Brains are conscious because of the computations that they perform, and if a computer is capable of simulating a brain (and the world it interacts with), it would therefore be conscious as well. Max Tegmark goes one step further in suggesting that not even a computer is needed to create a conscious being: a computer simulation can be represented as a static four-dimensional object, and this object arguably exists as a mathematical structure even if the computer were to disappear altogether. By this argument, there are mathematical structures describing computer simulations contain conscious entities, and feel as real to their inhabitants as simulated universes or 'real' universes such as our own. If this is true, then there are a vast number of mathematically possible universes with the same claim to physical existence as our own; and the existence of our universe becomes indistinguishable from the existence of the mathematical structure that describes our universe, and hence our universe is effectively just a mathematical structure. This essay focuses on the critical part of Tegmark's argument: can mathematical objects, as opposed to computer simulations, be conscious? What follows is a review of the critical part of Tegmark's account, and then some possible arguments against it. Despite some possible holes in the argument, there is one part of it that is undeniable, which is that formal systems can describe (and even be, at least while they are being calculated) universes as complex and worth exploring as our own. Mathematical objects can be identical to conscious beings in all of their essential details, even if they lack some final spark of subjective consciousness that comes from being simulated. The profound implications of this fact transcend the possibly unknowable question of whether entities in these mathematical objects are really conscious or not.
I am a PhD student in linguistics at Radboud University, Nijmegen and the Max Planck Institute for Psycholinguistics.
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