God is sophisticated
On the unusual dimensionality of our space-time
In one of my recent notes, I wrote that God is sophisticated. A sentence like this might give the impression that it was penned with the intention of publishing a book of quotations, but that is not why I used it.
We live in a spacetime with three spatial dimensions and one temporal dimension. I marvel at this observation because it means we inhabit a spacetime with the minimal number of temporal dimensions and almost the minimal number of spatial dimensions.
If any laws of physics could exist—even those based on mathematics different from what we know, even contradictory to it—then for any pair of positive integers (X, Y), one could construct a spacetime with X spatial dimensions and Y temporal dimensions where life could exist. With full freedom to establish the laws of logic, mathematics, physics, and requirements for the emergence of life, one could always adapt them to any spacetime and eventually obtain intelligent observers.
However, if that were the case, how can we justify that the spacetime we find ourselves in is almost minimal? After all, in the scenario described above, there is an infinite number of possible combinations. Why do we observe a combination that is only two dimensions different from the minimal one—the only special one in this set? Why, instead of 5008 spatial dimensions and 333 temporal dimensions, 45,345 and 123, 64,564 and 33,453,466, or any other combination, do we perceive exactly three spatial dimensions and one temporal dimension?
This puzzle has a very elegant solution. Namely, if we assume that for some reason God is limited to the mathematics and logic we know, then even if He created all universes with all possible combinations of dimensions of time and space, only in a universe with three spatial dimensions and one temporal dimension could intelligent observers exist.
Why? Spacetimes with fewer than three spatial dimensions would be too simple to lead to the emergence of beings complex enough to ask questions about their own existence. On the other hand, a number of spatial dimensions greater than three has the characteristic that planetary systems within such a spacetime are not stable, and thus do not form systems that allow for the emergence and evolution of life, like our Solar System. Regarding a number of temporal dimensions greater than one, they would lead to realities where any prediction of the future would be at least an order or two of magnitude more difficult than in ours, and even in our reality, forecasting is often very difficult and sometimes even impossible. Therefore, two or more temporal dimensions would prevent the existence of a cognitive niche, whose presence is necessary for the emergence of intelligent observers.1
But for God to be limited? That cannot be, so He must self-limit—but not like just anyone, rather like a virtuoso who does not play just anything but only the most magnificent musical compositions. God, therefore, must be sophisticated.
Sponsored by: Wiadomości giełdowe GPW
[gr-qc/9702052] On the dimensionality of spacetime