Stories with Tag gravity

• Orbit Spirograph (2019)

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  Posted: 2025-01-23 16:28:07

  Verbose tl;dr

  This blog post explores creating spirograph-like patterns by simulating gravitational orbits of multiple bodies. Instead of gears, the author uses Newton's law of universal gravitation and numerical integration to calculate the paths of planets orbiting one or more stars. The resulting intricate designs are visualized, and the post delves into the math and code behind the simulation, covering topics such as velocity Verlet integration and adaptive time steps to handle close encounters between bodies. Ultimately, the author demonstrates how varying the initial conditions of the system, like the number of stars, their masses, and the planets' starting velocities, leads to a diverse range of mesmerizing orbital patterns.

  In a 2019 blog post titled "Orbit Spirograph," Amit Patel, the author of Red Blob Games, explores the fascinating visual patterns created by simulating the gravitational interaction of two bodies, one significantly more massive than the other. He meticulously details the process of generating these intricate, spirograph-like orbital trajectories using a numerical integration method known as the leapfrog or Verlet method. This method is chosen for its computational efficiency and its ability to conserve energy reasonably well, leading to stable and visually appealing simulations.

  Patel begins by establishing the fundamental physics governing the interaction: Newtonian gravity. He describes how the force of gravity between the two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force then dictates the acceleration each body experiences, influencing their velocities and subsequent positions over time.

  The core of the blog post lies in the explanation of the leapfrog method. This method involves discretizing time into small steps and updating the positions and velocities of the bodies at each step. The "leapfrog" aspect comes from the staggered updates: velocities are calculated at half-time steps while positions are calculated at whole time steps. This approach provides a good approximation of the continuous orbital motion while remaining computationally tractable. Patel provides detailed equations and pseudocode for implementing the leapfrog method, making the concept accessible to readers with programming experience.

  Further enhancing the visual appeal, Patel introduces the concept of rendering the orbital paths with varying colors. He accomplishes this by assigning a color based on the orbiting body's speed, resulting in a gradient effect where faster segments of the orbit are depicted with different hues than slower segments. This visual representation adds another layer of information to the simulation, allowing for a more intuitive understanding of the body's changing velocity throughout its orbit.

  Beyond the basic two-body simulation, Patel briefly touches on the potential for extending the simulation to include more than two bodies, hinting at the increased complexity and computational demands of such a system. He also acknowledges the limitations of the simplified simulation, mentioning that real-world orbital mechanics can be influenced by factors not included in his model, such as the non-uniform distribution of mass within celestial bodies.

  In essence, Patel's "Orbit Spirograph" post provides a clear and engaging exploration of orbital mechanics through numerical simulation. By breaking down the underlying physics and providing a practical implementation of the leapfrog method, the post enables readers to generate and appreciate the beautiful and intricate patterns that arise from the dance of gravity between celestial objects.

  • spirograph
  • orbit
  • Orbital Mechanics
  • Simulation
  • Visualization
  • mathematics
  • physics
  • interactive
  • javascript
  • red blob games
  • 2019
  • gravity
  • celestial mechanics

  Summary of Comments ( 2 )
  https://news.ycombinator.com/item?id=42805421

  Verbose tl;dr

  HN users generally praised the Orbit Spirograph visualization and the clear explanations provided by Red Blob Games. Several commenters explored the mathematical underpinnings, discussing epitrochoids and hypotrochoids, and how the visualization relates to planetary motion. Some users shared related resources like a JavaScript implementation and a Geogebra applet for exploring similar patterns. The potential educational value of the interactive tool was also highlighted, with one commenter suggesting its use in explaining retrograde motion. A few commenters reminisced about physical spirograph toys, and one pointed out the connection to Lissajous curves.

  The Hacker News post "Orbit Spirograph (2019)" linking to Red Blob Games' article on orbital spirographs has a moderate number of comments, exploring various aspects of the topic.

  Several commenters expressed general appreciation for the visualizations and the interactive nature of the article, praising the clear explanations and the author's ability to make complex concepts accessible. One commenter specifically highlighted the value of interactive explanations, contrasting it with static images or videos.

  A recurring theme in the comments was the connection to celestial mechanics and how the visualizations relate to actual orbital movements. One commenter drew a parallel to the three-body problem and how the spirograph patterns could be seen as simplified representations of more complex gravitational interactions. Another commenter questioned the direct applicability to real-world orbital mechanics, pointing out the simplified assumptions of the model. This prompted a response from another user who clarified that the visualizations are meant to illustrate underlying principles rather than precisely simulate real orbits, highlighting the educational value of simplified models.

  There's also a discussion about the mathematical underpinnings of the spirographs. One commenter delved into the concept of epicycles, relating the historical context of using epicycles to model planetary motion to the spirograph patterns generated in the article. Another comment thread explored the use of different coordinate systems and their impact on the resulting visualizations.

  Some comments focused on the technical aspects of the implementation. One commenter inquired about the specific JavaScript library used for the interactive elements, prompting a response identifying the library. Another commenter discussed the potential for extending the visualizations to three dimensions.

  Finally, a few comments offered links to related resources, including other interactive simulations and articles on orbital mechanics. One comment specifically mentioned a website with interactive simulations of gravitational interactions.

  Overall, the comments on the Hacker News post reflect a positive reception of the article, demonstrating interest in the visualizations, the underlying mathematical concepts, and the connection to real-world orbital mechanics. The discussion ranges from general appreciation to more technical explorations, showcasing the diverse interests and expertise of the Hacker News community.

• Life on a Closed Timelike Curve

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  Posted: 2025-01-12 21:33:23

  Verbose tl;dr

  This paper explores the implications of closed timelike curves (CTCs) for the existence of life. It argues against the common assumption that CTCs would prevent life, instead proposing that stable and complex life could exist within them. The authors demonstrate, using a simple model based on Conway's Game of Life, how self-consistent, non-trivial evolution can occur on a spacetime containing CTCs. They suggest that the apparent paradoxes associated with time travel, such as the grandfather paradox, are avoided not by preventing changes to the past, but by the universe's dynamics naturally converging to self-consistent states. This implies that observers on a CTC would not perceive anything unusual, and their experience of causality would remain intact, despite the closed timelike nature of their spacetime.

  The paper "Life on a Closed Timelike Curve" by Toffoli and Margolus explores the hypothetical implications of biological life existing within a region of spacetime containing a closed timelike curve (CTC). CTCs, permitted by Einstein's general relativity, theoretically allow for time travel by creating loops in the fabric of spacetime. The authors specifically focus on how such a scenario would affect evolutionary processes and the development of complex organisms.

  They construct a simplified model of an ecosystem existing on a CTC using cellular automata, a computational model where cells on a grid evolve according to predetermined rules. This allows them to simulate the effects of time travel within a controlled environment. The CTC is incorporated into the model by introducing a region where the future state of the cells is directly influenced by their past states, effectively creating a causal loop. This loop mimics the effect of information being transmitted through time along the CTC.

  The authors then investigate how organisms represented by specific patterns within the cellular automata would evolve under these unusual conditions. They observe that traditional Darwinian evolution, driven by random mutations and natural selection, faces significant challenges in the presence of CTCs. The fixed nature of the temporal loop constrains the possible evolutionary trajectories, potentially preventing the emergence of novel traits. Moreover, the constant feedback loop introduced by the CTC can lead to stable but suboptimal configurations, hindering the optimization process usually associated with natural selection.

  Instead of relying solely on random mutations, the authors propose a new mechanism they term "evolution by self-consistency." In this framework, organisms adapt not just to their immediate environment but also to their own future states, accessible through the CTC. This leads to a sort of "pre-adaptation," where organisms develop traits that are advantageous not only in the present but also in the future, creating a self-consistent loop across time.

  The paper demonstrates that life on a CTC can indeed evolve towards complex and stable configurations, but through a fundamentally different process than Darwinian evolution. This "evolution by self-consistency" emphasizes the importance of global optimization and temporal coherence, rather than local adaptation driven by random mutations. The results suggest that the presence of CTCs would drastically reshape the landscape of biological evolution, leading to life forms with unique adaptations tailored to the peculiarities of closed-timelike-curve environments. While purely theoretical, the research provides valuable insights into the potential intersection of biology and exotic spacetime geometries, prompting further exploration of the profound implications of time travel for the fundamental laws of nature and the development of life itself.

  • physics
  • time travel
  • closed timelike curves
  • general relativity
  • causality
  • spacetime
  • theoretical physics
  • quantum physics
  • astrophysics
  • cosmology
  • quantum mechanics
  • gravity

  Summary of Comments ( 36 )
  https://news.ycombinator.com/item?id=42677158

  Verbose tl;dr

  HN commenters discuss the implications and paradoxes of closed timelike curves (CTCs), referencing Deutsch's approach to resolving the grandfather paradox through quantum mechanics and many-worlds interpretations. Some express skepticism about the practicality of CTCs due to the immense energy requirements, while others debate the philosophical implications of free will and determinism in a universe with time travel. The connection between CTCs and computational complexity is also raised, with the possibility that CTCs could enable the efficient solution of NP-complete problems. Several commenters question the validity of the paper's approach, particularly its reliance on density matrices and the interpretation of results. A few more technically inclined comments delve into the specifics of the physics involved, mentioning the Cauchy problem and the nature of time itself. Finally, some commenters simply find the idea of time travel fascinating, regardless of the theoretical complexities.

  The Hacker News post titled "Life on a Closed Timelike Curve," linking to a scientific paper exploring theoretical life in a closed timelike curve (CTC) spacetime, has generated several comments. Many commenters engage with the core concepts of the paper, grappling with the implications of CTCs and their potential paradoxes.

  A significant portion of the discussion revolves around the Novikov self-consistency principle, which the paper relies upon. This principle, suggesting that events within a CTC must be consistent with themselves, sparked debate about its validity and implications. Some commenters express skepticism about the principle, questioning whether it truly resolves paradoxes or merely sidesteps them. Others explore the philosophical ramifications of self-consistency, pondering the nature of free will and determinism in a universe with CTCs.

  Several comments delve into the specifics of the paper's model, discussing aspects like the use of game theory and the nature of the simulated organisms. Some users raise questions about the model's assumptions and limitations, while others offer alternative interpretations or suggest potential extensions of the research.

  The idea of "predestination paradoxes" receives considerable attention, with commenters presenting thought experiments and hypothetical scenarios to illustrate the complexities of causality in a CTC. The famous "grandfather paradox" is mentioned, along with variations and counterarguments.

  Some commenters also connect the theoretical discussion to broader topics in physics and computer science. Connections are made to quantum mechanics, information theory, and the concept of computation. A few users even draw parallels to science fiction, mentioning stories and films that explore similar themes.

  While there's general agreement on the fascinating nature of CTCs and the thought-provoking questions they raise, there isn't a consensus on the plausibility or implications of the paper's findings. The comments reflect a mix of curiosity, skepticism, and intellectual engagement, showcasing the diverse perspectives of the Hacker News community. The discussion doesn't reach definitive conclusions but serves as a platform for exploring the complex and often paradoxical nature of time travel and its potential impact on life.