In June 1946 Max Planck spoke in the Göttingen physics colloquium. Planck was 88 years old, had received the highest honors of his community, including a Nobel Prize in 1918 for his discovery of the quantum, and had profoundly changed how we think about physical reality. He knew something about problems, both in science and in life. He postulated the quantum, famously, “in an act of despair.” His first wife died young, as did four of his five children, the fourth, Erwin, killed by the Gestapo in 1945. Having lived through all of this, Max Planck decided to talk about problems that are nothing but distraction — scheinproblems.
Following the vertiginous developments in early 20th century physics, a handful of German words established themselves in the scientific lingua franca — ansatz and gedankenexperiment are two of them. Can we add scheinproblem, please?
Planck’s lecture is available here (in German). It is an attempt to classify non-problems, so that we may spot them instead of wasting our days and nights trying in vain to resolve unresolvable conundrums. With this, Planck gives us a valuable gift: time. Remember this is an 88-year-old speaking, and looking back the question occurs to him: what are we to do with our time among the living? Instead of addressing that unanswerable question, Planck turns it around and tells us what we shouldn’t do: give ourselves a headache over unanswerable questions — scheinproblems, as he calls them.
Not all hard problems are worthy of attention, Planck tells us. Proper unsolvability does not mean that we’re too dumb — it means that the problem is not what it pretends to be. Impossible to solve is not an extrapolation of hard to solve. There’s no hierarchy: easy, medium, hard, impossible. No. Impossible is different. Just as infinity is different from “a very big number.”
Here is an example from his lecture, for which he apologizes in advance because it may offend the audience’s intelligence. He says from where you’re sitting, this wall over here is the left wall of the lecture hall. But from where I’m standing, the left wall is over there. But so which is it? I present to you the unsolvable problem: which is the left wall of the lecture hall? Planck imagined disagreements and sleepless nights, but I’m imagining departments, institutes, and professorships of lecture hall chirality, students of the problem, journals, academic conferences — the whole shebang.
It’s amusing to just go wild with Planck’s lecture hall idea. But he gives us more than this nugget. What are these problems? Can we classify them? Or, more modestly: how can we spot them? In one type, he tells us, the correct answer is a matter of perspective. An electron, in a meaningful sense, is a particle from one point of view. From another point of view it really is a wave. This is similar to the lecture hall chirality problem, and an excuse to remember the enjoyable inter-generational disagreement whereby G.P. Thompson received the 1938 Nobel Prize in Physics for discovering the electron as a wave, whereas his father J. J. Thompson had received the 1906 Nobel Prize in Physics for discovering the electron as a particle.
Incidentally, some 24 years before Planck’s colloquium, Wittgenstein concluded that all philosophical problems are really scheinproblems, and fundamentally linguistic. Abstract language, divorced from real life, confuses our thinking. We end up pondering grammatically correct but meaningless sequences of words like “why can’t unicorns fly?” Wittgenstein doesn’t use the word “Scheinproblem” but describes the phenomenon accurately, in his Tractatus Logico-Philosophicus, 6.53. To Wittgenstein, natural science — as distinct from philosophy — is the set of solvable problems, meaning not scheinproblems. Planck asks in his colloquium how scheinproblems emerge as the scientist veers off course.
Scheinproblems require a questioning of the question. Apart from looking for multiple valid perspectives, we can look for wrong assumptions hidden in the statement of the problem. What’s the inside surface of the Möbius strip in the feature image of this post? The wrong assumption is that such a surface exists. Problems arising from wrong assumptions are not resolved by normal science, they can only be resolved by a paradigm shift. We don’t solve the scheinproblem by addressing the question as posed — we solve it by re-examining the question itself, and by rephrasing it, recognizing it for what it is and possibly posing a related real problem instead. Then we solve that. Think of gamble evaluation. Because changes in expected monetary wealth fail to predict human behavior, researchers in the 18th century asked what is wrong with money (a scheinproblem), or even what is wrong with human behavior (another scheinproblem). Much effort went into answering those questions. A better question, in my opinion, is to ask what is wrong with expectation values. I don’t answer either of the questions as posed, I replace them with a question I find more promising and answer it.
The scheinproblem is not so much solved as eliminated. I cannot overemphasize the difference between the type of solution required by a problem and the type of solution required by a scheinproblem. We don’t expect a stated problem to be resolved by identifying it as a scheinproblem. We expect the problem to be real, and for someone to give us an answer. Gentlemen, my cabinet advisors tell me the lecture hall chirality issue has been defeating the brightest heads of our times. Progress must be made, funding will be available. We want answers!
Another type of scheinproblem is an under-specified problem. There may not be an error in the assumptions behind the problem statement, but we may just not have enough information to solve the problem. In that case, if we fail to recognize the schein-nature of the problem, investigators will run off in different directions and introduce different additional assumptions. We may not even notice it when we’re doing this, and when two different camps meet further down the line, they will discover irreconcilable differences. Different schools of thought emerge, each born of its own additional tacit assumptions. They may even accuse each other — correctly — of introducing additional assumptions, recognizing the fault of the other, but not their own.
Encouragingly, Planck points out that a scientific scheinproblem may turn into a real problem, meaning a solvable problem, following scientific progress. His example is the alchemists’ search for a recipe to transform mercury into gold. This was an impossibility in the context of the tools available to the alchemists. It’s not a problem of chemistry but a problem of nuclear physics, which had not been discovered at the time the problem was stated, and the alchemists made no progress. But nuclear fission had been discovered 8 tumultuous years before the 1946 colloquium (by Planck’s student Lise Meitner, and their friend Otto Hahn): nuclear physics had progressed to understand that knocking a proton out of a mercury nucleus would indeed turn it into gold.
Let me spell out the analogy to economics: we laid the conceptual foundations in the 17th and 18th centuries. Probability theory starts in 1654 with a gambling problem, life annuities are priced in 1693, Daniel Bernoulli introduces expected utility theory in 1738. The mathematical tools available during this time are not so different from the cooking pots of the alchemists. Crucially, the concept of ergodicity and the importance of time-averaging were unknown. These tools became available in the 19th and 20th centuries. And examples abound: the exponential function is all-important in the context of growth, re-investment, reproduction, and evolution. It was properly written down for the first time by Euler in 1748 (see Eli Maor’s delightful book “e The story of a number“, p.156).
Why didn’t the alchemists immediately turn into chemists and nuclear physicists? Why did their goal not guide them to a solution? My answer to this question is a quote from the 1979 Tarkovsky movie Stalker (which featured two years ago in LML’s Science on Screen program):
With their eyes glued to the prize of making gold, the alchemists failed to listen to the only certain guide in the zone of science: childlike curiosity about nature’s true structure. Identifying a goal, a useful but as yet unknown result, can create a scheinproblem. The result may be wonderful if found, but actually unattainable, or to be found in a wholly unexpected direction.
While Planck’s colloquium was about natural science, let’s end on a philosophical note and return to Wittgenstein. Philosophical problems are scheinproblems, to be solved by identifying them as such. Oddly, this does not detract from their significance. As a problem’s significance increases, how much we can meaningfully say about it often decreases, and at the point of existential significance there is nothing left to say.
“The solution of the problem of life is seen in the vanishing of this problem.
(Is not this the reason why men to whom after long doubting the sense of life became clear, could not then say wherein this sense consisted?)”
— L. Wittgenstein, Tractatus Logico-Philosophicus 6.521.