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Scientists have tried over at least the past few hundred years (depending on your definitions) to build, from scratch, a perspective on the world which is as fr

Scientists have tried over at least the past few hundred years (depending on your definitions) to build, from scratch, a perspective on the world which is as free from human bias as possible. At the moment, the jewel in the crown is quantum physics: an inherently statistical theory, so detached from human biases and assumptions that many smart people have struggled to understand or accept it, despite its incredible predictive power. At the heart of the whole process is statistical inference: generalising the results of experiments or observations to the Universe as a whole. A "statistical crisis in science" would be terrible news. We may have been standing on the shoulders of the misinformed, rather than giants. Our "achievements", from particle accelerators to nukes and moon rockets, could have been flukes; if the underlying statistical approach of science was flawed, the predicted behaviour and safety margins of these devices could have been way off. We may be routinely bringing the world to the edge of catastrophe, if we don't understand the consequences of our actions. Oh wait, it seems like some "political scientists" have noticed that their results tend to be influenced by external factors. I hope they realise the irony in their choice of examples: > As a hypothetical example, suppose a researcher is interested in how Democrats and Republicans perform differently in a short mathematics test when it is expressed in two different contexts, involving either healthcare or the military. The article criticises scientists' ability to navigate the statistical minefield of biases, probability estimates, modelling assumptions, etc. in a world of external, political factors like competitive funding, positive publication bias, etc. and they choose an example of measuring how political factors affect people's math skills! To me, that seems the sociological equivalent of trying to measure the thermal expansion of a ruler by reading its markings. What do you know, it's still 30cm!

semi-extrinsic 12y ago
Saying that quantum mechanics is an inherently statistical theory is a blatant misrepresentation. Precisely the point that makes QM so weird is that it is not caused by statistics. In a (properly set up) double slit experiment, a single electron is simultaneously travelling through both slits and causing an interference pattern.
- ChrisLomont 12y ago
  >Saying that quantum mechanics is an inherently statistical theory is a blatant misrepresentation. Every axiomatic QM formulation (for example, [0]) I have ever seen has an axiom a statistical statement, usually about observables. Can you provide a set of axioms reproducing QM without such an axiom? If not, then it's inherently a statistical theory. In your example, where a single electron lands is completely governed by a probability distribution that is determined by the setup of the test. [0] http://en.wikipedia.org/wiki/Dirac%E2%80%93von_Neumann_axioms http://en.wikipedia.org/wiki/Dirac%E2%80%93von_Neumann_axiom...
- gsteinb88 12y ago
  Actually, that's an interpretation of quantum mechanics, not quantum mechanics itself. QM itself is in fact a statistical theory: the result of a calculation is a probability distribution of possible outcomes (even in the cases where the outcome might be deterministic). Taking your example of the double slit experiment, the calculation yields, in the case of two slits, a probability distribution with peaks and nulls corresponding to interference fringes. Close one slit and you get a different distribution without said interference. What you describe is an interpretation of those probability distributions, and there are many conflicting views on the interpretation of QM (though, to date, these interpretations have not led to conflicting numerical results in the calculations). Wiki has a reasonable list of the extant interpretations [1] but I'll also draw your attention to an interpretation that is inherently statistical: Quantum Bayesianism (Nature has a nice overview [2]). To be crude, the idea is to look at QM from the point of view of the experimentalist: what information does she have available to her? In the case of the double slit experiment, it's impossible to say from a measurement of the electron at the screen which slit it passed through, so you cannot condition the measurement on either one individually, but both together. QuBism is only one of the many interpretations of QM; others include the many-worlds interpretation (only deterministic in the crudest sense; any collapse of a wavefunction is thought to cause as many divergent universes as there are possible outcomes, but the one the experimentalist observes is still a statistical result), the copenhagen interpretation (also statistical, while the wavefunction is thought to represent the "true" state of a particle, its evolution under measurement is still non-deterministic), etc. Finally, in case anyone is interested in more in-depth reading, the Stanford Encyclopedia of Philosophy has some fantastic readings on these, and related, topics. Articles worth checking out are that on measurement in QM [3] and those on the various interpretations (e.g. [4-6]). [1] http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics http://en.wikipedia.org/wiki/Interpretations_of_quantum_mech... [2] http://www.nature.com/news/physics-qbism-puts-the-scientist-back-into-science-1.14912 http://www.nature.com/news/physics-qbism-puts-the-scientist-... [3] http://plato.stanford.edu/entries/qt-measurement/ http://plato.stanford.edu/entries/qt-measurement/ [4] http://plato.stanford.edu/entries/qm-copenhagen/ http://plato.stanford.edu/entries/qm-copenhagen/ [5] http://plato.stanford.edu/entries/qm-manyworlds/ http://plato.stanford.edu/entries/qm-manyworlds/ [6] http://plato.stanford.edu/entries/qm-modal/ http://plato.stanford.edu/entries/qm-modal/

semi-extrinsic 12y ago

Saying that quantum mechanics is an inherently statistical theory is a blatant misrepresentation. Precisely the point that makes QM so weird is that it is not caused by statistics. In a (properly set up) double slit experiment, a single electron is simultaneously travelling through both slits and causing an interference pattern.

ChrisLomont 12y ago
>Saying that quantum mechanics is an inherently statistical theory is a blatant misrepresentation. Every axiomatic QM formulation (for example, [0]) I have ever seen has an axiom a statistical statement, usually about observables. Can you provide a set of axioms reproducing QM without such an axiom? If not, then it's inherently a statistical theory. In your example, where a single electron lands is completely governed by a probability distribution that is determined by the setup of the test. [0] http://en.wikipedia.org/wiki/Dirac%E2%80%93von_Neumann_axioms http://en.wikipedia.org/wiki/Dirac%E2%80%93von_Neumann_axiom...
gsteinb88 12y ago
Actually, that's an interpretation of quantum mechanics, not quantum mechanics itself. QM itself is in fact a statistical theory: the result of a calculation is a probability distribution of possible outcomes (even in the cases where the outcome might be deterministic). Taking your example of the double slit experiment, the calculation yields, in the case of two slits, a probability distribution with peaks and nulls corresponding to interference fringes. Close one slit and you get a different distribution without said interference. What you describe is an interpretation of those probability distributions, and there are many conflicting views on the interpretation of QM (though, to date, these interpretations have not led to conflicting numerical results in the calculations). Wiki has a reasonable list of the extant interpretations [1] but I'll also draw your attention to an interpretation that is inherently statistical: Quantum Bayesianism (Nature has a nice overview [2]). To be crude, the idea is to look at QM from the point of view of the experimentalist: what information does she have available to her? In the case of the double slit experiment, it's impossible to say from a measurement of the electron at the screen which slit it passed through, so you cannot condition the measurement on either one individually, but both together. QuBism is only one of the many interpretations of QM; others include the many-worlds interpretation (only deterministic in the crudest sense; any collapse of a wavefunction is thought to cause as many divergent universes as there are possible outcomes, but the one the experimentalist observes is still a statistical result), the copenhagen interpretation (also statistical, while the wavefunction is thought to represent the "true" state of a particle, its evolution under measurement is still non-deterministic), etc. Finally, in case anyone is interested in more in-depth reading, the Stanford Encyclopedia of Philosophy has some fantastic readings on these, and related, topics. Articles worth checking out are that on measurement in QM [3] and those on the various interpretations (e.g. [4-6]). [1] http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics http://en.wikipedia.org/wiki/Interpretations_of_quantum_mech... [2] http://www.nature.com/news/physics-qbism-puts-the-scientist-back-into-science-1.14912 http://www.nature.com/news/physics-qbism-puts-the-scientist-... [3] http://plato.stanford.edu/entries/qt-measurement/ http://plato.stanford.edu/entries/qt-measurement/ [4] http://plato.stanford.edu/entries/qm-copenhagen/ http://plato.stanford.edu/entries/qm-copenhagen/ [5] http://plato.stanford.edu/entries/qm-manyworlds/ http://plato.stanford.edu/entries/qm-manyworlds/ [6] http://plato.stanford.edu/entries/qm-modal/ http://plato.stanford.edu/entries/qm-modal/