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OK, then one more quick final statement | 758 comments | Create New Account
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OK, then one more quick final statement
Authored by: Anonymous on Saturday, October 20 2012 @ 10:48 AM EDT

I think your whole hypothesis is built on a house of cards because it relies on a false assertion of the theory of computability and unsolvability.

You state:

Mathematicians have discovered a special category of algorithms called universal algorithms. Several universal algorithms are known. Each of these algorithms can compute every function which is computable provide we give them a corresponding program as input. In effect, any universal algorithm can emulate the behavior of every other algorithm. This is why we call them universal. This is like a glorified Swiss army knife but for computing. A single algorithm suffices to serve the purposes of all of them. [Footnote reference omitted]

However, Martin Davis, in the book Computability and Unsolvability, Dover Publications, Inc., New York, 1982, states, right on the first page (vii) of the Preface to the First Edition:

... The existence of universal Turing machines, another result of the theory, confirms the belief of those working with digital computers that it is possible to construct a single "all-purpose" digital computer on which can be programmed (subject of course to the limitations of time and memory capacity) any problem that could be programmed for any conceivable deterministic digital computer. This assertion is sometimes heard in the strengthened form: anything that can be made completely precise can be programmed for an all-purpose digital computer. However, in this form, the assertion is false.

So you have made an unwarranted logical leap from "Several universal algorithms are known. Each of these algorithms can compute every function which is computable provided we give them a corresponding program as input" [emphasis added] to "In effect, any universal algorithm can emulate the behavior of every other algorithm."

Furthermore, in an earlier article referenced by you in the lead story, you state:

Let's illustrate the importance of computation theory with one of the legal issues computation theory will help resolve. Consider the following list of statements.

  • All software is data.
  • All software is discovered and not invented.
  • All software is abstract.
  • All software is mathematics.
  • However, Davis, at page xviii, states:

    There is no algorithm that enables one to decide whether an alleged algorithm for computing the values of a function whose domain of definition is the set of positive integers, and all of whose values are positive integers, is indeed such an algorithm. [italics in original]

    Yet every "algorithm" performed by a digital computer is, in fact, a function having as its domain of definition the set of positive integers, and having all of its values as positive integers. After all, software is based on logic and gates, at least when it is executed on a digital computer (as opposed to an analog computer). But you can't tell me that the derivation of software that actually works for a particular useful purpose (e.g., that usefully provides answers to a real-world problem) doesn't involve invention, and your computability theory doesn't tell me how to write the algorithm. You can't even prove that such an algorithm exists, and once you allege to have such an algorithm, you can't even prove that it is an algorithm.

    In a way, the whole argument is analogous to shoveling dirt. The first shovel is probably worthy of a patent, because someone had to invent it at a time when there was no prior art and it wasn't obvious. That time has, of course, long passed. But we don't remove all possible ways of using the shovel from the realm of patentability just because the shovel is prior art. For example, a method of frying an egg on a shovel may be useful. If that method is new and non-obvious, it should be worthy of patent protection. Or a method of growing a plant in dirt held by a shove may be useful, novel, and non-obvious. Or a method of temporarily attaching a computer to a shovel may be useful, novel, and non-obvious (for example, to dispose of the computer when it is obsolete a week after you buy it).

    Or perhaps a computer-controlled method of using a shovel to remove dirt from a trench without having the trench collapse on workers inside the trench might be useful, novel, and non-obvious, remembering, of course, that the movement of the shovel has to be stable and not subject to growing oscillations.

    I'm not saying that any or all of these things are patentable -- just that they probably ought to pass the relatively low bar of being subject matter eligible for patenting. And at least to the extent that novel and non-obvious engineering judgements have to be made to get software to work, and further to the extent that the strong assertion concerning the existence of universal Turing machines is false, software should be patentable subject matter.

    Your response is welcome and would be appreciated.

    [ Reply to This | Parent | # ]

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