The thing with the time dimension is causation. Things that happened at t=0 influence t=1. The x, y, z dimensions have no such property. Stuff that happens on x

The thing with the time dimension is causation. Things that happened at t=0 influence t=1. The x, y, z dimensions have no such property. Stuff that happens on x=0 have no effect on x=1. Probability and entropy arise as a result of the causative nature of time, thus creating an arrow: "The arrow of time." There is no "The arrow of space." Probability in mathematics has certain axioms and the equations that arise from these axioms somehow apply very well to the real world. Like theories in physics probability is in itself a theory about the way the world works. It is also the axiomatic basis which we use to verify other theories. We assume probability is true. All other science arises as a result. Thus with probability being the axiomatic foundation of our sciences there is, as a result, no science behind itself. To use probability to verify theories of physics like gravity is one thing, but then what do we use it to verify the theory of probability itself? Nothing. We just assume it's true. That being said, I have not read the books described in the article but is understandable why at some point there is no rigor. It's because rigor at this point doesn't exist. When it comes to time, probability and entropy we are at the foundational assumption of all science. The only tools at this point are philosophical conjecture and random speculation. There is a difference with time and the other dimensions. We can see it with our eyes when we watch the world unfold and entropy rise... we literally have no clue why it's like this, this is one of the fundamental limits of our understanding.