Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes

I argue that data becomes temporarily interesting by itself to some self-improving, but computationally limited, subjective observer once he learns to predict or compress the data in a better way, thus making it subjectively simpler and more beautiful. Curiosity is the desire to create or discover more non-random, non-arbitrary, regular data that is novel and surprising not in the traditional sense of Boltzmann and Shannon but in the sense that it allows for compression progress because its regularity was not yet known. This drive maximizes interestingness, the first derivative of subjective beauty or compressibility, that is, the steepness of the learning curve. It motivates exploring infants, pure mathematicians, composers, artists, dancers, comedians, yourself, and (since 1990) artificial systems.Comment: 35 pages, 3 figures, based on KES 2008 keynote and ALT 2007 / DS 2007 joint invited lectur

Alternative Modes for Teaching Mathematical Problem Solving: An Overview

Various modes are proffered as alternatives for teaching mathematical problem solving. Each mode is described briefly, along with general purposes, advantages and disadvantages. Combinations of modes are suggested; general issues identified; recommendations offered; and feedback from teachers summarized

Sounds of Waitakere: Using practitioner research to explore how Year 6 recorder players compose responses to visual representations of a natural environment

How might primary students utilise the stimulus of a painting in a collaborative composition drawing on a non-conventional sound palette of their own making? This practitioner research features 17 recorder players from a Year 6 class (10–11-year-olds) who attend a West Auckland primary school in New Zealand. These children were invited to experiment with the instrument to produce collectively an expanded ‘repertoire’ or ‘palette’ of sounds. In small groups, they then discussed a painting by an established New Zealand painter set in the Waitakere Ranges and attempted to formulate an interpretation in musical terms. On the basis of their interpretation, drawing on sounds from the collective palette (complemented with other sounds), they worked collaboratively to develop, refine and perform a structured composition named for their chosen painting. This case study is primarily descriptive (providing narrative accounts and rich vignettes of practice) and, secondarily, exploratory (description and analysis leading to the development of hypotheses). It has implications for a range of current educational issues, including curriculum integration and the place of composition and notation in the primary-school music programme

Co-Adventurers in Discovery: Collaborative Research Between Undergraduate Students and Faculty

There are many opportunities available beyond the classroom for undergraduate students to engage in cutting-edge scholarship. Some of the opportunities include study abroad, internships, and independent study. We strongly suggest that students experience such programs. Independent study courses can serve not only to sharpen the student’s engagement skills with the open-ended questions of current research, but also to enhance his or her own relationship with faculty. In this article we share the experiences of a biology student and a mathematics faculty member coming together as co-adventurers learning from each other about the mechanisms and mathematics involved in cardiac arrhythmia through collaborative mathematical modeling research. Biology and mathematics have a long history of an explosive synergy that enriches and extends both fields (Cohen, 2004) (Reed, 2004), and this synergy led us to the fruitful journey reported here. As there is no end in sight for opportunities to engage in such multi-disciplinary student-faculty collaborative research, we encourage everyone to take advantage of such opportunities