phenomena already known to him, such as gravity, the properties of the chemical elements, and the luminosity of the sun, remained to be explained. He was claiming that these phenomena would only ever appear as list of facts or rules of thumb, to be memorized but never understood or fruitfully questioned. Every such frontier of fundamental knowledge that existed in 1894 would have been a barrier beyond which nothing would ever be amenable to explanation. There would be no such thing as the internal structure of atoms, no dynamics of space and time, no such subject as cosmology, no explanation for the equations governing gravitation or electromagnetism, no connections between physics and the theory of computation . . . The deepest structure in the world would be an inexplicable, anthropocentric boundary, coinciding with the boundary of what the physicists of 1894 thought they understood. And nothing inside that boundary – like, say, the existence of a force of gravity – would ever turn out to be profoundly false.
Nothing very important would ever be discovered in the laboratory that Michelson was opening. Each generation of students who studied there, instead of striving to understand the world more deeply than their teachers, could aspire to nothing better than to emulate them – or, at best, to discover the seventh decimal place of some constant whose sixth was already known. (But how? The most sensitive scientific instruments today depend on fundamental discoveries made after 1894.) Their system of the world would for ever remain a tiny, frozen island of explanation in an ocean of incomprehensibility. Michelson’s ‘fundamental laws and facts of physical science’, instead of being the beginning of an infinity of further understanding, as they were in reality, would have been the last gasp of reason in the field.
I doubt that either Lagrange or Michelson thought of himself as pessimistic. Yet their prophecies entailed the dismal decree that no matter what you do, you will understand no further. It so happens that both of them had made discoveries which could have led them to the very progress whose possibility they denied. They should have been seeking that progress, should they not? But almost no one is creative in fields in which they are pessimistic.
I remarked at the end of Chapter 13 that the desirable future is one where we progress from misconception to ever better (less mistaken) misconception. I have often thought that the nature of science would be better understood if we called theories ‘misconceptions’ from the outset, instead of only after we have discovered their successors. Thus we could say that Einstein’s Misconception of Gravity was an improvement on Newton’s Misconception, which was an improvement on Kepler’s. The neo-Darwinian Misconception of Evolution is an improvement on Darwin’s Misconception, and his on Lamarck’s. If people thought of it like that, perhaps no one would need to be reminded that science claims neither infallibility nor finality.
Perhaps a more practical way of stressing the same truth would be to frame the growth of knowledge (all knowledge, not only scientific) as a continual transition from problems to better problems, rather than from problems to solutions or from theories to better theories. This is the positive conception of ‘problems’ that I stressed in Chapter 1. Thanks to Einstein’s discoveries, our current problems in physics embody more knowledge than Einstein’s own problems did. His problems were rooted in the discoveries of Newton and Euclid, while most problems that preoccupy physicists today are rooted in – and would be inaccessible mysteries without – the discoveries of twentieth-century physics.
The same is true in mathematics. Although mathematical theorems are rarely proved false once they have been around for a while, what does happen is that mathematicians’ understanding of what is fundamental improves. Abstractions that were originally studied in their own right are understood as aspects of more general abstractions, or are related in unforeseen ways to other abstractions. And so progress in mathematics also goes from problems to better problems, as does progress in all other fields.
Optimism and reason are incompatible with the conceit that our knowledge is ‘nearly there’ in any sense, or that its foundations are. Yet comprehensive optimism has always been rare, and the lure of the prophetic fallacy strong. But there have always been exceptions. Socrates famously claimed to be deeply ignorant. And Popper wrote:
I believe that it would be worth trying to learn something about the world even if in trying to do so we should merely learn that we do not know much