Last week’s dehydrated potato problem is a clear and instructive example of a “mental illusion,” as the solution is as surprising as it is counterintuitive. And it is also a good example of lateral thinking, because if it is approached in a way other than the conventional one, which would consist of posing the corresponding equations, it is solved without the need for calculations. The “trick” is to adopt the potato point of view, that is, to realize that in 100 kilos of potatoes with 99% water there is 1% dry potato, that is, 1 kilo, and to If 1 kilo is 2% of the weight (since dehydration reduces the water to 98%), there must be 50 kilos.
The perforated bead problem also admits an elegant and ingenious “lateral” solution: if the volume of the solid part is independent of the diameter of the hole, we can give this diameter any value, and the simplest thing is to give it the value 0, with This is to calculate the volume of a sphere of radius 3 mm: V = 4/3 π.3³ = 113.04 mm³, and since the density of gold is 19.3, the count will weigh 2.18 grams.
Some readers rightly commented that to solve the problem in this way we have to admit a priori that the volume sought is independent of the diameter of the hole, that is, we have to assume that the statement is correct and that no data is missing, which led us to talk about abduction.
Nothing to do with alleged abductions of humans by evil aliens. Well, although the esoteric meaning of the term is better known, in the jargon of logic abduction is a syllogism whose premise is not certain, but only probable. The name of this type of “unsafe” syllogism is due to the fact that in them the attention is diverted – abducted – from the conclusion to focus on the premise. In the counting problem, for example, abductive reasoning leads us to ask whether the volume is really independent of the diameter of the hole.
The American scientist and philosopher Charles S. Peirce, in the late nineteenth century, proposed the concept of abduction as a key to creative thinking
Since, both in everyday life and in scientific research, we are almost never sure of anything, in reality most of our reasoning is abductive: perfect syllogisms have a place only in courses in logic and in pure mathematics. And this led the American scientist and philosopher Charles S. Peirce, at the end of the 19th century, to propose the concept of abduction – redefined by him – as the key to creative thinking. For Peirce, abduction is not a mere anomaly or imperfect variant of deduction, but rather, on an equal footing with this and with induction, it constitutes the basic trinomial of thought, and especially of the generation of new ideas. Abduction proposes hypotheses, deduction draws conclusions from these hypotheses, and induction tests these conclusions against experience to reinforce or refute the proposed hypotheses. Abduction, deduction, and induction are thus the three legs of inference. And the pillars of the scientific method.
According to Peirce, there are three types of people when it comes to mental attitude: artists, practical people, and scientists. Artists see the world as if it were a great painting; for practical people the world is an “opportunity”; and scientists are engaged in “diligent investigation of the truth for the mere eagerness of penetrating the reason for things.” In their most inspired moments, and although they are not always aware of it, all three types of people use abduction creatively, which Peirce associates with surprise and redefines in this way: “We observe the surprising fact C [c de “conclusión”]; yes A [premisa] were true, C would be obvious; therefore A is likely to be true ”. This is how the human mind works, seeking order from surprise. And so science advances.
Carlo Frabetti is a writer and mathematician, member of the New York Academy of Sciences. He has published more than 50 popular science works for adults, children and young people, including ‘Damn physics’, ‘Damn mathematics’ or ‘The great game’. He was a screenwriter for ‘La bola de cristal’.