From: scottlgu@gmail.com   
      
   Abstraction   
   Could computers understand and represent irrational numbers without   
   knowing the exact values, which may be necessary to build sciences ?   
   Humans can. How about uncountable set ? Are there somethings in human   
   intelligence which exceed the power of Turing Machine? The measurement   
   of generic intelligence is critical to further development of   
   artificial intelligence (AI). However, there are various bottlenecks   
   and issues in the existing methods: Turing Test and its variants,   
   which cannot really measure intrinsic intelligence capabilities. Based   
   on the studies of knowledge development, several essential design   
   goals for intelligence measurement are identified to address these   
   issues. A new method: Gu Test is proposed, to meet some of these   
   design goals, distinguish strong AI and regular machines, and provide   
   insights for future directions of AI. Further improvement could be   
   done in future.   
      
      
   1. The Measurement of Generic Intelligence   
      
   Could computers understand the concepts of irrational numbers and   
   represent these numbers and the theories based on these numbers   
   without knowing their exact values ? Such concepts and theories are   
   necessary to build sciences and advanced human intelligence. How about   
   uncountable set, etc. ? Such intrinsic intelligence capabilities are   
   important milestones for machine intelligence levels.   
      
   The measurement of generic intelligence capabilities is critical to   
   AI, to estimate the current status and look for future improvement,   
   etc. However, the existing measuring methods, such as Turing Test and   
   its variants, are mainly behavior-based, knowledge-based, or task-   
   based, etc. There are various bottlenecks and issues in these   
   solutions. They cannot really measure intrinsic intelligence   
   capabilities.   
      
   People could design algorithms on Turing Machine or its improved   
   models. These are mathematics models limited by Goedel's incompleteness   
   theorems. Even worse, there are still problems to implement these   
   models physically.   
      
   Current computers use rational numbers to approximate irrational   
   numbers. Due to the sensitivity to intial conditions in nonlinearity,   
   there are problems in such approximations. How do human intelligence   
   works in real physical situations ?   
      
   Are there somethings in human intelligence which exceed the power of   
   Turing Machine and its current improvements? A good measurement should   
   point to possible bridges between mathematics models, physical   
   implementations, and human intelligence. Gu Test, is a new measurement   
   to address these issues, distinguish strong AI from regular machines,   
   and provide insights for future directions, etc.   
      
   The following sections will discuss Turing Test and its variants with   
   their bottlenecks and issues first. Several design goals are   
   identified to address these issues and better measure generic   
   intelligence. Gu Test, is proposed to achieve these design goals. Some   
   directions for future work are discussed.   
      
      
   2. Turing Test and Chinese Room concern   
      
   Alan Turing described an imitation game in his paper Computing   
   Machinery and Intelligence [1], which tests whether a human could   
   distinguish a computer from another human only via communication   
   without seeing each other.   
      
   It is a black box test, purely based on behavior. Computers could pass   
   this kind of tests by imitating humans.   
      
   So John Seale raised a Chinese Room issue [2], i.e., computers could   
   pass this test by symbolic processing without really understanding the   
   meanings of these symbols.   
      
   More important, there are bottlenecks of communication or storage, in   
   expression or in capacity, and the issues of blackbox test and   
   understanding, etc., as described below, which make the current ways   
   of symbolic processing inadequate as generic intelligence.   
      
   Turing Test uses interrogation to test, so it only can test those   
   human characteristics which already be understood well by humans and   
   can be expressed in communication. Humans still have very limited   
   understanding of life, psychology, and intelligence. Some people could   
   manage to understand each others by face to face, analogy, metaphor,   
   implying, suggestion, etc.,  on things which cannot be purely done in   
   symbolic processing. Some people may not. Humans do not know why these   
   methods work or do not work yet. So these intrinsic intelligence   
   abilities not understood well yet could not be expressed or tested via   
   interrogation behind veils. Turing Test does not work in these cases.   
   This is the bottleneck in expression.   
      
   Even if the bottleneck in expression could be resolved in some   
   problems, the capacity in communication or storage could still be an   
   issue if purely relying on symbolic processing: say, how to represent   
   the value of an irrational number, and how many irrational numbers   
   they could represent, finite or infinite, countable or uncountable,   
   etc. ? The current von Neumann architectures only have finite memory   
   units. Turing Machine has infinite but countable memory units. Could   
   Turing Machine be enhanced with uncountable memory units ?   
      
   Since the methods of face to face, analogy, metaphor, implying,   
   suggestion, etc., does not work in Turing Test or other blackbox   
   tests, is it still possible for computers to be programmed to   
   understand things like irrational numbers or uncountable sets ? There   
   is a blackbox test issue to verify this.   
      
   Assume infinite but countable storage as in Turing Machine, or   
   interrogators with infinite testing time, and a computer is able to   
   compute the value of an irrational number a digital by a digital. In   
   blackbox test, how could these interrogators know the computer is only   
   going to display a huge rational number with the same digitals as a   
   portion of an irrational number, or it is going to display a true   
   irrational number? This issue could be resolved by whitebox tests, to   
   review the program in the computer to verify whether they really   
   understand.   
      
   Turing Test cannot resolve these bottlenecks and issues.   
      
      
   3. Variants of Turing Test   
      
   There are several variants of Turing Test which aim at improving on   
   it.   
      
   One is Feigenbaum test. According to Edward Feigenbaum, "Human   
   intelligence is very multidimensional", "computational linguists have   
   developed superb models for the processing of human language grammars.   
   Where they have lagged is in the 'understand' part", "For an artifact,   
   a computational intelligence, to be able to behave with high levels of   
   performance on complex intellectual tasks, perhaps surpassing human   
   level, it must have extensive knowledge of the domain." [3].   
      
   Feigenbaum test is actually a good method to test the knowledge in   
   expert systems. The test tries to produce generic intelligence by   
   average out of many expert systems. That is why it needs to test   
   extensive knowledge.   
      
      
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