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So, if I was going to argue about things not existing, the concept of pi, the irrational number, would be my first target. It's just an artifact of bean countin

So, if I was going to argue about things not existing, the concept of pi, the irrational number, would be my first target. It's just an artifact of bean counting that people chase their tails over. To say that pi is a non-repeating fraction with infinite decimal places, is to say that we cannot ever precisely know the boundary and definition of a circle, forever zooming in on a point never met. That we find circles, and capitulate to what must be their true or approximate location is a cheat, and mere luck at the integrity of atoms or planck space or what have you. But still, it's garbage in the same way that the divide-by-zero rule is garbage. Granted, dividing something into nothing isn't a practical operation. But, I can divide zero into as many parts as I like, and it's still zero. So, if people want to keep stacking infinitesimally small tenths, hundreths, thounsandths, millionths and so on, to the end of any particular number, forever, well, forever sounds like an infinite quantity to me, and I'll argue to point that out. Unroll the circumference of a circle. Where does it end? Approximately near X? Approximately??? Tell me the area of a circle. Approximately within this fuzzy boundary? Approximately??? I am dubious.

drdeca 10y ago
Are you objecting that infinite precision or irrational numbers do not physically exist? That may be. Or it might not. Whether (physical) space is infinitely divisible or not is, I think, an open question. I think it is even plausible that the answer might be that it can be described equally well both ways? Not sure. I don't mind thinking about abstract objects which do not physically exist. (Though, I generally consider abstract objects to exist in some sense, though you may disagree, and that's fine.) If you don't care to think about them, that's fine also. I believe that thinking about them is often useful. Treating pi as existing allows for reasoning about things more efficiently, even if it turns out that it results in inaccuracies in predictions about the physical world which are far smaller than our ability to measure/notice. (If we can't notice the results of the error, it doesn't seem to be much of a problem.) That doesn't mean you have to accept pi as actually existing. I think it would be to your benefit to at least accept its use though. I do consider it to actually exist.

drdeca 10y ago

Are you objecting that infinite precision or irrational numbers do not physically exist? That may be. Or it might not. Whether (physical) space is infinitely divisible or not is, I think, an open question. I think it is even plausible that the answer might be that it can be described equally well both ways? Not sure. I don't mind thinking about abstract objects which do not physically exist. (Though, I generally consider abstract objects to exist in some sense, though you may disagree, and that's fine.) If you don't care to think about them, that's fine also. I believe that thinking about them is often useful. Treating pi as existing allows for reasoning about things more efficiently, even if it turns out that it results in inaccuracies in predictions about the physical world which are far smaller than our ability to measure/notice. (If we can't notice the results of the error, it doesn't seem to be much of a problem.) That doesn't mean you have to accept pi as actually existing. I think it would be to your benefit to at least accept its use though. I do consider it to actually exist.