just viewed a you tube item.....the Banach/Tarski Paradox
but can you deal with such things?
These mathematical artifacts have to do with the semantics of language or qualities of human language and not with reality. Let me explain by analogy. When you go into McDonalds and buy a Big Mac, there's a pretty picture on the menu. When you sit down at the table and open your Styrofoam container what you look at is a blob of food that doesn't look like anything that was showing in the picture. What this means is our words are not the reality they represent. Words are like a map. No matter how much detail you add to the map, reality always has more detail. So this means our maps of reality are not the reality they represent.
The paradoxes listed in the video occur in mind-space even though by showing a sphere in the video the author was implying reality. In mind space, with semantics, semantic connections are being made because our minds flex. Our mind is closing meaning between two points by bending to make the connection. There is nothing in our imagination preventing us from making the connection between two points of meaning. Connecting the dots is easy in one's imagination. Reality, however, does not flex the same way.
Reality dictates what is real by uncountable waves of energy interacting in every possible direction. Rogue waves converge causing experimental errors and other unexplainable events in reality not in accordance to some language of mathematics we use to represent reality's behaviors.
Mathematics is just a language. Just like every language there are an unlimited amount of things you can say with words. There are an unlimited amount of things you can write about in mathematics. And just like words, in mathematics, there's a smaller subset of language that loosely maps with reality. The Banach–Tarski Paradox is a cute story. It may map to some part of reality in some limited context. But it most likely does not.
What I mean by loosely is in order for any mathematical pattern to be identified to exist in nature it always has to be bounded by a limited scope. Reality is so much more messy that our representations of it. Technology is great but it never lasts long and it's always breaking. If you really want to impress me take something with a thousand parts and predict exactly when it will break and exactly how it will break.
The problem with reality is it has no scope. If it did have scope then we could predict the exact moment when a particular radio active decay would occur with exact precision. Instead, what we have is everything is connected to everything else without any scope. Our imaginations have a limited scope created by our experiences which is very different than reality.
