The act of observation now had a complicated description that took into account what the experimenter was doing.īut all this mathematics didn’t get at what actually happened when the properties of a particle were being measured. Heisenberg (and later, Erwin Schrödinger) came up with equations that described particles in terms of a wavefunction, where simple numbers became entities of infinite dimensions that lived in exotic mathematical spaces.
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How to describe this phenomenon flummoxed theorists. Bohr and his protégé, Werner Heisenberg, were trying to figure out how to talk about the weird behaviour of quantum particles: how they appeared to ‘know’ when they were being observed, for example, and to act as a particle when observed and a wave when not observed. The great debates about quantum physics kicked off in the 1920s. Yet it’s in the work of these philosophers that I began to see answers to some of our most fundamental questions about reality – answers that stem from recognising that we are not only asking the wrong questions we are asking nonsensical ones. Contemporaries of Einstein and Bohr, Wittgenstein and Russell didn’t engage with the quantum revolution directly. Yet it was only when I dived into the parallel milieu of Cambridge Philosophy, at the time of Ludwig Wittgenstein and Russell’s ascendancy, that I began to feel like my qualms about mathematics and physics might be addressed. Recent experiments in quantum information theory have shown that our most basic assumptions about reality, such as when something can be considered to have been observed and to have definite physical properties, are in the eye of the beholder.Īttempts to address these paradoxes date back to the dawn of quantum mechanics, when Albert Einstein and Niels Bohr debated how to interpret the baffling phenomena they’d uncovered. But quantum theory exposed that, too, as a fantasy: even though we could define rules and equations for physical laws, we could not explain what they meant. His attempt was published, with his collaborator Alfred North Whitehead, in the loftily titled Principia Mathematica (1910-13) – a dense three-volume tome, in which Russell introduces the extended proof of 1 + 1 = 2 with the witticism that ‘The above proposition is occasionally useful.’ Published at the authors’ considerable expense, their work set off a chain reaction that, by the 1930s, showed mathematics to be teetering on a precipice of inconsistency and incompleteness.Įventually, I turned to physics, hoping to reground my Platonist aspirations in the eternal laws that governed the physical reality of the cosmos.
The mathematician and philosopher Bertrand Russell spent much of his career trying to shore up this house built on sand. These problems with mathematics turned out to be well known. Each rested on self-evident axioms that, while apparently true, seemed to be based on little more than consensus among mathematicians.
My proofs seemed more like arguments than irrefutable calculations. Yet, as I churned out proofs for my doctoral coursework, the human element of mathematics began to discomfit me.
These statements, I was told, were true at the beginning of time and would be true at its end, long after the last mathematician vanished from the cosmos. I could prove the number of primes to be infinite, and the square root of two to be irrational (a real number that cannot be made by dividing two whole numbers). Somewhere out there was a perfect circle all the other circles we could see were pale copies of this single Circle, dust and ashes compared with its ethereal unity.Ĭhasing after this ideal as a young man, I studied mathematics. I knew a bit about philosophy and was taking a survey class in the humanities, but Plato’s theory of ideal forms arrived as a revelation: this notion that we could experience a shadow-play of a reality that was nonetheless eternal and immutable. A mathematics and English nerd – a strange combination – I played cello and wrote short stories in my spare time. I first learnt about Plato’s allegory of the cave when I was in senior high school.
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