Jan M. Żytkow

Analytical chemistry; the science of many models

SummaryWe argue that physical reductionism is a one-sided view of science. While it has successfully guided detection of elementary building blocks in many domains of science, and reduction of different sciences to the elementary objects, properties and interactions in physics, it provides little help for other scientific activities and is particularly ill suited to describe analytical chemistry. Analytical chemistry focuses on (1) empirical meaning of chemical concepts and on (2) understanding the structure of any particular sample. The primary theoretical tool of analytical chemistry is (3) model construction. Considering that activities (1–3) are complementary to formation of reductionist theories, analytical chemistry is as much in the forefront of research as theoretical physics, expanding our knowledge in other, equally indispensable directions. In this paper we briefly describe (1) and (2), and then we concentrate on model formation and the role of models in science. Models combine knowledge of basic building blocks, knowledge of structure, and elements of empirical meaning. Models play an essential role in preparation for measurements and in developing new measurement procedures. They expand our capability for knowledge verification and systematization. They are critical in understanding the hidden structure of objects and processes and in identifying new phenomena. A model is a product of synthesis and describes structured objects and situations, usually complex, as combinations of basic elements. Basic elements are provided by reductionistic theories which are the product of knowledge analysis and describe simple elements of nature and their interaction viewed from a singular perspective of either gravity, or electromagnetism, thermal phenomena, and the like. Model construction, not theory construction, is a basic theoretical tool in domains such as chemistry, which study complex systems and phenomena. We analyse the process of model creation, pointing out that it oscillates between solvability of equations and adequacy of description. As an example we analyse model construction in the domain of ion selective electrodes.

Is Analytical Chemistry an autonomous field of science

SummaryAnalytical Chemistry is an autonomous branch of science. It provides empirical meaning for chemical concepts, and it has a significant component of a science of the artificial within chemistry. Processes of sample analysis and model construction that are characteristic to Analytical Chemistry, inherently involve discovering of new objects and of deeply hidden regularities. This places the discipline at the frontier of research. Moreover, it is particularly beneficial for the methodology of science to study sample analysis and model construction using the examples from Analytical Chemistry. For the same reason the methodological self-reflection of a chemist-analyst can make an original contribution to our understanding of science as a whole.

Integration of knowledge and method in real-world discovery

An architecture which controls automated discovery of empirical knowledge must integrate a robotic component which interacts with the real world, knowledge network which accumulates knowledge, a discovery method, and the currently executed discovery tasks. We describe such an architecture implemented in the FAHRENHEIT system, concentrating on the integration and interaction between elements. The robotic component includes hardware connections to the external instruments and manipulators, operational procedures to control the hardware, and a process that controls outstanding requests for measurements and manipulations. Knowledge network describes the actual state of knowledge about the world, including all discoveries that have been made. The state of knowledge expands as the discovery process continues. Operational procedures are expanded and refined as a result of discoveries. Better procedures, in turn, allow FAHRENHEIT to collect better data and to improve its knowledge. The discovery method consists of a network of generic goals and plans for goal execution. Discovery goals require search, so most of the generic plans are solution schemes to search problems. All search problems are defined by the application of a uniform search template. Actual goals and plans executed at any given time form a recursive network of instances of generic goals and plans. The instances are selected based on the generic network of goals and plans, and the current state of knowledge. The selected plans are search instances. At any given time a number of search instances of various types may be in progress, each of them plan leading to new discoveries.

Theories that Combine Many Equivalence and Subset Relations

Knowledge comes in different species, such as equations, contingency tables, taxonomies, rules, and concepts. We show how starting from contingency tables, simple tests can distinguish various special forms of 2-D knowledge. Our experience in data mining with the application of the 49er system shows that the exploration of even a modestly sized database frequently leads to large numbers of regularities. The problem that we address in this paper comes from the recurring observation of users who show serious confusion when faced with thousands of regularities discovered in a database. As a response, 49er uses tests which classify regularities into different categories and applies automated methods which combine large numbers of regularities in each category into concise, useful forms of taxonomies, inclusion graphs and other multi-dimensional theories. We focus on detection of 2-D regularities which can be represented by equivalence and implication relation, and we show how taxonomies and subset graphs can capture large numbers of regularities in those categories. We illustrate the presented algorithms by applications on two databases.

Mining patterns at each scale in massive data

An important but neglected aspect of data analysis is discovering phenomena at different scale in the same data. Scale plays the role analogous to error. It can be used to focus data exploration on differences that exceed the given scale (error) and to disregard those smaller. We introduce a discovery mechanism that applies to bi-variate patterns, in particular to time series. It combines search for maxima and minima with search for regularities in the form of equations. If it cannot find a regularity for all data, it uses other discovered patterns to divide data into subsets, and explores recursively each subset. Detected patterns are subtracted from data and the search continues in the residuals. Our mechanism does not skip patterns at any scale. Applied at many scales and to many data sets, it seems explosive, but it terminates surprisingly fast because of data reduction and the requirements of pattern stability and significance. We show application of our method on a time series of a half million datapoints. Our example shows that even simple data can reveal many surprising phenomena, and our method leads to fine conclusions about the environment in which they have been gathered.

The first phase of real-world discovery: determining repeatability and error of experiments**The work described in this paper was supported by Office of Naval Research under the grants No. N00014–88-K-0226 and N00014–90-J-1603

Using un-repeatable data and forgetting about measurement error are two cardinal sins in empirical sciences. A machine discovery system must be able to handle both before attempting serious discoveries. We describe an application of the discovery system FAHRENHEIT in a science laboratory, focused on the preparatory stage of the empirical discovery process, i.e. the investigation of repeatability and the measurement of error. To cope with real-world empirical discovery, FAHRENHEIT has been reorganized as a distributed multi-process system and a robotic component including external manipulators and measuring instruments. We present the application of FAHRENHEIT to an experiment in which the system discovers repeatability conditions and error in the context of dispensing liquids in a chemistry laboratory. We then present the theory of the process. Many quantitative discovery systems distinguish between dependent and independent control variables. We argue that to handle repeatability and error, independent variables should be divided further into two categories: theory formation variables and experiment refinement variables. The former have been used by BACON, FAHRENHEIT and other empirical discovery systems to re-discover scientific laws. The latter are used to determine the repeatability and error, prior to the system discovery of the main theory using theory formation variables.