Discovering The Law of Gravity: As an Infant

Yucong Duan

International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation(DIKWP-SC)

World Artificial Consciousness CIC(WAC)

World Conference on Artificial Consciousness(WCAC)

(Email: duanyucong@hotmail.com)

Introduction

From the earliest moments of my existence, I was captivated by the movements and interactions of objects around me. Toys fell to the ground when released, leaves fluttered down from trees, and the moon traced a consistent path across the night sky. My innate curiosity drove me to understand the forces governing these phenomena. Through observation, experimentation, and logical reasoning, I embarked on a journey to uncover the fundamental principles that dictate the attraction between masses.

In this narrative, I will detail how, starting from basic sensory experiences as an infant, I independently observed, experimented, and logically deduced the Law of Gravity. Each concept evolved explicitly from my experiences, ensuring that my understanding is grounded in reality and free from subjective definitions.

Chapter 1: Observing Objects in Motion1.1 Early Experiences with Falling ObjectsDropping Toys

• Observation: When I released a toy from my hand, it always fell straight down to the ground.

• Reflection: Objects have a natural tendency to move downward when not supported.

• Semantics: The downward movement is consistent and predictable.

Stacking Blocks

• Experiment: Building towers with blocks and watching them collapse when they became too tall.

• Observation: The blocks fell downward, scattering upon hitting the ground.

• Reflection: There is a force acting on the blocks that pulls them toward the Earth.

1.2 Noticing Consistency in DirectionFalling Objects Always Descend

• Observation: Whether I dropped a spoon, a ball, or a feather, all objects moved toward the ground.

• Reflection: The downward direction is consistent regardless of the object's composition or shape.

Semantics:

• Downward Direction: Defined relative to my position and the surface I'm on; objects move toward the Earth's center.

Chapter 2: Differentiating Mass and Weight2.1 Feeling the Weight of ObjectsLifting Different Toys

• Experiment: Comparing how it felt to lift a light stuffed animal versus a heavy book.

• Observation: Heavier objects required more effort to lift.

• Reflection: Objects have a property called mass, influencing how heavy they feel.

2.2 Understanding MassDefining Mass

• Concept: Mass is a measure of the amount of matter in an object.

• Semantics: Mass relates to the resistance of an object to changes in its motion (inertia).

Distinguishing Mass from Weight

• Observation: While mass is inherent to the object, weight seems to be the force experienced due to gravity acting on the mass.

• Semantics: Weight is the gravitational force exerted on an object's mass.

Chapter 3: Investigating the Acceleration of Falling Objects3.1 Timing Falling ObjectsSimple Experiments

• Experiment: Dropping two objects of different masses simultaneously from the same height.

• Observation: Both objects hit the ground at the same time (neglecting air resistance).

• Reflection: The acceleration due to gravity is the same for all objects, regardless of mass.

3.2 Understanding AccelerationDefining Acceleration

• Concept: Acceleration is the rate of change of velocity of an object.

• Mathematical Expression:

  a=ΔvΔta = \frac{\Delta v}{\Delta t}a=ΔtΔv​

• $a$: Acceleration

• $\Delta v$: Change in velocity

• $\Delta t$: Change in time

Acceleration Due to Gravity

• Observation: The acceleration of falling objects is constant and directed downward.

• Semantics: Denoted as $g$, the acceleration due to gravity near Earth's surface.

Chapter 4: Exploring Gravitational Force4.1 Newton's Second Law and GravityApplying Newton's Second Law

• Law: $F=m\times a$

• Observation: The force acting on a falling object is its mass times the acceleration due to gravity.

• Mathematical Expression:

  $$F=m\times g$$

• $F$: Gravitational force (weight)

• $m$: Mass of the object

• $g$: Acceleration due to gravity

4.2 Universal Nature of GravityQuestioning the Reach of Gravity

• Reflection: If gravity acts on objects near the Earth's surface, does it also act on objects farther away, like the moon?

Hypothesis:

• Gravity is a universal force acting between any two masses, not just objects near the Earth's surface.

Chapter 5: Observing Celestial Movements5.1 Watching the Moon and StarsRegular Patterns

• Observation: The moon follows a consistent path across the sky, and stars maintain relative positions.

• Reflection: Celestial bodies move in predictable ways, possibly influenced by gravity.

5.2 Considering the Moon's MotionThe Moon's Orbit

• Hypothesis: The moon is in constant free fall toward the Earth but has sufficient tangential velocity to keep missing it, resulting in orbit.

• Semantics: The gravitational pull between Earth and the moon keeps the moon in orbit.

Chapter 6: Formulating the Law of Universal Gravitation6.1 Proposing the Gravitational Force EquationFactors Influencing Gravitational Force

• Hypothesis: The gravitational force between two masses depends on:

• The masses of the two objects (m1m_1m1​ and m2m_2m2​)

• The distance ($r$) between their centers

• Mathematical Expression:

  F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}F=Gr2m1​m2​​

• $F$: Gravitational force between the two masses

• $G$: Gravitational constant

• m1,m2m_1, m_2m1​,m2​: Masses of the two objects

• $r$: Distance between the centers of the two masses

6.2 Understanding the Inverse Square LawImpact of Distance

• Observation: As distance increases, gravitational force decreases rapidly.

• Reflection: The force is inversely proportional to the square of the distance.

Semantics:

• Inverse Square Law: A physical quantity is inversely proportional to the square of the distance from the source.

Chapter 7: Verifying the Law with Planetary Motion7.1 Kepler's Laws of Planetary MotionObserving Planetary Orbits

• Observation: Planets orbit the sun in elliptical paths with predictable periods.

• Reflection: Gravitational force could explain the centripetal force required for orbital motion.

7.2 Calculating Orbital MechanicsApplying the Law to Planets

• Equation for Centripetal Force:

  F=mv2rF = m \frac{v^2}{r}F=mrv2​

• Setting Gravitational Force Equal to Centripetal Force:

  GMmr2=mv2rG \frac{M m}{r^2} = m \frac{v^2}{r}Gr2Mm​=mrv2​

• $M$: Mass of the sun

• $m$: Mass of the planet

• $v$: Orbital velocity

• $r$: Orbital radius

Deriving Kepler's Third Law

• Resulting Relation:

  v2=GMrv^2 = G \frac{M}{r}v2=GrM​

• Conclusion: The Law of Universal Gravitation explains planetary motions consistent with Kepler's observations.

Chapter 8: Gravitational Constant and Units8.1 Determining the Gravitational ConstantChallenges in Measurement

• Observation: The gravitational force between everyday objects is tiny and difficult to measure.

• Solution: Use precise experiments, such as the Cavendish experiment, to determine $G$.

8.2 Units and DimensionsUnderstanding Units

• Gravitational Constant $G$:

  G=6.67430×10−11 N⋅m2/kg2G = 6.67430 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2G=6.67430×10−11N⋅m2/kg2

• Semantics: $G$ provides the proportionality factor that scales the gravitational force appropriately.

Chapter 9: Implications of the Law of Gravity9.1 Predicting TidesGravitational Effects of the Moon and Sun

• Observation: The ocean's tides correlate with the positions of the moon and sun.

• Explanation: The gravitational pull from the moon and sun affects Earth's water, causing tides.

9.2 Gravitational Potential EnergyConcept of Potential Energy

• Definition:

  U=−Gm1m2rU = -G \frac{m_1 m_2}{r}U=−Grm1​m2​​

• Interpretation: Objects have gravitational potential energy due to their positions relative to each other.

Chapter 10: Reflecting on the Discovery10.1 The Universality of GravityApplicability Across the Universe

• Reflection: Gravity acts between all masses, from apples falling from trees to galaxies influencing each other.

10.2 The Elegance of Mathematical RelationshipsSimplicity and Power

• Observation: A single equation explains a vast array of phenomena.

• Appreciation: The Law of Universal Gravitation unifies terrestrial and celestial mechanics.

Conclusion

Through observation, experimentation, and logical reasoning, I was able to discover and formulate the Law of Universal Gravitation. Starting from basic experiences with falling objects and extending my inquiry to celestial bodies, I developed a comprehensive understanding of how masses attract each other. By grounding each concept in reality and evolving the semantics explicitly, I arrived at a law that not only explains everyday phenomena but also governs the motions of planets and stars.

This exploration demonstrates that complex scientific concepts can emerge naturally from simple observations. By avoiding subjective definitions and relying on direct experiences, profound ideas become accessible and meaningful. The Law of Gravity not only provides insight into the fundamental forces of nature but also serves as a cornerstone for further advancements in physics and astronomy.

Epilogue: Implications for Learning and AI

This narrative illustrates how foundational scientific principles can be understood through direct interaction with the environment and logical reasoning. In the context of artificial intelligence and cognitive development, it emphasizes the importance of experiential learning and the evolution of semantics from core experiences.

By enabling AI systems to observe patterns, formulate hypotheses, and derive laws from observations, we can foster the development of intuitive understanding similar to human learning. This approach avoids reliance on predefined definitions and promotes the natural discovery of scientific relationships.

Note: This detailed narrative presents the conceptualization of the Law of Gravity as if I, an infant, independently observed and reasoned it out. Each concept is derived from basic experiences, emphasizing the natural progression from simple observations of falling objects to the understanding of universal gravitation. This approach demonstrates that with curiosity and logical thinking, foundational knowledge about physics can be accessed and understood without relying on subjective definitions.

References

1. International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation (DIKWP-SC),World Association of Artificial Consciousness(WAC),World Conference on Artificial Consciousness(WCAC). Standardization of DIKWP Semantic Mathematics of International Test and Evaluation Standards for Artificial Intelligence based on Networked Data-Information-Knowledge-Wisdom-Purpose (DIKWP ) Model. October 2024 DOI: 10.13140/RG.2.2.26233.89445 .  https://www.researchgate.net/publication/384637381_Standardization_of_DIKWP_Semantic_Mathematics_of_International_Test_and_Evaluation_Standards_for_Artificial_Intelligence_based_on_Networked_Data-Information-Knowledge-Wisdom-Purpose_DIKWP_Model

2. Duan, Y. (2023). The Paradox of Mathematics in AI Semantics. Proposed by Prof. Yucong Duan:" As Prof. Yucong Duan proposed the Paradox of Mathematics as that current mathematics will not reach the goal of supporting real AI development since it goes with the routine of based on abstraction of real semantics but want to reach the reality of semantics. ".