Are mathematical explanations causal explanations in disguise? 

2024, Philosophy of Science

(with Campbell, D., Montelle, C. and Wilson, P.)

https://doi.org/10.1017/psa.2024.8 

We argue that purported mathematical explanations conceal contingent facts in their conditionals, and thus there is no fundamental difference between a mathematical explanation of a physical phenomenon and an ordinary application to mathematics to a physical phenomenon.  

On the continuum fallacy: is temperature a continuous function?  

2023, Foundations of Physics 

(with Campbell, D., Montelle, C., and Wilson, P.)  

https://doi.org/10.1007/s10701-023-00713-x 

This paper argues against the widely-held misconception that temperature is necessarily represented as a continuously varying function. It also argues that discontinuum models of temperature variation may actually have greater explanatory relevance and empirical adequacy in some cases.   

Does topology provide sufficient structure for non-causal explanations?

2023, PhD thesis (Foundations of Applied Mathematics), University of Canterbury, NZ

https://ir.canterbury.ac.nz/items/abeca6d2-8aea-4d0a-a456-a4fce5a823b0

This thesis examines some foundational issues in the applicability of topology to the natural world and their bearing on allegedly non-causal (topological) explanations of dynamical and complex systems. 

Not so distinctively mathematical explanations: topology and dynamical systems 

2022, Synthese  

(with Campbell, D., Montelle, C., and Wilson, P.)

https://doi.org/10.1007/s11229-022-03697-9  

This paper argues that distinctively mathematical explanations are actually causal explanations in disguise because they sneak in reasoning about particular forces in the associated conditional.  

A mathematical model of Dignaga’s hetu-cakra 

2020, Journal of Indian Council of Philosophical Research

https://doi.org/10.1007/s40961-020-00217-3 

This paper provides a formulation to deconstruct styles of analogical reasoning in Indian philosophy using the ideas of bounded rationality and the Buddhist method of reasoning through analogies.  

Foundations of Thermal Physics

1. Thermodynamics at small scales: A case for stochastic thermodynamics at strong coupling (under review; draft here)

(This is a chapter from my Cambridge PhD thesis)

I argue that extending thermodynamics to small systems exposes background assumptions that are largely invisible in its traditional macroscopic domain. Using mesoscopic stochastic thermodynamics, I examine the underappreciated weak-coupling idealization—negligible system–environment interaction—which normally secures an unambiguous split between heat and work. 

2. On the relational character of thermal physics

(with Rodriguez-Warnier, Pascal)

We distinguish between various aspects of the relational character of thermal concepts like entropy, heat-work distinction, equilibrium and coarse-graining identifying which of their aspects are epistemic, subjective or seemingly anthropocentric, and which ones are rather objective and means-relative.  

3. Do fluctuation theorems ground the Second Law? (proposal here; for Pittsburgh postdoc)

I examine whether fluctuation theorems — particularly Jarzynski Equality — provide a robust foundation for the Second Law within stochastic thermodynamics. I focus on stochastic systems strongly coupled to their thermal bath, where the system-bath interaction potential is comparable in magnitude to the system’s internal energy. I argue that examining strong coupling reveals conceptual ambiguities that remain disguised in the standard weak-coupling regime, where the interaction potential is negligible and typically neglected. These ambiguities, as I intend to examine, potentially cast doubt on the claim that fluctuation theorems universally ground the Second Law at stochastic levels.

4. Projection operators and non-equilibrium temperature

(with te vrugt, Michael and Hoyningen-Huene, Paul)

We look into the interpretations of temperature fields in Mori-Zwanzig formalism and examine its implications for obtaining a consistent definition of non-equilibrium temperature when the assumption of local thermal equilibrium is relaxed.   

Philosophy of Mathematical Modelling 

1. What role do low-level symmetries play in high-level representations?? 

I argue that low-level symmetry, either in the physical low-level structure of complex systems or in how low-level interactions inherent in such systems scale up, is crucial to explain the stability of high-level representations, apart from the requirements of stochastic independence and the law of large numbers (which cancels out low-level variations) . 

2. Are there physicalist grounds for some mathematical assertions? 

(with Campbell, D., Montelle, C. and Wilson, P.)

We claim that some mathematical ideas may be deeply grounded in conservational principles, building upon Mark Levi's brilliant book, The Mathematical Mechanic (Princeton University Press, 2012) that provides various ways of understanding the physical basis of various mathematical results.  

Buddhist Philosophy and the History of Indian astronomy 

1. On the Nature of Mathematical Knowledge: Reflections from Modelling and Buddhist Philosophy (under contract, draft available via email)

(Proceedings of the Maynooth Consonances Conference on Mathematics, Language, and the Moral Sense of Nature, 2023) 

This paper argues that a perspectival, contextual and mind-dependent view of mathematical models can be read closely to the ontological middle ground proposed by the Buddhist philosophical school of Madhyamaka, which argues no concept exists independently of human thought. 

2. The tale of a medieval Indian scroll: mathematical discoveries (slides available)

(with Montelle, C., Cidami, S. and Dhammaloka, J. : part of a University of Canterbury project on the history and mathematics of medieval astronomical scroll)

We investigate the historical and the mathematical origins of a rare seven-metre-long-medieval-Sanskrit scroll which, we believe, holds important lessons for historians of science.