[The Mozart Problem] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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The Mozart Problem
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Posted by: Jason Cawley
Popper imagined a deterministic theory sufficient to predict all the actions of a genuis of the caliber of Mozart, composing a symphony. He thought it so implausible he considered it evidence against determinism. Kurzweil wants Chopin preludes instead. Before he has them, he remains unimpressed by computational universality. The practical problems and potential capabilities of algorithmic music aside, there is a philosophical issue here, which I think has been misdiagnosed.
Those involved in the argument seem to think that it turns on questions of prior metaphysical principle (in the case of Popper) or of some missing additional trick needed to create strong AI. I'll stick to Popper for now. My idea is to grant all the positions of NKS that seem to run against Popper's attitude, and then to show that his judgment remains sound. Just not for the reasons he thought.
So we stipulate that there is a complete deterministic theory of humans (brains, or more if more turns out to matter), taking human specifications and initial states, and returning as output all the controls needed to drive a human emulator. I imagine it as something like a Mathematica function, parallel to CellularAutomaton.
Its input format is HumanSim[human, initialstate, lengthoftime]. Its output can be put in a parameterized function of the whole behavior expression depending upon it. The first argument is a bare number that enumerates possible lists of rules, each sufficient to specify the entire range of behavior of one human being. The initial state may, without loss of generality, include interaction information (FoldList fashion) to specify the external environment, or if there is anything pseudorandom in the rules involved, a random seed. The external specification might be fantastically difficult, but we assume we can encode anything that actually matters for the evolution of any human system. Notice however that it must be encoded outward from its effects on human rule tables, and you would have to deduce anything it implies about externals. For simplicity's sake, imagine the function can return data from some person's life as movies to a viewer, or its raw instructions to behavior subsystems can be queried in machine readable form. If the third argument is left to run from some parameter values for the others, you get the forward deterministic movie of that person's life.
Notice, we have therefore assumed far more than strong AI. We have a complete enumeration of possible humans and possible trajectories for human behaviors. We can scan the inputs programmatically or by any other method we can specify. We can query the outputs. We can tweak only the exteral environment and see what it does to the time-forward behavior, and so ask questions of our virtual humans, if we find that useful or efficient.
All of this is simply stipulated: the deterministic simple programs view is true by mere hypothesis and we have already succeeded in constructing this function. Now our mission is to find Wolfgang Amadeus Mozart and ask him about his next symphony. Cherchez la femme! My claim is that we have not solved the problem. That we have not solved the problem "in principle". That we have at best removed a few distracting issues subject to frequent philosophical contention, but that the real problem remains before us.
Reality is measure epsilon in possibility space.
What resources are allowed us to address the problem? I do not grant one countable infinity. I do not grant infinite running time on a slow Turing machine. I give a lot, but strictly finite resources. You have the efforts of 1 million human beings - a scale set by the largest corporations. You have computers 1000 times faster than any that exist today, as many as the people. And you have 1000 years. And you have all the Mathematica's you want running the above function, trying initials or searching through outputs. Your people can interview virtual humans to ascertain whether they are Wolfgang Amadeus Mozart. You can set one computer simulating an interviewer asking others whether they are. You can specify any effective procedures or programs you please, to search within the space of all possible humans in all possible environments from all possible prior states.
And I claim you can't begin to find him. You might purely theoretically find a man of the same name and circumstances, creating wonderfully involved pastries in his bakery. You might find a great classical composer, who sounds like Chopin. You will certainly find scads of people who never existed and are nothing like him. But the mission is to find the real Wolfgang Amadeus Mozart, with his actual experiences and memories, and ask him about his next symphony. The target is not a point - a range of initials were part of that real man's life, and minor changes to his environment would not change who he was. But the target set is modest, and the space is beyond astronomical.
Reality is measure epsilon in possibility space.
Solving strong AI is easy compared to this problem - so I claim. Writing algorithmic music software so good it makes Mozart quality symphonies is easy compared to this problem. Writing the HumanSim function may be incredibly difficult, but is child's play compared to using the thing once it is written, to solve a problem this hard. So I claim. Anyone who thinks differently is welcome to give a solution within the stipulated resources, with the above assumptions.
Suppose we start at the other end. Having realized that our aiming at all possible humans has dramatically expanded the search space, beyond a level we can deal with for the problem at hand, we might instead hope to arrive at the tiny outcome box by getting the right initial much farther back. We therefore further stipulate that we have a deterministic, computational, fundamental theory of physics, along the lines suggested by NKS. We have found the rule of the universe (we do not need to consider 10^800 string theories), and it starts from a simple initial condition, so we do not have to search over an enourmous space of those. If we run it forward long enough, the truth and determinism of this rule (given by hypothesis) must eventuate in the historical Wolfgang Amadeus Mozart, in all his glory and all his mortality.
But we can't run it forward far enough. We can't make it to the epoch when the universe becomes transparent to light. It is exceedingly doubtful we can run it for a day of real time when the universe is at its smallest. OK, but perhaps we can shortcut portions of its evolution. After all, at a coarser level it has simpler descriptions.
But as soon as you go up to those instead of the full underlying theory, you will throw out detailed configuration information, and your transitions may become multivalued. If this were not a problem you would not have needed the underlying generator in the first place, because you would have had an exhaustive deterministic description at the higher level. We know by the time we reach the overlying emergent level of QM, we have already gone multivalued. Some of the differing details necessary for single valued deterministic evolution have been lumped into the same bins, by then.
If you throw out details of the configuration, you have left the path forward from the posited whole universe simple initial. There is no longer one world-path to follow, but a branching possibility space. If you keep the details because they matter, you must calculate every detail, and you cannot. If you discard them even though they can matter, you must scan a space of possibilities.
Either way, the historical uniqueness of definite individuals remains. It is not accessible horizontally from an origin because the entire universe cannot be calculated. It is not accessible vertically because entire possibility spaces, for anything complex enough, cannot be calculated. Because all complex systems require real computational work, and in general we cannot shortcut that work, the massive calculation that is history adds something fundamental that we cannot replace formally.
What we might actually do instead is constrain the search with empirical data, slicing off great swaths from abstract possibility space with a blade built from observation, over and over again. That way we exploit prior calculation that history has already performed for us. For a space as large as HumanSim, however, that would still be almost arbitrarily hard. Or we might write a function less general than HumanSim - say SymphonyMaker - that does not try to find Wolfgang Amadeus Mozart, but merely to make pleasant music.
Dreams of the power of formalism need to be tempered by consulting external reality, because reality is measure epsilon in possibility space. There is information in reality that is - pragmatically but strictly - not recoverable by formalism. Even if there are purely formal underlying causes for all of reality, even if they are simple and deterministic, and even if we can in principle find them.
Formalism is often much more useful practically, when it aims at possibility spaces we can actually span.
Posted by: Lawrence J. Thaden
How will the HumanSim model account for the strictly human phenomenon: insight?
Posted by: Enexseenge
Simple...
Incentive..
No need for insight if you will only exist for a moment...
( i mean to say here that we exist for more then a moment, so we function with incentives which are in relation to the inevitable circumstances which arise due to our "lag" here. By liberty of our involvement with the environment, we see the need to use incentives to structure our functionality. We do this mainly because they correlate well with innate properties of our bodies, and incentives are easy to hold within a structure that is maintained in retrospect)
And besides, that insight is only expressed within a context which is very available to parts of the individual which will assemble an interpretation of an event and compound it into something that would be considered "insight". Which makes insight more like "guessing" don’t you think?
Functionality is in connection with an agenda which is held in retrospect, and only by altering the retro-state can functionally be altered, how else would the ridged aspects of structure be altered, for without that retro state there would be no “structure” to be altered.. any other way is too fast to accommodate the speed of this construct. This works for even inanimate things like inorganic structures, then again when you expand it to that scope the word “agenda” becomes quite more then an “agenda” but more so an innate property of a certain configuration..
Is that not what a human agenda is? A innate property of a certain configuration?
“strictly human phenomena”
Come on, you are just playing with your self here… Information is physical! Information is what is playing here, not “humans” phenomena “strictly for them”…
Posted by: Iconasostacles
As I understand it, the potential of wolfram-style systems to model reality offers a vast, functional leap forward constrained within the necessary limitation of all computational systems. The mere fact that a computation occurs puts it ever so slightly out of phase with any other computation that it might model. There will always be this slight disparity that is largely synonymous with the threshold of computational equivalence.
Like the 'velocity of light' or 'a first moment' or 'knowability' there is a faint ceiling which is co-terminal with the imagined structure of Reality as we know it.
This limit, this faint mismatch, is articulated in the different between a perfect simulation of Mozart and the "real" Mozart. Computations cannot function without some slight remainder just as it was historically asserted that all forms arise within the unknowable "tao." This unknowable is not merely the general backdrop of all forms and process but the specific differential between the structural possibilities of an entity and the 'actualness' of that entity.
We are all phenomenologically aware of the slight differential between "everything that makes us up" and "our essence." The latter quality, which matches or exceeds our complexity of comprehension, seems to fuzz out, vanish, dissipate into meaninglessness. It is almost not there -- but somehow it is there. All of these qualifications amount to complementary descriptoins of its nature.
So, if I am following Jason, I would affirm the "in principle" impossibiltiy of locating the real Mozart within pattern space AND simultaneously affirm the inevitable (even imminent) capacity of pattern-mining to produce novel Mozart-like symphonies, biological templates, life-strategies, etc.
Posted by: AdamL
I've been reading this one over and over every now and then since it was posted. It's not easy stuff. I think Jason's point in everyday terms is that the validity of a model should not depend on it's thoroughness or completeness in ability to model all that exists. Reality is smaller than possibility space, and models are smaller than reality. The stuff Davies writes about regarding cosmic programs is applicable, if I understand Jason correctly. That a model is an accurate model of reality does not depend on it being the same size or having the same breadth of reality. To use an analogy, a bioshphere in a lab can never have the capacity to reproduce the scope of the biological events on earth, but will still be an accurate model of those biological events on earth. If Popper is saying that a model that cannot reproduce what perhaps is the height of the universe's own production, the consequence may be that there cannot be a model of the universe. If instead one assumes that a model is meant to imitate but not fully reproduce it's subject - ie., a model is of process and not evaluated on practical production possibilities. Those practicalities may be or not be totally independantly of the model. We could in fact have a perfect model of the universe, but by the fact that it is a model it is not the universe. The universe may in fact be able to reproduce itself but to hold that as a precondition to a valid model (and to require the model to be of the same scope as it's parent) would be an error. The one is a case of a limitation of inputs, rather than a deficiency in the model.
Looking to get some feedback on whether I am getting this or not.
Posted by: Jason Wesley Ellis
I like the image of your observational blade slicing off impossible, because unobserved, possibility spaces. Personally I am amazed that this universe exists,,,, maybe there are others, universes where your blade is not quite as sharp.
possibility space is the important thing in this discussion. the problem is "what is possible?"
maybe there is a universe out there whose only function is to record, with redundancy, our universe. Maybe our universe does this on it's own, without redundancy,,,,
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