*2.2.2 Spectacular successes*

*Connectivity and Functional Specialization in the Brain*

rejected upon examination).

ordered structure.

understanding.

*2.2.1 Baffling failures*

Importantly, models admit deliberately inserted counterfactual variations (e.g. A could have second thoughts and imagine C owning an expensive watch and asking for time because it had accidentally stopped) and generate the corresponding predictions (e.g., a satisfactory marriage) without revisiting the path (i.e., skipping over the sequence "C will stay with us, board the train with us, etc.)). Similarly, the model allows assessing global impact of local changes in one of the components without giving consideration to other components (e.g., one does need to trace the chain of coordinations in order to realize that failure in one element (e.g., D does not come to the station) will fail the entire chain and cancel the prediction). Crucially, models 'resist' relaxation of constraints, requiring forceful (deliberate) insertion of variations (i.e., under the model, the thoughts of D failing to appear, or C owning an expensive watch, etc. do not come to mind, as opposed to being

To summarize, eliminating degrees of freedom in mental models entails remov-

ing from consideration an otherwise exploding multitude of alternatives, thus making predictions both attainable and usable (i.e., delivered within the time window demanded by the situation). Models admit local variations consistent across the model (e.g. Macbeth's decision to kill Duncan in scene 7 is consistent with what happened to him in scene 2, etc.) and suppress spurious variations. As a result, understanding yields the experience of having succeeded in grasping "general relations in multitudes of particulars", thus turning an intractable mess into a well

The next section turns from literary scenarios to realistic ones, seeking to illustrate the extremes (amazing successes and baffling failures) in the operation of

Children at an early age often fail to connect and coordinate events taking place right in front of them, as follows. The child is shown a toy which is subsequently placed under a cover allowing her to retrieve the toy. After a few successful repetitions, the toy is transferred, in full view of the child, to another spot where it is placed under another cover. After some hesitation, the child looks for the toy, not in

Claudius Galen, an outstanding philosopher and physician in the Roman Empire, formulated a theory of blood production and processing in the body (circa 150 AD). The theory asserted that blood is produced in the liver from ingested food, rises to the lungs through the right side of the heart, crosses through pores to the left side where it is mixed with inhaled air and, finally, gets distributed throughout the body and consumed by the tissue (the surplus is expelled with sweat and urine). In this schema, heart remains a reservoir where blood is collected and treated (mixed with air) on its way from the source (liver) to the sink (tissues). In the XIth century, Galen's works were translated into Latin and became a dogma that dominated medical profession for over 500 years. Ironically, bloodletting was one of the most frequent treatment modalities in the medieval medicine, but neither the viewing of blood streams spurting from incisions nor the evidence of heart's incessant beating in one's own chest could cause questioning of the dogma. In 1628, English physician William Harvey published a book presenting a simple and cogently argued model of blood circulation. Moreover, he pointed out absurdities inherent in the dogma (e.g., the liver would have to produce several times the body weight in blood every day if the blood was being absorbed). Despite their undeniable strength (a simple model

**2.2 From children's games to revolutionary discoveries**

the spot to where it was just moved but in the previous one [20].

**76**

In the 1820–1835 time period, Michael Faraday formulated key ideas of the field theory postulating relations between electric and magnetic phenomena which, in the preceding decades, were commonly viewed as being totally unrelated. Expressed in a mathematical formalism by James Clerk Maxwell, the Faraday - Maxwell model of electromagnetism depicted propagation of electric and magnetic fields as tightly coordinated processes. Faraday's conceptualization of fields envisioned material entities of a kind that are not perceptually accessible but permeate space and carry force. In a brilliant feat of expansive insight, Maxwell realized the existence of relations between electromagnetic waves, light and perception of color. These findings have been propelling advances in physics and technology, until the present day and into the foreseeable future.

Modern physics (quantum mechanics, astrophysics) deals with entities that are not directly observable. Literature reports that key ideas concerning quantum processes were formulated by Werner Heisenberg (circa 1925) following an insight he allegedly received when taking a walk in the park at night and observing a passer by appearing in illuminated areas under lamp posts and disappearing in the shadows when leaving those areas [23]. The position and movement of the person between the posts remained undetermined, suggesting the idea of indeterminate states of electrons in the atom when transiting between energy levels (somewhat similar to indeterminate states of characters in a play when transiting between scenes, as in **Figure 1**). Quantum mechanics proved to be the most successful physical theory ever formulated, predicting the outcomes of particle interactions with unparalleled accuracy.

As reported in [24], an explosion on a DC-10 passenger airliner incapacitated one of three engines and demolished the hydraulic system, causing loss of control mechanisms for the remaining two engines except for their thrust levers. Hydraulic systems are built with triple redundancy, bringing the odds of losing control due to hydraulic system failure to less than one in a billion. Accordingly, no protocol has been ever created for handling such occasions and no training was ever offered. When the aircraft started pitching violently up and down (a phugoid pattern), the pilot had a short time window to figure out how to suppress phugoids and land the aircraft. According to pilot's recollections, a simplified model was formed in his mind that accounted for the location of the remaining two engines and suggested a maneuvering strategy using differential thrust. The strategy was not only unfamiliar but grossly counterintuitive, requiring decelerating when the aircraft was climbing and accelerating when it was heading down. When flight conditions were reproduced in a simulator, numerous pilots failed to figuring out a course of action and kept crashing (could not make the runway after dozens of attempts) [24].

Samuel Reschevsky, a chess prodigy born in 1911 in Poland, learned the game at the age of four and at the age of eight was defeating champions of his country in tournaments, as well as beating scores of opponents, including master-level players, in public demonstrations of simultaneous play. Although cognitive difficulties faced in chess have been always appreciated, there were no satisfactory methods for quantifying them until the era of chess computers. Chess algorithms required hardware with operating speed at or above <sup>8</sup> 10 position evaluations per second in order to compete with expert players capable of carrying out at most one or two position evaluations per second. Understanding the game compensates for the 1: <sup>8</sup> 10 disadvantage in speed: expert players perceive configurations of pieces as compositions of "complexes", deriving game plans from apprehending coordinations between the "complexes" [25]. Findings in [25] suggest that expert game models take the form of simultaneous structures, not unlike the matrix in **Figure 1**. A novice's perception is limited to a few adjacent cells in the matrix (2–3 moves look-ahead involving 2–3 pieces) while expert models can include a hierarchy of matrices encompassing the entire configuration and extending to 10–15 moves look-ahead Position analysis involves envisioning variations for some of the moves, constrained by the entire web of coordinations across the matrix. As a result, experts are not distracted into considering spurious (weak) moves, no more than novices waste effort in considering illegal moves [26].

To summarize, the previous section associated understanding with the development of mental models representing entities, their behavior and different forms of behavior coordination in the form of simultaneous memory structures. It was suggested that simultaneous coordination suppresses combinatorial explosion, confining the process to an infinitesimally small volume in the vast combinatorial space (considering possible move combinations in chess, similar to considering possible letter combinations in playwriting, quickly brings one to the realm of counting protons in multiple universes). Prediction, explanation and planning are enabled by mental modeling. This section reviewed extreme cases when modeling processes failed to establish coordination between a few directly observable and persistent entities and succeeded in quickly coordinating multiple, transient and/or unobservable ones. Summarily, suggestions and observations in Section 2 define the main challenges facing a theory of understanding:


The next part focuses on the emergence of understanding.
