How to Solve Problems
I’ve some mixed feelings about writing on this topic. The reason is that it’s so ordinary to solve problems that it’s almost not worth talking about. What is life, after all, if not the continual creating and solving of problems? And death simply what one calls a problem that one couldn’t solve? But a theory of problem-solving may itself be useful for solving some problems, so here we are.
My reference for developing this theory is Gilbert Simondon. Best known as a philosopher, he was also a psychologist because back when he was getting educated and attaining his academic appointments those weren’t yet distinct subjects in France. His daughter recounts his early life and career in some detail for those interested in his biography.
One course he taught was recently published in English: Imagination and Invention. Simondon creates a fascinating theory of how images, which for him are not simply mental or wholly ‘subjective’, are formed and develop, and then how they can serve as the basis of an invention. As is typical, Simondon works to blend and modulate classic distinctions and fields in order to overcome their latent problems. In this way he practices what he preaches in the very act of preaching. I heartily recommend the book.
It’s that final section, on Invention, that I want to focus on. I will here quote Simondon at length, then comment on that quote.
To what situation does invention correspond? To a problem, which is to say, to an interruption due to an obstacle or a discontinuity acting as a barrier to an operative implementation [accomplissement opératoire] that is continuous in its project. What is problematic is a situation that dualizes an action, chops it up by separating it into segments, either for lack of a middle term or because the fulfillment of one part of the action destroys another equally necessary part; the two fundamental problematic modes are hiatus and incompatibility; both amount to an action’s failure to adapt to itself intrinsically, across the various sequences and subsets it presupposes; solutions show up as restorations of continuity, enabling the progressiveness of operative modes along paths previously invisible within the structure of the given reality. Invention is the emergence of an extrinsic compatibility between the milieu and the organism and of an intrinsic compatibility between the subsets of the action. Detours, the fabrication of instruments, and the association of several operators all represent different means of re-establishing intrinsic and extrinsic compatibility. When a problem is resolved, the dimension of the final act of the result encompasses, in its dimensional characteristics, the operative regime that produced it; for instance, in a classical tale, a rolling boulder stuck in the middle of a narrow path cannot be moved by individual travelers trying to move it separately, since it is too heavy, though it is easily pushed aside by the travelers working together; here the problem cannot be solved as it is initially given, when the road is a place of passage where multiple individual itineraries do not compound [couplage]; rather the group of travelers exists virtually from the point of view of the result, since it is only at that moment that they can all resume their travel, even though they arrived at the obstacle at different times depending on their particular trip. The compounding of efforts, visible in the unity of the result, points back to the act of resolution and to invention; within the conditions of the problem, the lines of a possible solution already appear, albeit negatively; the accumulation of people stopped by the boulder, one after the other, progressively constitutes a simultaneity of expectations and needs, thus a tension towards the simultaneity of departures once the obstacle is removed; the virtual simultaneity of imagined departures points back to the simultaneity of efforts in which the solution lies. Anticipation and foresight are not enough since each traveller is perfectly capable of imagining how he would go on walking if the boulder were pushed aside; what is needed is that anticipation return to the present by altering the structure and conditions of the ongoing action; in this case, it is collective anticipation that alters each of the individual actions by constructing a system of synergy.
Hence there is a structuring return of the content of the anticipation onto the formula of the present action; it is a return of information, or rather a return of organization whose source is of the order of magnitude of the result—the regime of the operation thought of as carried out and complete. Invention sets up a certain kind of retroaction, a recurring input (“feedback”) which goes from the regime of the completed result to the organization of the means and subsets within a mode of compatibility. In the example of the boulder, the organization of compatibility in the form of synergy amounts to setting the force of each traveler against a fraction of the boulder to be moved; since the boulder is not divisible this can take place only if the boulder is pushed at the same moment by all the travelers. The root of the solution is a communication between two orders of magnitude, that of the result (the road reopened to all) and that of the problem-event (a barrier across the path of each one), whose data are altered: within the new perspective of a collective (and no longer individual) result, the operation amounts to each traveler moving a fraction of the boulder; the collective result is still compatible with the individual result, the path being opened to each one when it is open to the group; similarly, the individual action of pushing is compatible with the sum of the actions of other individuals thanks to the additive simultaneity of parallel thrusts; it is this intrinsic compatibility that enables the extrinsic compatibility of the relation between a single person’s force and the weight of a fraction of the boulder.
In such a case, invention is facilitated by the fact that the subjects are at the same time virtual operators; the interruption of the action caused by the problem-event prompts a shift to the order of magnitude of the result, which is that of compatibility; the different interruptions of the originally independent trips generates the collective of stopped travelers, thereby creating through a negative effect the field within which the compatible action can unfold; the association through a community of intentions within a homogeneous group is a particular case, since it requires neither instrumental mediation nor a division of labor. As soon as the problem can find a solution only in an order of magnitude very different than that of the individual and of the elementary gesture, because of size or complexity, it becomes necessary to resort to heterogeneous mediations, and the task of invention bearing on these mediations is considerable; but invention preserves its functional place as a transfer system between two different orders of magnitude; simple machines such as a lever or a capstan, even the inclined plane or the winch display in their structure the essential function of transfer such devices materialize. With a capstan or a hoist, a single operator, in each of his gestures, acts as if he were moving the fraction of the load that is compatible with his strength; yet he moves the entire, indivisible load, albeit only a small distance. Invention in such a case, while respecting the principle of conservation of work, consists in varying both factors, intensity of force and displacement, in order to adapt them to the capacities of the organism of the operator. The problem is solved when a communication is established between the action system of the subject who encounters the problem and the regime of reality of the result; the subject is part of the order of reality in which the problem is posed; he is not part of the order of imagined results; invention is the discovery of mediation between two orders, a mediation thanks to which the action system of the subject may gain purchase on the production of the result through coordinated action.
What Simondon points to here is the role that nonlinearity plays in invention. As he says, there is a disconnect between the current state of affairs and the world once the problem has been solved. The future must come back to affect the present.
The challenge, then, is to imagine that future state wherein the problem is solved, to communicate that vision so that it makes sense to all parties involved, work backwards from the solution to formulate its conditions of possibility in the present, and then to modify the present to match those conditions.
Lots of people, it seems to me, have trouble with this for various reasons. Here’s a non-exhaustive list:
They lack a clear sense of the problem
They can’t articulate it to those others whom they need to solve it
The problem they want to solve may not be a problem in the same sense, or at all, for those necessary others
Related: They don’t want to have to rely on others or to care about those others’ problems, so they don’t allow those others to reformulate the problem at hand in a way that has them voluntarily participate in solving it
There may be lots of preparation necessary before one can accomplish the ultimate solution
They don’t want to do the work of solving the problem
Other forces are at work that hamper their ability to focus on solving the problem
Since this is just a theory of problems and their solutions, I won’t claim that it will help with any particular problem one may face. But perhaps it can help to clarify the situation and lead to better problems, which might allow one to find a suitable solution.