4 ms·
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 pe
by 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 agoNo? 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 agoI'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 agoModeling media besides math: digital electronic circuits, analog electronic circuits, legos, quantum mechanical phenomena, gears, computer simulation, wetware, mythology, clocks, BZ reactions, ...
- Groxx 14y agoMany of which are reducible to math. Though I'm not sure what legos have been "unreasonably effective" at predicting.
- Sniffnoy 14y agoSeveral 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 agoBut 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 agoDid 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.
- jblow 14y agoAnd the point is that it's not about modeling! What happens is that we invent crazy math that is not supposed to have applicability, then some years go by and it's like, oh my God, quantum mechanics is somehow exactly all about the operation of unit Hermitian matrices... how crazy is that?? etc. If it were some kind of model that we are able to successively refine, the progress of discovery would look something like a Taylor series, and it would be no surprise that we are eventually able to model phenomena within some tolerance epsilon. But that is not what is happening! Rather, it's that we discover that some large and sophisticated piece of math, for which we had not thought of any particular applicability, turns out to exactly represent specific advanced physical phenomena. This happens over and over.
- 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."