Consider the real tree

The botanist wants to know how well a real tree grows under nominal conditions, how round is the tree trunk.

The real tree evolved in a hologram world, it grew well where the previous epoch left a depressed hemispherical mound of decaying nutrients.  That is the self sampling problem, the uncertainty of what is nominal. Nothing ever became completely disconnected between epochs.  If everything is local then how to two separated physicists compare outcomes except by hoping across local surfaces? The local surface jumps are of the physicists creation, designed for the experiment, thus moidfying the history, ex ante.

Nash and his pigeons.  The rate at which one pigeon can sample its neighbor is finite and known imprecision, each pigeon knows the bounds.  A signal from the periphery to the interior takes about three steps before it is drowned by sample uncertainty.

So we get small flocks, irregular circles, ready to fly off in a moment of non-adiabatic motion. They are circular to begin with because in a hologram world, a circle is the smallest surface area for a target and sufficient density for reproduction. They know error bounds, and when it is exceeded, they know adiabatic conditions are gone. This is a 1 D line of symmetry, distance from neighbors, into a 2-D surface circular, the hologram effect. We would expect to see that inside the tree trunk, for real, but maybe not in theory, I dunno.

Mouse and scroll bar.  We did that one. density matrix is low rank, 3 bit computing is all we devote to the mouse. So, in a scroll bar, we go from 0 D to 1D, devoting three move types to vertical, and one move to escape the bar. Our tracking filter was maximum entropy, and matched mouse cursor to rectangle function, using separate IO manager extracted from X Window.

It is what Weinberg is working on, quantizing experiment and environment, finding a general solution for the physicist.

The sandbox is data driven, the pit boss does what it has to do, and theory can all be ex post, or soon priced thereof.  The idea behind sandbox is that our human trade space is much lower resolution than compute space, the bitcoin assumption. With power of attorney, the auto pit process can manage the pit boss function; because the computer manages congestion among bots much more accurately than human pit bosses manage human traders. Humans in the model supply trades and bounds to the bots with power of attorney. Traders buy their own pricing insurance while paying their fair share for currency risk.

I think it boils down to a queuing problem over finite channels. Hawkins flow is needed to maintain quantization and keep the density matrix moving along the manifold aibatically.