Numbers, the universe and complexity beyond us, Data structures Math Foundations 177

In mathematics, we want to write things down. That way we can check what we are actually talking about. Other people can look at it, and assess whether it makes sense or not. We can more easily compare what we are thinking about with other, perhaps related concepts, objects, patterns. But what if we want to write down a natural number so big that it doesn t fit onto our page, or perhaps our hard drive, or even Google s hard drives What if that number we are thinking about is so big that it doesn t even fit in our universe, even if we write in a very tiny fashion Have we then crossed the boundary from mathematics and science into mysticism and philosophy In this video we discuss various approaches to the philosophy of mathematics, including not only Platonism, the default position for most mathematicians, but also the Aristotelian realist philosophy proposed by the Sydney School led by James Franklin. Then we concretely estimate just how big, and how small the un