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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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How does the Author analyze the concept of 'possible worlds' in Copenhagen in relation to the idea of a multiverse and alternate history?

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Dr. Rishabh Pathak


 

The article on Michael Frayn's play "Copenhagen" analyzes the concept of 'possible worlds' in relation to the idea of a multiverse and alternate history by delving into the narrative quantum cosmology presented in the play. Here is how the analysis unfolds:

1. **Possible Worlds Theory**: The article adopts the approach of possible worlds theory to examine how 'possible worlds' are projected in Copenhagen. Possible worlds theory, often used in philosophy and narratology, posits that there are multiple ways the world could have been or could be, representing different scenarios or realities. In the context of the play, these possible worlds are explored as counterfactuals or 'drafts' that present alternate versions of events and interactions between the characters.

2. **Multiverse**: The article draws parallels between the concept of possible worlds in narratology and the idea of a multiverse in physics. Physics has proposed the existence of a multiverse, where multiple parallel universes coexist, each with its own set of physical laws and possibilities. In Copenhagen, the proliferation of possible worlds mirrors the notion of a multiverse, suggesting a myriad of potential outcomes and realities stemming from the characters' choices and actions.

3. **Alternate History**: By presenting a multitude of counterfactuals and alternate historical scenarios, the play offers an alternate history that challenges linear narratives and deterministic views of events. Frayn's exploration of these possible worlds in Copenhagen blurs the boundaries between fact and fiction, inviting the audience to consider the implications of different choices and paths taken by the characters. This approach not only enriches the storytelling but also prompts reflections on the nature of history, causality, and the complexity of human decision-making.

Overall, the article's analysis of 'possible worlds' in Copenhagen in connection to the multiverse and alternate history underscores the play's narrative richness and philosophical depth. By intertwining quantum concepts with narrative possibilities, Frayn creates a compelling exploration of uncertainty, choice, and the multiplicity of realities that shape our understanding of the world.

 

Frayn, M. (2000). Copenhagen. s

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