1 n Where Do New Ideas Come From? How Do They Emerge? Epistemology as Computation (Information Processing) NKS 2007 Wolfram Science Conference July 15,

1

n

Where Do New Ideas Come From? How Do They Emerge?

Epistemology as Computation (Information Processing)

NKS 2007 Wolfram Science Conference

July 15, 2007 – University of Vermont, Burlington

Gordana Dodig-Crnkovichttp://www.idt.mdh.se/personal/gdc/

Department of Computer Science and EngineeringMälardalen University, Sweden

2

Greg Chaitin - Alan Turing Lecture on Computing and Philosophy,Epistemology as Information Theory: From Leibniz to the Omega Numberhttp://www.idt.mdh.se/ECAP-2005/

E-CAP 2005 SwedenEuropean Computing And Philosophy Conference

3

“Understanding is compression of information.”

However:

“In other words, the normal, Hilbertian view of math is that all of mathematical truth, an infinite number of truths, can be compressed into a finite number of axioms. But there are an infinity of mathematical truths that cannot be compressed at all, not one bit!”

Greg Chaitin Epistemology as Information Theory:

From Leibniz to the Omega Number

4

In the conclusion of Epistemology as Information Theory: From Leibniz to Ω, Chaitin leaves us with the following assignment: “In fact, I believe that this is actually the central question in biology as well as in mathematics; it's the mystery of creation, of creativity: Where do new mathematical and biological ideas come from? How do they emerge?”

5

- Info-computational universe

- Organisms are information-processing computational systems

-We as other living organisms are open systems

- Interaction is central for all life

- Evolution is the basic mechanism that helps us understand cognition, from

simplest cognitive systems (organisms) to more and more complex ones

- Persistent patterns of interaction with the environment leave trace

on the cognitive structures of the organism

- Epistemology naturalized on the most basic level by info-computationalism

Where Do New Ideas Come From? How Do They Emerge?

6

Investigations into Information Semantics and Ethics of Computing

Computation InformationComputation as Information ProcessingEthics of ComputingOpen Problems RevisitedResearch ResultsFuture Research

http://www.diva-portal.org/mdh/theses/abstract.xsql?dbid=153

Dodig-Crnkovic G., Bookrest 2Oil on kanvas

7

Dodig-Crnkovic G., Ab Ovo. Information: Between the Anvil and Hammer – Orphean Theme, oil on canvas

Information

The informational Universe: Paninformationalism

A special issue of the Journal of Logic, Language and Information (Volume 12 No 4 2003) dedicated to the different facets of information.

A Handbook on the Philosophy of Information (Van Benthem, Adriaans) is in preparation as one volume Handbook of the philosophy of science. http://www.illc.uva.nl/HPI/

8

Computation

The computing Universe: Pancomputationalism

Zuse was the first to suggest (in 1967) that the physical behavior of the entire universe is being computed on a basic level, possibly on cellular automata, by the universe itself which he referred to as "Rechnender Raum" or Computing Space/Cosmos.

Computationalists: Zuse, Wiener, Fredkin, Wolfram, Chaitin, Lloyd, Seife, ..

Computing: Computer Science, Computer Engineering, Software Engineering and Information Systems, according to ACM/IEEE (2001). The German, French and Italian languages use the respective terms "Informatik",

"Informatique" and “Informatica” (Informatics in English) to denote Computing.

9

Computing Nature and Nature Inspired Computation

In 1623, Galileo in his book The Assayer - Il Saggiatore, claimed that the language of nature's book is mathematics and that the way to understand nature is through mathematics. Generalizing ”mathematics” to ”computation” we may agree with Galileo – the great book of nature is an e-book!

Natural computation includes computation that occurs in nature or is inspired by nature. Computing

Inspired by nature: Evolutionary computation Neural networks Artificial immune systems Swarm intelligence

Simulation and emulation of nature:Fractal geometry Artificial life

Computing with natural materials: DNA computing

Quantum computing

Journals: Natural Computing and IEEE Transactions on Evolutionary Computation.

10

Turing Machines Limitations - Self-generating Systems

According to George Kampis, complex biological systems must be modeled as self-referential, self-organizing systems called "component-systems" (self-generating systems), whose behavior, though computational in a generalized sense, goes far beyond Turing machine model.

“a component system is a computer which, when executing its operations (software) builds a new hardware.... [W]e have a computer that re-wires itself in a hardware-software interplay: the hardware defines the software and the software defines new hardware. Then the circle starts again.”

(Kampis, p. 223 Self-Modifying Systems in Biology and Cognitive Science)

11

Computation as Information Processing

With information as the primary stuff of the universe, and computation as its time-dependent behavior (dynamics), we have a Dual-aspect Universe: informational structure with computational dynamics.

Information and computation are closely related – no computation without information, and no information without dynamics (computation).

12

How is Knowledge Generated? Epistemology Naturalized

Naturalized epistemology (Feldman, Kornblith, Stich) is, in general, an idea that knowledge may be studied as a natural phenomenon -- that the subject matter of epistemology is not our concept of knowledge, but the knowledge itself.

“The stimulation of his sensory receptors is all the evidence anybody has had to go on, ultimately, in arriving at his picture of the world. Why not just see how this construction really proceeds? Why not settle for psychology?” (Epistemology Naturalized, Quine 1969; emphasis mine)

I will re-phrase the question to be: Why not settle for computing?

Epistemology is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief.

13

Naturalist Understanding of Cognition

According to Maturana and Varela (1980) even the simplest organisms possess cognition and their meaning-production apparatus is contained in their metabolism. Of course, there are also non-metabolic interactions with the environment, such as locomotion, that also generates meaning for an organism by changing its environment and providing new input data.

Maturana’s and Varelas’ understanding of cognition is most suitable as the basis for a computationalist account of the naturalized evolutionary epistemology.

14

Naturalist Understanding of Cognition

A great conceptual advantage of cognition as a central focus of study is that all living organisms posess some cognition, in some degree.

15

Universe Computer, Not A Typewriter

What is the mechanism is of the evolutionary development of cognitive abilities in organisms?

Critics of the evolutionary approach mention the impossibility of “blind chance” to produce such highly complex structures as intelligent living organisms. Proverbial monkeys typing Shakespeare are often used as an illustration.

Chaitin - Bennet counter argument: The universe is not a typewriter, but a computer, so a monkey types random input into a computer.

16

Universe Computer, Not A Typewriter

“Quantum mechanics supplies the universe with “monkeys” in the form of random fluctuations, such as those that seeded the locations of galaxies. The computer into which they type is the universe itself.

From a simple initial state, obeying simple physical laws, the universe has systematically processed and amplified the bits of information embodied in those quantum fluctuations.

The result of this information processing is the diverse, information-packed universe we see around us: programmed by quanta, physics give rise first to chemistry and then to life; programmed by mutation and recombination, life gave rise to Shakespeare; programmed by experience and imagination, Shakespeare gave rise to Hamlet.

You might say that the difference between a monkey at a typewriter and a monkey at a computer is all the difference in the world.“(Lloyd 2006)

17

Universe Computer, Not A Typewriter

The universe computer on which a monkey types is at the same time the hardware and the program, in a way similar to the Turing machine.

An example from biological computing is the DNA where the hardware (the molecule) is at the same time the software (the program, the code). In general, each new input restructures the computational universe and changes the preconditions for future inputs. Those processes are interactive and self-organizing. That makes the essential speed-up for the process of getting more and more complex structures.

18

So: Where Do New Mathematical And Biological Ideas Come From? How Do They Emerge?

It seems to me that new ideas come through continuous interactions of an cognizing agent with the world (including other agents, directly or via artifacts). Humans, just as other biological organisms, are only a tiny open subset of the universe, and the universe we inhabit has definitely an impact on us.

A part of the new ideas is the consequence of the re-configuration and reshaping of already existing elements in the biosphere, like in component-based engineering. Life learns from both already existing elements and from something that comes from the outside of our horizon (new discovery).

19

The universe is a huge (quantum mechanical) computer - for us an infinite reservoir of new and surprising facts.

For even if the universe as a whole would be a totally deterministic mechanism, for humans it is impossible to predict all of its behavior.

Chaitin has already shown that there are incompressible truths. In order to be able to predict the Universe-computer we would need the Universe-computer itself to compute its next state.

Pancomputationalism does not contradict creativity. New ideas, new structures emerge from the existing ones as a consequence of recombination and restructuring and interaction (discovery).

So: Where Do New Mathematical And Biological Ideas Come From? How Do They Emerge?

20

Computation, Information, Cognition:

The Nexus and the Liminal

Editor(s): Gordana Dodig Crnkovic and Susan Stuart

Cambridge Scholars Publishing Titles in Print as of July 2007

http://www.c-s-p.org/Flyers/Computation--Information--Cognition--The-Nexus-and-the-Liminal.htm