Everything is computable...
Recently I read an article that presented a novel idea by Nicolas Gisin . In a nutshell, Gisin says that only a certain number of digits of real numbers have physical meaning. After some number of digits, for example, the thousandth digit, or maybe even the billionth digit, their values are essentially random. This is very interesting because it means that there are no noncomputable numbers. Provided this idea is correct, we can easily decide if for example there are three 4s in the decimal expansion of π! The real problem of course is to agree on the number of significant digits. Once this problem is settled, then we can answer any question about physical real numbers. Another consequence of this idea would be that real numbers might be directly representable in even present computer hardware. What is left is to examine deeply this idea and see if it is actually valid.