Consciousness and how it got to be that way

Thursday, October 22, 2009

Flatland and Free Will

In my previous post I asked why, if we do not have free will and the path of the universe is set in stone, we should have a seemingly privileged timepoint called "now". With no free will, there are no more degrees of freedom as you're reading this "now" "in the present" then there are degrees of freedom for something that happened ten minutes ago, or in 1588. In this setting "now" seems especially arbitrary and one wonders why nervous systems of this sort, i.e. that are constrained to one gradually changing temporal perspective, would ever appear - since events are all settled anyway. If we live in four-dimensional block of frozen space-time, why can't we see the whole thing? Why do we seem limited to one slowly shifting level within it?

Another way of looking at it (and responding to TGP's statement that "now" is a given) is to imagine a visit to Flatland. In Abbott's original conception, Flatland appears to three-dimensional beings as a plane in which 2-dimensional creatures like squares and circles are going about their lives, unaware (and unable to be aware) that above or below them, they were being observed by extra-dimensional beings. Abbott used Flatland as a way of arguing by analogy how fourth-dimensional objects would interact with and appear in our own three-dimensional universe (see the link for the full treatment).

If you look at our universe as four-dimensional space-time, then you can consider Flatland to not be two-dimensional, but three-dimensional plane-time. In a no-free-will Flatland, their universe would look to us like a tall box, with time-tracks - set-in-stone of every square and circle twisting through it like tunnels in an ant colony. If you wanted to be a three-dimensional sadist, you could climb up on a ladder and look at Mr. Square at the moment of his death in a two-dimensional hospital. Then you climb back down and again insert yourself into Flatland to find him enjoying lunch in a park the day after his twenty-third birthday. "You will die on the following date and time; I know, because I already saw it." Do you see why this is strange? From your three-dimensional standpoint, no-free-will Flatland is a giant, static sculpture. Why would the awareness of any entity in that block be constrained to any one plane within it?

By the same argument, in no-free-will space-land (where we live, if you don't believe in free-will anyway), we're stuck in a block of four-dimensional space-time. Fourth dimensional sadists are free to go scrambling up and down this block like you just did on Mr. Square's universe, except the fourth-dimensional sadists are looking for nasty tidbits to relay to unfortunate three-dimensional suckers like you. A fourth-dimensional sadist could pop in ninety seconds from now and tell you that you getting smooshed by a rabid slime mold on 19 July, 2025, and it knows because it already saw it happen. And in a very real sense, in a non-free-will universe, it already has happened. The disconnect is that you haven't experienced it yet, and in a no-free-will universe, that's what seems strange. If the events happening now are just as certain as the events happening then, why isn't seeing the future the same as turning your head to look at the other side of the room you're in? It's all already there.

An implication is that if we again assume a literal interpretation of multidimensional models of the universe, if the universe has a finite set of dimensions, it would necessarily be deterministic. The highest dimension would be a static one, and Mr. Square can't have free will if we don't.


  1. I think the Flatland analogy confuses the issue of free will more than it clarifies it. Maybe some fifth-dimensional sadist told the fourth-dimensional sadist that he was always going to tell you about your third-dimensional smooshing (into a two-dimensional object, right?) thus transferring the question of free will up n dimensions.

  2. I still think Flatland is a useful analogy for those who see a pre-destined universe as a four-dimensional block of frozen space-time, which some do. You're correct that in this model, we ourselves as three dimensional beings must have a fourth dimension across which the state of the other three can change, so that we can change states in the third dimension, and climb around on Flatland's 3D block of plane-time. If time as the fourth dimension is taken literally by various models of the universe (six in the standard model I think?), there are multiple dimensions above us, but as long as there aren't infinite dimensions then the highest would necessarily be static.

    The backdrop of this issue for me is that I do believe there is such a thing as free will, but I recognize the incompatibilities between this belief and our understanding of the physical world (and therefore, nervous systems) so far. Consequently I'm actually happy that the concept of "now" seems incoherent in a deterministic universe because it's apparently incoherent.

  3. A very interesting post! It gives great food for thought, however I fear that you may be taking too literally, the idea that time is a +1th dimension. To simply "tack time on to space as an extra dimension" does not work as in your analogies. Just because we can traverse space does not mean that we can traverse time in a lower dimensional space. To put this mathematically precisely, a two dimensional world with time is represented by R^2 x R. That is, a 2-tuple consisting of a two dimensional space vector and a time scalar. One can still only traverse the two dimensional space vector.

    That said, I find your post very interesting and it made me think. I have recently started thinking of such things in my blog (, with a post firstly on determinism in flatland, and then a subsequent post on the implications this has on free will in flatland.

  4. I definitely took this quite literally and knew I could be doing so erroneously; but it's a good vehicle for thinking about it. But my question is that I'm not sure what an addtional dimension can mean if it can in principle not be traveresed (i.e. R^2 x R in the representation you used). I'll visit your post and see! Thanks for your comment.