"Time" not a dimension.

[lilphil1989]

In addition to providing a more accurate description of the nature of physical reality, the concept of time as a numerical order of change can also resolve Zeno’s paradox of Achilles and the Tortoise....
Here, the researchers explain that the paradox can be resolved by redefining velocity, so that the velocity of both runners is derived from the numerical order of their motion, rather than their displacement and direction in time.

Seriously? Zeno's paradox just arises from incorrect use of the word "never". The sum of the amount of time taken for each step in the "paradox" forms a convergent geometric series. So it's invalid to say that Achillles will never pass the tortoise, rather one should say that Achilles will not pass the tortoise before the time that the sum converges to.

---

It seems like these guys are just creating a false dichotomy. Time as the order of events OR as a "dimension" in a 3+1 spacetime. But there's no reason to think that the two should be mutually exclusive.

Perhaps you shouldn't be taking this too seriously, it's to be published in Physics Essays, which has something of a reputation for publishing odd or even outright silly papers which would have little to no chance of being published elsewhere.

Forgive me if this is a boneheaded question -- my science-fu is distinctly weak -- but if we erase the concept of time dilation...

Time dilation is an observable physical phenomenon. They're not really suggesting getting rid of the concept of time dilation, they're just recasting it as changes in "the velocity of material change".