computable vs cantgotu worlds

A hyper-reductionist view of the universe is that the universe is essentially computation present across different scales and complexity. Ordered information then becomes the true currency of existence where order is defined a sequence of organization that can predictably help serve a complex purpose. If we look at the history of the universe across time-scales, we can observe that information is moving towards a path of increasing order as depicted by technologist Ray Kurzweil in his book ‘Singularity is Near’ where he mentions the different epochs of information evolution which started after the Big Bang with primitive matter first storing ordered information at the quantum scale giving rise to various stable elements whose ordered and complex combinations down the road eventually gave rise to biological DNA which is again information of very high order that further enabled the creation of complex nervous systems which enabled real time processing of higher order information later enabling the creation of computers as external symbiotic tools to help in further ordering of information. So computation is essentially woven into the fabric of reality by virtue of design and this is one of the ideas that physicist David Deutsch tries to capture in his book ‘Fabric of Reality’ which tries to link the different existing foundational branches of science to construct a comprehensive ‘Theory of Everything’ to explain reality. A crucial element of explaining reality lies in linking theory of computation formulated by computer scientist Alan Turing with existing laws of physics. To explore the linkage between computation and physics, David Deutsch performs a thought experiment using a universal virtual reality (VR) generator with infinite computational power that should ideally be able to simulate any logical possible physical environment where all information can be programmed into a series of logical instructions which can be executed by a universal turing machine in order to virtually simulate the environment. The universal VR generator however hits a computational limit when trying to compute certain type of environments which are logically possible but is incomputable due to a mechanism known as diagonal argument formulated by mathematician George Cantor. To understand the diagonal argument, consider that the instructions for simulating a logically possible physical environment can be represented by a matrix where the rows of the matrix represents the exhaustive set of programs needed to simulate the physical environment and column elements represents the progression of each program at different moments in time. However, according to the diagonal argument, we can use the diagonal of the matrix to construct a new program which is not part of the list of programs contained in the rows which were supposed to be exhaustive, by selectively altering the parameters of the diagonal so as to not exactly match with any of the existing programs and this process can be infinitely repeated leading to the conclusion that there are certain logically possible environments which cannot be simulated by a universal computer making them theoretically incomputable. David Deutsch labelled these environments as Cantgotu environments named after George Cantor crediting his diagonal argument which explains the incomputability of these environments. The theoretical possibility of Cantgotu environments hinders the hope of linking computation theory with reality but David Deutsch introduces the Turing Principle which states that it is possible to build a universal computer whose repertoire includes any computation that any other physically possible object can perform. This implies that while we cannot compute Cantgotu environments which are a mathematical possibility, the Turing principle guarantees that we can compute anything that actually happens in physical reality. Anything that happens in physical reality is bounded by the laws of physics and thereby possesses a certain programmatic order within its immense complexity preventing the uncomputable infinite variations as seen in Cantgotu environments. The laws of physics fine-tunes the universe for comprehensibility which allows us to simulate smaller subsets of the universe in our minds or even computers which would not have been possible if the universe was not computable. This reinforces the view that the universe is essentially a large scale computation and can be programmatically reduced to series of instructions which can theoretically be executed by a universal computer to produce a copy of the universe. The universe however operates on a very different paradigm of computing which would be intractable for a universal classical computer which although has infinite computing power is a sequential processor of instructions. Information in the universe fundamentally exists in the quantum scale within sub-atomic particles which are building blocks of the universe and information computation at the quantum scale happens parallelly on a massive scale rather than sequentially providing ground for a whole new world of computing i.e. quantum computing (which I have covered in another article - ‘quantum interference manipulation’) which would be the necessary next step if we want to truly build a universal computer capable of simulating the universe.