### Research Experiences for Undergraduates (REU) Seminar

Topic: Meaningless Statements

Speaker: **Fred S. Roberts**, DIMACS

Date and time: Friday, June 15, 2001, 12:00 noon

Location: DIMACS Center, Room 431, Rutgers University, Piscataway, NJ

Lunch will be served.

A statement involving scales of measurement is called
meaningless if its truth or falsity can depend on the particular
versions of scales that are used in the statement. We will develop
the mathematical foundations of a theory of measurement that will
allow us to make the notion of meaningless statement precise. We will
then give a variety of examples of meaningless statements. For
example, we will show that the conclusion that a given solution to a
problem is optimal might be meaningless and in particular we will
describe such results for shortest path problems, for graph coloring
problems arising from frequency assignments, and for scheduling
problems. We will also discuss limitations (through functional
equations) on the possible averaging functions which allow meaningful
comparisons in different applications such as choosing new
technologies, comparing the abilities of different groups of students,
etc.

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