Can we 'see' photons, black holes, curved spacetime, quantum jumps, the expansion of the universe, or quanta of space? Physics challenges appearances, showing convincingly that our everyday vision of reality is limited, approximate and badly incomplete. Established theories such as quantum theory and general relativity and investigations like loop quantum gravity have a reputation of obscurity. Many suggest that science is forcing us into a counterintuitive and purely mathematical understanding of reality. I disagree. I think that there is a visionary core at the root of the best science. Where 'visionary' truly means formed by visual images. Our mind, even when dealing with abstract and difficult notions, relies on images, metaphors and, ultimately, vision. Contrary to what is sometimes claimed, science is not just about making predictions: it is about understanding, and, for this, developing new eyes to see. I shall illustrate this point with some concrete cases, including the birth of quantum theory in Einstein’s intuition, curved spacetimes and quanta of space.

The serious scientific application of the atomic theory began in the eighteenth century, with calculations of the properties of gases, which had been studied experimentally since the century before. This is the topic with which we begin this chapter. Applications to chemistry and electrolysis followed in the nineteenth century, and are considered in subsequent sections. The final section of this chapter describes how the nature of atoms began to be clarified with the discovery of the electron.

Maxwell's discovery of the equations for the electromagnetic field was one of the greatest achievements of nineteenth-century physics. The laws of electrostatics, magnetostatics and the magnetic fields produced by steady currents were established by the 1820s. Faraday's discovery of electromagnetic induction in 1831 led to his concept of magnetic field lines and the visualisation of the laws of induction as being determined by the rate of cutting of the field lines. Maxwell mathematised Faraday's model of magnetic field lines by adopting a mechanical model of the aether. His theoretical investigations led to the introduction of the displacement current and the discovery that light is electromagnetic radiation.