Physical theory requires the continuum
It has been argued that digital physics, grounded in the theory of finite state machines and hence discrete mathematics, cannot do justice to a physical theory whose mathematics requires the real numbers, which is the case for all physical theories having any credibility.
But computers can manipulate and solve formulas describing real numbers using Symbolic computation, thus avoiding the need to approximate real numbers by using an infinite number of digits. Before symbolic compoutation, a number—in particular a real number, one with an infinite number of digits— was said to be computable if a Turing machine will continue to spit out digits endlessly. In other words, there is no "last digit". But this sits uncomfortably with any proposal that the universe is the output of a virtual-reality exercise carried out in real time (or any plausible kind of time). Known physical laws (including quantum mechanics and its continuous spectra) are very much infused with real numbers and the mathematics of the continuum.
"So ordinary computational descriptions do not have a cardinality of states and state space trajectories that is sufficient for them to map onto ordinary mathematical descriptions of natural systems. Thus, from the point of view of strict mathematical description, the thesis that everything is a computing system in this second sense cannot be supported".[24]
Moreover, the universe seems to be able decide on their values in real time, moment by moment. As Richard Feynman put it:
"It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?"[25]
He then answered his own question as follows:
"So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this speculation is of the same nature as those other people make—'I like it,' 'I don't like it'—and it is not good to be prejudiced about these things".[25]