From: mk_thisisit
Predicting the future is a concept deeply explored through the lens of chaos theory. Professor Adam Kanigowski, winner of the European Mathematical Society’s main prize, discusses this topic at the National Museum of Technology in Warsaw [00:00:00].
The Future: Theoretically Written, Practically Elusive
Professor Kanigowski asserts that if all parameters were known with infinite precision, the future would be knowable [00:01:35]. Theoretically, predicting the future is possible [00:00:51]. However, in practice, this is unattainable due to inherent measurement errors [00:01:48]. The inability to precisely measure the present moment means that even minute disturbances can lead to vastly different future states [00:02:38].
The Butterfly Effect
The Butterfly Effect is a core concept within chaos theory, illustrating how a minimal disturbance from an actual state can lead to an “absolutely different future” [00:02:43]. For instance, a butterfly flapping its wings can subtly change wind force, which, despite seeming insignificant, can have colossal consequences [00:00:21]. This phenomenon highlights why predicting the future with certainty is practically impossible [00:02:01].
Order Within Chaos
Despite the term “chaos,” the Butterfly Effect can be viewed as an underlying order [00:02:54]. Chaos arises when predictions diverge significantly from the actual state after a period, but the law governing this divergence can still be considered a form of order [00:03:19].
Applications and Challenges
Chaos theory has various applications, particularly in fields aiming for long-term prediction:
- Weather Prediction: The Butterfly Effect originated from meteorologist Edward Lorenz’s work on weather forecasting [00:04:34]. He concluded that long-term weather prediction is impossible due to deterministic chaos, where even a minimal temperature or wind disturbance can lead to colossal changes [00:04:47].
- Stock Market Movements: Similar to weather, predicting stock market movements for increasingly longer periods depends on measurement precision [00:09:10].
- Biological Evolution: Chaos can describe how systems evolve, including the development of species [00:12:47]. Minimal disturbances in initial conditions can determine which species survive and thrive [00:13:08].
- N-Body Problem: The problem of predicting the movements of multiple celestial bodies (like Earth, Sun, and Moon) is inherently complex [00:14:43]. While a two-body system has a known solution, the three-body problem, for example, is notoriously difficult to solve due to the terrifying number of variables [00:15:10]. Even celestial body movements cannot be predicted beyond approximately 2 million years [00:13:47].
The Role of Measurement Precision
The ability to predict for a longer period is directly tied to the precision of measurements. The speed at which information is lost is exponential, described by the Lyapunov exponent [00:10:26]. If temperature is measured with an accuracy of one millionth, prediction can be extended to three days, compared to only one day with lower accuracy [00:09:34]. This highlights a continuous effort in computing to slow down the Butterfly Effect [00:09:47].
Optimization Theory
Given the practical impossibility of perfect prediction, mathematicians utilize optimization theory. This field focuses on correcting decisions over time to steer towards an expected result, despite initial errors [00:29:22]. It’s about making optimal corrections along the way to stay close to a desired outcome [00:30:20].
Chaos Theory and Determinism vs Indeterminism
Chaos theory is primarily developed within the framework of classical, Newtonian physics, which assumes a deterministic world [00:18:25]. In a purely deterministic view, if one knew the state of every elementary particle, the future would be entirely written [00:34:08].
However, the quantum world challenges this deterministic view, exhibiting non-intuitive phenomena like particles being in multiple places simultaneously [00:17:46]. Mathematics is only beginning to learn how to study quantum phenomena [00:18:37]. Hypotheses like Quantum ergodicity suggest that if one knows more about velocity, position becomes evenly distributed, akin to having zero information about position [00:19:18]. The fundamental unpredictability at the quantum level means predictions are described using probability theory [00:35:00].
The distinction between "chaos" and "order" in this context is crucial:
While chaos theory describes systems highly sensitive to initial conditions, leading to seemingly random outcomes, these systems are still governed by underlying deterministic laws. The “chaos” emerges from our inability to precisely measure and predict due to this sensitivity.
Is Mathematics Discovered or Created?
Professor Kanigowski believes that important mathematics is discovered, not created [00:46:17]. He holds an idealistic view that “somewhere there is some book which has in which everything is written” [00:37:38]. Differential calculus, for example, is seen as discovered [00:07:24]. The challenge lies in uncovering these pre-existing truths.
The Future of Prediction
In the near future, it is unlikely that large-scale events can be predicted for longer periods due to the sheer number of variables [00:52:39]. Instead, the focus shifts to understanding the probability of a given event [00:52:49]. Mathematical advancements and increasing computational power allow for more precise measurements and longer prediction times, but the exponential loss of information remains a fundamental hurdle [00:42:25].
The dynamic processes in the modern world have intensified, making prediction potentially more difficult than in past centuries [00:41:36]. However, the motivation for mathematicians remains the inherent curiosity about the world and the desire to discover its underlying principles [00:50:50].