Uncertainty is an essential topic in all disciplines beyond metrology
A message to a metrologist who tends to stick to the definition of a term from his perspective
Prologues
Many people today say that we live in uncertain times and that uncertainty worsens. The Google Books Ngram Viewer shows that "uncertainty" has doubled since 1950, with a unique trend, as shown in Figure 1. Since in metrology (the science of measurement), reporting all measurement and calibration results requires an explicit description of their uncertainty, it is not an exaggeration to say that uncertainty budgeting could cover half of our work. Therefore, we tend to extend the metrology concept to other fields and consider the word belonging only to our field. Such attitude could not be blamed because this is also a natural human tendency, as suggested by Abraham Maslow, who wrote: "I suppose it is tempting if the only tool you have is a hammer, to treat everything as if it were a nail."
I am going to write more articles about measurement uncertainty in the future. Before I do, I would like to look at uncertainty from other perspectives that might be held by experts in different fields and by ordinary individuals. However, because meeting them is not easy, I will take advice from ChatGPT instead. Although bias is often an issue in AI language models, I expect ChatGPT to help us broaden our knowledge and perspective on uncertainty. At the very least, ChatGPT is expected to give us a message from a different perspective than ours.
Why uncertainty matters more now
First, I ask this question with more introduction to ChatGPT to test its general understanding and perspective on uncertainty in conjunction with the increasing use of the word 'uncertainty'. Let me copy it here and comment later.
Uncertainty has become more important in the current age due to several reasons:
1. Rapid Technological Advancements: Technology is advancing at an unprecedented rate, leading to rapid changes in industries, economies, and societal structures. These changes introduce uncertainties as it becomes challenging to predict the impacts of emerging technologies on various aspects of life.
2. Global Interconnectedness: Globalization has increased the interdependence among nations economically, politically, and socially. Events in one part of the world can have far-reaching consequences across the globe, amplifying uncertainties and making it difficult to anticipate and mitigate risks.
3. Geopolitical Instability: The geopolitical landscape is characterized by increased tensions, conflicts, and economic imbalances among nations. Political uncertainties stemming from geopolitical events, trade disputes, and geopolitical rivalries add layers of unpredictability to global affairs.
4. Climate Change: Climate change presents significant uncertainties regarding its impacts on ecosystems, economies, and societies. Extreme weather events, shifts in climate patterns, and rising sea levels introduce unpredictability, challenging existing infrastructure and adaptation strategies.
5. Societal Changes: Societal changes, including demographic shifts, cultural transformations, and changes in consumer behavior, contribute to uncertainties in various sectors such as healthcare, education, and urban planning.
6. Pandemics and Health Crises: Global pandemics, such as the COVID-19 pandemic, highlight the vulnerabilities of societies and economies to health crises. The unpredictable nature of infectious diseases and their socio-economic impacts underscore the importance of addressing uncertainties in public health preparedness and response.
Overall, uncertainties pervade various aspects of modern life, necessitating adaptive and resilient strategies to navigate an increasingly complex and unpredictable world.
Regarding ChatGPT's response above about uncertainty as a general term, I think it is superior to the average person who has done a lot of reading. It also identifies more causes than any expert in a particular field could list. However, I am afraid it lacks a unified understanding and explanation of how all these causes are related. Now, ChatGPT is a good or even better interviewee for the original purpose of this article.
How ChatGPT understand uncertainty
I asked ChatGPT to explain the concept of uncertainty by giving an example of how AI might be wrong about a fact because of uncertainty. I got the following answers:
Suppose you ask an AI language model like me, “What is the population of New York City?” Now, let’s assume that the AI has been trained on a vast amount of data, including population statistics from various sources. It has learned that the population of New York City is approximately 8.4 million people.
However, the AI’s answer may still be subject to uncertainty due to several factors:
Data Quality: The AI relies on the quality and accuracy of the data it has been trained on. If the data sources used to train the AI contain errors or inaccuracies, the AI’s estimate of the population may also be incorrect.
Temporal Variability: Population figures can change over time due to factors such as births, deaths, migration, and changes in census methodologies. The AI may not have access to the most up-to-date population data, leading to a potentially outdated estimate.
Geographical Variability: Population estimates may vary depending on the geographical boundaries considered. New York City’s population can be defined differently based on whether it includes only the five boroughs or extends to the broader metropolitan area. The AI may provide a population estimate for a specific definition, but it may not clarify the geographical scope of its estimate, leading to uncertainty.
Sampling Error: If the AI’s training data is based on a sample rather than a complete population, there is a possibility of sampling error. The AI’s estimate may be subject to uncertainty, especially if the sample is not representative of the entire population.
Model Limitations: The AI’s algorithms and models may have inherent limitations or biases that affect the accuracy of its predictions. It may not account for certain factors or nuances that could influence population estimates, leading to potential inaccuracies.
Given these sources of uncertainty, the AI’s answer to the question about the population of New York City may be incorrect or imprecise. While the AI can provide a reasonable estimate based on the information it has been trained on, it’s essential to recognize that its answer is subject to uncertainty and may not always be entirely accurate. This example illustrates how uncertainty can arise even in AI systems that are trained on vast amounts of data.
Although ChatGPT does not describe the uncertainty of the population of New York City in terms of a number, it adequately explains the concept of uncertainty by citing five sources of uncertainty similar to those I am trying to list. It is interesting to see ChatGPT's response as if it acknowledges the existence of uncertainty in its prediction. Yet, new AI language models have recently produced highly biased results and stopped serving.
Origins of uncertainty from human tendency to ethics
Humans try to understand and describe a problem based on their knowledge or perspective. This essential human trait leads to fundamental uncertainty in answering the world's problems. For example, when we look at flowers in a garden through a window, our description of the flower can change due to our condition as an observer. From this context, let me list the origins of uncertainty individually. ChatGPT helped me again:
1. Subjectivity and bias: Our understanding of the world is inherently subjective, shaped by our individual experiences, beliefs, values and cultural backgrounds. This subjectivity can lead to biases and limitations in how we perceive and interpret issues, potentially obscuring important aspects or alternative viewpoints. Recognising and addressing these biases is essential to reducing uncertainty and promoting more inclusive and comprehensive approaches to problem solving.
2. Limitations of models and frameworks: When we approach a problem, we often rely on conceptual models, frameworks or mental schemas to make sense of it. However, these models are simplifications of reality and may not fully capture the complexity and nuance of the problem. As a result, there is uncertainty about how well our models match reality and whether they provide sufficient insight to address the problem effectively.
3. Interdisciplinary perspectives: Complex problems often require interdisciplinary approaches that integrate insights from different disciplines and perspectives. However, integrating different perspectives can introduce uncertainty, as different disciplines may have conflicting theories, methodologies or priorities. Managing this interdisciplinary uncertainty requires collaboration, open dialogue and a willingness to reconcile divergent viewpoints.
4. Contextual and situational factors: The context in which a problem arises, including social, cultural, economic and political factors, can significantly influence our understanding and approach to addressing it. However, contextual factors are often dynamic and multifaceted, adding layers of uncertainty to problem-solving efforts. Recognising and addressing these contextual uncertainties is essential to developing contextually appropriate and effective solutions.
5. Unforeseen consequences and emergent properties: Attempts to solve complex problems can lead to unintended consequences or unexpected emergent properties that were not originally anticipated. These unanticipated outcomes introduce uncertainty into the effectiveness and sustainability of our interventions. Embracing uncertainty means acknowledging the possibility of unintended consequences and adopting adaptive, iterative approaches to problem solving.
6. Ethical and value-based considerations: Ethical considerations and value judgments play an important role in how we define and prioritise problems and evaluate potential solutions. However, ethical dilemmas and conflicting values can introduce uncertainty into decision-making processes, particularly when different stakeholders hold divergent views. Engaging in transparent, inclusive deliberation processes can help to manage these ethical uncertainties and promote consensus-building around shared values and goals.
Recognising and embracing possible sources of uncertainty requires humility, reflexivity and openness to alternative viewpoints, ultimately enriching our problem-solving approaches and enhancing our capacity to effectively address future challenges.
Uncertainty from an epistemological perspective
From this perspective, uncertainty reflects the inherent limitations of human knowledge and understanding. It recognises that our knowledge of the world is always incomplete, provisional, and subject to revision. I ask ChatGPT to add some points to consider uncertainty from this perspective. In the meantime, I have refined ChatGPT's response and presented as follows:
Fundamental limitations of knowledge: Uncertainty arises from the recognition that there are fundamental limits to what we can know about the world. Our perceptions are limited by our senses, our reasoning is constrained by our cognitive abilities, and our observations are influenced by our biases and perspectives. As a result, our understanding of reality is always partial and imperfect.
Complexity and interconnectedness: The world is inherently complex and interconnected, with countless variables and factors influencing events and phenomena. Uncertainty arises from our inability to fully grasp the intricacies of these interactions and predict their outcomes with certainty. Even seemingly straightforward systems can exhibit emergent behavior and unpredictable dynamics.
Probabilistic nature of knowledge: Uncertainty is often expressed in terms of probabilities and likelihoods, reflecting our understanding that many phenomena are inherently stochastic or probabilistic in nature. Probability theory provides a formal framework for quantifying uncertainty and making informed decisions in the face of incomplete information.
Fallibility and revisionism: Recognising uncertainty reminds us of our fallibility as knowers and the importance of humility in our pursuit of knowledge. It encourages a spirit of skepticism, open-mindedness, and willingness to revise our beliefs in light of new evidence or perspectives. Embracing uncertainty can lead to a more nuanced and nuanced understanding of the world.
Pragmatic approaches to uncertainty: Despite the inherent uncertainty in our knowledge, we still need to make decisions and take actions in various domains of life. Pragmatic approaches to uncertainty emphasize making decisions based on the best available evidence, acknowledging uncertainty, and being prepared to adapt and adjust as new information emerges.
Uncertainty arises from our limited knowledge and understanding of epistemic uncertainty. Because of its probabilistic nature, knowledge has an inherent randomness or variability in the system itself, called aleatory uncertainty. Distinguishing between these two types of uncertainty can help us to better understand and address the sources of uncertainty in a given situation. In metrology, a systematic effect corresponds to epistemic uncertainty, while random uncertainty is a type of aleatory uncertainty.
Uncertainty in various disciplines
Again, I ask ChatGPT to list several disciplines where uncertainty is studied more quantitatively, along with concrete examples for each:
1. Statistics: Statistics provides rigorous methods for quantifying uncertainty. For example, confidence intervals in polling data provide a range of values within which the true population parameter is likely to lie with a certain level of confidence.
2. Economics: Economic models often incorporate uncertainty, with concepts like expected utility theory quantifying decision-making under uncertainty. For instance, in finance, option pricing models such as the Black-Scholes model use probabilistic assumptions to estimate the value of financial derivatives.
3. Finance: Finance utilizes quantitative methods to assess and manage financial risks. Value at Risk (VaR) is a widely used measure in risk management, quantifying the potential loss in value of a portfolio over a specified time horizon with a given confidence level.
4. Operations Research: Operations research employs mathematical optimization techniques to make decisions under uncertainty. For example, stochastic programming models in inventory management account for uncertain demand and supply conditions to optimize inventory levels.
5. Engineering: Engineering disciplines utilize probabilistic methods to design reliable systems and structures. In structural engineering, probabilistic risk assessment (PRA) quantifies the likelihood of failure in a structure under various loading and environmental conditions.
6. Environmental Science: Environmental scientists use probabilistic modeling to assess environmental risks and impacts. Climate models simulate future climate scenarios based on probabilistic projections of greenhouse gas emissions and other variables.
7. Computer Science: Computer science employs probabilistic algorithms and machine learning techniques to handle uncertainty in data and decision-making. Bayesian networks are used in artificial intelligence for probabilistic reasoning and decision-making under uncertainty.
8. Public Health: Public health researchers apply statistical methods to quantify uncertainty in epidemiological studies and disease modeling. For example, epidemiological models estimate the spread of infectious diseases like COVID-19 by incorporating uncertain parameters such as transmission rates and effectiveness of interventions.
9. Psychology: Psychology utilizes quantitative methods to study uncertainty’s cognitive and behavioral aspects. Decision-making under uncertainty is investigated using experiments that measure risk preferences, such as the Iowa Gambling Task, which assesses individuals’ decision-making in a probabilistic environment.
10. Sociology: Sociology employs quantitative methods to analyze societal responses to uncertainty and risk. Survey research often includes statistical techniques to measure public attitudes and perceptions towards uncertain events or social phenomena.
I agree that ChatGPT's answers above make sense as far as each proposed discipline is concerned. Furthermore, prioritising statistics is reasonable because it underpins the uncertainty of all other disciplines. However, ChatGPT did not include metrology here, which we believe is one of the most critical areas regarding uncertainty. In response to my request for its addition, it has finally included metrology as follows:
11. Metrology: Metrology focuses on quantifying and minimising measurement uncertainty. Measurement uncertainty is crucial in fields such as manufacturing, quality control, and scientific research. For example, in manufacturing, the uncertainty associated with dimensional measurements of mechanical parts is assessed using methods like the Guide to the Expression of Uncertainty in Measurement (GUM) to ensure product quality and compliance with specifications.
Methodologies for expressing uncertainty numerically
Finally, I ask ChatGPT to respond to this topic. I try to ask it, expecting any other methodology rather than statistics. Look at its response as follows:
1. Standard Deviation (σ): The standard deviation measures the dispersion or spread of a set of data points around the mean (average) value. It quantifies the average distance of data points from the mean and provides a measure of the variability or uncertainty within the dataset.
2. Standard Error (SE): The standard error is a measure of the variability of sample means around the population mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size. The standard error is often used to quantify the uncertainty associated with sample statistics, such as the mean or proportion.
3. Confidence Interval (CI): A confidence interval is a range of values calculated from sample data that is likely to contain the true population parameter with a certain level of confidence. It provides a measure of the uncertainty surrounding an estimated parameter, such as a population mean or proportion. Common confidence levels include 95% and 99%.
4. Margin of Error (MOE): The margin of error is a measure of the uncertainty associated with survey estimates due to sampling variability. It is typically expressed as a percentage and represents the range within which the true population parameter is likely to fall with a certain level of confidence. The margin of error is often used in opinion polls and surveys.
5. Prediction Interval: Unlike a confidence interval, which estimates the range of possible values for a population parameter, a prediction interval estimates the range of possible values for an individual observation or future data point. It accounts for both sampling variability and random error, providing a measure of the uncertainty surrounding a predicted outcome.
6. Bayesian Credible Interval: In Bayesian statistics, a credible interval is similar to a confidence interval but is based on the posterior distribution of a parameter rather than the sampling distribution. It represents the range of values within which the true parameter value is likely to fall with a certain level of credibility, based on the observed data and prior beliefs.
7. Probability Distribution Functions (PDF): Probability distribution functions describe the likelihood of different outcomes in a random process or experiment. Common probability distributions include the normal distribution, binomial distribution, Poisson distribution, and exponential distribution. These distributions quantify the uncertainty associated with random variables and provide a basis for probabilistic modeling and inference.
These methodologies provide various ways to quantify and express uncertainty numerically, each with its own assumptions, interpretations, and applications. Depending on the context and the nature of the data or problem at hand, different methodologies may be more appropriate for characterizing and communicating uncertainty effectively.
What do you think of ChatGPT's answer above? It's too long and redundant. Nevertheless, ChatGPT's answers make sense. I also have no idea other than what the statistics suggest. To summarise the list above, presenting a PDF would be the best way to express uncertainty numerically. Alternatives would show other indicators, such as some dispersion corresponding to the PDF.
Epilogue
We certainly live in a world of increasing uncertainty. Uncertainty is undoubtedly a subject of interest to many disciplines, including metrology. I want to be advised on this subject by someone who is not a metrologist but has read many books on uncertainty from different fields of knowledge. For this article, I have chosen ChatGPT as my interviewee. Although I have much more knowledge and experience in dealing with measurement uncertainty, I cannot say that I am much superior to ChatGPT in terms of knowledge and understanding of uncertainty from a general point of view.
I ask ChatGPT to list disciplines where uncertainty is studied more quantitatively. Unfortunately, metrology was not spontaneously mentioned until ten disciplines were listed. Note that statistics are the first to be mentioned. Under these circumstances, does it make sense to impose metrology terminology on all disciplines? For example, although metrologists consider the term 'error' for uncertainty to be taboo, it is still widely used in other fields. We should accept that the standard error of statistics is much more widely used than uncertainty. Our recent work on measurement uncertainty has been brilliant, and we are willing to share our achievements with other disciplines. What should we do in this situation? I would like to repeat the exact words that ChatGPT gave when explaining the origin of uncertainty.
Recognising and embracing possible ‘disagreement between two disciplines’ requires humility, reflexivity and openness to alternative viewpoints, ultimately enriching our problem-solving approaches and enhancing our capacity to effectively address future challenges.
ChatGPT advised me in preparing this article. He was a balanced interviewee and a teacher with a wide range of knowledge.
