Scientific Laws: Math Or Not?

Scientific laws are conclusions based on repeated experiments and observations that describe or predict a range of natural phenomena. They are often formulated as one or several statements or equations, and many can be reduced to a mathematical equation. For example, Newton's Law of Universal Gravitation can be written as Fg = G * (m1 * m2 / d^2), where Fg is the force of gravity, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them. However, scientific laws do not express absolute certainty, as mathematical laws do, and they do not explain the underlying mechanisms or causes of the phenomena they describe. Instead, they are distillations of the results of repeated observations, and their applicability is limited to circumstances resembling those already observed.

Scientific laws are based on repeated experiments or observations

A scientific law is a generalized rule to explain a body of observations in the form of a verbal or mathematical statement. They are often framed as mathematical statements, according to NASA. For example, E = mc^2 is a scientific law that can be reduced to a mathematical statement, where 'c' refers to the speed of light in a vacuum. Many other scientific laws take mathematical forms and can be stated as equations. For instance, Newton's Law of Universal Gravitation can be written as an equation where Fg is the force of gravity, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them. Ohm's law, Newton's law of universal gravitation, the early laws of aerodynamics, Hooke's law, and Boyle's law are other examples of scientific laws that take mathematical forms.

Scientific laws are not the same as scientific theories. Theories are explanations of natural phenomena, whereas laws are observations. Theories are verifiable explanations, while laws are predictions. Laws are narrower in scope than theories, which may entail one or several laws. For example, the theory of gravity explains why an apple falls to the ground when dropped, while the law of gravity can be used to make predictions about events and perform calculations.

Scientific laws are also distinct from facts. Facts are simple, one-off observations that have been shown to be true. Laws are generalized observations about the relationship between two or more things in the natural world based on a variety of facts and empirical evidence. For example, "Apples fall down from this apple tree" is a fact, while "The strength of gravity between any two objects (like an apple and the Earth) depends on the masses of the objects and the distance between them" is a law.

Scientific laws are also different from hypotheses and postulates, which are proposed during the scientific process before validation by experiment and observation. Laws differ from hypotheses and postulates in that they have been verified to a higher degree.

Scientific laws are not absolute, unlike mathematical laws

Scientific laws are based on repeated experiments or observations and describe or predict a range of natural phenomena. They are developed from data and can be further developed through mathematics. They are typically expressed in terms of a single mathematical equation. For example, Newton's Law of Universal Gravitation can be written as an equation where Fg is the force of gravity, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

However, scientific laws do not express absolute certainty, unlike mathematical laws. They are not laden with ontological commitments or statements of logical absolutes. A scientific law may be contradicted, restricted, or extended by future observations. For example, Ohm's law only applies to linear networks, and Newton's law of universal gravitation only applies in weak gravitational fields. The applicability of a law is limited to circumstances resembling those already observed, and the law may be found to be false when extrapolated.

Mathematical laws, on the other hand, express absolute certainty. They are not subject to change or contradiction. For example, the law of conservation of energy, expressed mathematically as ΔU = Q - W, states that energy is conserved in any given system, and this law holds true regardless of the specific circumstances or conditions.

The nature of scientific laws has been a subject of much discussion in philosophy. While they are considered to be empirical conclusions reached through the scientific method, they do not explain the underlying mechanisms or causes of the observed phenomena. They are also narrower in scope than scientific theories, which may encompass one or several laws.

Scientific laws are general rules to explain a body of observations

Scientific laws are general rules that explain a body of observations. They are based on repeated experiments or observations and describe or predict a range of natural phenomena. For example, Newton's Law of Universal Gravitation states that the force of gravity between two objects depends on their masses and the distance between them. This law can be expressed mathematically as Fg = Gm1m2/d^2, where Fg is the force of gravity, G is the universal gravitational constant, m1 and m2 are the masses of the objects, and d is the distance between them.

Scientific laws are developed from data and can be further refined through mathematics. They are based on empirical evidence and are widely accepted as true, but they do not express absolute certainty like mathematical laws. A scientific law may be contradicted, restricted, or extended by future observations, and its applicability is limited to circumstances similar to those already observed. For example, Ohm's law only applies to linear networks, and Newton's law of universal gravitation only holds true for weak gravitational fields.

While scientific laws can be expressed mathematically, they do not explain the underlying mechanisms or causes of the observed phenomena. They are descriptive and predictive, but not explanatory. For example, Newton's Law of Gravity describes how two bodies interact with each other, but it does not explain what gravity is or how it works. That explanation came later with Einstein's Theory of Relativity.

Scientific laws are often simple and concise, such as the third law of thermodynamics: "For every action, there is an equal and opposite reaction." They are fundamental to science, aiming to summarise and describe our environment through repeated observations and experiments. Scientific laws are universal, applying everywhere in the universe, and they are true within their regime of validity.

Scientific laws are different from scientific theories

Scientific laws and scientific theories are both based on tested hypotheses and supported by a large body of empirical data. However, they have distinct roles and characteristics that differentiate them.

A scientific law describes an observed phenomenon in nature and predicts the results of certain initial conditions. It is a generalized observation about the relationship between two or more things in the natural world, often framed as a mathematical statement. For example, the law of universal gravitation describes the behaviour of two objects in a certain circumstance. Laws are based on repeated experiments or observations and are universally accepted within the scientific community. They are typically expressed in terms of a single mathematical equation. However, they do not explain why the phenomenon exists or what causes it. Laws are narrower in scope than theories and are limited to circumstances resembling those already observed.

On the other hand, a scientific theory explains why things happen as they do and provides a logical explanation for observed phenomena. It describes how nature behaves under specific conditions and seeks to serve as a definitive explanation. For example, a theory might use gravity to explain the parabolic trajectory of a baseball. Theories are broader in scope than laws and are supported by rigorous testing. They are proposed during the scientific process and are validated by experiments and observations. Theories tend to be as broad as their supporting evidence permits, and they may compete to provide the best explanation for a new discovery.

While laws and theories have distinct roles, they are both essential for understanding the natural world. They work together to provide a comprehensive understanding of scientific phenomena.

Scientific laws are different from facts

Scientific laws, on the other hand, are descriptive generalizations about how some aspect of the natural world behaves under certain circumstances. They are inferred from specific facts and are applicable to a defined group or class of phenomena. For example, "The strength of gravity between any two objects depends on the masses of the objects and the distance between them". This is a law because it describes the behaviour of two objects in a certain circumstance. If the circumstance changes, the implications of the law would also change.

Scientific laws are based on repeated experiments or observations and describe or predict a range of natural phenomena. They are developed from data and can be further developed through mathematics. They are often formulated as one or more statements or equations that can be used to predict the outcome of an experiment. For example, Newton's Law of Universal Gravitation can be written as an equation: Fg = G * (m1*m2)/d^2, where Fg is the force of gravity, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

Scientific laws do not express absolute certainty, unlike mathematical laws. They do not explain why a phenomenon exists or what causes it. They are also not hypotheses or postulates, as they have been verified to a higher degree. Laws are narrower in scope than theories, which may include one or several laws.

In summary, scientific laws are generalized observations about the natural world based on facts and empirical evidence, often expressed as mathematical statements. They are different from facts, which are simple, proven observations, as laws describe the behaviour of natural phenomena under certain circumstances.

Frequently asked questions