This is a poor argument, because the universe is uncomputable. We have models that apply on short time scales, but it's fundamentally not computable either in practice or in principle.

On long enough scales - and they're not that long when you're talking about billions of years - we don't even know if the solar system is stable.

Bio-computability has the same issue at smaller scales. There are islands of conceptual stability in a sea of noise, but good luck to you if you think you can compute this sequence of comments on Hacker News given the position of every atom in the original primordial soup.

The universe is not clockwork. The concept of computability is essentially mechanical, and it's essentially limited - not just by conceptual incompleteness theorems, but by the fact that any physical system of computation has physical limits which place hard bounds on precision and persistence.

> because the universe is uncomputable

We have no evidence to suggest that is true. If no individual process in the universe exceeds the Turing computable - and we have no evidence it does, or that anything exceeding the Turing computable can even exist - then the universe itself would be existence-proof that it is computable. Now, we can't be 100% sure, because we'd have to demonstrate that every physical interaction everywhere is individually Turing computable. But we also have nothing that even hints of evidence to the contrary.

Note that it is possible the universe is not computable from within with full precision due to e.g. lack of compressibility.

> On long enough scales - and they're not that long when you're talking about billions of years - we don't even know if the solar system is stable.

That has zero relevance to whether or not it is computable. If it is computable, then any such instability is simply an effect of a computation.

In other words you're committing the logical fallacy of begging the question - your conclusion rests on your premise, as you're trying to argue that the universe is computable by using processes as evidence that can only be uncomputable if the universe as a whole is uncomputable.

> The universe is not clockwork.

That is irrelevant to whether or not it is computable.

> but by the fact that any physical system of computation has physical limits which place hard bounds on precision and persistence.

This is also in general irrelevant to whether or not a system is computable. We can operate symbolically on entities that requires any arbitrary (including infite) precision and persistence within various constraints. E.g. we can do math with 1/3 to infinite precision for a whole lot of calculations.

Unless you can show specific processes that demonstrably happens with a precision that is impossible to simulate without the computation becoming infinite, this argument doesn't get you anywhere. Note that it would be insufficient to show a process that appears to have infinite precision in a way that would take infinite time to calculate unless there is demonstrably no way to lazily calculate it to whatever precision you actually try to observe in a finite amount of time, as such a system can be simulated.

Length of time would also not be a problem unless you can show why such a simulation needs to run at full speed to work, rather than impose a subjective time on the inside of the simulation that can vary with computational complexity.

Space complexity is also irrelevant unless you can show limits on the theoretical maximum capacity of an outside simulator.

Now to the question of whether life is computable, then if the universe is computable, then life is too, but if the universe is not, life might still be, and so this is largely a digression from the original point I made.