Sorry that I haven't yet read the book and doing so would be necessary to do justice to your argument, but I would like to comment: I very much agree with the general hypothesis that intelligence can be modeled in terms of motion, though I think you need to step back and put motion into its larger context. As Newton said, "For every action, there is an equal and opposite reaction." While any particular action can be modeled as a vector, the reaction is a non-linear distribution through the context. Much as water being pushed aside by a ship and filling in behind it means an equal amount of water moves in the opposite direction of the ship. How we generally conceive of this cumulative activity is as thermodynamics. The motions of many such entities creating an overall balance, with all the myriad resulting peaks and troughs of temperature and pressure, creating vortices, waves though the underlaying mediums, smoothness, uniform action, choppiness, etc.
This operates on many physiological levels, from our body temperature, to the activities of large numbers of people. I would argue much of the subconscious aspects of our brain work thermodynamically as well, while it is our conscious rational, sequencing function that is the vector perception.
Remember that the brain is divided into two hemispheres and while the left side is considered the logical, rational, linear function, it is the right, emotional, intuitional side which operates more as a scalar function. Think temperature or pressure, where all the information in our minds is constantly jostling around, with those instinctive connections rising to the surface as intuition, the emotional effects of conflicting impulses and or too much information, otherwise known as stress, etc.
So part of our mind is focused on that forward motion through our context, that is the vector and part is like a body of water, interacting with that environment on a more complex contextual level.
This also goes to the main point I keep making in these debates, that we equate time with that mental effect of forward motion and so think of it is the present moving from one event to the next and so on this narrative basis, history and essentially civilization is based. Physics then codifies this perception by treating time as simply measures of duration between such events. The deeper reality though, is that it is just this activity which creates change and so it is those events which form and dissolve into the next, as the energy is constantly changing form. So it is actually the events which go future to past. To wit, tomorrow becomes yesterday because the earth spins, not the earth traveling some flow of time from yesterday to tomorrow. Duration is simply the state of the present, while these events come and go and is not external to any point of the present.
The problem this poses for physics is that it makes time an effect of activity and as such, more like temperature than space. Which means spacetime is just a clever mathematical correlation between measures of distance and duration, not the underlaying fabric of reality.
Yes measures[i/] of distance and duration are fundamentally connected, but then so are measures of temperature, or pressure and volume, but no one insists temperature or pressure are another dimension of space!! This explains why all clocks run at their own rates, yet remain in the same present. In fact a faster clock will burn through its energy proportionally faster and so age quicker, thus falling into the past before a slower clock of the same energy content. Whereas if time were simply a vector from past to future, the faster clock should move into the future before the slow clock. Now it will evolve quicker, but require more energy to sustain its continued existence. The hare is long dead, while the tortoise still plods along.
Safe to say this steps on too many professional toes to even be given consideration, but that's why I try focusing on its more practical applications, like mind/brain function.