1. E.g. logistic equation: xt+1 = lambda*xt*(1-xt).
Interpret xt as population at time t as proportion of what is possible. lambda is rate of poputlation growth.
(1-xt) is dampening effect. Nonlinear equation.
2. This simple equation displays very odd behavior.
For lambda < 1, population goes to 1.
For lambda > 1, < 3.57, population is stable or oscillating between two points.
For lambda > 3.57, performance is chaotic: apparently random results, extremely dependent on starting value of x. E.g. x=.4 and x=.35 makes a huge difference.
3. This is chaos: slight differences in initial conditions lead to exponentially diverging results over time.
4. So a process, though deterministic, is inherently unpredictable.
5. Although it may show regularities: "attractors": stable states into which a system can slip, but out of which it can be perturbed.
1. Weather: the butterfly effect: a butterfly flapping its wings in Texas can have a big effect on Ontario's weather a few days later.
2. Simple pendulum: can go into chaotic, seemingly random motion.
3. Dripping faucet.
4. Biological systems: ecologies, cardiac rhythms, neurons?
5. Economics: stock market, economy in general.
General idea: several variables related to each other nonlinearly can produce very complex behavior. Cf. fractals. A dynamic system is any system that can be described by means of an evolution equation.
Tim van Gelder, "What might cognition be if not computation?"
1. Example: Watt's governor
Steam engine driving a flywheel running machinery.
Want speed of wheel to be constant despite fluctuations of workload and steam pressure.
Representational strategy: develop computer program with structures that represent steam pressure, etc., and do calculations to adjust speed of wheel.
But Watt's solution was very different: attach spindle to flywheel with two arms, each with a metal ball. When spindle goes to fast, balls fly out by centrifugal force, making the arms adjust the throttle valve on the steam engine, reducing pressure and slowing flywheel.
2. Connectionist systems are dynamical systems. The state of the system is the activations of the various units, and the evolution equation is the equation that updates the activation of the various units. Always nonlinear.
Hypothesis (Smolensky): cognition is state-space evolution in a connectionist dynamical system.
3. Van Gelder's view is more radical: take the Watt governor as a prototype, and dispense with any notion of explicit represenation, and dispense with connectionist structure as well: just give equations that describe the behavior of the system.
1. The Watt governor is too primitive to suggest the equations to be used for how thinking evolves.
2. Without such a model, the idea that the mind is a dynamical system is much too vague: we need to know what kind of dynamical system it is. Maybe it's a dynamical representational system. Or connectionist, or something else now not understood.
3. van Gelder's model has the same limitations as Brook's robots, blindly responding to the world. We need a model of mind as both situated in the world and able to think about it with a fair degree of freedom, which requires the representational theory of mind.
Cognitive science has tended to ignore social aspects of knowledge.
1. Traditionally, understanding of knowledge has been individualistic. E.g. Plato, Descartes. Knowledge is possessed by individuals. Rationality is an individual matter.
2. This view challenged by Peirce, 1860s. "interest in an indefinite community" is an "indispensable requirement of logic." (Writings vol. 3, p. 285). For Peirce, truth was a matter of what the community of inquirers would eventually agree on.
3. Kuhn, 1962. Structure of Scientific Revolutions. The scientific community is a crucial unit for understanding development: shared values, methods, etc.
4. Solomon, 1993. "Social empiricism." Individuals are caught up in their personal biases. But science as a social enterprise can be rational in a way that no individual is: what gets accepted in the society is in fact the most empirically adequate. A scientfic community is rational in that eventually everyone reaches the empirically correct conclusion, even if they do it for somewhat biased reasons.
But: this is still too individualistic. It neglects the extent to which individuals have acquired the socially approved interest of doing good experiments and accepting good theories. Cf. Longino's Science as social knowledge.
5. Need for communitarian view, that analogously to political philosophy, takes community as basic, not simply derived from individual position. Descriptively and normatively, for knowledge as for politics, community is not simply derived from individuals.
Social epistemology is now an active research area in philosophy.
Distributed artificial intelligence (DAI) investigates principles by which computers that each possess some degree of intelligence can collectively have accomplishments that no individual computer could easily have on its own. DAI is also called multi-agent systems.
Many AI applications are inherently distributed, for example controlling a set of intelligent robots working together or bringing together a number of expert systems with complementary areas of expertise.
Distributed computing differs from parallel computing in that the latter typically involves simple nodes of similar kinds communicating with each other in straightforward ways. For example, in connectionist systems, each neuron-like node is an uncomplicated device that updates its activation based on the activation of the nodes to which it is linked and the weights on those links. Intelligence is an emergent property of the operation of numerous interacting nodes, not of each individual node. In contrast, in distributed artificial intelligence, it is assumed that each node has much greater computational power than the simple units in connectionist systems, including the capacity to communicate in more complicated ways with other nodes.
Huberman's results on the advantages of cooperation among computational agents: n interacting problem solvers do better than n problem solvers working separately.
1. Examples:
- Physics papers with 30 authors
- Blue Jays knowledge of baseball
- Businesses cooperating on projects
- Navy ship navigation: 7 people (Ed Hutchins, Cognition
- Visual Cognition group
- Get more examples from students.
2. Shared knowledge, goals. Conversation and coordination required to work towards these goals.
1. Collaborators. Scientists at the same or different institution who are working on common projects will communicate frequently.
2. Students and teachers. Communication links exist between scientists and scientists-in-training. If, as in cognitive psychology and many other fields, the students function as collaborators on research projects, the links are particularly tight. Research methods and skills are communicated along with more easily described verbal information.
3. Colleagues. Scientist working in the same university department may see each other regularly and exchange ideas.
4. Acquaintances. Scientists who regularly attend the same conferences and workshops will get to know each other and may exchange information irregularly.
See my papers on cognitive and social aspects of science.
1. Greater productivity.
2. Greater creativity: combine insights.
1. Possible lack of reliablility: e.g. fraud in scinece.
2. Confusion, bureacracy, inflexibility.
3. Time cost in communication.
1. In science, as in many other parts of life, knowledge is socially distributed. Understanding of the applications of knowledge will require attention to how social structures and processes make possible the communication of individual cognitive structures.
2. Many interesting normative questions arise too: How should communities of knowers, e.g. science researchers in Canada, be organized so as to encourage the development of knowledge?
3. The social challenge to cognitive science can be met by supplementing CRUM with social/computational considerations.
Culture is the way of life of a society, including beliefs and behaviors.
Examples:
Computational Epistemology Laboratory.
This page updated Nov. 17 2008