about maths: strictly speaking, off topic, but justified.
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From: tonyb on 16 Mar 2010 04:18 > > >> Now put yourself back in the early 20th century. A certain > > >> hypothesis is found in your hypothesis space. It is the idea > > >> that matter -- yes hard and palpable matter -- possesses > > >> wave-like characteristics. What probability do you assign > > >> to this hypothesis? Well, after you stop laughing, you > > >> rate it about P = 10^-104, toss it aside, and then keep > > >> dipping into your "space" for something else. > > > > I disagree. > > > I think that at that time many experiments were exhibiting wave > > > phenomena, all with a very high level degree of model-data > > > probability. So high in fact, that we had to modify some cherished > > > hypothesis. > > > (or put the other way round, classical models were producing very low > > > probabilities for these datasets) > > > My conjecture is that if we had been more formal about this process, > > > we would have moved to the wave hypothesis *sooner* > > > You're armchair quarterbacking. > > I'm not entirely sure what you mean by that (I'm from the UK) > My point is simply, if you had done the 2 slits/particle interference > experiment, and then measured the probability of each model, given the > data, > even with an extremely large prior for classical physics, the data > would have still overridden that prior. > Imagine modelling an interference pattern with a mixture of two > Gaussian distributions - the maximum likelihood model will be really > really bad - to be equally speculative P = 10^-204 > Very quickly the data would have won the argument - certainly much > quicker than a group of conservative old farts who didn't want to > violate Newton's majesty Another case in point. Part of Einstein's genius was to genuinely accept the truth of experimental data. If we'd used this approach, I doubt we would have repeated the M-M experiment so many times before letting go of the aether What I'm proposing is nothing more than an automated honesty tool. TonyB
From: jmfbahciv on 16 Mar 2010 09:14 rabid_fan wrote: > On Mon, 15 Mar 2010 07:00:41 -0500, jmfbahciv wrote: > >> If so, what are the verbs? >> > > Not verbs, but predicates. > I'll ask the damn question again...if you claim that math is a language, what are the verbs? /BAH
From: tonyb on 16 Mar 2010 09:03 On 15 Mar, 21:16, rabid_fan <r...(a)righthere.net> wrote: > On Mon, 15 Mar 2010 10:28:40 -0700, tonyb wrote: > > Couldn't we formalize this process? > > > Given a finite set of resources to investigate a massive hypothesis > > space, how would I attempt to decide which experiments to do? > > Easy! We can put a hundred monkeys in front of a hundred > keyboards and, give or take 10^130 years, amid the massive > gibberish will arise a massive hypothesis space. > > Now put yourself back in the early 20th century. A certain > hypothesis is found in your hypothesis space. It is the idea > that matter -- yes hard and palpable matter -- possesses > wave-like characteristics. What probability do you assign > to this hypothesis? Well, after you stop laughing, you > rate it about P = 10^-104, toss it aside, and then keep > dipping into your "space" for something else. I've just realized - you've missed (ignored?) the point once again! These are *not* subjective priors (i.e. not guessed by people), they are objective probabilities taken from previous experiments relating to the supporting hypothesis After this experiment is done, its data+model will itself have create another objective prior to add to our belief network.
From: rabid_fan on 16 Mar 2010 10:18 On Tue, 16 Mar 2010 08:14:01 -0500, jmfbahciv wrote: > > I'll ask the damn question again...if you claim that math is a language, > what are the verbs? > I will answer the damn question again: not verbs, but predicates. Another, more general, name for mathematics, is, guess what, logic: http://www.cs.rochester.edu/~nelson/courses/csc_173/predlogic/
From: rabid_fan on 16 Mar 2010 10:49
On Tue, 16 Mar 2010 01:18:09 -0700, tonyb wrote: >> Very quickly the data would have won the >> argument - certainly much quicker than a group of conservative old >> farts who didn't want to violate Newton's majesty The essence of the problem is human bias. You are proposing a solution involving an automated system. A more realistic approach, and one that would generate far more fruitful and lasting consequences, is to provide the means, through training and education, for all humans, and especially scientists, to transcend their innate stubbornness and bias. Every scientist must develop insight into the foibles of the human mind and must be made to understand how easily human judgment can be mislead and beguiled. Many business organizations rely on formalized decision methods to select employees. In most cases, these methods are completely ludicrous because they usually involve some totally unsophisticated and ignorant human resource subordinate blindly applying the rules. Ideally, only a person thoroughly experienced in human complexity and diversity should be entrusted with personnel decisions. Automated methods cannot compensate for human stupidity. If our society cannot properly edify its citizens and its professionals, then it simply does not deserve the quality and progress that it may crave. |