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I have seen that is is debated if the universe is digital, computable or non-computable. what specific consequence could this have in the format of the laws of physics? Or would that mean that we will not be ever capable or writing equations?

Qmechanic
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    That's not a debate in mainstream physics. That most of the universe is non-computable for all practical purposes has been known intuitively since the days of Newton and it has found a sure mathematical footing at the end of the 19th, early 20th century, I believe (but I am not a science historian, so I can't give you relevant references for the timeline). Having said that, computability is not a scientific requirement for anything, so it really doesn't matter to physics proper. – CuriousOne Jun 05 '15 at 17:42

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Non-computability is unrelated to the fact of not being to be able to write laws. One example of an algorithm that can be defined and could be included in a law of physics but whose solution cannot be computed is the busy beaver.

However, so far, apart from possible inherent randomness in QM, there is currently no evidence that indicates that the physical laws are non-computable.

Of course, even if the laws are computable, that doesn't mean that they can answer all questions. As Godel showed any formal system has statements that cannot be proved (see Count Iblis answer).

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This means that the universe cannot be simulated by a Turing Machine, it's not related to being able to write down th equations of physics. If the laws of physics are non-computable, you then also lift the restrictions any computing device is subject to and expand that to whatever the non-computable laws of physics would allow.

E.g. classical physics is known to be non-computable, and the laws of classical physics allow you to build a computer that is capable of accelerating so that each clock cycle is half of the previous clock cycle. This means that you can perform an infinite number of computations in a finite period of time. The halting problem can then be circumvented. E.g. if the Riemann hypothesis is true but unprovable, then this computer could still verify that it is correct. it would bypass the unprovability (i.e. the lack of a finite length proof) by checking that all the infinite number of non-trivial zeros are on the critical line.

Count Iblis
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