John Norton: Approximation and Idealization
TLDRThe speaker, John Norton, discusses the nuances of approximation and idealization in scientific models and theories, emphasizing the importance of distinguishing between the two for clear communication in scientific discourse. He delves into the complexities of taking limits in statistical physics, illustrating the potential pitfalls of idealizing systems as infinite. Norton also addresses the debate between reductionism and emergence in physics, suggesting that both perspectives can be valid depending on the level of analysis, and encourages a careful approach to understanding infinite systems and their implications for scientific understanding.
Takeaways
- 📅 The speaker announces upcoming lectures by Leo Cadof, including the annual Nurur lecture and talks for the applied math and philosophy departments.
- 🎓 John Norton is introduced as a prominent figure in the philosophy of science, known for his diverse contributions and clever explanations in various scientific fields.
- 🧐 The lecture focuses on the concepts of approximation and idealization, emphasizing the importance of distinguishing between the two in scientific discussions.
- 🔍 Norton argues that taking limits to infinity, a common practice in statistical physics, can be a particularly challenging and error-prone process.
- 🚫 The speaker warns against the assumption that infinite idealizations are always accurate representations of finite systems, as they may not possess the expected properties.
- 🤔 The debate between reduction and emergence in statistical physics is discussed, suggesting that terminological differences may underlie disagreements between experts.
- 🔄 The renormalization group method is highlighted as a powerful tool in statistical physics, which operates by approximation rather than by dealing with infinite systems directly.
- 💡 The speaker suggests that the perceived conflict between reductionists and emergentists may stem from professional specialization and different interpretations of 'levels' in scientific theories.
- 📚 Norton's work on approximation and idealization in scientific theories is available on his website, offering further reading for those interested in the topic.
- 🤝 The lecture concludes with an invitation for further exploration and discussion, acknowledging the complexity and nuance of the issues presented.
Q & A
What is the main topic of the lecture given by John Norton?
-The main topic of the lecture is the difference between approximation and idealization, and why it matters in the context of scientific theories and models.
What is the purpose of using specific terms like 'approximation' and 'idealization' in scientific discussions according to John Norton?
-The purpose of using specific terms is to facilitate clear communication and to distinguish between inexact descriptions and the representation of novel systems with properties that provide those inexact descriptions.
Can you explain the example of the pot of skew and how it illustrates the concept of approximation?
-The pot of skew boiling at 100° C is used to illustrate an inexact description of its temperature. The approximation '100° C' is not exactly correct because the boiling point can change with impurities, but it is an exact truth for pure water at standard pressure, demonstrating the concept of approximation.
What is the significance of the difference between approximation and idealization in statistical physics?
-In statistical physics, the difference is significant because taking limits to infinity to generate idealizations can be a complex and error-prone process. Often, what we refer to as infinite idealizations are actually approximations and do not necessarily involve infinite systems.
Why is the limit process in statistical physics considered to be especially difficult and fraught with potential errors?
-The limit process is difficult because it involves taking the number of components in a system towards infinity, which can lead to properties that are not what we expect or need for our approximations. Infinite systems might not have the properties that we assume they have when we start with finite systems.
What is the thermodynamic limit in statistical physics, and why is it problematic?
-The thermodynamic limit is a process where both the number of components and the volume of the system go to infinity while keeping their ratio (density) constant. It is problematic because it can lead to qualitative changes in behavior and discontinuities that are not present in finite systems, such as the spontaneous excitation of an infinite one-dimensional crystal.
What is the renormalization group method in statistical physics, and how does it relate to the concepts of approximation and idealization?
-The renormalization group method is a technique used to study the behavior of systems near their critical points. It involves generating transformations based on physical assumptions about the independence of thermal properties from internal degrees of freedom. This method works by approximation, not by infinite idealization, emphasizing the importance of understanding the behavior of systems with very large but finite components.
What is the debate over reduction and emergence in the context of phase transitions in statistical physics?
-The debate is whether phase transitions can be fully explained by the reduction of thermodynamics to statistical physics (reductionism) or whether they represent an emergent phenomenon that cannot be fully understood from the properties of individual components alone (emergence).
What does John Norton suggest as the reason for the ongoing debate between reduction and emergence in phase transitions?
-Norton suggests that the debate stems from a professional divide between philosophers and physicists, who tend to conceptualize levels differently. Philosophers often focus on relations between theories, while physicists focus on the differences between systems at various scales.
How does the concept of 'levels' play a role in the debate over reduction and emergence?
-The concept of 'levels' is central to the debate because it determines the framework within which reduction and emergence are discussed. Philosophers may view levels as self-contained theories, while physicists may view them as collections of processes at particular scales, leading to different interpretations of reduction and emergence.
Outlines
📅 Upcoming Lectures and Events
The speaker announces various upcoming events, including the annual Nurur lecture by Leo Cado, scheduled for the following Tuesday at Somerville House. The lecture series is aimed at the general public and is not restricted to specialists in physics or philosophy. Additional lectures by Leo Cado on scientific simulation and prediction, and another for the philosophy department, are also highlighted, taking place later in the week at different venues.
🎓 Introduction to John Norton
The introducer praises John Norton for his contributions to the philosophy of science, highlighting his wide range of topics, clever explanations, and impressive graphics. Norton's extensive publication record and his role as director of the Pittsburgh Center for History and Philosophy of Science are also mentioned, emphasizing his significant impact on the field.
🔍 The Distinction Between Approximation and Idealization
John Norton begins his talk by addressing the confusion surrounding the terms 'approximation' and 'idealization', explaining his specific use of these terms throughout the lecture. He emphasizes the importance of distinguishing between the two concepts, with approximation referring to inexact descriptions and idealization to novel systems that provide exact descriptions. Norton also discusses the process of generating idealizations by taking limits to infinity, particularly in statistical physics, and the potential pitfalls of this process.
🌡️ The Concept of Approximation Illustrated
Norton uses the example of boiling water to illustrate the concept of approximation. He explains that while it is an inexact description to say water boils at 100°C, this is an exact truth for pure water at standard pressure. He further discusses how this inexact description serves as an approximation for real-world scenarios where water's boiling point can be affected by various factors.
🚀 The Dynamics of Skydiving and Bacterial Growth
The speaker provides examples of skydiving and bacterial growth to demonstrate the use of approximations and idealizations. In the case of skydiving, the initial speed of the diver is approximated by a formula that is an exact description for an idealized scenario of falling in a vacuum. For bacterial growth, Norton points out the limitations of using an exponential formula when considering an infinite number of bacteria, as it leads to irrational numbers and an impractical model.
⚠️ The Pitfalls of Infinite Systems
Norton warns of the dangers associated with infinite systems, explaining that they may not possess the properties expected of large, but finite, systems. He uses a geometric system to illustrate how a property that stabilizes as a system grows larger can fail to deliver an idealization when the limit is taken to infinity, leading to a divergence between the limit property and the limit system.
🔬 The Thermodynamic Limit in Statistical Physics
The speaker delves into the thermodynamic limit, a concept used in statistical physics to study systems with a large number of components. Norton explains how this limit can lead to a qualitative change in behavior, such as the spontaneous excitation of an infinite one-dimensional crystal, which contrasts with the behavior of finite systems. He highlights the challenges and the need for caution when dealing with such idealizations.
🔧 Renormalization Group Methods
Norton discusses renormalization group methods, which are used to understand the behavior of physical systems near critical points. He emphasizes the importance of the transformation based on the physical assumption that thermal properties can be independent of internal degrees of freedom. However, he also points out the limitations of these methods when applied to systems with an infinite number of components, as the partition function becomes undefined.
🤔 Philosophical Implications of Infinite Systems
The speaker reflects on the philosophical implications of working with infinite systems, particularly in the context of reductionism and emergence. He suggests that the debate between these two perspectives may be influenced by professional tendencies among physicists and philosophers to focus on different levels of description. Norton proposes that understanding these differences can help reconcile the seemingly conflicting views on reduction and emergence.
🌐 The Concept of Levels in Physics and Philosophy
Norton explores the concept of levels in both physics and philosophy, suggesting that the way these levels are defined and used can lead to different interpretations of reduction and emergence. He discusses the molecular description level and the thermodynamic level, highlighting the different starting points and the potential for misunderstanding when these levels are conflated or not clearly distinguished.
🔄 The Debate Over Reductionism and Emergence
The speaker engages with the ongoing debate over whether phase transitions are a result of reduction from thermodynamics by statistical physics or an example of non-reductive emergence. Norton suggests that both sides of the debate may be correct, depending on the sense of 'level' being discussed, and that the key to resolving the debate lies in understanding the different professional perspectives and the scales at which they operate.
📚 Conclusions and Further Reading
In conclusion, Norton emphasizes the importance of distinguishing between approximation and idealization, warns of the dangers of discussing infinite systems, and attempts to bring clarity to the debate between reductionism and emergence. He invites the audience to visit his website for more information, including papers on approximation and idealization, and his thoughts on the physics of transitions.
🤝 Audience Q&A and Discussion
The speaker engages in a Q&A session with the audience, discussing topics such as the relationship between infinite systems and mathematical precision, the conceptual framework for understanding finite and infinite cases, and the practical implications of approximation in various fields. The discussion highlights the importance of careful consideration when dealing with infinite systems and the potential for confusion between mathematical and physical descriptions.
Mindmap
Keywords
💡Approximation
💡Idealization
💡Limit of a Function
💡Statistical Physics
💡Thermodynamic Limit
💡Renormalization Group
💡Phase Transition
💡Emergence
💡Reductionism
💡Critical Phenomena
Highlights
Introduction of the concept of approximation and idealization in scientific theories and their importance in distinguishing between exact and inexact descriptions.
The potential confusion and misuse of terms in scientific literature, emphasizing the need for clear definitions and distinctions.
The exploration of the challenges and complexities involved in taking limits to infinity in statistical physics, suggesting the need for careful consideration.
The assertion that infinite idealizations often only provide approximations and may not necessarily involve infinite systems.
Discussion on the role of approximations in scientific simulations and predictions, highlighting the limitations and potential pitfalls.
The debate over reductionism and emergence in statistical physics and thermodynamics, suggesting that both perspectives have merit.
The presentation of the idea that terminological differences may underlie the debate between reduction and emergence, proposing a reconciliation.
The use of the boiling point of water as a simple example to illustrate the concept of approximation in scientific descriptions.
The introduction of the skydiver analogy to explain the relationship between inexact descriptions and idealizing systems.
The presentation of the bacterial growth model to demonstrate the limitations of taking limits to infinity in certain scientific models.
The geometric system example illustrating the divergence between limit properties and limit systems, emphasizing the need for careful limit analysis.
The thermodynamic limit discussion in statistical physics, pointing out the potential for qualitative changes in system behavior.
The renormalization group methods and their role in understanding the behavior of systems near critical points, despite their technical complexity.
The caution against the dangers of idealization, especially when dealing with infinite systems and the potential for indeterminism.
The distinction between approximation and idealization in the context of renormalization group transformations, highlighting the importance of finite systems.
The conclusion that systems work by approximation rather than infinite idealization, emphasizing the importance of understanding the behavior of finite systems.
Transcripts
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