; saw; upvoted apropos reference already.
    - Sniffnoy 14y ago
      I'm confused by your statement that "Math's not the only modeling medium that can be Unreasonably Effective", because it's not clear to me what the notion of a "non-mathematical model" means. (That is to say, it's not clear to me that you're even correct in the weaker assertion that "Math's not the only modeling medium.") Can you explain?
      - kjhughes 14y ago
        Modeling media besides math: digital electronic circuits, analog electronic circuits, legos, quantum mechanical phenomena, gears, computer simulation, wetware, mythology, clocks, BZ reactions, ...
        Groxx 14y ago
        Many of which are reducible to math. Though I'm not sure what legos have been "unreasonably effective" at predicting.
        Sniffnoy 14y ago
        Several of those are, in fact, math. (In particular, computer simulation.) The others are mostly phsyical models, which I must admit, I had not thought of. So that yields two; mathematical models (that is to say, formal models) and physical models (that is to say, real-world models). (The line can perhaps be a bit blurry in the case of e.g. digital electronic circuits, but, well, I'm not claiming there's a sharp line.) That leaves "mythology", which I'm not convinced is a proper modeling medium at all.
        lutusp 14y ago
        But those are examples of modeling math, with a superficial layer of physical material. Another way to say it is the degree that these are useful models, is the same degree to which they reflect mathematics. With the possible exception of mythology.
    - jblow 14y ago
      Did you read the essay? Actually, both of them? The reason mathematics is considered Unreasonably Effective is because we have never seen anything with similar effectiveness. Ever.
  - lutusp 14y ago
    > The surprising thing is that the models generate predictions far beyond the domains they were designed for (and far beyond the original knowledge of the people making the models), and that the predictions are so mindbogglingly accurate that there seems to be Something Else going on. Yes -- and I can't resist citing antimatter as a perfect example. Dirac's Equation had two symmetrical results (sort of like a quadratic), and Dirac wasn't sure about the physical meaning of one of them. After antimatter was detected, Dirac was asked why he didn't simply predict antimatter himself based on a literal interpretation of his equation's implications. He replied, "Pure cowardice."
    - im3w1l 14y ago
      But in the end antimatter didn't have negative energy anyway?
      - lutusp 14y ago
        Yes, true, the term "antimatter" has always been somewhat of a misnomer. "Antimatter" differs from matter in a number of ways, but there's only one kind of gravitational mass-energy.
Variance 14y ago
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...

by crusso 14y ago

sheeps 14y ago

http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_...

kjhughes 14y ago

Math is but a medium for modeling. Any model can have predictive power. The challenge is in determining which surprising aspects of the model have faithful correspondence to the domain and which are nonessential artifacts of the modeling medium.

jblow 14y ago
No. The surprising thing is that the models generate predictions far beyond the domains they were designed for (and far beyond the original knowledge of the people making the models), and that the predictions are so mindbogglingly accurate that there seems to be Something Else going on. See the Unreasonable Effectiveness of Mathematics link below.
- kjhughes 14y ago
  No? Surprising thing: Math's not the only modeling medium that can be Unreasonably Effective. Unreasonable Effectiveness of Mathematics: Know; saw; upvoted apropos reference already.
  - Sniffnoy 14y ago
    I'm confused by your statement that "Math's not the only modeling medium that can be Unreasonably Effective", because it's not clear to me what the notion of a "non-mathematical model" means. (That is to say, it's not clear to me that you're even correct in the weaker assertion that "Math's not the only modeling medium.") Can you explain?
    - kjhughes 14y ago
      Modeling media besides math: digital electronic circuits, analog electronic circuits, legos, quantum mechanical phenomena, gears, computer simulation, wetware, mythology, clocks, BZ reactions, ...
      - Groxx 14y ago
        Many of which are reducible to math. Though I'm not sure what legos have been "unreasonably effective" at predicting.
      - Sniffnoy 14y ago
        Several of those are, in fact, math. (In particular, computer simulation.) The others are mostly phsyical models, which I must admit, I had not thought of. So that yields two; mathematical models (that is to say, formal models) and physical models (that is to say, real-world models). (The line can perhaps be a bit blurry in the case of e.g. digital electronic circuits, but, well, I'm not claiming there's a sharp line.) That leaves "mythology", which I'm not convinced is a proper modeling medium at all.
      - lutusp 14y ago
        But those are examples of modeling math, with a superficial layer of physical material. Another way to say it is the degree that these are useful models, is the same degree to which they reflect mathematics. With the possible exception of mythology.
  - jblow 14y ago
    Did you read the essay? Actually, both of them? The reason mathematics is considered Unreasonably Effective is because we have never seen anything with similar effectiveness. Ever.
- lutusp 14y ago
  > The surprising thing is that the models generate predictions far beyond the domains they were designed for (and far beyond the original knowledge of the people making the models), and that the predictions are so mindbogglingly accurate that there seems to be Something Else going on. Yes -- and I can't resist citing antimatter as a perfect example. Dirac's Equation had two symmetrical results (sort of like a quadratic), and Dirac wasn't sure about the physical meaning of one of them. After antimatter was detected, Dirac was asked why he didn't simply predict antimatter himself based on a literal interpretation of his equation's implications. He replied, "Pure cowardice."
  - im3w1l 14y ago
    But in the end antimatter didn't have negative energy anyway?
    - lutusp 14y ago
      Yes, true, the term "antimatter" has always been somewhat of a misnomer. "Antimatter" differs from matter in a number of ways, but there's only one kind of gravitational mass-energy.

Variance 14y ago

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...