3 ms·
It seems quite likely that cutting off Pi at the quintillionth decimal place will not hurt your simulation simply because your knowledge of the initial conditio
by roywiggins 5y ago
It seems quite likely that cutting off Pi at the quintillionth decimal place will not hurt your simulation simply because your knowledge of the initial conditions in the physical universe won't be exact either. If a quintillion digits aren't enough, run your simulation with another quintillion places. Eventually you will match reality to within the accuracy of your ability to measure.
Any issues introduced by using a finite approximation to Pi will eventually be swamped by the uncertainty in the initial conditions. If there's no uncertainty in the initial conditions, there will still be some finite approximation to Pi that will give you results as accurate as you can measure...
- katmannthree 5y agoYes, you can generally find ways to manage life with limited precision. Doing so is useful enough that it’s an entire field (applied mathematics). For many cases though it is a better choice to stick with these particular carefully designed constructs (real, imaginary, and complex numbers) because they are easier to deal with and help keep you from getting bogged down in avoidable numerical tangles. Managing error accumulation is a huge deal for some types of simulations and every little bit counts, to the point of carefully ordering your operations to minimize precision loss with the widest numbers you can afford to use.