And: how, exactly, should the average effect of all these different structures be computed? How should the sum over the infinite number of possibilities be written down and added up when the time came to test the theory: to make a prediction, and calculate some tangible, physical quantity which an experiment could actually measure?

On one level, the obvious response to both questions was: “use whatever gives the right answers” – but choices which did that were hard to find … and some of them smacked of contrivance. Infinite sums were notorious for being either intractable, or too pliable by far. I jotted down an example – remote from the actual tensor equations of ATMs, but good enough to illustrate the point:

Let S = 1 – 1 + 1 – 1 + 1 – 1 + 1 –…

Then S = (1–1) + (1–1) + (1–1) +…

= 0 + 0 + 0…

= 0

But S = 1 + (–1+1) + (–1+1) + (–1+1)…

= 1 + 0 + 0 + 0…

= 1

It was a mathematically naïve “paradox”; the correct answer was, simply, that this particular infinite sequence didn’t add up to any definite sum at all. Mathematicians would always be perfectly happy with such a verdict, and would know all the rules for avoiding the pitfalls – and software could assess even the most difficult cases. When a physicist’s hard-won theory started generating similarly ambiguous equations, though, and the choice came down to strict mathematical rigor and a theory with no predictive power at all … or, a bit of pragmatic side-stepping of the rules, and a theory which churned out beautiful results in perfect agreement with every experiment … it was no surprise that people were tempted. After all, most of what Newton had done to calculate planetary orbits had left contemporary mathematicians apoplectic with rage.

Violet Mosala’s approach was controversial for a very different reason. She’d been awarded the Nobel prize for rigorously proving a dozen key theorems in general topology – theorems which had rapidly come to comprise a standard mathematical toolbox for ATM physicists, obliterating stumbling blocks and resolving ambiguities. She’d done more than anyone else to provide the field with solid foundations, and the means of making – careful, measured – progress. Even her fiercest critics agreed that her mathematics was meticulous, beyond reproach.

The trouble was, she told her equations too much about the world.

The ultimate test of a TOE was to answer questions like: “What is the probability of a ten-gigaelectronvolt neutrino fired at a stationary proton scattering off a down quark and emerging at a certain angle?” … or even just: “What is the mass of an electron?” Essentially, Mosala prefixed all such questions with the condition: “Given that we know that space-time is roughly four-dimensional, and total space is roughly ten-dimensional, and the apparatus used to perform the experiment consists, approximately, of the following…”