I USA utropas varje år april månad till Mathematics Awareness Month, framför allt som ett slags paraply för en mängd olika lokala aktiviteter med det gemensamma syftet att skänka matematiken den uppmärksamhet i samhället ämnet förtjänar. Ett specifikt tema utses varje år, och i år är temat The Future of Prediction. I aprilnumret av tidskriften Notices of the American Mathematical Society ägnas en särskild avdelning åt detta tema, inklusive en text av yours truly, rubricerad Our desperate need to predict the future, där jag tar chansen att inskärpa några vetenskapsteoretiska poänger jag tidigare snuddat vid i Kapitel 6 av min bok Here Be Dragons och i min tidigare bloggpost No nonsense.1 Så här inleder jag den aktuella texten:
- In 1814, Pierre Simon de Laplace envisioned a demon who could pinpoint the exact present positions and movements of all particles and then calculate all of their future trajectories, thereby accurately predicting everything that will ever happen. He understood, however, that this task would be forever beyond mere human capabilities. Due to what we now know of as sensitive dependence on initial conditions, this brute force approach to predicting the future does not work (other than in certain limited situations with limited time horizon). Instead, we’d like to find regularities in the past and assume “by induction” that they will continue into the future. Unfortunately, there seems to be no way to defend induction - the extension of past regularities into the future - without reverting to circularity by pointing out that induction has served us well in the past and thus can be expected to do so in the future.
Nevertheless, we rely on induction to make predictions. We simply do not know any other way. Good applied mathematicians and good scientists know that the extent to which these predictions are reliable depends on how closely the state of the system we are trying to predict will remain within the envelope of what has already been observed. The further we push atmospheric CO2 levels above those of the last several million years, the less reliably we can predict the future climate. Moore’s law - the exponential curve that fits several decades of computer hardware development so well - eventually predicts the physically impossible.
Today we face unprecedented challenges of the following kind.
Fotnot
1) Min nya text har också beröringpunkter med förra veckans bloggpost Aaronson om Newcombs paradox, som även den behandlar ämnet prediktion. Newcombs paradox kan ju ses som en illustration av hur känslan av fri vilja tycks gå upp i rök om vi blir alltför bra på att prediktera mänskligt beteende. I sista stycket av Notices-artikeln berör jag samma fenomen, om än inte med något fullt lika skruvat exempel.
