Is interaction a computation?

My understanding of Seth Lloyd’s thesis [1][2][3] is that information is fundamental and any interaction (change, dynamics) involves computation. This is in line with John A. Wheeler’s “it from bit” program. You can reach Wheeler’s classic essay from the link below.


There is an implication of this claim for theory construction. See below.


“A mathematical problem is computable if it can be solved in principle by a computing device. Some common synonyms for “computable” are “solvable”, “decidable”, and “recursive”. Hilbert believed that all mathematical problems were solvable, but in the 1930’s Gödel, Turing, and Church showed that this is not the case. There is an extensive study and classification of which mathematical problems are computable and which are not.” – [4]

Implication for theory construction

Most real numbers are not computable. If someone insists on “interaction” being a computation then they have to construct the dynamical theory using integer numbers. In such a theory space and time have to be discrete.

Even when the theory is based on complex, quaternion, or octonion numbers the basis elements of these have to be discrete variables. In my opinion this is too limiting. Maybe “interaction” is not a computation. Edward Witten expressed a similar thought.

“On the real numbers, I’ve got to plead ignorance or agnosticism. It is something I wonder about, but I’ve tried to imagine what it could mean to not use the continuum of real numbers, and the one logician I tried discussing it with didn’t help me.” – Edward Witten [5]







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