Can, Can't, and Probably

Draft for the author · not yet in her words

Physics usually tells us what will happen, given where things start and the laws that move them. In 2012 David Deutsch proposed asking a different question. Constructor theory, developed since with Chiara Marletto at Oxford, asks which transformations are possible and which are impossible, and why. Its working unit is a task: turning one thing into another. A constructor is anything that can carry out the task and remain able to do it again: a catalyst, a cell, a machine, a person.

I found the field late and recognized it at once, because my work has always dealt with what can come into being. Marletto's argument that life could arise under laws containing no design, so long as those laws allow information to be copied, says that the information is not inside the thing. It is in which changes the arrangement allows. That is the principle I set down early: understanding the universe is predicated on understanding relationships.

Where I part company

Constructor theory draws a hard line between can and can't. I would change possibilities to probabilities. A clean yes and a clean no are an exact one and an exact zero, and I do not trust exact endpoints; they usually stand in for what we have not yet measured. In a liquid-metal droplet, a ring of pinned atoms did not make crystallizing impossible. It made it far less likely, until the metal had cooled hundreds of degrees further. The arrangement changed the odds, and the odds changed the future available to it.

The evolution I describe in this book, quantum and probabilistic rather than fixed, works the same way. Nothing is guaranteed and almost nothing is forbidden. What matters is what tilts the odds, and whether that tilt can be held long enough to matter.

Deutsch, D. "Constructor Theory." Synthese 190 (2013). Deutsch, D. and Marletto, C. "Constructor Theory of Information." Proc. R. Soc. A 471 (2015). Marletto, C. "Constructor Theory of Life." J. R. Soc. Interface 12 (2015). Marletto, C. The Science of Can and Can't (Viking, 2021). Leist, C. et al. ACS Nano 19 (2025).