Maximizing Accuracy in Modeling Physical Phenomena through the Power of Information Theory
One of the major challenges in measuring physical variables and assessing uncertainty lies in the fact that all statistical methods without exception, are focused on identifying, calculating the relative uncertainties of all variables considered in the already constructed model, verifying computer uncertainties, as well as on determining the consistency of experimental data. It cannot diminish the importance and necessity of these steps. However, balancing simplicity with model accuracy is crucial in achieving high measurement accuracy, and incorporating uncertainty associated with all variables in the model structure can aid in achieving this balance. It is important to recognize the impact of ignoring such uncertainties, as it can affect the reliability of the measurement results and lead to poor decision-making. Therefore, incorporating the uncertainty associated with all variables in the model structure can significantly improve the accuracy and reliability of measurements, leading to better decision-making and problem-solving.
—In these challenging times, it is imperative that we strive to comprehend the hazy, complex nature of our surroundings.—
To address this issue, research has developed a method for estimating the limit of measurement accuracy at the model-building stage. This approach considers factors such as the storage, transmission, processing, and use of information by the thinker, without disturbing the observed object through mental acts. By selecting the optimal quantitative and qualitative set of variables to accurately reproduce the observed phenomenon within the finite amount of information contained in the model, this method enables the calculation of precise values for the threshold difference between the model and the real phenomenon. As a result, this method can significantly increase the accuracy of measurement theory.
The author begins by discussing the challenges of modeling complex systems, which can involve large amounts of data and a high degree of uncertainty. Traditional modeling methods, such as statistical analysis, may not be sufficient to capture the complexity of these systems. The author argues that information theory provides a more powerful approach, as it can quantify the amount of information contained in a system.
The article then goes on to discuss several key concepts in information theory, such as entropy, mutual information, and channel capacity. These concepts provide a way to measure the amount of information contained in a system, as well as the amount of information that can be transmitted through a communication channel. The author argues that these concepts can be applied to physical systems, such as experimental physics or engineering, to enhance the accuracy of modeling.
By presenting the model as a channel through which information flows from the object of study to the thinker, it becomes possible to apply it to a wide range of physical phenomena and technological processes.
The article presents a theoretical proof of the ε-equation as a fundamental limit in modeling physical phenomena using the framework of information theory. The ε-equation has a physical interpretation as the initial conceptual comparative uncertainty ε inherent in any physical or mathematical model, which is solely determined by the amount of information in the model and is independent of the measurement process.
This equation imposes a lower bound on the achievable measurement accuracy in both experimental setups using state-of-the-art test benches and numerical calculations performed with high-speed computers. This is because the value of ε is solely determined by the design of the model structure and the finite amount of information available in the model prior to conducting any experiment, and it is not related to the measurement process itself.
Furthermore, the ε-equation is applicable to models that use dimensional and non-dimensional variables derived from any system of units, including different base quantities and derived variables.
The method outlined in this paper presents a conceptual decomposition of the modeling process into its components in terms of sources of the model comparative uncertainty. It was developed considering the presentation of the model as a channel for transmitting information from the object of study to the thinker, and it is applicable to any physical phenomena and technological processes. The method reveals the relationship between the structure of the model and its comparative uncertainty and allows you to identify research problems associated with choosing the most preferable model for a particular object.
The article provides several examples of the application of information theory to the modeling of physical phenomena, how this theory has been successfully applied to complex systems, demonstrating its potential as a valuable trust tool for researchers and practitioners in a variety of fields including the usage of the bandwidth of information channels to test the preferred model structure for the most appropriate method for measuring various physical variables, such as the speed of sound, physical constants, and the amount of information accumulated on Earth.
In these challenging times, it is imperative that we strive to comprehend the hazy, complex nature of our surroundings. It is crucial to acknowledge that, despite the meticulous and precise research methods utilized, science is inherently uncertain. Moreover, the very act of thinking and analyzing as a scientist can limit the accuracy and reliability of the findings. Therefore, we must explore various effective tools to identify the root causes of inaccuracies in replicating natural and technological processes. The information method is one such reliable, theoretically proven tool with significant promise in this regard.
Translation of the article: Unleashing the Power of Information Theory: Enhancing Accuracy in Modeling Physical Phenomena, in Journal of Applied Mathematics and Physics, 11(3), 2023. https://www.scirp.org/pdf/jamp_2023032715355822.pdf
Cite this article in APA as: Menin, B. (2023, April 14). Maximizing accuracy in modeling physical phenomena through the power of information theory. Information Matters, Vol. 3, Issue 4. https://informationmatters.org/2023/04/maximizing-accuracy-in-modeling-physical-phenomena-through-the-power-of-information-theory/