Book contents
- Frontmatter
- Contents
- Acknowledgements
- Part I Mathematical Recreations and Abstract Games
- Part II Mathematics: game-like, scientific and perceptual
- 6 Game-like mathematics
- 7 Euclid and the rules of his geometrical game
- 8 New concepts and new objects
- 9 Convergent and divergent series
- 10 Mathematics becomes game-like
- 11 Mathematics as science
- 12 Numbers and sequences
- 13 Computers and mathematics
- 14 Mathematics and the sciences
- 15 Minimum paths: elegant simplicity
- 16 The foundations: perception, imagination, insight
- 17 Structure
- 18 Hidden structure, common structure
- 19 Mathematics and beauty
- 20 Origins: formality in the everyday world
- References
- Index
14 - Mathematics and the sciences
Published online by Cambridge University Press: 05 November 2012
- Frontmatter
- Contents
- Acknowledgements
- Part I Mathematical Recreations and Abstract Games
- Part II Mathematics: game-like, scientific and perceptual
- 6 Game-like mathematics
- 7 Euclid and the rules of his geometrical game
- 8 New concepts and new objects
- 9 Convergent and divergent series
- 10 Mathematics becomes game-like
- 11 Mathematics as science
- 12 Numbers and sequences
- 13 Computers and mathematics
- 14 Mathematics and the sciences
- 15 Minimum paths: elegant simplicity
- 16 The foundations: perception, imagination, insight
- 17 Structure
- 18 Hidden structure, common structure
- 19 Mathematics and beauty
- 20 Origins: formality in the everyday world
- References
- Index
Summary
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
[Einstein 1921]Scientists abstract
When Galileo did his famous experiment of rolling a marble down a straight chute and timing its descent, he abstracted away the friction of the marble against the chute and the inevitable errors in his measurement of the time taken. When he argued that the flight of a cannonball could be analysed into a steady motion horizontally and an entirely separate accelerating motion vertically, he ignored the resistance of the air which would have had negligible effect on his marble in a chute but greatly distorts the flight of a cannonball from a perfect parabola.
Galileo's experiments were concrete and physical but his conclusions, which he believed to be Laws of Nature ordained by God, were precise and mathematical. His results fit Einstein's dictum. The abstract model can be analysed with great confidence to make predictions – but the predictions will not fit reality perfectly. Plato compared the use of mathematics for the study of reality to, ‘fitting a sandal to the foot’. It's a good analogy: the sandal should fit as closely as possible – if it doesn't it will be uncomfortable! – but no one mistakes one for the other [Young 1928: 204].
- Type
- Chapter
- Information
- Games and MathematicsSubtle Connections, pp. 148 - 162Publisher: Cambridge University PressPrint publication year: 2012