# What are the Steps Needed to Make a Scientific Law?

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I don't know if this initial post is clear but I will try to explain what I mean. Newton's Law of Gravity is presumably based on numerous observations and tests which led to the belief of a fundamental Law of Science.

What are the steps to make a Law of Science?

I am guessing the following:

Observation

Hypothesis

(Tests for Reproducibility)

Theory

(Tests for Reproducibility, Falsification and Exceptions)

Principle (e.g. the Anthropic Principle)

Law

However, I am a bit confused about the order of events and look for help here.

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laws aren't really part of the progression.

they are mainly leftovers from the early days of science.

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Laws are for mathematics, not science.

Science deals in theory, which is the pinnacle achievement.

(Principle would probably be an axiom, not an outcome)

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What are the steps to make a Law of Science?

To have a theory that is very well supported, and was first proposed a few centuries ago before we quit calling such things laws.

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OK guys, so I take it that the order would be:

Observation

Hypothesis

Theory?

I reluctantly take the point that a Principle is an axiom but look at the definition:

maxim: a saying that is widely accepted on its own merits

(logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident

wordnetweb.princeton.edu/perl/webwn

However, because the OP was based on my own meandering thoughts, I looked up Wiki for a tighter definition and found the following:

Within most fields of study, and in science in particular, the elevation of some principle of that field to the status of "law" usually takes place after a very long time during which the principle is used and tested and verified; though in some fields of study such laws are simply postulated as a foundation and assumed. Mathematical laws are somewhere in between: they are often arbitrary and unproven in themselves, but they are sometimes judged by how useful they are in making predictions about the real world. However, they ultimately rely on arbitrary axioms.

http://en.wikipedia.org/wiki/Principle_(disambiguation)

which proves the point that, if you look hard enough, you can always find something to back up your hypothesis - or have I just invented a new theory?

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OK guys, so I take it that the order would be:

Observation

Hypothesis

Theory?

Not necessarily.

For example, Dirac's prediction of anti-particles (1928) was purely theoretical and based on "taking the square root" of an operator. Just like taking the square root of a number you get two solution, plus and minus.

Dirac predicted anti-matter without any observational motivation. It was only after did Anderson (1932) discover anti-particles in nature.

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laws aren't really part of the progression.

they are mainly leftovers from the early days of science.

Laws are for mathematics, not science.

Science deals in theory, which is the pinnacle achievement.

(Principle would probably be an axiom, not an outcome)

To have a theory that is very well supported, and was first proposed a few centuries ago before we quit calling such things laws.

All three of these responses are wrong.

What is a scientific law? Here are a few: the Stefan–Boltzmann law, aka the Stefan–Boltzmann equation. Gauss's law, aka Gauss's flux equation aka Gauss's flux theorem. Faraday's law of induction, aka the Maxwell–Faraday equation. Gauss' law + Gauss' law for magnetism + Faraday's law of induction + Ampere's law, aka Maxwell's equations.

Law is a synonym for equation.

A scientific theory must yield predictions, and very specific predictions, of the outcome of an experiment. Laws, aka equations, are the thing that distinguish a scientific theory from hand-waving pseudoscience.

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Law is a synonym for equation.

I'll stipulate up front that you know far more about each of those concepts than myself, but I would argue that your quote above is precisely why my previous comment that "laws are for math, not science" remains entirely accurate. Science can use and benefit from those mathematical laws, but the laws themselves reside entirely in the domain of maths.

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I'll stipulate up front that you know far more about each of those concepts than myself, but I would argue that your quote above is precisely why my previous comment that "laws are for math, not science" remains entirely accurate. Science can use and benefit from those mathematical laws, but the laws themselves reside entirely in the domain of maths.

I disagree. The Stefan-Boltzmann equation is about as uninteresting to mathematicians as are the equations that accountants use to balance their books. Just because something is stated mathematically does not mean that it is in the domain of mathematics. Science requires mathematical statements. Pseudoscience does not.

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I Just because something is stated mathematically does not mean that it is in the domain of mathematics.

I really do not understand this statement.

Surely any statement in mathematics is within the domain of mathematics.

What you mean is statements in mathematics are not necessarily of great interest to and are not solely the interest of practising mathematicians.

I think what INow is stating is the difference between mathematical modelling of nature and nature.

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Laws are for mathematics, not science.

Mathematics is a branch of science though...

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Mathematics is a branch of science though...

I think so, but plenty of physicists, chemist etc. and mathematicians disagree. I am sure you can find posts on this in this forum.

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I do not think that cartoon is very fair. There is plenty of cross-fertilisation between physics and mathematics.

That said, it is still funny.

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I think so, but plenty of physicists, chemist etc. and mathematicians disagree.

For them I believe perhaps they should try to redefine science...

science • noun

1 the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment. 2 a systematically organized body of knowledge on any subject.

It looks to me that both definitions on science apply to mathematics. It is clearly an essential element in the systematic study of the structure and behaviour of the physical and natural world. It is also clearly a subject of a systematically organized body of knowledge.

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I do not think that cartoon is very fair. There is plenty of cross-fertilisation between physics and mathematics.

I don't disagree. I do, however, wish to reiterate my point that the laws are in the math, not the science. The science uses the math.

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I think what INow is stating is the difference between mathematical modelling of nature and nature.

I took iNow's statement quite differently:

"laws are for math, not science"

That is pure bunk. (Sorry to be so blunt, iNow). Laws are precisely what distinguishes real physics from the nonsense that predominates over in the speculation and pseudoscience sub-forum.

Just because people are using mathematics does not mean they have moved from the domain of science to mathematics. At least in physics, exactly the opposite is true: Until people use mathematics, they are not doing physics.

==================

Mathematics is a branch of science though...
I think so, but plenty of physicists, chemist etc. and mathematicians disagree.

Count me in!

Mathematics is distinct from the sciences. It does not use the scientific method because the scientific method is all about relating scientific conjectures to reality. Conforming to reality is not an immediate concern in mathematics.

Suppose some future physicist working in the field of string theory devises an experimental test of that theory. Now suppose that the experiment is performed and that it entirely falsifies the theory. (All it takes in science is one stupid experiment to toss a vast body of knowledge into the trash bin of failed scientific theories.)

String theory has motivated the development of a lot of interesting mathematics. If some experiment does falsify string theory as a scientific theory, it will not say anything about the validity of the mathematic theorems developed as a consequence of developing string theory. Those theorems, assuming they were properly derived, remain true.

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For them I believe perhaps they should try to redefine science...

There is the question of physical and natural world.

Merged post follows:

Consecutive posts merged

Mathematics is distinct from the sciences. It does not use the scientific method because the scientific method is all about relating scientific conjectures to reality. Conforming to reality is not an immediate concern in mathematics.

From what I have learnt by doing mathematics research is that there is a kind of "scientific method" applied.

The presenting of mathematics seems to be very deductive. That is moving from a general setting to the specific. The research and development of mathematics is much more inductive and is based on observations of simple examples.

There is "Popper-like" falsifiability in mathematics. Simply find a counter example.

What makes me think that mathematics is science is that one does not seem to be able to do whatever you want in mathematics. There seems to be something behind it all.

But we digress...

I completely agree with you on some points. Mainly, mathematics is necessary in physics. It is the link, at least in principle between the "mathematical world" and the "physical world "that makes the mathematical constructions found in physics, physics.

Edited by ajb
Consecutive posts merged.

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Mathematics is distinct from the sciences.

So you are effectively disputing the definition of science as given in the Oxford English Dictionary?

And this one as well?

Mathematics Noun

* S: (n) mathematics' date=' math, maths (a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) [/quote']

Edited by doG

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So you are effectively disputing the definition of science as given in the Oxford English Dictionary?

On technical definitions the Oxford English Dictionary is not the best source.

The objections, which I believe DH will agree are

1) Is the mathematical word part of or distinct from the physical/natural world?

2) Does a Popper-like scientific method based on falsifiability via experiment exist for mathematics?

Another option could be to simply widen what we mean by science to overcome any of these (and other) issues. I'd like to say "mathematical sciences" to distinguish "natural science". Of course in practice these two are often not as distinct as one may like.

Simplifying we have

1) Observation and description of some phenomena.

2) Formulation of a hypothesis to explain the phenomena.

3) Use hypothesis to predict other phenomena.

4) Preform test to investigate said phenomena.

5) Loop

I claim that in philosophy and practice mathematics does indeed follow the scientific method. The test take the form of examples, counter examples and ultimately proofs. The biggest departure from "natural sciences" is that one is not restricted to physical phenomena in the universe and that the tests are far more demanding and stringent.

Edited by ajb

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Actually I would not necessarily call them equations, precisely as it conjures mathematical equations, but rather mechanistic models.

Laws in sciences tend to be very specific models that can be described mathematically precisely because they are so well defined. However they do describe physical relationships rather than mathematical ones. Most constants used throughout physics and chemistry are based on empirical studies and have no direct relationship from purely mathematically derived relations. They just behave and scale in a way that can be described mathematically.

Edited by CharonY

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However they do describe physical relationships rather than mathematical ones.

I don't quite agree, but understand what you are saying. Relationships are mathematical. What one then has to do is relate these relationships to nature and in particular things we can observe. One should make a clear distinction between the mathematical model and the natural phenomena it models.

This is Wigner's "Unreasonable Effectiveness of Mathematics in the Natural Sciences".

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Mathematics is a branch of science though...

I think so, but plenty of physicists, chemist etc. and mathematicians disagree. I am sure you can find posts on this in this forum.

I don't consider math a branch of science. Math is a branch of philosophy dealing with numbers and anything related to numbers. Here's the important bit: in math you can choose any premises you like, and granted these premises deduce theorems and prove them to be necessarily true. Certainly you can also work by induction and make uncertain theorems. I think you still have to accept the principle of non-contradiction and some of the more fundamental premises used in logic.

Science is also a branch of philosophy. In science, you start with certain premises relating to the real world:

1) Observability: you are able to observe the world.

2) Objectivity: the laws of physics are the same regardless of the persons conducting the experiments.

3) Repeatability: the laws of physics are such that experiments may be repeated and give the same results.

4) Understandability: the laws of physics can be understood or at least accurately approximated.

1),2), and 3) are derived from the scientific method. If something does not follow these criteria, it cannot be studied by the scientific method and so are not science. 4) is derived from the fact that anyone bothers to do science. I may have missed some premises of science, but you get the idea.

If you take philosophy and add to it these as starting premises, you get science. If you take philosophy and add to it the requirement that it deals with numbers or numberlike things, you get math.

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I don't consider math a branch of science. Math is a branch of philosophy dealing with numbers and anything related to numbers.

There are plenty of things in mathematics that do not need the real numbers. Though, most things I know can (for a finite number of them) at least be represented as matrices over the real (or complex) numbers.

The objects themselves should not be confused with their (many) representations.

A representation is a map from the abstract structure to a vector space that allows us to describe the abstract structure in a more familiar setting.

Here's the important bit: in math you can choose any premises you like, and granted these premises deduce theorems and prove them to be necessarily true. Certainly you can also work by induction and make uncertain theorems. I think you still have to accept the principle of non-contradiction and some of the more fundamental premises used in logic.

According to Hilbert's ideas (which have influenced modern mathematics ever since) you are free to change what ever axioms you like. Thus he would clearly state that mathematics is not a science. He believed in mathematical formalism which described mathematics as a "game in which you can set the starting rules".

However, in practice this does not seem so. In order to get non-trivial and interesting structures you are not so free. It really appears that there maybe some wider structure here that we are "probing".

This ties in with the ideas of Tegmark, who states that the universe is inherently mathematical. If this were true we would not need to make much of a distinction between models and nature.

Science is also a branch of philosophy. In science, you start with certain premises relating to the real world:

1) Observability: you are able to observe the world.

2) Objectivity: the laws of physics are the same regardless of the persons conducting the experiments.

3) Repeatability: the laws of physics are such that experiments may be repeated and give the same results.

4) Understandability: the laws of physics can be understood or at least accurately approximated.

1),2), and 3) are derived from the scientific method. If something does not follow these criteria, it cannot be studied by the scientific method and so are not science. 4) is derived from the fact that anyone bothers to do science. I may have missed some premises of science, but you get the idea.

All these also apply to mathematics, with the proviso one is not restricted to the natural world in a strict sense. (Not subscribing to Tegmark's ideas.)

If you take philosophy and add to it these as starting premises, you get science. If you take philosophy and add to it the requirement that it deals with numbers or numberlike things, you get math.

I have no idea how to define mathematics in a way that really get to the heart of what mathematicians do or why they do it. That said, almost everyone would recognise mathematics when it is presented to them.

I guess the widest interpretation of science is "a body of knowledge acquired by systematic investigation and accumulation of evidence". Mathematics would definitely be included in that.

I do agree with you that philosophy + scientific method = science.

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Just to return to the OP briefly, IMHO, I would suggest Natural Selection to be a Law of Nature. It can be expressed in mathematical terms but its rigorous theoretical reproducibility and aesthetic qualities can be found in natural events, for example in industrial melanism in B. betularia . It appears Earth-wide as a natural Law but its Universality remains to be proved. Natural Selection provided me with the impetus to suggest that it should be categorised as a Law and not merely as a theory. If, indeed, Laws are equations then it stays as a theory.

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