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Notes on Emergent Inference
References are listed at the bottom. Entries are arbitrarily labeled, for now,
but I do intend to renumber them more adequately as their number grows. Last
updated 09-20-2011.
(AAA) What is Emergent Inference?
EI is a new type of inference. EI was recently discovered (see [1] and
references therein). EI is a mathematical property of causal sets.
There are several other types of inference, but EI has a distinguishing
feature: it is not man made. There is a very important consequence to this
feature: EI was available to evolution since
the beginning of life.
(AAB) What are, exactly, your claims?
My claims are [1]:
Claim C1. Knowledge base. Any finite system susceptible to mathematical analysis
can be represented as a causal, where the nature of the elements
of the set is irrelevant.
Claim C2. Natural structure. Any causal set has a natural structure,
where information appears organized and associated into units called blocks.
Claim C3. Feedback and hierarchies. Structures described by block systems
are, in turn, causal sets, and have natural structures of their own.
This claim describes feedback as natural self-organization, and the structures
as fractals with self-similar levels that obey a power scaling law.
Claim C4. The functional. To every causal set there corresponds a set
of permutations of its elements that are compatible with the partial order,
called the legal permutations of the set. The structures referred to in claim C2
can be found in the set of permutations by a search process where the functional
of emergence is optimized.
The following corollary is a consequence of claims C1-C4:
Corollary L1. The structure of systems. Any finite system amenable to
mathematical analysis has a natural hierarchical structure that can be found by
emergent inference.
(AAC) Have you made any conjectures?
Yes [1]:
Conjecture K1. Emergence and self-organization. Observed phenomena of emergence and self-organization in complex
dynamical systems bear a causal relationship to local properties and
interactions of the components of the system, and are explained by corollary L1.
Conjecture K2. Intelligence. Emergent behavior and feedback in complex systems such as the
brain give rise to a series of phenomena collectively known as intelligence.
This conjecture also implies that intelligence has a source from first
principles, and that the source is the phenomenon of emergence in causal sets.
(ABC) Is EI Turing-equivalent?
EI is not an algorithm or a virtual machine. The notion of Turing equivalence
does not apply to EI.
(ABA) Can EI be simulated by a computer program?
No. EI is a mathematical property, not an algorithm. In other words, given the
causal set, given the structures. The structures already exist as
soon as a causal set is given, they can not be simulated by a
computer program.
EI has been compared to the concept of mathematical limit. Just as EI, the
mathematical limit is a mathematical property (of continuous functions). Just as
EI, the concept of limit can not be replaced with anything else. It would be
unconceivable to attempt to build a 747 while ignoring the concept of limit,
because Newton's equations of motion are based on that concept and the rest of
Aeronautical Engineering is based on Newton's equations. It would also be
unconceivable to try to develop Artificial Intelligence while ignoring the
structures of EI.
However, there is a big difference between EI and the concept of limit: in EI,
there is no notion of continuity. A mathematical limit can not be approximated
by a finite algorithm, but it can be approximated as accurately as desired by an
infinite algorithm that is truncated when the desired accuracy has been
achieved. This is possible when the functions are continuous. But it is not
possible when chaos exists, as in the case of a hurricane, because the butterfly
effect defeats the assumed continuity.
In the case of EI, the structures can never be approximated by a finite
algorithm or by the convergence of an infinite one, because the notion of
continuity does not exist and the butterfly effect is always present. The
correct structures can only be found by the application of EI.
(ABB) If EI can not be simulated by a program, then what is the SCA
algorithm?
The SCA algorithm ([2], Section 3) merely searches the set of permutations of
claim C4 for the permutations with the minimum value of the functional of
emergence. The structures are already there, SCA does not create them. In fact,
any procedure can be used for the search as long as it finds the optimum
permutations. For example, the study of small systems ([1], Section 4) relies on
a simple inspection of the set of permutations, because this set isn't too
large. It has also been suggested that the Cuthill-MacKey algorithm ([3],
Section 4.5) be used to initiate the search. Any search procedure that finds the
optimum permutations is acceptable.
(AAD) Did evolution take advantage of emergent inference?
EI turns raw sensory information into structures that represent meaningful
features of the environment. Since EI is a mathematical property, EI does all
that mechanically, without any pre-requisites and without the need for any
previously existing intelligent capabilities. It would be very surprising if
evolution
didn't take advantage of such a powerful feature to improve survival. The
prominent biologist Stuart Kauffman supports this view, and believes that
emergence plays as much of a role in evolution as Darwinian natural selection. While evolution was promoting only survival, the unintended
consequence of the application of EI was intelligence.
(AAK) Is there emergence in the brain?
I believe there is.
(AAE) Does emergent inference have any practical consequences or
applications?
The discovery of EI has immediate practical applications in Software
Engineering. Four of the great unsolved automation problems (GUAP) of Software
Engineering of the last four decades
have exact mathematical solutions, and these solutions can be found only by EI.
The four problems are: Object-oriented analysis, software refactoring, the
integration of man-made software, and self-programming. None of the four
problems has been fully automated. Currently, approximate solutions to
any of the four problems can be obtained only by human analysts. This is so
because the human brain is the only known source of EI. But it also makes
software analyst-dependent and prevents automation in computer-related
applications. In addition, parallel programming is under way.
More in general, EI is a new mathematical tool for solving problems of
organization and structure in all complex dynamical systems. Computer programs
running on a computer are just an example of such systems. The brain is another.
The discovery of EI is expected to have a significant impact in all disciplines that deal with
complex systems, including SE and Computer Science in general, Complex Systems
Science, Engineering, Neuroscience, Foundational Physics, Evolutionary Biology,
and others, as well as technologies such as image recognition, natural language
processing, and automation in general.
(AAF) Are there any available tools for EI-based refactoring, OO analysis,
integration, or self-programming?
No. EI is a recent discovery. To my knowledge, no commercial development on any
of the unsolved problems of SE has yet been undertaken. I myself only conduct
research on the subject, but do not intend to undertake any development.
(AAG) How was EI discovered?
The discovery of EI was the result of a long process of research on the
refactoring of software. An account of the research can be found in the
Introduction of [1]. The original motivation for the research was the observation of
extraordinary self-organization properties in canonical matrices. The key
finding was the discovery of the functional via the correspondence between
canonical matrices and causal sets. Causal sets are one of the most prevalent and fundamental objects in
Mathematics, and are the (invisible) root of many applications in Physics,
Engineering and technology. It is easy to represent complex systems such as
software or sets of mathematical equations as causal sets.
(AAH) What is a model? [1]
A model is an abstraction of the features of an observed system,
a simplification that contains only those features that the model designer
considers to be the most important for some particular purpose, while
other less important or less influential features are neglected. The intent of
the model is to simplify the calculations and gain in understanding by
preserving only the most critical features and ignoring unnecessary detail. The
model does not have to resemble the real system at all, for example the continuous model of matter, where
solid, liquid, or gaseous matter is represented as a continuous and the
molecular structure is ignored, is enormously useful for studies of the sea, the
atmosphere, and in general the motion of gases, liquids and solids. A model
always refers to some system, and is associated with a theory for that system.
By applying the theory, the model can be used to calculate results and predict
expected behavior. In order to be useful, a model must be capable of producing
useful results that agree with observation. Because of the approximation,
a model is restricted in its range of applications, and can not be used beyond
this range. The model designer must specify what the range is. A model that is powerful enough can play a very
important role in science. For example, the Standard
Model is fundamental for particle physics.
(AAJ) What is a minimalist model?
Particularly useful are the so called
minimalist models (Phys. Today, Sept. 2011, p.19), which represent only one or very few features or the system and
are intended to isolate only those aspects of the behavior of the system that
are controlled by those features in cases where the system is too complicated
and can not be understood as a whole. For example, the Bohr model of the
hydrogen atom was not entirely correct, but was essential for the development of
the Schroedinger equation of Quantum Mechanics. Another example is the proposed
CFS brain model, which is also minimalist and intended to describe the mechanism of
emergent inference.
(AAI) How is a metaphor different from a model?
A model is very different from a metaphor. A model is supposed to be founded on
rigorous mathematics and experimental fact, otherwise it would not be possible
to use it for quantitative calculations or expect it to produce useful results.
Instead, metaphors are not intended for quantitative calculations. What can one
do with a metaphor? A firefighter who sees smoke can use the metaphor "where
there is smoke there is fire" to find the fire. Using the metaphor "where there
is structure there is inference," a scientist who finds structures in a
self-organizing system will be able to find the inference that caused the
structures to exist. Metaphors are used as familiar reminders of useful
associations.
(AAL) What is a conjecture? [1]
A conjecture is a statement that can not be proved, but is supported by some
existing evidence, and provides a conceptual framework for further research in
some discipline. A stated conjecture prompts other researchers to examine it,
contribute their views and results, and generate scrutiny and debate. A
conjecture can be proved or disproved. Sometimes a conjecture can never be
proved or disproved, and the scrutiny continues for ever. In either one of the
three cases, the conjecture can be very beneficial to science. Proving an
important conjecture is an equally important step forward. Disproving a
conjecture is also a step forward because it prevents rediscoveries and
validates other competing conjectures. Sometimes one single observation that
contradicts a conjecture is sufficient to disprove it, partially or totally. But
the most useful conjectures are the ones that remain under scrutiny forever. The
process of examination constantly contributes new ideas and new lines of
research to the discipline. A reasonable conjecture is always very useful to
science.
References
[1] Emergence and self-organization in partially ordered sets. Sergio
Pissanetzky. Complexity, Volume 17, Issue 2, November/December 2011, Pages:
19–38. Article first published online : 22 OCT 2011, DOI: 10.1002/cplx.20389.
Note: The type of partially ordered sets discussed in this publication are know
as causal sets, or causets.
[2] The matrix model of computation. Sergio Pissanetzky. Proc. 12th
Multi-conference on Systemics, Cybernetics and Informatics, pp. 184-189 (2008).
[3] Sparse Matrix Technology. Sergio Pissanetzky. Academic Press, London, 1984.
MIR, Moscow, 1988.
[4] Structural emergence in partially ordered sets is the key to intelligence.
Sergio Pissanetzky. Artificial General Intelligence. Lecture Notes in Artificial
Intelligence, a subseries of Lecture Notes in Computer Science, Springer, pp.
92-101 (2011). Note: The type of partially ordered sets discussed in this
publication are know as causal sets, or causets.
[5] A new universal model of computation and its contribution to learning ,
intelligence, parallelism, ontologies, refactoring, and the sharing of
resources. Sergio Pissanetzky. Int. J. of Information and Math. Sciences
(previously known as Int. J. of Computational Intelligence), Vol. 5, no. 2, pp.
143-173 (2009). Available on-line.
[6] Emergent inference, or how can a program become a self-programming AGI
system? Sergio Pissanetzky. Workshop on Self-programming in AGI systems. AGI-11
conference, Google Headquarters, Mountain View, CA. August 3-6, 2011. Full text
PDF, slides and slide notes are
available.
[7] Artificial Intelligence. A modern Approach. Stuart J. Russell and Peter
Norvig. Third Edition. Prentice Hall Series in Artificial Intelligence, 2010.
[8] Self-Programming through Imitation. J. Storrs Hall. Workshop on
Self-Programming in AGI Systems. Fourth Conf. on Artificial General
Intelligence. Mountain View, CA, 3-7 Aug. 2011. Available from http://www.iiim.is/agi-workshop-self-programming/.
[9] Thinking Outside the Box: Creativity in Self-Programming Systems. Stefan
Leijnen. Workshop on Self-Programming in AGI Systems. Fourth Conf. on Artificial
General Intelligence. Mountain View, CA, 3-7 Aug. 2011. Available from http://www.iiim.is/agi-workshop-self-programming/.
[10] NOVA Science Now. How does the brain work? Broadcast on PBS, hosted by
astrophysicist Neil deGrasse Tyson.
[11] Answering Descartes: Beyond Turing. Stuart Kauffman. Proc. of the 2011
European Conf. on Artificial Life (ECAL 11), 20th Anniversary Edition: Back to
the Origins of Alife, pp.11-22, 2011.
[12] Organizing principles of real-time memory encoding: neural clique
assemblies and universal neural codes. L. Lin, R. Osan, and J. Z. Tsien. Trends
in Neuroscience, Vol 29, pp. 48-57, (2006).