Why? If there is a number that can't be computed, and there's no evidence that it's physically present, what's the contradiction here?
Computers are only limited in creating things that can be proven because creating something is a proof that it exists. This has a more formal meaning if you look at the Curry-Howard correspondence.
They exist in the mathematical sense that they are basically the solution to an equation. We know the equation, we know there is a solution, but we don't know what the solution is, and it has no physical relevance. Many mathematicians (constructivists) would say that this means that they don't exist until you can find a way of finding the exact solution.
For many of these numbers, we know that there cannot be any rigorous procedure by which they can be found, because if there was, there would be a logical contradiction.
Why? If there is a number that can't be computed, and there's no evidence that it's physically present, what's the contradiction here?
Computers are only limited in creating things that can be proven because creating something is a proof that it exists. This has a more formal meaning if you look at the Curry-Howard correspondence.
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They exist in the mathematical sense that they are basically the solution to an equation. We know the equation, we know there is a solution, but we don't know what the solution is, and it has no physical relevance. Many mathematicians (constructivists) would say that this means that they don't exist until you can find a way of finding the exact solution.
For many of these numbers, we know that there cannot be any rigorous procedure by which they can be found, because if there was, there would be a logical contradiction.