  Although quantum states nicely express interference effects, the outcomes of
experiments are not states, but correspond to probability distributions. Twenty
years ago we proved that probability distributions leave open a choice of
quantum states to explain experiments that is resolvable only by a move beyond
logic, which, inspired or not, can be characterized as a guess. Guesses link
the inner lives of investigators to their explanations of experimental results.
Recognizing the inescapability of guesswork in physics leads to avenues of
investigation, one of which is presented here.
  We invert the quest for the logical foundations of physics to reveal a
physical foundation of logic and calculation, and we represent this foundation
mathematically, in such a way as to show the shaping and re-shaping of
calculations by guesswork. We draw on the interplay between guessing and
computation in digital contexts that, perhaps surprisingly, include living
organisms. Digital computation and communication depend on a type of
synchronization that coordinates transitions among physically distinct
conditions represented by "digits." This logical synchronization, known to
engineers but neglected in physics, requires guesswork for its maintenance. By
abstracting digital hardware, we model the structure of human thinking as
logically synchronized computation, punctuated by guesses.
  We adapt marked graphs to mathematically represent computation and represent
guesses by unpredictable changes in these marked graphs. The marked graphs
reveal a logical substructure to spatial and temporal navigation, with
implications across physics and its biological applications. By limiting our
model to the logical aspect of communications and computations, we unveil
logical structure in relation to guesswork, applicable not just to electronics
but also to the functioning of living organisms.
