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https://aeon.co/essays/for-sergiu-klaine...be-divined
EXCERPTS: ‘A physical theory,’ Klainerman said, ‘is a mathematical theory verified by experimental facts.’ The two fields, from this perspective, are not merely related. They are more like two strands that emanate from separate starting points yet inexorably converge. The quandary raised by Wigner may, to some degree, stem from a gap that exists between what we perceive as mathematical reality and as physical reality – a gap that, Klainerman suggests, philosophers have been circling for a very long time.
He cites Plato, who argued that mathematical objects may in fact be more real than the objects we experience with our senses. A circle, in Plato’s view, is not the thing you draw on a piece of paper or trace with a compass. Those are approximations – imperfect embodiments of the ideal form of a circle, which exists independently of any attempt to render it. The drawn circle not only has flaws but is ephemeral, whereas the mathematical circle – a set of points equidistant from a common centre – is built to last.
For most of the history of science, this distinction could be set aside. You could remain agnostic about the ultimate nature of mathematical objects and still do acceptably good physics, because the objects under study – planets, pendulums, electromagnetic fields – were, at least in principle, observable. You could check your equations against the world. The mathematical structure was a description of something you could almost always see.
In many instances today, that is no longer true. Theoretical physics has arrived at a place where some of its fundamental objects are so far removed from ordinary experience that direct observation may be impossible in principle, not merely in practice. [...] For objects like these, mathematics may provide more than a useful description; it may offer the only means by which they can be understood at all... (MORE - details)
EXCERPTS: ‘A physical theory,’ Klainerman said, ‘is a mathematical theory verified by experimental facts.’ The two fields, from this perspective, are not merely related. They are more like two strands that emanate from separate starting points yet inexorably converge. The quandary raised by Wigner may, to some degree, stem from a gap that exists between what we perceive as mathematical reality and as physical reality – a gap that, Klainerman suggests, philosophers have been circling for a very long time.
He cites Plato, who argued that mathematical objects may in fact be more real than the objects we experience with our senses. A circle, in Plato’s view, is not the thing you draw on a piece of paper or trace with a compass. Those are approximations – imperfect embodiments of the ideal form of a circle, which exists independently of any attempt to render it. The drawn circle not only has flaws but is ephemeral, whereas the mathematical circle – a set of points equidistant from a common centre – is built to last.
For most of the history of science, this distinction could be set aside. You could remain agnostic about the ultimate nature of mathematical objects and still do acceptably good physics, because the objects under study – planets, pendulums, electromagnetic fields – were, at least in principle, observable. You could check your equations against the world. The mathematical structure was a description of something you could almost always see.
In many instances today, that is no longer true. Theoretical physics has arrived at a place where some of its fundamental objects are so far removed from ordinary experience that direct observation may be impossible in principle, not merely in practice. [...] For objects like these, mathematics may provide more than a useful description; it may offer the only means by which they can be understood at all... (MORE - details)