One sometimes hears popular science programmes claiming that the scientific revolution began when Galileo had the bright idea of finding out about the world by doing experiments. However, whilst Galileo was not the first person in history to perform an experiment, he was the first person in history to claim that the language of natural philosophy should be exclusively mathematical, a view he expressed in this well-known passage from The Assayer:
“Philosophy [i.e. physics] is written in this grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.”
Why had nobody thought before to frame the theories of natural science in mathematical language? The problem was that before Galileo philosophers took the world to be full of sensory qualities: colours, smells, tastes, sounds. Intuitively one cannot capture the redness of a tomato, or the spicy taste of curry, or the sweet smell of flowers, in the austere, abstract language of mathematics. Galileo got around this problem by stripping the world of sensory qualities and locating them in the immaterial soul.
For Galileo, the spicy taste of curry isn’t really in the curry; rather it’s in the soul of the person tasting the curry. The sweet smell of the flowers isn’t really in the flowers; it’s in the soul of the person smelling them. Even colours for Galileo resided not ‘out there’ on the surface of objects but within the human soul. By stripping external objects of any qualities other than shape, Galileo created a world which could be exhaustively described in mathematical geometry.
In other words, it was a change in our philosophical conception of the world which made mathematical physics possible, and that change was a matter of placing the sensory qualities we encounter in conscious experience outside of the material world studied by physics.
This is the start of mathematical physics, which subsequently proved to be a great success. Once we can capture nature in mathematics, we can start to frame laws of nature in mathematical language. A short while later we have Newton’s laws of motion and gravity. And five centuries of developing more and more accurate mathematical models of the world’s causal structure has enabled us to manipulate it in all sorts of extraordinary ways, giving us lasers and microwave ovens and flights to the moon.
It is tempting to take this success as evidence for a kind of physics-fundamentalism, according to which mathematical physics is on its way to giving us a complete account the nature of space, time and matter. But this is the wrong conclusion to draw. The success of mathematical physics resulted from limiting the scope of enquiry. By putting the sensory qualities we encounter in conscious experience –colours, smells, tastes, sounds – outside of the domain of the physical sciences, we are able to give a purely mathematical description of what’s left over. But those qualities that Galileo took out of the material world still exist somewhere and must still be accounted for somehow. If the spicy taste of the curry isn’t really in the curry then where is it? Galileo thought it was in the soul, but if we don’t want to believe in souls then we need to find a place in the natural world for the sensory qualities Galileo believed were located in souls.
How are we going to do that? Do we need to move to a ‘post-Galilean’ picture of the world, which somehow accommodates both the causal structure we learn about from physics and the sensory qualities we encounter in our conscious experience? Or perhaps Galileo wrong to think that the sensory qualities can’t be accounted for in mathematical terms. Is there perhaps a way of thinking of the spiciness of curry or the sweet smell of flowers which would allow us to capture their nature in mathematical language?
These are very difficult questions. But if we’re ever going to find the answers, I think we’re going to need to keep some philosophers handy.