The short and not-as-sarcastic
-as-it-appears answer is, "anything a Turing Machine
(TM) can do." This is because, by definition, a Universal Turing Machine
(UTM) can be encoded with the state
of any other extant Turing Machine.
In my opinion, there are really two interesting approaches as to what a UTM would
do. First, this question could be read to ask what the upper boundary
of a UTM's capabilities is. Alternatively, the question could be read as a commentary on human behaviour
seeking the likely tasks a UTM would be asked to perform by a human user.
As to the upper boundary approach, this is a question best suited for answer by the mathematical philosphers
. One answer is that the limit of a UTM's possible functions is the sum of all possible tasks in the universe. This is possible if the UTM is thought of as a "thing that can do anything any other thing can do," a definition well suited to the kind of raw abstractions
that drive non-philosophers nuts.
What will really bake your noodle
is the idea that the UTM could produce results/functions that are not available to any single Turing Machine. For example, assume that there are only ten possible functions in the entire universe. In this model, any single TM can perform one or more of the ten possible functions. My hypothesis is that a UTM may allow an eleventh function not available to any single TM alone. In other words, the ability to perform all ten functions unlocks the eleventh function.
The presence of the eleventh function raises the question of whether the eleventh function was "there" all along, or was instead created by the UTM as a result of its capability to perform all ten prior functions. If the eleventh function was created by the UTM, could a TM be built to perform only
that function? Would the UTM's ability to perform eleven functions give rise to a twelfth? Thirteenth? Is there some limit to the number of new funtions a UTM could create? If there is a limit, how is that limit determined?
Similarly, if the eleventh function was there all along, how many other functions lie dormant, waiting for the UTM to discover? It appears that regardless of whether the eleventh function was dormant or created, there must be some underlying rules to determing when a new function is discovered. Is that in itself a function for which a TM can be constructed? As you can see, the upper boundary approach to answering what a UTM would do can quickly lead to a number of much more complicated questions. Perhaps that is why the question has captivated the researchers attempting to answer it.
The second approach--"to what purpose would people put the UTM?"--seems less fruitful in generating interesting questions. It can be reduced to the same debate as "how would people use nuclear power
?" or "how would people use a sharp stick
?" People would use the UTM for war
, to make their grocery list, to make their grocery list shorter, and anything and everything people use anything to do.
There. I think I managed to turn a dubious nodeshell
into a meaningfull starting point for a debate
. Questions and comments are, as always, very much appreciated.