A surprising number of mathematicians, even quite prominent ones, believe in a realm of perfect mathematical entities hovering over the empirical world – a sort of Platonic heaven. Alain Connes of the Collège de France once declared that ‘there exists, independently of the human mind, a raw and immutable mathematical reality,’ one that is ‘far more permanent than the physical reality that surrounds us’. Roger Penrose, another unabashed Platonist, holds that the natural world is only a ‘shadow’ of a realm of eternal mathematical forms.
The rationale for this otherwordly view appeared first in the Republic. Geometers, Plato observed, talk of perfectly round circles and perfectly straight lines, neither of which are to be found in the sensible world. The same is true of numbers, since they must be composed of perfectly equal units. The objects studied by mathematicians must therefore exist in another world, one that is changeless and transcendent. Seductive though this picture of mathematics might be, it doesn’t tell us how mathematicians are supposed to get in touch with this transcendent realm. How do we come to have knowledge of mathematical objects if they lie beyond the world of space and time? Contemporary Platonists tend to do a bit of hand-waving when confronted with this question. Connes invokes a special sense, ‘irreducible to sight, hearing or touch’, that allows him to perceive mathematical reality; Penrose believes that human consciousness somehow ‘breaks through’ to the Platonic world. Kurt Gödel, among the staunchest of 20th-century Platonists, wrote that ‘despite their remoteness from sense experience, we do have something like a perception’ of mathematical objects, adding, ‘I don’t see any reason why we should have less confidence in this kind of perception, i.e. in mathematical intuition, than in sense perception.’
But mathematicians, like the rest of us, think with their brains
source;
The rationale for this otherwordly view appeared first in the Republic. Geometers, Plato observed, talk of perfectly round circles and perfectly straight lines, neither of which are to be found in the sensible world. The same is true of numbers, since they must be composed of perfectly equal units. The objects studied by mathematicians must therefore exist in another world, one that is changeless and transcendent. Seductive though this picture of mathematics might be, it doesn’t tell us how mathematicians are supposed to get in touch with this transcendent realm. How do we come to have knowledge of mathematical objects if they lie beyond the world of space and time? Contemporary Platonists tend to do a bit of hand-waving when confronted with this question. Connes invokes a special sense, ‘irreducible to sight, hearing or touch’, that allows him to perceive mathematical reality; Penrose believes that human consciousness somehow ‘breaks through’ to the Platonic world. Kurt Gödel, among the staunchest of 20th-century Platonists, wrote that ‘despite their remoteness from sense experience, we do have something like a perception’ of mathematical objects, adding, ‘I don’t see any reason why we should have less confidence in this kind of perception, i.e. in mathematical intuition, than in sense perception.’
But mathematicians, like the rest of us, think with their brains
source;
Mathematics on Ice
Jim Holt
- Naming Infinity: A True Story of Religious Mysticism
TITLE Available for free download at Ether Books | |
| Peter Cheevers | Not Even A Recall – Where’s That Revolver? |
| Peter Cheevers | Violence in Chichester? No, Never |
| Peter Cheevers | I Never Saw A Woman Look So Wistfully |
| Peter Cheevers | A Night On The Moon |
| Peter Cheevers | All Flesh Is Grass |
| Peter Cheevers | No Atheists In Foxholes |
| Peter Cheevers | The Rats' Somme |
| Peter Cheevers | To Self-help or Not to Self-help? |
| Peter Cheevers | Wearing Theory like a Versace Waistcoat |
| Peter Cheevers | The Nonsense of Living in the Now |
No comments:
Post a Comment