It might be informative to extend this for a case where new strong evidence supports a model with very low a priori probability. This will show that "an extraordinary claim requires extraordinary evidence". I can't think of an example at the moment though.
Thanks for the input. This could be an idea for a new video. Such a case would illustrate the principle you mentioned. I think Jaynes actually did have a couple of examples in that direction.
Any new theory that's been just formed could be described in those terms. It's newly been formed because something like the theory was a' priori considered unlikely but the model is suggested because new evidence supports it in comparison with the established theories.
I've been thinking whether Relativity vs Newton's laws fits in this category. Its tricky deciding what the a priori probability of Relativity is. You could say that any theory that isn't Newton's laws is unlikely, but then there is the action at a distance problem, and the theoretical elegance of Relativity. I suppose most new theories have similar considerations.
Actually, I think relativity is an extreme example, as Einstein's reasoning around the principle of invaraince and how that applies to Maxwell's equations and the Newtonic problems you mentioned could very well be said to have increased the prior probability for relativity to plausible even before data. Normally model-building is more driven by data and less by basic principles, in which case you would need strong evidence in order to form a new model.
Yes, relativity is not a great example. You're Quantum Theory example is more data driven - you assigned an a priori probability of 0.5 but in the absense of any data (i.e. not even any knowledge of the photoelectric effect), Quantum Theory would seem ridiculous. Its necessary to make clear the starting point.
Well I assigned 50% probability before the ten digit precision magnetic moment data, but more to illustrate the impact of that particular data than anything else. Quantum field theory was really well established in advance. But there may be some instances earlier in the developement of quantum theory that may be used as an illustration. The trouble is to get a fix on the measurement precision in the experiments that led to quantum theory.
Maybe I should think about a completely different example. For isntance, a tweaked version of the medical example from clip 3 and 10 with a very rare disease, like smallpox or the bubonic plague (rare now). Or perhaps a murder mystery with some extraordinary claim (the butler didn't do it).
I quite like this example - quantum theory is so weird that it may have been the most difficult revolution in the history of physics. The data and the theory gradually developed over more than 50 years. Was there a turning point where it could no longer be denied ? Perhaps the prediction of the spectral lines of hydrogen by the Schrödinger equation ?
Perhaps, but seem to remember that these spectral lines were predicted by Bohr's semi-classical models too. Still, that was an earlier step in the quantum direction. The problem is still to get hold of the data and the data uncertainties.
Indeed. It could be that I could use the Michelson-Morely experiment (1887) in order to check the then extraordianry claim that either Earth wasn't moving relative to the aether or there's no aether at all. The data seems to be available. That must wait, though, since I haven't covered continuous distributions, yet.
lol what the fuck you guys talking about this shit is boring get a life and or die :D
U83r1337hax 3 years ago
It might be informative to extend this for a case where new strong evidence supports a model with very low a priori probability. This will show that "an extraordinary claim requires extraordinary evidence". I can't think of an example at the moment though.
BrunoTheQuestionable 4 years ago
Thanks for the input. This could be an idea for a new video. Such a case would illustrate the principle you mentioned. I think Jaynes actually did have a couple of examples in that direction.
Any new theory that's been just formed could be described in those terms. It's newly been formed because something like the theory was a' priori considered unlikely but the model is suggested because new evidence supports it in comparison with the established theories.
trondreitan 4 years ago
I've been thinking whether Relativity vs Newton's laws fits in this category. Its tricky deciding what the a priori probability of Relativity is. You could say that any theory that isn't Newton's laws is unlikely, but then there is the action at a distance problem, and the theoretical elegance of Relativity. I suppose most new theories have similar considerations.
BrunoTheQuestionable 4 years ago
Actually, I think relativity is an extreme example, as Einstein's reasoning around the principle of invaraince and how that applies to Maxwell's equations and the Newtonic problems you mentioned could very well be said to have increased the prior probability for relativity to plausible even before data. Normally model-building is more driven by data and less by basic principles, in which case you would need strong evidence in order to form a new model.
trondreitan 4 years ago
Yes, relativity is not a great example. You're Quantum Theory example is more data driven - you assigned an a priori probability of 0.5 but in the absense of any data (i.e. not even any knowledge of the photoelectric effect), Quantum Theory would seem ridiculous. Its necessary to make clear the starting point.
BrunoTheQuestionable 4 years ago
Well I assigned 50% probability before the ten digit precision magnetic moment data, but more to illustrate the impact of that particular data than anything else. Quantum field theory was really well established in advance. But there may be some instances earlier in the developement of quantum theory that may be used as an illustration. The trouble is to get a fix on the measurement precision in the experiments that led to quantum theory.
trondreitan 4 years ago
Maybe I should think about a completely different example. For isntance, a tweaked version of the medical example from clip 3 and 10 with a very rare disease, like smallpox or the bubonic plague (rare now). Or perhaps a murder mystery with some extraordinary claim (the butler didn't do it).
trondreitan 4 years ago
I quite like this example - quantum theory is so weird that it may have been the most difficult revolution in the history of physics. The data and the theory gradually developed over more than 50 years. Was there a turning point where it could no longer be denied ? Perhaps the prediction of the spectral lines of hydrogen by the Schrödinger equation ?
BrunoTheQuestionable 4 years ago
Perhaps, but seem to remember that these spectral lines were predicted by Bohr's semi-classical models too. Still, that was an earlier step in the quantum direction. The problem is still to get hold of the data and the data uncertainties.
trondreitan 4 years ago
Yes indeed. You would think such crucial data would be more widely available.
BrunoTheQuestionable 4 years ago
Indeed. It could be that I could use the Michelson-Morely experiment (1887) in order to check the then extraordianry claim that either Earth wasn't moving relative to the aether or there's no aether at all. The data seems to be available. That must wait, though, since I haven't covered continuous distributions, yet.
trondreitan 4 years ago
Sounds good.
I'm still trying to work out how we can be moving relative to the Cosmic Microwave Background !
BrunoTheQuestionable 4 years ago