Its a good article with stimulating ideas I should take the time to read properly, but it seems to omit this feature of the arrow of time which I have noticed:

Its a good article with stimulating ideas I should take the time to read properly, but it seems to omit this feature of the arrow of time which I have noticed: In a basic gravitational simulation time would be completely reversible except that quantised integration is lossy. If data could be recorded to infinite precision it would be possible to integrate the simulation back and forth between any two points in time and thus re-calculate separate states precisely and repeatedly, there would be no irreversible arrow. The only reason I see that for example, a simulated glass will not perfectly reassemble itself after being virtually smashed is that quantization noise accumulates on every iteration, and in accordance with the 'butterfly effect' the noise which enters at the units of least precision, also trickles upward in significance on every iteration. But if a simulation was run using enormous word lengths for all its data then the noise would have longer to travel (up the word-lengths) until it made a significant difference to the virtual model. The model data might also be clipped at intervals in an attempt to remove this 'direction dependent noise'. Theoretical ideas about time which consider analog system real numbers or values of matter might not notice this effect, that the state of things becoming more intertwinned with each other through time, which ever direction viewed from, requires more and more precision to represent. It would not be a problem with infinite precision math. I dont know about the precision scheme of the physical universe, it sounds like quantum physics does find limits.