Mathematicians who call themselves ultrafinitists think that extremely large numbers are holding back science, from logic to cosmology, and they have a radical plan to do something about it
At a certain point, I realized that from another perspective, the big divide seems to be between those who see continuous distributions as just an abstraction of a world that is inherently finite vs those who see finite steps as the approximation of an inherently continuous and infinitely divisible reality.
Since I’m someone who sees math as a way to tell internally-consistent stories that may or may not represent reality, I tend to have a certain exasperation with what seems to be the need of most engineers to anchor everything in Euclidean topography.
But it’s my spouse who had to help our kids with high school math. A parent who thinks non Euclidean geometry is fun is not helpful at that point.
Yeah there is an important difference there. I think though that it’s not clear whether the world is fundamentally discrete or continuous. As far as I know there is no evidence either way on this (though I remember reading that space and time must have the same discreteness/continuousness).
At a certain point, I realized that from another perspective, the big divide seems to be between those who see continuous distributions as just an abstraction of a world that is inherently finite vs those who see finite steps as the approximation of an inherently continuous and infinitely divisible reality.
Since I’m someone who sees math as a way to tell internally-consistent stories that may or may not represent reality, I tend to have a certain exasperation with what seems to be the need of most engineers to anchor everything in Euclidean topography.
But it’s my spouse who had to help our kids with high school math. A parent who thinks non Euclidean geometry is fun is not helpful at that point.
Yeah there is an important difference there. I think though that it’s not clear whether the world is fundamentally discrete or continuous. As far as I know there is no evidence either way on this (though I remember reading that space and time must have the same discreteness/continuousness).