The legendary Scott Alexander recently posted an article promoting Max Tegmark’s mathematical universe hypothesis as a salvo in favor of atheism in the ongoing theism/atheism debate. While I am skeptical of theism myself, I have a couple problems with the mathematical universe hypothesis that lead me to find it unconvincing, which I hope to lay out in this post. These arguments are based on our immediate, subjective experience of existing in whatever reality we exist in, and as a result I believe they are fairly convincing arguments as to the nature of that reality.

My first point of contention with the mathematical universe hypothesis is the fact that we have a subjective experience of moving forward through time. I contend that if all we were was mathematical objects, we would not expect that. Now, it might seem like this critique is misguided. One of the most basic types of mathematical objects Scott mentions in his post is cellular automata, which have a series of temporally arranged steps. Indeed, a universe with a temporal dimension is something that could easily be modeled by and exist as a mathematical object. However, if it is merely that object and nothing more, there is a problem. Even though this object might mathematically describe temporal evolution and change, the object that describes all of the temporal states of this system exists “all at once.” That is to say, if we have a system such as a cellular automata, every temporal step of that system is part of the mathematical object describing the system, so if the universe described is merely that mathematical object and nothing more, all of its temporal states are described “simultaneously,” and exist side by side with each other. The subjective experience of moving forward through those states seems to be something that has to exist externally from the mathematical object, as some actuality that instantiates the states described by the object in order one at a time. If it was merely the mathematical object and nothing more, every described universe would be a “block universe” with every state in its temporal evolution simultaneously instantiated. So, it seems there must be something more than mere math to make the actualities of a described system appear one at a time and in a specific order. Since our subjective experience of time is one of the most fundamental things we can directly observe, it would seem that whatever universe we are existing as conscious observers within must be more than mere math. The fact that we experience temporal movement and an arrow of time implies that whatever fundamental structure we are living out, it must be something “on top of” the base math that all at once describes every physical state across the dimension of time. So from this fundamental observation of what we subjectively experience as time, the mathematical universe hypothesis is called into serious doubt.

There is another point based on direct subjective experience that I believe undermines the mathematical universe hypothesis. That is the existence of states of emotional valence, of positive and negative emotions. When it comes to the general existence of consciousness within a mathematical object, I do not object. Consciousness can simply be what it “feels like” to be whatever mathematical object is being described. However, what I find incredibly strange under this hypothesis is that there are things that feel good and bad. Good and bad emotional states are one of the most fundamental things we can experience, and indeed, I hold that it is so fundamentally true that feeling good is good and feeling bad is bad that a moral system of maximizing pleasure less pain is so immediately implied as to almost be self-evident. It simply is good to feel pleasure and bad to feel pain, and we can know this with subjective immediacy to a depth that is unreachable by any other supposed moral or ethical facts. Emotional valence is the fountainhead of value, from which what it even means for something to be good or bad arises. But if we are merely mathematical objects, from whence arises the feelings of pleasure and pain that are so fundamental? How does an equation encode what it subjectively feels like to experience joy or suffering? I can countenance the idea that there is something that it “feels like” to be a given mathematical object which explains consciousness within such a mathematical universe, but the idea of a mathematical object encoding emotional valence seems much more unlikely. While we could imagine that there is some utility function that encodes the emotional valence within a given universe, we quickly realize that you could switch out disutility for utility while leaving the function the same, meaning that pain rather than pleasure would be described by the same mathematical object. Therefore, it seems like there must be something beyond the equations that specifies whether positive or negative valence is being experienced. Essentially, there must be another “layer” above the functions that accounts for the subjective experience of pleasure or pain and the fact that the feeling of them cannot be switched out with each other without the immediate qualia being different from how they are in actuality. Whether good or bad emotions are being felt is something that seems beyond math by itself’s ability to describe.

These are the main objections I have to Tegmark’s mathematical universe hypothesis. Since both derive from immediate and unquestionable subjective experience, I believe these objections are very deep and powerful, and cast serious doubt on the hypothesis. While I am skeptical of theism for various other reasons, in this ongoing debate I simply don’t think that the mathematical universe is a viable atheistic explanation of reality.