Saturday, May 5, 2012
Different Approaches For Knowledge System Development (v3)
1) Introduction
To really understand how humans develop intelligence and knowledge systems, people have to retrace the whole history of philosophy and mathematics back to ancient itme, and study various kinds of methodologies for different purposes.
This article is not a complete review of philosophies and sciences. It only addresses the essentials and methodologies for knowledge development, for the interests of sciences, philosophy, education, and artificial intellignece, etc. So although Dmitri Mendeleev and Albert Einstein are extremely important scientists, they are not discussed here since they essentially followed the classic scientific approach: Galileo-Newton approach.
It does not try to cross the boundary between knowledge and religions. Only religious rites are mentioned.
By approach, it means coherent approach in this paper. Coherence does not guarantee correctness. However, incohenrence is always prone to problems and errors.
2) Various Approaches
Several approaches from ancient time are identified here. They are: Pythagoras-Plato approach; Socrates-Stoicism approach; Euclid-Archimedes approach; Yi-Jing approach from ancient China; approaches from ancient India; approaches from other countries, etc.
Some approaches from medieval age played important roles in sciences: they are Ibn al-Haytham's approach, Al-Biruni's approach, and Avicenna's approach, etc.
Galileo-Newton approach, the foundation of current sciences, evolved from Euclid-Archimedes and Ibn al-Haytham approaches. But there are differences between them. Some non-classic approaches from Charles Darwin, Adam Smith, Sigmund Freud, etc., are also different from Galileo-Newton approach.
The following sections will first discuss the strengths and limitations of the first three ancient approaches, the medieval approaches, then Galileo-Newton approach. Several non-classic approaches and important theoretic issues will also be discussed.
The ancient approaches from Yi-Jing, India, and other countries, would be discussed in separate articles, if possible.
3) Pythagoras-Plato Approach
Thales is a pioneer in mathematical proof. Egyptians and Babylonians might know Thales Theorem before him, but he was likely the first one providing a valid proof for it.
Although Thales tried to explain natural phenomena not based on mythology, he is a Hylozoist who believed everything is alive, and there is no difference between the living and the dead. He did not develop a coherence approach, but had significant influences on Pythagoras.
The first philosopher should be Pythagoras, who built a coherent systematic view. He formed a school of scholars to study philosophy, mathematics, music, etc.
Pythagorean are famous for Pythagorean Theorem. They are pioneers in mathematics, a systematic study. They also proposed a non-geocentric model that the Earth runs around a central fire which suggests both the Sun and the Earth are not the center of universe. They might develop or formulate the idea the Earth is round.
Pythagoras also taught religious rites and practices in his school, so came his beliefs. He and Plato believed there be a perfect and persistent abstract world, and an imperfect and sensible world. They pursued the beauty of abstract perfection. Plato followed this philosophy and developed it into maturity.
Pythagorean made many early contributions to knowledge. They tried to construct complicated things with simpler ones. They believed whole numbers be simple and perfect, and tried to represent all numbers with quotient of two whole numbers. Here they faced the first mathematical crisis: some, actually most of the numbers, cannot be expressed in such a way. They called these irrational numbers.
This discloses the problems of Pythagoras-Plato approach: the way they construct or interpret mathematics may not fit into the reality. The beauty of mathematics may not be able to explain an sensible world. Constructivism is important. But how to construct, and to what extent it works ?
Such an issue even has a consequence on modern sciences and technologies: how macro nonlinearity and micro quantum phenomena are related to irrational numbers ? How should irrational numbers be handled on computers ?
The issue of irrational numbers is actually related to measurement. Euclid described it in a better way as mentioned in Section 5, which is not understood properly by many modern mathematicians. Measurement is again associated to nonlinear, chaos, deterministic uncertainty, or computer modelling, etc. So people better think of this issue as a tip of an iceberg, rather than a solved problem which they could forget about it.
4) Socrates-Stoicism approach
Socrates led different beliefs. He did not take the beauty of abstraction as a doctrine. There is a Socratic method. He asked people to question each other. When people discuss their arguments explicitly, they could find the problems and understand them better.
Socrates asked many questions, but did not give many answers. This might be a good attitude. Socrates taught by playing a role model. By admitting his ignorance, he suggested other people also to admit their ignorance.
Admitting their ignorance is not beautiful, not even pleasant, but an extremely critical step to make further progresses. However, this attitude is offensive to many people. Socrates was voted to death eventually, probabily under accumulated anger from others.
Then Socrates played a role model again by accepting the death to show the rule of laws.
Also, "Aristotle attributed to Socrates the discovery of the method of definition and induction, which he regarded as the essence of the scientific method." (from wikipedia).
Socrates promoted rationale and ethics, which was followed by Cynicism and Stoicism. However, the strange behaviors of Cynicism actually showed the frustrations faced by this approach: they did not find effective ways to discover much more knowledge. This task would be achieved by Euclid-Archimedes, Ibn al-Haytham, Galileo-Newton, Darwin approaches later.
Sophism was an enemy to Socrates, and is also an enemy to future sciences. It does not provide a coherent approach.
Aristotelianism is not coherent, too. Although Aristotle adored Socrates and claimed he was against sophism, his way is actually a mixture of Socrates, Plato and sophism without coherence. So he included assertions like a flying arrow is at rest in his book.
His syllogism is an unsuccessful summarization and simulation of the methods in mathematical proofs. Aristotle did not know how the logic really works in mathematics. So he missed a very important factor: how to make the premises in syllogism valid and concrete, i.e. the first principle. Euclid provided a solution on this issue for some problems later.
Since Aristotle did not know how to apply logic and reasoning correctly, he did not know how to build coherent theories. His book The Physics brought little values to physics, but many misleadings. He just put togather whatever he knew or believed into huge collections without paying attention to coherence.
Aristotle was actually a naturalist. He made some contributions to zoological taxonomy based on observation. He is not the first one using observation. And he does not have a coherent approach.
5) Euclid-Archimedes Approach
Euclid is the first one who established a concrete systematic theory for a domain. He is more like a scientist, than a pure mathematician.
He did not concern much of the beauty of abstraction. In the proof of the number of prime numbers, he used the word "measure", instead of a number divides another number. Many modern mathematicians think not being abstract enough is Euclid's limitation.
However, Euclid using measurement for division, implies the accurate value of irrational numbers cannot be measured by rational numbers. Measurability is still a critical problem in modern sciences and computer modelling. So, such an expression is not Euclid's limitation, but his insight. He caught the essentials of the problems.
He usually constructed solutions rather than just proving the existence of unknown solutions. His system is incredible concrete after more than two thousand years, much more concrete than many of modern mathematics.
He constructed the geometry system by some simple axioms, and derived other theorems from these axioms. Although this looks like Pythagorean's way to construct complicated numbers by simpler whole numbers, they are different.
Euclid guarantees the correctness of derived theorems by making axioms simple and straightforward, thus self-evident. So Euclid solved the first principle issue in certain extent. Pythagorean did not show why whole numbers could be used to express all numbers, they just believed it be the beauty. Euclid's geometry is a good example of correct logic.
Euclid's approach mainly works in mathematics, and cannot find all theorems and laws in real needs. When Euclid worked on optics, his approach for first principle faced a problem: he did not have justified reasons to choose emission theory instead of intromission theory, although no justified reasons to make the opposite choice at that time, too. These limitations are partially solved by Ibn al-Haytham approach and Galileo-Newton approach, only partially.
Euclid was truly thought as a scientist in early days. Only after Galileo founded Physics, Euclid retired from scientists, and became a mathematician only.
Archimedes, one of the greatest engineers, was highly influenced by Euclid.
6) Medieval approaches
Pythagoras is very insightful in mathematics, philosophy, music, religious practices, etc. Plato developed the philosophy in his style into maturity. Socrates and Stoicism knew the way to develop rationale and ethics. Euclid and Archimedes designed theoretic and real systems in rigorous forms.
They all made big contributions to knowledge development, and still have big influences so far, but also with problems. Their accomplishments are still in very limited extent. It is some medieval scholars who brought in some new factors critical to future sciences.
Ibn al-Haytham used some procedure to do scientific research: observe, form conjectures, Testing and/or criticism of a hypothesis using experimentation, etc. He used this procedure to prove intromission theory.
However, this procedure is not a complete scientific approach. He can only use it to reach individual results, still under Euclid's geometry view. Although he did some brilliant work in optics, due to this geometry view and his way of thinking, he cannot gain deep and comprehensive understanding of physics.
More important, Ibn al-Haytham did not tell how to build big theories and establish new paradigns in sciences. Those are critical tasks for scientific revolutions, which were left to Galileo-Newton approach and Darwin non-classific approach, etc.
Al-Biruni put an emphasis on experimentation. He tried to conceptualize both systematic errors and observational biases, and used repeated experiments to control errors. He might also be a pioneer of comparative sociology.
Avicenna discussed the philosophy of science and summarized several methods to find a first principle. He developed a theory to distinguish the inclination to move and the force. He discussed the soul and the body, the perceptions. Probably he is a very important scholar misunderstood by many modern people.
Only after their efforts, big scientific progresses became possible.
7) Galileo-Newton Approach
Although Nicolaus Copernicus started the new age of sciences, he (and Johannes Kepler) still followed Euclid-Archimedes approach, a geometry view.
It is Galileo Galilei who formed many substantial understanding of the physical world and triggered a scientific revolution with his comprehensive and systematic thinking. Galileo showed how these systematic thinking could lead to new world theories and establish new paradigms in physical sciences, which is different from Ibn al-Haytham's approach. Without such a way to think, people cannot build a new big theory from individual isolated conclusions. But he did not summarize well what really make these differences.
Isaac Newton developed his great theories based on Galileo's approach. So this classic scientific approach is named as Galileo-Newton approach. Although Newton did a great work, he did not explain why he could do these, i.e., summarize well what are the real differences between their approach and Ibn al-Haytham's approach. Francis Bacon cannot explain the real differences too. The mechanisms behind these differences are left to be explained by future philosophers.
Galileo-Newton approach mainly work in worlds without considering the affects from life. Thomas Robert Malthus and John Maynard Keynes followed this classific scientific approach and tried to apply it to life and human societies. They made some progresses, but very limited. And they missed something very important to human beings.
There are still fundamental limitations in this approach. It does not work well in artificial intelligence, psychology, economics, and other humanity and social sciences, etc. Those fields relate to humans. Measurability and modelling are still big concerns. People could look at Newton's four rules of reasoning stated in his Mathematical Principles of Natural Philosophy, to figure out what the limitations really are:
"1.We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
2.Therefore to the same natural effects we must, as far as possible, assign the same causes.
3.The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
4.In experimental philosophy we are to look upon propositions collected by general induction from phænomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions".
Two issues are identified here: 1) Galileo, Newton or Bacon did not summarize well what are the differences and the mechanisms behind these differences between the classific scientific approach and Ibn al-Haytham's approach. 2) Galileo-Newton approach itself has fundamental problems when applied to life and humans. Actually, many important knowledge systems were not built with this approach.
8) Non-Classic Approaches
Although as great academic contributors, Charles Darwin, Adam Smith, and Sigmund Freud built their theories not with Galileo-Newton approach. These three are listed here in the descending order of closeness to sciences. No surprise, their theories relate to humans.
Some people classified Charles Darwin as a follower of Francis Bacon's methodology. It is not true. Darwin did much more than observation, induction, etc., empiricism methods, to construct his great theories for life and human history. He is the greatest historian in history. He established a paradigm to combine sciences, life, and humanity, etc.
The differences between Darwin's approach and Ibn al-Haytham's approach, and the differences between Darwin's approach and Galileo-Newton approach, are to be illustrated by future philosophers.
People also should pay attention to the differences between Darwinism and Social Darwinism. They actually took opposite positions on many issues.
Epicurus, Arthur Schopenhauer, Friedrich Nietzsche also illustrated many important opinions, related to human natures. Their ways are different from classic approaches, either.
9) The Progresses in Natural Sciences So Far
After Galileo-Newton approach was established, many theories in natural sciences were proposed such as periodic table, genetics, relativity theories, quantum theories, etc. They mainly followed Galileo-Newton approach. Relativity theories are just refinements to Newton dynamics, just as Kepler refined Copernicus' circle orbits with ellipse orbits. Today people know planets do not run in ellipse orbits, too. So people do not know whether relativity theories are the final theories.
There are good examples for work cross different approaches, such as the synthesis of evolution and genetics theories in life sciences. But people do not have good theories in psychology and intelligence yet, and do not know whether Galileo-Newton approach would work well in these fields. Even in biology, most mechanisms can not be explained yet.
10) Inadequate Summarizing Efforts
Many people tried to summarize the knowledge systems, such as: Francis Bacon, René Descartes, David Hume, Immanuel Kant, etc.
Georg Wilhelm Friedrich Hegel, Karl Marx, Bertrand Russell even made more ambitious efforts.
Just they all missed some or many important aspects.
11) Gödel Theorems and the Limitations of Mathematics and Positivism
Gödel theorems illustrate the intrinsic problems in mathematics systems beyond certain complexity. There are foundational crisis in mathematics as in http://en.wikipedia.org/wiki/Foundations_of_mathematics#Foundational_crisis.
More important, mathematics cannot explain all the potentials in reality.
Positivism is an ideal goal for Galileo-Newton approach. However, as said, Charles Darwin, Adam Smith, Sigmund Freud and many others built their theories and systems not strictly with this approach.
In the whole knowledge system, positivism is more like a Utopia, rather than a reality. Even so, as one of important doctrines in sciences, positivism should not be ignored, especially in the conclusion stage.
12) Future Researches
Some of the challenges for future are identified here:
1. How could people construct big theories and establish new paradigms ? These are the mechanims missed in Ibn al-Haytham's approach. Galileo, Newton, Darwin did their well. But they did not summarize well how they achieved these. Francis Bacon, René Descartes, David Hume, Immanuel Kant, etc., did not summarize these well, too.
2. Identify the limitations in Galileo-Newton approach.
3. Identify the limitations in Darwin's approach.
4. Develop an approach for future researches on life, psychology, and intelligence, etc.
It is up to future philosophers to figure these out and illustrate the mechanisms behind these.
(I delete the content related to computer intelligence and Gu Test in this version. Those are already presented in a seperated paper: Gu Test: A Measurement of Generic Intelligence)
Wednesday, April 18, 2012
Gu Test: A Measurement of Generic Intelligence (v3)
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 Gödel'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 and exponential divergence in nonlinear chaotic phenomena, there are problems in such approximations. In reality, nonlinearity is the normal rather than the exception. How does humans' intelligence guide their behavior 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.
Here, the bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding, still remain in Feigenbaum test as well as in other variants of Turing Test. There are differences between knowledge, concepts and data. The "understanding part" is still to be resolved.
One more issue of Feigenbaum test is: individual humans may not have very extensive knowledge in many domains, but they have potentials. So extensive knowledge may not be necessary, but tests for potentials are.
Another variant is Shane Legg and Marcus Hutter's solution [4], which is actually agent-based, a good test for tasks. Their solution tries to test generic intelligence by average out of many tasks. It still uses behavior imitation and comparison. So it is a blackbox test and a variant of Turing Test.
In their framework, an agent sends its actions to the environment and received observations and rewards from it. If their framework is used to test strong AI, then it assumes that all the interactions between humans and their environment could be modeled by actions/observations/rewards. This assumption has not been tested yet. The bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding, still remains.
Furthermore, there are differences between humans and the definitions of agents. Humans can play some roles of agents, but they are not just agents. They could make paradigm evolution or shift, which usually means gain deeper observations, take better actions, and gain more rewards than what already in any definitions.
Even if Turing Test is enhanced with vision and manipulation ability, or with methods like statistical inference, etc., it still does not resolve the bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding.
These issues could be solved by concept understanding, whitebox test, etc. The measurement of generic intelligence is not just producing the digitals of one or a few irrationl numbers.
4. The Design Goals for Generic Intelligence Measurement
Based on the analysis done in previous sections, some design goals are proposed here:
1) Resolve Chinese Room issue, i.e., to test the real understanding, not just behavior imitating or symbolic processing.
2) Resolve the bottleneck in expression, by not purely relying on interrogation. Find some ways to test those intrinsic intelligence abilities which have not been understood and expressed well.
3) Resolve the bottleneck in capacity, by levergae of the differences between concepts, knowledge and data.
4) Use whitebox test to resolve blackbox test issue.
5) Involve as less domain knowledge as possible, since regular humans may not have much knowledge in specific domains. But include those essential intrinsic capabilities commonly necessary in many domains, with which humans have the potentials to develop intelligence in many domains.
6) Include sequential test levels, since humans are able to make continuous progresses in intelligence.
7) Include a framework to test structured intelligence and be able to make paradigm evolution or shift, since humans have such abilitities.
5. Gu Test
Based on these design goals, Gu Test is proposed. It should include sequential test levels, and be able to test structured intelligence and make paradigm evolution or shift gradually.
The current efforts are to achieve the design goals 1) to 6). The work to meet goal 7) will be left to future researches.
The first test step of Gu Test is: to test whether testees could understand irrational numbers without knowing their exact values. It is a white box test. Average humans with certain basic education can. Current computers most likely cannot. An advanced step could be: to test the understanding of uncountable sets.
These test the real understanding; They do not rely on interrogation, but test some intrinsic ability. Humans have this ability without the issues of bottlenecks in expression or capacity, but they probably do not know why they have this ability yet; It tests some concepts and knowledge which cannot be represented as data; Irrational number is a primitive concept developed in Pythagoras' age, who is a poineer in philosophy and mathematics; The concept is necessary to so many domains, but involves very little domain-specific knowledge. Uncountable set is an advanced concept.
Due to these characteristics, Gu Test is very different from Turing Test and its variants by testing the understanding parts.
Irrational number and Uncountable set are just mathematics concepts. Physical concepts are in complete different dimensions. To make generic intelligence understand physical concepts and represent them would be very different challenges.
6. Comparison With other Test Methods
As said, Gu Test is very different from behavior-based tests, knowledge-based tests, task-based tests, etc. It is a whitebox test, requiring humans to analyze whether a system achieves certain intelligent levels with certain internal capabilities.
So Gu Test represent a complete paradigm shift from previous test methods. And it is not comparable with those previous test methods.
7. Future Research
Much more work need be done to extend Gu Test to include various test levels and meet design goals 7).
The analysis on the bottlenecks and issues of Turing Test, would naturally lead to the questions of the power and limitations of Turing Machine, and what the better models are for artificial intelligence. Does it need uncountable memory units ? If yes, how to implement it. If not, how to enhance the power. People probably have to revisit Church-Turing thesis. It is possible to build models exceeding the power of Turing Machine mathematically. However, it would be a challenge to develop such a model matching physical reality.
To really understand the essentials of intelligence, people have to study the history of knowledge development, philosophy, mathematics, sciences, etc.
References
[1] Turing, A. M., 1950, "Computing machinery and intelligence". Mind 59, 433–460.
[2] Searle, John. R., 1980, "Minds, brains, and programs". Behavioral and Brain Sciences 3 (3): 417-457.
[3] Feigenbaum, Edward A., 2003, "Some challenges and grand challenges for computational intelligence". Journal of the ACM 50 (1): 32–40.
[4] Legg, S. & Hutter, M., 2006, "A Formal Measure of Machine Intelligence”, Proc. 15th Annual Machine Learning Conference of Belgium and The Netherlands, pp.73-80.
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 Gödel'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 and exponential divergence in nonlinear chaotic phenomena, there are problems in such approximations. In reality, nonlinearity is the normal rather than the exception. How does humans' intelligence guide their behavior 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.
Here, the bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding, still remain in Feigenbaum test as well as in other variants of Turing Test. There are differences between knowledge, concepts and data. The "understanding part" is still to be resolved.
One more issue of Feigenbaum test is: individual humans may not have very extensive knowledge in many domains, but they have potentials. So extensive knowledge may not be necessary, but tests for potentials are.
Another variant is Shane Legg and Marcus Hutter's solution [4], which is actually agent-based, a good test for tasks. Their solution tries to test generic intelligence by average out of many tasks. It still uses behavior imitation and comparison. So it is a blackbox test and a variant of Turing Test.
In their framework, an agent sends its actions to the environment and received observations and rewards from it. If their framework is used to test strong AI, then it assumes that all the interactions between humans and their environment could be modeled by actions/observations/rewards. This assumption has not been tested yet. The bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding, still remains.
Furthermore, there are differences between humans and the definitions of agents. Humans can play some roles of agents, but they are not just agents. They could make paradigm evolution or shift, which usually means gain deeper observations, take better actions, and gain more rewards than what already in any definitions.
Even if Turing Test is enhanced with vision and manipulation ability, or with methods like statistical inference, etc., it still does not resolve the bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding.
These issues could be solved by concept understanding, whitebox test, etc. The measurement of generic intelligence is not just producing the digitals of one or a few irrationl numbers.
4. The Design Goals for Generic Intelligence Measurement
Based on the analysis done in previous sections, some design goals are proposed here:
1) Resolve Chinese Room issue, i.e., to test the real understanding, not just behavior imitating or symbolic processing.
2) Resolve the bottleneck in expression, by not purely relying on interrogation. Find some ways to test those intrinsic intelligence abilities which have not been understood and expressed well.
3) Resolve the bottleneck in capacity, by levergae of the differences between concepts, knowledge and data.
4) Use whitebox test to resolve blackbox test issue.
5) Involve as less domain knowledge as possible, since regular humans may not have much knowledge in specific domains. But include those essential intrinsic capabilities commonly necessary in many domains, with which humans have the potentials to develop intelligence in many domains.
6) Include sequential test levels, since humans are able to make continuous progresses in intelligence.
7) Include a framework to test structured intelligence and be able to make paradigm evolution or shift, since humans have such abilitities.
5. Gu Test
Based on these design goals, Gu Test is proposed. It should include sequential test levels, and be able to test structured intelligence and make paradigm evolution or shift gradually.
The current efforts are to achieve the design goals 1) to 6). The work to meet goal 7) will be left to future researches.
The first test step of Gu Test is: to test whether testees could understand irrational numbers without knowing their exact values. It is a white box test. Average humans with certain basic education can. Current computers most likely cannot. An advanced step could be: to test the understanding of uncountable sets.
These test the real understanding; They do not rely on interrogation, but test some intrinsic ability. Humans have this ability without the issues of bottlenecks in expression or capacity, but they probably do not know why they have this ability yet; It tests some concepts and knowledge which cannot be represented as data; Irrational number is a primitive concept developed in Pythagoras' age, who is a poineer in philosophy and mathematics; The concept is necessary to so many domains, but involves very little domain-specific knowledge. Uncountable set is an advanced concept.
Due to these characteristics, Gu Test is very different from Turing Test and its variants by testing the understanding parts.
Irrational number and Uncountable set are just mathematics concepts. Physical concepts are in complete different dimensions. To make generic intelligence understand physical concepts and represent them would be very different challenges.
6. Comparison With other Test Methods
As said, Gu Test is very different from behavior-based tests, knowledge-based tests, task-based tests, etc. It is a whitebox test, requiring humans to analyze whether a system achieves certain intelligent levels with certain internal capabilities.
So Gu Test represent a complete paradigm shift from previous test methods. And it is not comparable with those previous test methods.
7. Future Research
Much more work need be done to extend Gu Test to include various test levels and meet design goals 7).
The analysis on the bottlenecks and issues of Turing Test, would naturally lead to the questions of the power and limitations of Turing Machine, and what the better models are for artificial intelligence. Does it need uncountable memory units ? If yes, how to implement it. If not, how to enhance the power. People probably have to revisit Church-Turing thesis. It is possible to build models exceeding the power of Turing Machine mathematically. However, it would be a challenge to develop such a model matching physical reality.
To really understand the essentials of intelligence, people have to study the history of knowledge development, philosophy, mathematics, sciences, etc.
References
[1] Turing, A. M., 1950, "Computing machinery and intelligence". Mind 59, 433–460.
[2] Searle, John. R., 1980, "Minds, brains, and programs". Behavioral and Brain Sciences 3 (3): 417-457.
[3] Feigenbaum, Edward A., 2003, "Some challenges and grand challenges for computational intelligence". Journal of the ACM 50 (1): 32–40.
[4] Legg, S. & Hutter, M., 2006, "A Formal Measure of Machine Intelligence”, Proc. 15th Annual Machine Learning Conference of Belgium and The Netherlands, pp.73-80.
Friday, March 23, 2012
The Growth of Souls -- Brain, Heart and Pleasure
Brain: there are two types of intelligence: task-oriented and world-oriented.
Heart: it is the heart which makes people relevant, adhensive, or committed to somethings, somewhere, or some other people, etc.
Pleasure: it could be fast-changing, diversified, and temporary. So better let you choose pleasure, not pleasure choose you.
Souls combine hearts with brains and pleasure, and make people coherent.
To think of growth and future, is to understand your soul, with your brain, heart and pleasure.
Genes are not completely selfish. Be serious and meticulous to what already committed and what going to commit. Try to understand the past and future with coherence.
Heart: it is the heart which makes people relevant, adhensive, or committed to somethings, somewhere, or some other people, etc.
Pleasure: it could be fast-changing, diversified, and temporary. So better let you choose pleasure, not pleasure choose you.
Souls combine hearts with brains and pleasure, and make people coherent.
To think of growth and future, is to understand your soul, with your brain, heart and pleasure.
Genes are not completely selfish. Be serious and meticulous to what already committed and what going to commit. Try to understand the past and future with coherence.
Wednesday, February 22, 2012
Bildungsromans and Children
This is a late celebration of Charles Dickens' 200th birthday, which passed early this month.
David Copperfield and Great Expectations are two of the best novels from Charles Dickens, and possibly two of the best Bildungsromans. They illustrate different aspects of human natures.
Great Expectations contains many twisted personalities. The protagonist Pip was actually trapped. He did not realized this completely even in the end of the current version of the novel, which is a bad story. In Dickens' original version, Pip got out from the trap in the end, a correct one for a Bildungsroman.
David Copperfield is about healthy development. There are three successful couples in the novel: Copperfields, Strongs, and Traddleses.
Betsey Trotwood is a close family member. After David came, her life started to flow and became meaningful.
Clara Peggotty is a very special friend.
Letting children be aware of twisted characters is equally important as healthy development. Charles Dickens actually wrote Great Expectations a decade later after David Copperfield, with deeper thinking. It would be good to be cautious and prevent your children from being twisted and caught in traps.
David Copperfield and Great Expectations are two of the best novels from Charles Dickens, and possibly two of the best Bildungsromans. They illustrate different aspects of human natures.
Great Expectations contains many twisted personalities. The protagonist Pip was actually trapped. He did not realized this completely even in the end of the current version of the novel, which is a bad story. In Dickens' original version, Pip got out from the trap in the end, a correct one for a Bildungsroman.
David Copperfield is about healthy development. There are three successful couples in the novel: Copperfields, Strongs, and Traddleses.
Betsey Trotwood is a close family member. After David came, her life started to flow and became meaningful.
Clara Peggotty is a very special friend.
Letting children be aware of twisted characters is equally important as healthy development. Charles Dickens actually wrote Great Expectations a decade later after David Copperfield, with deeper thinking. It would be good to be cautious and prevent your children from being twisted and caught in traps.
Tuesday, January 31, 2012
Gu Test: A Measurement of Generic Intelligence (v3)
Abstraction
Could computers understand and represent irrational numbers without knowing the exact values, and uncountable sets? Humans can. 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 solve these issues. A new method: Gu Test is proposed, to distinguish strong AI and regular machines, meet some of these design goals, and provide insights for future directions of AI. Further improvement could be done in future.
1. The Measurement of Generic Intelligence
Measurement is so important in sciences and technologies. Just as clocks are necessary to advanced studies of motion and speed, centrifugal governors are critical to make steam engines usable, etc.
The measurement of generic intelligence is also 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. So they cannot really measure intrinsic intelligence capabilities.
People could design algorithms on Turing Machine or its improved models. These are mathematics models limited by Gödel's incompleteness theorems. Even worse, there are problems to implement them physically. 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 resolve these issues and distinguish strong AI from regular machines.
The following sections will discuss Turing Test and its bottlenecks and issues; the variants of Turing Test: Feigenbaum test, Shane Legg and Marcus Hutter's solution, etc; the design goals to achieve better measurement of generic intelligence; Gu Test, and some directions for future work.
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.
Here, the bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding, still remain in Feigenbaum test as well as in other variants of Turing Test. There are differences between knowledge, concepts and data. The "understanding part" is still to be resolved.
One more issue of Feigenbaum test is: individual humans may not have very extensive knowledge in many domains, but they have potentials. So extensive knowledge may not be necessary, but tests for potentials are.
Another variant is Shane Legg and Marcus Hutter's solution [4], which is actually agent-based, a good test for tasks. Their solution tries to test generic intelligence by average out of many tasks. It still uses behavior imitation and comparison. So it is a blackbox test and a variant of Turing Test.
In their framework, an agent sends its actions to the environment and received observations and rewards from it. If their framework is used to test strong AI, then it assumes that all the interactions between humans and their environment could be modeled by actions/observations/rewards. This assumption has not been tested yet. The bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding, still remains.
Furthermore, there are differences between humans and the definitions of agents. Humans can play some roles of agents, but they are not just agents. They could make paradigm evolution or shift, which usually means gain deeper observations, take better actions, and gain more rewards than what already in any definitions.
Even if Turing Test is enhanced with vision and manipulation ability, or with methods like statistical inference, etc., it still does not resolve the bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding.
These issues could be solved by concept understanding, whitebox test, etc. The measurement of generic intelligence is not just producing the digitals of one or a few irrationl numbers.
4. The Design Goals for Generic Intelligence Measurement
Based on the analysis done in previous sections, some design goals are proposed here:
1) Resolve Chinese Room issue, i.e., to test the real understanding, not just behavior imitating or symbolic processing.
2) Resolve the bottleneck in expression, by not purely relying on interrogation. Find some ways to test those intrinsic intelligence abilities which have not been understood and expressed well.
3) Resolve the bottleneck in capacity, by levergae of the differences between concepts, knowledge and data.
4) Use whitebox test to resolve blackbox test issue.
5) Involve as less domain knowledge as possible, since regular humans may not have much knowledge in specific domains. But include those essential intrinsic capabilities commonly necessary in many domains, with which humans have the potentials to develop intelligence in many domains.
6) Include sequential test levels, since humans are able to make continuous progresses in intelligence.
7) Include a framework to test structured intelligence and be able to make paradigm evolution or shift, since humans have such abilitities.
5. Gu Test
Based on these design goals, Gu Test is proposed. It should include sequential test levels, and be able to test structured intelligence and make paradigm evolution or shift gradually.
The current efforts are to achieve the design goals 1) to 6). The work to meet goal 7) will be left to future researches.
The first test step of Gu Test is: to test whether testees could understand irrational numbers without knowing their exact values. It is a white box test. Average humans with certain basic education can. Current computers most likely cannot. An advanced step could be: to test the understanding of uncountable sets.
These test the real understanding; They do not rely on interrogation, but test some intrinsic ability. Humans have this ability without the issues of bottlenecks in expression or capacity, but they probably do not know why they have this ability yet; It tests some concepts and knowledge which cannot be represented as data; Irrational number is a primitive concept developed in Pythagoras' age, who is a poineer in philosophy and mathematics; The concept is necessary to so many domains, but involves very little domain-specific knowledge. Uncountable set is an advanced concept.
Due to these characteristics, Gu Test is very different from Turing Test and its variants by testing the understanding parts.
Irrational number and Uncountable set are just mathematics concepts. Physical concepts are in complete different dimensions. To make generic intelligence understand physical concepts and represent them would be very different challenges.
6. Future Research
Much more work need be done to extend Gu Test to include various test levels and meet design goals 7).
The analysis on the bottlenecks and issues of Turing Test, would naturally lead to the questions of the power and limitations of Turing Machine, and what the better models are for artificial intelligence. Does it need uncountable memory units ? If yes, how to implement it. If not, how to enhance the power. People probably have to revisit Church-Turing thesis. It is possible to build models exceeding the power of Turing Machine mathematically. However, it would be a challenge to develop such a model matching physical reality.
To really understand the essentials of intelligence, people have to study the history of knowledge development, philosophy, mathematics, sciences, etc.
References
[1] Turing, A. M., 1950, "Computing machinery and intelligence". Mind 59, 433–460.
[2] Searle, John. R., 1980, "Minds, brains, and programs". Behavioral and Brain Sciences 3 (3): 417-457.
[3] Feigenbaum, Edward A., 2003, "Some challenges and grand challenges for computational intelligence". Journal of the ACM 50 (1): 32–40.
[4] Legg, S. & Hutter, M., 2006, "A Formal Measure of Machine Intelligence”, Proc. 15th Annual Machine Learning Conference of Belgium and The Netherlands, pp.73-80.
Could computers understand and represent irrational numbers without knowing the exact values, and uncountable sets? Humans can. 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 solve these issues. A new method: Gu Test is proposed, to distinguish strong AI and regular machines, meet some of these design goals, and provide insights for future directions of AI. Further improvement could be done in future.
1. The Measurement of Generic Intelligence
Measurement is so important in sciences and technologies. Just as clocks are necessary to advanced studies of motion and speed, centrifugal governors are critical to make steam engines usable, etc.
The measurement of generic intelligence is also 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. So they cannot really measure intrinsic intelligence capabilities.
People could design algorithms on Turing Machine or its improved models. These are mathematics models limited by Gödel's incompleteness theorems. Even worse, there are problems to implement them physically. 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 resolve these issues and distinguish strong AI from regular machines.
The following sections will discuss Turing Test and its bottlenecks and issues; the variants of Turing Test: Feigenbaum test, Shane Legg and Marcus Hutter's solution, etc; the design goals to achieve better measurement of generic intelligence; Gu Test, and some directions for future work.
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.
Here, the bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding, still remain in Feigenbaum test as well as in other variants of Turing Test. There are differences between knowledge, concepts and data. The "understanding part" is still to be resolved.
One more issue of Feigenbaum test is: individual humans may not have very extensive knowledge in many domains, but they have potentials. So extensive knowledge may not be necessary, but tests for potentials are.
Another variant is Shane Legg and Marcus Hutter's solution [4], which is actually agent-based, a good test for tasks. Their solution tries to test generic intelligence by average out of many tasks. It still uses behavior imitation and comparison. So it is a blackbox test and a variant of Turing Test.
In their framework, an agent sends its actions to the environment and received observations and rewards from it. If their framework is used to test strong AI, then it assumes that all the interactions between humans and their environment could be modeled by actions/observations/rewards. This assumption has not been tested yet. The bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding, still remains.
Furthermore, there are differences between humans and the definitions of agents. Humans can play some roles of agents, but they are not just agents. They could make paradigm evolution or shift, which usually means gain deeper observations, take better actions, and gain more rewards than what already in any definitions.
Even if Turing Test is enhanced with vision and manipulation ability, or with methods like statistical inference, etc., it still does not resolve the bottlenecks of communication or storage, in expression or in capacity, and the issue of blackbox test and understanding.
These issues could be solved by concept understanding, whitebox test, etc. The measurement of generic intelligence is not just producing the digitals of one or a few irrationl numbers.
4. The Design Goals for Generic Intelligence Measurement
Based on the analysis done in previous sections, some design goals are proposed here:
1) Resolve Chinese Room issue, i.e., to test the real understanding, not just behavior imitating or symbolic processing.
2) Resolve the bottleneck in expression, by not purely relying on interrogation. Find some ways to test those intrinsic intelligence abilities which have not been understood and expressed well.
3) Resolve the bottleneck in capacity, by levergae of the differences between concepts, knowledge and data.
4) Use whitebox test to resolve blackbox test issue.
5) Involve as less domain knowledge as possible, since regular humans may not have much knowledge in specific domains. But include those essential intrinsic capabilities commonly necessary in many domains, with which humans have the potentials to develop intelligence in many domains.
6) Include sequential test levels, since humans are able to make continuous progresses in intelligence.
7) Include a framework to test structured intelligence and be able to make paradigm evolution or shift, since humans have such abilitities.
5. Gu Test
Based on these design goals, Gu Test is proposed. It should include sequential test levels, and be able to test structured intelligence and make paradigm evolution or shift gradually.
The current efforts are to achieve the design goals 1) to 6). The work to meet goal 7) will be left to future researches.
The first test step of Gu Test is: to test whether testees could understand irrational numbers without knowing their exact values. It is a white box test. Average humans with certain basic education can. Current computers most likely cannot. An advanced step could be: to test the understanding of uncountable sets.
These test the real understanding; They do not rely on interrogation, but test some intrinsic ability. Humans have this ability without the issues of bottlenecks in expression or capacity, but they probably do not know why they have this ability yet; It tests some concepts and knowledge which cannot be represented as data; Irrational number is a primitive concept developed in Pythagoras' age, who is a poineer in philosophy and mathematics; The concept is necessary to so many domains, but involves very little domain-specific knowledge. Uncountable set is an advanced concept.
Due to these characteristics, Gu Test is very different from Turing Test and its variants by testing the understanding parts.
Irrational number and Uncountable set are just mathematics concepts. Physical concepts are in complete different dimensions. To make generic intelligence understand physical concepts and represent them would be very different challenges.
6. Future Research
Much more work need be done to extend Gu Test to include various test levels and meet design goals 7).
The analysis on the bottlenecks and issues of Turing Test, would naturally lead to the questions of the power and limitations of Turing Machine, and what the better models are for artificial intelligence. Does it need uncountable memory units ? If yes, how to implement it. If not, how to enhance the power. People probably have to revisit Church-Turing thesis. It is possible to build models exceeding the power of Turing Machine mathematically. However, it would be a challenge to develop such a model matching physical reality.
To really understand the essentials of intelligence, people have to study the history of knowledge development, philosophy, mathematics, sciences, etc.
References
[1] Turing, A. M., 1950, "Computing machinery and intelligence". Mind 59, 433–460.
[2] Searle, John. R., 1980, "Minds, brains, and programs". Behavioral and Brain Sciences 3 (3): 417-457.
[3] Feigenbaum, Edward A., 2003, "Some challenges and grand challenges for computational intelligence". Journal of the ACM 50 (1): 32–40.
[4] Legg, S. & Hutter, M., 2006, "A Formal Measure of Machine Intelligence”, Proc. 15th Annual Machine Learning Conference of Belgium and The Netherlands, pp.73-80.
Imperial Selection, Socratic Method, and Sophism
There is an issue related to knowledge development: how to evaluate the knowledge owned by people.
In ancient China, Imperial Selection (科举) was used to select people with some talents. It was started in Han Dynasty (206 BCE – 220 CE), initially with recommendation, then relying more and more on examinations later. Examinations should be blackbox tests ideally, in which the grades are made only based on the answers.
Examinations are also used in university admission. In 1970's, recommendation was resumed in university admission in China in a short period (工农兵学员). Then it has been switched back mainly to examinaitions up to now.
Both recommendation and examination are not good enough to evaluate scientific researches. Socratic method promotes open discussion fairly and honestly. When you want to question others' points, raise the questions face to face so the other parties would have a chance to answer. It should be a fair play. Thesis defence is similar to Socratic method.
However, Socratic method is vulnerable to sophism. Sophism could make fair and honest discussion impossible. Socrates was even voted to death.
Very few people could resist against sophism and keep away from it. Those who really can could benefit from sciences.
In ancient China, Imperial Selection (科举) was used to select people with some talents. It was started in Han Dynasty (206 BCE – 220 CE), initially with recommendation, then relying more and more on examinations later. Examinations should be blackbox tests ideally, in which the grades are made only based on the answers.
Examinations are also used in university admission. In 1970's, recommendation was resumed in university admission in China in a short period (工农兵学员). Then it has been switched back mainly to examinaitions up to now.
Both recommendation and examination are not good enough to evaluate scientific researches. Socratic method promotes open discussion fairly and honestly. When you want to question others' points, raise the questions face to face so the other parties would have a chance to answer. It should be a fair play. Thesis defence is similar to Socratic method.
However, Socratic method is vulnerable to sophism. Sophism could make fair and honest discussion impossible. Socrates was even voted to death.
Very few people could resist against sophism and keep away from it. Those who really can could benefit from sciences.
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