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7593.Gams M. - Computational Analysis of Human Thinking Processes (Invited Paper) (2004).pdf

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International Journal of Computational Cognition (http://www.YangSky.com/yangijcc.htm)
Volume 2, Number 3, Pages 1?19, September 2004
Publisher Item Identifier S 1542-5908(04)10301-1/$20.00
Article electronically published on May 27, 2003 at http://www.YangSky.com/ijcc23.htm. Please cite this
paper as: hMatjaz Gams, ?Computational Analysis of Human Thinking Processes (Invited Paper)?,
International Journal of Computational Cognition (http://www.YangSky.com/yangijcc.htm), Volume 2, Number 3, Pages 1?19, September 2004i.
COMPUTATIONAL ANALYSIS OF HUMAN THINKING
PROCESSES (INVITED PAPER)
MATJAZ GAMS
Abstract. Human creative thinking is analyzed, in particular through
the principle of multiple knowledge. It is claimed that current digital
computers, however fast, cannot achieve true human-level intelligence,
and that the Church-Turing thesis might be inadequate to encapsulate
top human thinking mechanisms. We try to show this by introducing and analyzing a two- and one-processing entity. Formally, we
want to compare performance of a single program/process performed
by a Turing machine, and two programs/processes performed by two
interaction Turing machines that can dynamically change each othc
ers programs based on dynamic unconstrained input. �03
Yang?s
Scientific Research Institute, LLC. All rights reserved.
1. Introduction
Can we define computing processes in animals, humans and computers?
Do they formally differ? Why are we intelligent and creative (Gomes et al.
1996, Haase 1996, Turner 1995, Wiggins 2001) and which cognitive processes
differ us from animals on one side and from computers on the other?
The best formal model of computing is the Turing machine. Digital computers are very good real-life implementations of formal Turing machines.
The science that is interested in dealing with intelligence and consciousness
in computers is artificial intelligence (AI). It is the science of mimicking
human mental faculties in a computer (Hopgood 2003).
But while it is rather easy to reproduce several human mental abilities
- like playing chess - with digital computers, it is very hard to implement
true intelligence or consciousness. In recent years it is more or less becoming evident that the mathematical model of the universal Turing machine
(Figure 1) is not sufficient to encapsulate the human mind and the brain
(Gams 2001).
Received by the editors January 16, 2003 / final version received May 26, 2003.
Key words and phrases. Weak artificial intelligence, strong artificial intelligence, AI,
cognitive science, computational model of human mind.
1
c
�03-2004
Yang?s Scientific
Research Institute, LLC. All rights reserved.
2
MATJAZ GAMS
Figure 1. The Turing machine can compute anything a
human can, according to the strong-AI interpretation of
the Church-Turing thesis.
It is only fair to observe that there are different viewpoints regarding
human/computer subject (Gams et al. 1997). Even some very smart and
successful researchers still say that current computers are intelligent and
conscious. But this position is much less common than a decade ago, and
is often denoted as ?strong AI? (Sloman 1992).
There are several ways of structuring different AI approaches. Here we
are interested in weak and strong AI. Strong AI says that computers are
in principle computationally as powerful as digital computers, while weak
AI highlights practical or principal differences (Gams 2001). Strong AI is
philosophically based on an implication of the Church-Turing thesis claiming - in simple words - that all solvable functions can be mechanically solved
by the Turing machine (Copeland 1997). More difficult functions cannot be
solved by in our physical world existing computing mechanisms. Therefore,
humans are in principle computationally as capable as digital computers.
Another consequence directly following from the Church-Turing thesis is
that there is no possible procedural formal counterexample or counterproof
to show potential human stronger computing, i.e. supercomputing mechanisms.
The last two arguments dominated scientific human/computer debates
for the last five decades. Not only are they theoretically correct, no widely
accepted counterexample was found in real life. So, scientifically speaking,
there is nothing wrong with the Church-Turing thesis ? as long as we stay
in formal definable domains.
On the other hand, where are intelligent and conscious computers? One
thing is to play a game like chess brilliantly, another to show at least some
COMPUTATIONAL ANALYSIS OF HUMAN THINKING PROCESSES
3
level of true intelligence and consciousness, recognized by humans. Not only
that, analysis of capacity growth highlight the problem.
The exponential growth of computer capabilities (Moore 1975; Hamilton 1999) is constant over more than half of the century. E.g. the speed
of computing roughly doubles each 18 months. On the other hand, human capabilities have been practically the same during the last century,
despite some small constant growth in IQ tests in recent decades. Since
computer performance grows pretty linearly on a logarithmic scale, computers in more and more areas sooner or later outperform humans. Regarding symbolic calculating possibilities, computers outperformed humans
practically immediately, and several other areas followed. Currently, computers are outperforming best humans in most complex games like chess or
in capabilities like mass memory (See Figure 2).
It is hard to objectively measure intelligence, but one of the most common
definitions is performance in new, unknown situations. The other idea is by
Penrose (1991) that humans recognize intelligence based on some intuitive
common sense. We shall accept this position.
Memory capacity
Computers
Humans
1T
20G
1G
20M
1M
1K
Crossing
point
20K
Time
Figure 2. Computer capabilities progress exponentially ?
i.e. linearly on a logarithmic scale. Due to the much faster
growth rate, computers outperform humans in more and
more complex domains, currently in mass memory capacity.
Putting this basic intelligence (or consciousness) of humans and computers on the same graph, we again see that human performances remain unchanged in the last century, similar to Figure 2. But in this case, computer
basic intelligence remain indistinguishable from zero over the same period
(Figure 3). Growing exponentially, computers would by now have to be at
least a little intelligent and consciousness, e.g. at least like a little child, if
there were any correlation between speed of computing and intelligence.
4
MATJAZ GAMS
Intelligence, consciousness
So there must be something wrong with the strong AI thesis that digital computers will soon become truly intelligent (Wilkes 1992). Computer
computing power and top human properties do not seem to be related.
Human-level intelligence
Un unknown barrier
Computer intelligence
1940 1950 1960 1970 1980 1990 2000 2010 2020 2030
Figure 3. In top human properties like intelligence and
consciousness, computer performance remains indistinguishable from zero, contradicting exponential growth in
computing capabilities.
The discussion about the Turing machine sometimes resembled discussions between scientists and mentalists (Angell 1993; Abrahamson 1994;
Dreyfus 1979), but mostly it remained inside two scientific disciplines (Penrose 1989): strong and weak AI. Other related disciplines are cognitive
sciences and studies of Turing machines. One of our main interests is to
present formal computing mechanisms encapsulating human thinking.
2. Formal Model
Formally, can a single processing entity like the Turing machine (or a
human mental creative process) perform as well as two Turing machines
(two human mental creative processes) interacting with each other?
Here we often use term ?human mental process? since it is obvious that
some of thinking is rather trivial. In general, in this section we discuss top
mental processes like thinking, intelligence and consciousness.
In computer science, one of the key concepts is related to the Turing
machine. As long as we deal with formal domains, the universal Turing
COMPUTATIONAL ANALYSIS OF HUMAN THINKING PROCESSES
5
machine can perform exactly the same function as two of them (Hopcroft et
al. 1979). The main reason is that two functions can be performed as one
integrating function. We call this the paradox of multiple knowledge and
later try to show the neglected differences.
If we make experiments in classification and machine learning areas (Breiman
et al. 1984, Mantaras et al. 2000), the evaluation procedure is fairly well
defined. The computing entity with problem domain knowledge is denoted
as a model of the domain. It can be used to predict or perform tasks in this
domain, e.g. classify a new patient on the basis of existing knowledge. The
probability of correct solution is denoted as pi, 0i� The probability that
a combination of two or more models will perform correctly in a situation s
is denoted by qs. For example, for two models in a situation where the first
model succeeds (T) and the second fails (F), the probability that the combination will be successful is denoted by qTF (see Table 1). It is assumed
that 0s� and qFF = 0, qTT=1. Note that qTF is not related to concepts
like true false often used in machine learning.
Table 1. Analyses of four combinations of combining two processes.
s
ps
ps , d = 0
(F, F ) (1 ? p1 )((1 ? d)(1 ? p2 ) + d) (1 ? p1 )(1 ? p2 )
(F, T )
(1 ? p1 )(1 ? d)p2
(1 ? p1 )p2
(T, F )
p1 (1 ? d)(1 ? p2 )
p1 (1 ? p2 )
(T, T )
p1 ((1 ? d)p2 + d)
p1 p2
ps , d = 1
1 ? p1
0
0
p1
qs
qF F (= 0)
qF T
qT F
qT T (= 1)
Explanation of Table 1: The first column denotes all possible situations
of two sps ps d = 0ps d = 1qs (F, F )(1 ? p1 )((1 ? d)(1 ? p2 ) + d)(1 ? p1 )(1 ?
p2 )1 ? p1 qF F (= 0)(F, T )(1 ? p1 )(1 ? d)p2 (1 ? p1 )p2 0qF T (T, F )p1 (1 ? d)(1 ?
p2 )p1 (1 ? p2 )0qT F (T, T )p1 ((1 ? d)p2 + d)p1 p2 p1 qT T (= 1)
models. The first letter denotes the success/failure of the first model, the
second of the second model. General probability of each combination is
presented in column 2. There, p1 and p2 represent classification accuracy
of the first and the second model, and d represents dependency of the two
models. Columns 3 and 4 represent two special cases with d = 0 (independent) and d = 1 (totally dependent i.e. identical). The success rate of the
combining mechanism is represented in the fifth column (qs).
An example: Suppose that in 3/3 of all cases the two models perform
identically, and each model alone again classifies with 0.5. Suppose that in
case when one model fails and the other succeeds, the combining procedure
always chooses the correct prediction. From this data it follows pFF = pTT
= 0.75/2 = 0.375, pFT = pTF = 0.25/2 = 0.125, and p1 = p2 = 0.5. The
6
MATJAZ GAMS
mathematical calculation returns d = 0.5 meaning that the second model is
identical to the first one in one half of classifications and independent in the
other half of classifications. The parameters of combining mechanism are:
qFF = 0, qTF = qFT = qTT = 1. Classification accuracy of the combined
model is 0.625. This is 0.125, i.e. 12.5% in absolute terms better than the
best single model, which is quite a substantial increase.
The question we want to analyze is: when do two models perform better
than the best model? The ?technical? version of our Principle of multiple
knowledge (Gams 2001) claims that it is reasonable to expect improvements
over the best single model when single models are sensibly combined. Combining different techniques together is in recent years often denoted as the
?blackboard system? (Hopgood 2003).
There is another, ?strong? version of the Principle of multiple knowledge.
It states that multiple models are an integral and necessary part of any creative, i.e. truly intelligent process. Creative processes are top-level processes
demanding top performance, therefore ?single? processes cannot achieve top
performance. In other words: a sequential single model executable on the
universal Turing machine will not achieve as good performance as combined
models in majority of real-life domains. Secondly, no Turing machine executing a single model, e.g., no computer performing as a single model, will
be able to achieve creative performance.
First, we analyze the technical version of the principle.
3. Analysis
In this section we perform analyses of two computing entities, i.e. models.
The probability of successful performance of two models is obtained as a sum
over all possible situations; for two independent models it is (see Table 1):
pM =
X
ps qs = p2 (1 ? p1 ) qF T + p1 (1 ? p2 ) qT F + p1 p2
s?S
and for two dependent models by including d:
p?M
=
X
ps qs
s?S
=
p?M can
(1 ? d)( p2 (1 ? p1 ) qF T + p1 (1 ? p2 ) qT F + p1 p2 ) + dp1 .
be expressed in relation to pM :
p?M = (1 ? d)pM + dp1 .
COMPUTATIONAL ANALYSIS OF HUMAN THINKING PROCESSES
7
Here we assumed p1 ? p2 . For 0 < d < 1, the accuracy p?M lies between p1 and pM . Therefore, whenever two combined independent models
indicate better overall performance than the best model alone, dependent
models will also indicate it, and the improvement of accuracy p?M ? p1 will
be directly proportional to pM ? p1 with a factor of 1 ? d. This is an
important conclusion, but should not mislead us into thinking that we analyze two independent models, which is quite an irrelevant case in real life.
Rather, we analyze any two computing entities, in real life or in formal domains, but only by eliminating too dependent behavior to focus
on the most relevant performance. Final conclusions will be relevant for all
combinations of two processing entities, as mentioned above.
As mentioned, interaction is the most important part of the supercomputing mechanisms that enables improvements over the Turing machine.
But for the purpose of analyses of beneficial conditions, we concentrate on
independent cases and assume reasonable interaction.
Now we continue analyzing two independent models to reveal basic conditions in the 4-dimensional (p1 , p2 , qT F , qF T ) space, under which any
combined dependent models are more successful than the best single model
alone. This conclusion has already simplified the problem space. We can
further shrink the analyzed 4-dimensional space into a 3-dimensional space
by predefining one variable. Now we can graphically show conditions under
which two models perform better than the best one of them alone. We shall
analyze 4 cases:
(1)
(2)
(3)
(4)
p1 = p2 = p;
qT F = qF T = q;
predefined qF T ;
predefined p1 .
Case 1: p1 = p2 = p. This is the case where both models have the same
classification accuracy. We analyze under which conditions is pM greater or
equal to max(p1 , p2 ); therefore we compare max(p1 , p2 ) ? pM and derive:
1 ? qT F + qF T .
The combining mechanism must on average behave just a little better
than randomly to obtain the improvement.
Case 2: qT F = qF T = q. Again we compare two and the best single model
and obtain:
q?
max(p1 , p2 ) ? p1 p2
.
p1 (1 ? p2 ) + p2 (1 ? p1 )
8
MATJAZ GAMS
In this case there are three variables and we can plot the corresponding
hyperplane, which shows under which conditions two models perform better
the best single one.
In Figure 4 we show the lower bound for q that enables successful combined classification depending on p1 and p2 . If p1 = p2 , q must be at least
0.5. This is consistent with the case 1: qT F + qF T > 1. Another conclusion: the greater the difference between p1 and p2 , the greater must be q to
achieve the improvement over the best single model. This seems intuitively
correct as well, and can also be analytically analyzed. If models perform
similar, we need to guess just a little better than random when combining
models. But if one model is substantially better than the other, one has
problems determining when to trust the less successful model.
Figure 4. In the space above the hyperplane two models
outperform the best single one. In terms of parameters, we
analyze lower bound of q.
The improvement is possible for all (p1 , p2 ) pairs. No improvement for
qT F + qF T < 1 is possible. Unlike in case 1, qT F + qF T > 1 by itself does
not guarantee an improvement.
COMPUTATIONAL ANALYSIS OF HUMAN THINKING PROCESSES
9
Figure 5. For qF T = 0.5, the space where two classifiers
perform better than the best one, shrinks compared to Figure 4.
.
Case 3: predefined qF T . Now we predefine one value of the variable qF T ,
and get the condition:
qT F ?
max(p1 , p2 ) ? (1 ? p1 )p2 qF T ? p1 p2
.
p1 (1 ? p2 )
Two cases for qF T = 0.5 and qF T = 0.999 are presented in Figure 5 and
Figure 6.
The improvement space in Figure 5 is smaller than in Figure 4. For
qF T = 0.5, in a large proportion of the (p1 , p2 ) pairs, improvement is not
possible (the top wing of the surface). For qF T = 0.999 in Figure 6, which
means nearly perfect guessing when the better model fails and the worst
one succeeds, improvement is feasible in nearly the whole (p1 , p2 ) plane, for
nearly all values of qT F . When the first model classifies better than the
second one (p1 > p2 ), the lower bound for qT F is roughly proportional to
10
MATJAZ GAMS
Figure 6. For qF T = 0.999, two combined models often
perform better than the best single one.
the difference between p1 and p2 . Good estimates of the correctness of a
better model play a major role in determining the overall success.
Case 4: predefined p1 . In this case, the following condition is obtained:
max(p1 , p2 ) ? p1 (1 ? p2 ) qT F + (1 ? p1 )p2 qF T + p1 p2 .
Two cases, p1 = 0.5 and p1 = 0.999, are graphically represented in Figures 7 and 8. They show the same influence of the difference between p1 and
p2 : the greater the difference, the harder it is to obtain an improvement.
Improvements are in general possible under similar conditions as observed
in previous cases.
Overall, analyses strongly indicate that in many real-life domains, improvements can be obtained by sensibly combining two models/processing
entities. Here we presented four special cases, which indicate general conditions and relations:
COMPUTATIONAL ANALYSIS OF HUMAN THINKING PROCESSES
11
Figure 7. For a predefined value of p1 = 0.5, p2 > p1 , a
large part of the space is again beneficial for the two models.
? The best situation when combining models is obtained when p1 =
p2 , i.e. when models perform similarly good
? with fixed qF T and qT F , increasing difference between p1 and p2
proportionally decreases the portion of the space where combining
is beneficial, meaning that the biggest the difference in quality, the
more difficult it is to get an improvement over the best model, and
? it is more important that the better model is well estimated than
the worse model, which has generally less effect on the success of a
combination.
These conclusions can be verified in real tests as well (Gams 2001).
What is the meaning of these formal analyses? First, they show, but
not prove, that in many reasonable situations in real-life we can expect
meaningful improvements when sensibly combining two good, but not too
similar programs/models. To show that two models are beneficial in a general real-life domain on average, we need much more complex analyses and
of course ? gathering statistics from experiments in practical tasks. Both
12
MATJAZ GAMS
Figure 8. The same analysis for a predefined value of p1 = 0.999.
studies strongly indicate that multiple knowledge is indeed beneficial. For
analytical analyses refer to (Gams 2001), while there have been countless reports about practical combining two models/methods/programs in various
domains from pattern recognition to classification.
In relation to formal computing theory, e.g. the Turing machine (TM) the
puzzle remains because ? as mentioned - it is always possible to construct
another TM that performs exactly the same as a combination of two TMs. In
relation to models/programs, we refer to the paradox of multiple knowledge,
since it is always possible to construct a model/program, that will perform
exactly the same as a combination of two single models/programs.
In the next session we show that it is possible to resolve this contradiction
by introducing computing machines, stronger than the universal TM or even
only by interaction multiple structure.
4. Supercomputing
Soon after the introduction of the universal Turing machine it has been
known that, at least in theory, stronger computing mechanisms exist. Alan
COMPUTATIONAL ANALYSIS OF HUMAN THINKING PROCESSES
13
Turing himself introduced the universal TM only for simulating procedural/mechanic thinking of a human while accessing that this might not
be sufficient for creative thinking. At the same time he found no formal
reason why computers in future should not outperform human in thinking
and even feelings. His estimate of this event was around year 2000, and
obviously, this is far from realized.
Turing already proposed a stronger computing mechanism ? the Turing
machine with an oracle, capable of answering any question with always correct Yes/No (1947; 1948). This formal computing mechanism is obviously
stronger than the universal Turing machine, and can easily solve several
problems like the halting problem, i.e. whether a TM performing a program will stop or not under any condition. The only problem is that there
is no known physical implementation of a guru, while digital computers are
very good implementations of the universal Turing machine. Also, the Turing machine with a guru does not seem to perform like humans. However,
there are several other stronger-than-TM computing mechanisms with interesting properties (Copeland 2002). Terms like ?hypercomputation? and
?superminds? (Bringsjord, Zenzen 2003) are introduced.
History is full of interesting attempts in the stronger-than-UT direction.
Scarpellini (1963) suggested that nonrecursive functions, i.e. those demanding stronger mechanisms than the universal Turing machine, are abundant
in real life. This distinction is important, since obviously most of simple processes are computable, and several simple mental processes are computable
as well. But some physical processes and some mental ? i.e. creative processes are very probably not. One of the debatable computing mechanisms
are quantum computers. Clearly, no digital computer can compute a truly
random number, while this is trivial in quantum events.
Komar (1964) proposed that an appropriate quantum system might be
hypercomputational. This is unlike Penrose who proposed that only the
undefined transition between quantum and macroscopic is nonrecursive.
Deutch (1992) also reports that although a quantum computer can perform computing differently, it is not in principle stronger than the universal
TM. Putnam (1965) described a trial-and error Turing machine, which can
compute also the Turing-uncomputable functions like the halting problem.
Abramson (1971) introduced the Extended Turing machine, capable of storing real numbers on its tape. Since not all numbers are Turing-computable,
Turing machines cannot compute with those numbers, and are there inferior in principle. Boolos and Jeffrey (1974) introduced the Zeus machine,
a Turing machine capable of surveying its own indefinitely long computations. The Zeus machine is another version of the stronger-than-UTM.
It is also proposed as an appropriate computing mechanism by Bringsjord
14
MATJAZ GAMS
(Bringsjord, Zenzen 2003). Karp and Lipton (1980) introduced McCullochPitts neurons, which can be described by Turing machines, but not if growing at will. Rubel (1985) proposed that brains are analog and cannot be
modeled in digital ways.
One of the best-known authors claiming that computers are inferior to
human creative thinking is Roger Penrose (1989; 1994). His main argument is that human superiority can be formally proven by extending the
Goedelian argument: in each formal system a statement can be constructed
that can not be formally proven right or wrong. The statement it similar to
the ?liar statement? (Yang 2001), which says something about itself. Humans immediately ?see? the truth of such statements since they deal with
similar situations all the time in real life, but formal systems cannot. According to Penrose, the reason for ?seeing? is that humans are not abided by
limitations of formal systems; they are stronger than formal systems (computers). Furthermore, since humans ?see? the truth and cannot describe it
formally, the solution is not procedural, i.e. Turing computable, therefore,
humans use nonrecursive mechanisms. The other major idea by Penrose
is related to supercomputing mechanisms in the nerve tissue. This is the
Penrose-Hameroff theory (Hameroff et al. 1998). The special supercomputing mechanisms are based on quantum effects in connections between
neurons.
Several of these theories are well in accordance with our principle of multiple knowledge. Principles are general theories, and should be supported by
many more specific theories and also interpretations of the principles. The
undoubtedly valid hypothesis of course is, that there is another, strongerthan-UTM mechanism. The principle is consistent with that, but also with
much softer interpretations, e.g. that multiple interacting processes with
open input are sufficient for supercomputation. This structural/processing
interpretation is related to the question where intelligence in humans is. Is
it in a genome? In one genome not, but the brain and the mind is to a
large extend dependent of it. However, it is the genome itself that enables
construction of the brain and supermind. So the intelligence comes only
through appropriate structure.
In relation to the Penrose-Goedelian argument, it can be derived from
the principle of multiple knowledge, that humans in a flash introduce any
new mechanism necessary whenever the current computing mechanism gets
Goedelized. So, while any formal system can be Goedelized also in our mind
processes, it can also be extended so rapidly and consistently, that there is
no way in real life that the mind gets actually trapped with any specific
case. The Turing machine is not time-dependent, while most cases in real
life are. Therefore, there is no practical sense in formally showing that any
COMPUTATIONAL ANALYSIS OF HUMAN THINKING PROCESSES
15
formal system can be Goedelized, when there is no time for it. Thinking in
the mind resembles a multi-process in society of multiple constantly interacting processes that can only be frozen in time for a particular meaningless
moment.
Similar performance is achieved by growing communities of final number
of mathematicians. What we argue with the principle of multiple knowledge, is that one human brain and mind in reality performs like a community of humans. The idea is similar to the Society of minds (Minsky
1987; 1991), where Minsky presented the mind as a society of agents, but
presented no claim that this computing mechanism is stronger than a universal Turing machine. Minsky also introduced the blackboard idea - that
multiple knowledge representations are in reality stronger than single knowledge representations. However, Minsky seems inclined to the validity of the
Church-Turing thesis, which he often presented to public.
One of the stronger-than-UTM that we find relevant are interaction Turing machines. Wegner in 1997 presented his idea that interaction is more
powerful than algorithms. The major reason for superior performance is in
an open truly interactive environment, which not only cannot be formalized, it enables solving tasks better than with the Turing machine. This
resembles our principle, but can be interpreted in a simpler form as well.
Consider social intelligent agents on the Internet (Bradshaw 1997), which
already fit the interaction demand (see Figure 9). Such agents are already
in principle stronger than stand-alone universal Turing machines, although
these are just common computers with the addition of open Internet communication. Therefore, current computers, if able to truly interact with the
open environment, should already suffice.
Quite similar to the interaction TM are ?coupled Turing machine? (Copeland,
Sylvan 1999). The improvement is in the input channel, which enables undefined input and thus makes it impossible for the universal Turing machine
to copy its behavior.
Similar idea of introducing mechanisms that cannot be copied by the
universal Turing machines comes from partially random machines (Turing
1948, Copeland 2000). These Turing machines get random inputs and therefore can not be modeled by a Turing-computable function as shown already
by Chruch.
The problem with these ideas is that it is hard to find physical evidence
for these mechanisms in real life around us. For example, there is no oracle
in real world that would always correctly reply to a Yes/No question. On
the other hand, nearly all practical, e.g. mathematical and physical tasks
are computable, i.e. Turing computable. There is no task we are not able
to reproduce by a Turing machine. Copeland (2002) objects to this idea
16
MATJAZ GAMS
INPUT
INPUT
Figure 9. Some stronger-than-universal Turing Machines
resemble this graphical representation, consistent with the
principle of multiple knowledge.
citing Turing and Church. Referring to the original statements presented
by the founders of computer science, one observes discrepancies between
mathematical definitions and interpretations later declared by the strong AI
community. Original mathematical definitions are indeed much stricter, e.g.
referring to mathematical definitions. Yet, to fully accept Copeland?s claims,
humans should produce one simple task that can be solved by humans and
not by computers.
The example we propose is simply lack of intelligence and consciousness
in computers. There is a clear distinction between the physical world and
the mental world. The Turing machine might well be sufficient to perform
practically all meaningful practical tasks in practical life. But the mental
world is a challenge that is beyond the universal Turing machine. Every
moment in our heads a new computing mechanism rumbles on joining and
interacting with others. In computing terms, our mind performs like an
unconstrained growing community of at any time final number of humans.
COMPUTATIONAL ANALYSIS OF HUMAN THINKING PROCESSES
17
5. Confirmations / Discussion
In this paper we have shown basic advantages when combining two mental processes/programs/models. There is practical relevance of combining
several processes/programs/models, and the principal one related to humanlevel intelligence and consciousness. The first is denoted as the general version of the principle and the last as intelligent version of the principle of
multiple knowledge.
As mentioned, there have been many confirmations of the principle of
multiple knowledge, e.g., in machine learning where several hundreds of
publications show that multiple learning mechanisms achieve better results;
in simulations of multiple models and formal worst-case analyses, which
show that reasonable multiple processes can outperform best single-ones;
when fitting the formal model to real-life domains showing that it can be
done sufficiently good.
There are also reasonable confirmations that human thinking is highly
multiple. In historic terms, the progress of human race and its brains/mind
also strongly indicate that multiple thinking is in strong correlation to intelligence and consciousness. At the anatomic level, especially through the
split brain research, there is the significant left-right brain asymmetry showing that humans do not think in one way as programs on Turing machines
do.
We argue that digital computers might be inadequate to perform truly
intelligent and consciousness information processing. Currently, there are
several supercomputing or hypercomputing mechanisms proposed. We have
proposed our principle of multiple knowledge differentiating between universal Turing machines and human brains and minds. Thinking processes in
our heads perform like a group of actors, using different computing mechanisms interacting with each other and always being able to include new
ones.
The principle of multiple knowledge is in a way similar to the Heisenberg principle, which discriminates the physical world of small (i.e. atomic)
particles from the physical world of big particles. Our principle differentiates between universal Turing computing systems and multiple interaction
computing systems like human minds.
In analogy to physics, existing computer single-models correspond to
Newtonian models of the world. Intelligent computer models have additional
properties thus corresponding to quantum models of the world valid in the
atomic universe. The Heisenberg?s principle of uncertainty in the quantum
world is strikingly similar to multiple interaction computing introduced here.
18
MATJAZ GAMS
Weak AI basically says that the universal Turing machine is not strong
enough to encapsulate top human performances. The Principle of multiple
knowledge does not directly imply that digital computers cannot achieve
creative behavior. Rather, it implies that current computers need substantial improvements to become creative, and that just increased performances
won?t be enough. But human mental processes might as well indeed be in
principle different compared to computer systems.
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Department of Intelligent Systems, Jozef Stefan Institute, Jamova 39, 1000
Ljubljana, Slovenia, Europe
E-mail address: matjaz.gams@ijs.si
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