With all due respect LJ, I see this argument similar to "the anything is possible" argument. Both may be theoretically possible but don't represent an actual intellectual concept.
I don't understand your argument here at all.
I am saying that while I think it's possible to construct a mathematical model that could output a "correct" verdict in a criminal trial, it would require an astonishingly complex set of inputs in order to replicate human reasoning. Therefore, for practical purposes as of 2015, I believe it's impossible to construct a sufficiently robust mathematical model to do this job (and I suggest that the modelling may have to be so complex as to require the use of things such as AI, fuzzy logic and quantum computing.
Look: you can build a mathematical model that will accurately tell you the real-world probability (and standard deviations etc) of pulling three blue balls in a row out of a sack that originally contained 20 blue balls and 20 red balls. And if you actually conduct that experiment in the real world a whole bunch of times, the real-world results you get will converge towards the results predicted by the model.
But imagine another scenario. If you're a heterosexual male, you probably glance at women sometimes in the street or in a store or on public transport, and you make a pretty instant assessment of whether you find that woman physically attractive. Your input into that process is usually no more than your vision. For the sake of this argument, imagine that in your head you might be grading any particular woman on a scale from 1 to 5, with 1 being not at all attractive to you, and 5 being wow, super attractive to you.
So imagine now that you are trying to build a computer model that could take the same input - a still or moving image of a woman - and accurately model whether or not you would find that woman physically attractive and where on the 1-5 scale you would place her. Stop and think about that. This is something that you can do in your head pretty instantly. But even though you don't realise it, there are a truly astonishing number of highly nuanced (and often abstract) thought processes going on in that split second before you reach your decision. The precise (and minutely differing) position and size of the woman's eyes, nose, mouth etc. The way she wears her hair. What you can discern of her physical body type (which would include complex understanding of how clothes hang on a body, how they reflect the underlying body type, how they can disguise body type). More abstract things still, such as the way the woman "carries herself". A comparison between the woman and other women whom you find attractive (or not). Society's definitions of what constitutes "physical attractiveness" in a woman*
This is an incredibly complex set of operations being carried out inside your mind in a split second. Most of these operations are extremely difficult to translate into a mathematical form, and some of them are mind-blowing difficult to translate into a mathematical form. I therefore propose that it would be nigh-on impossible for anyone today to build a mathematical model that came anywhere even close to accuracy in mirroring/predicting how you would rate the physical attractiveness of any given woman, based on the single input of a still or moving image of that woman.
That's what I'm trying to say here.
* For example, in Europe during the Renaissance, the prevailing cultural norm among the higher social classes was that the most beautiful women had a body type that we would now classify as very overweight or obese (i.e. "Rubenesque"). And that would have obviously impacted heavily on how a given person at that point in history would have rated the physical attractiveness of a given woman that he saw.....