Heuristic methods

The heuristic methods are a type of scientific methods.

The term heuristic derives from the Greek "heuriskein", which means "to discover". The term "method" derives from the Greek "methodos", composed of the terms "meta", which means "beyond", and "hodos" meaning "way". An example of heuristic methods is the consistency tests applied to guarantee that a hypotheses is internally consistent and in agreement with previous formalisms [1].

Heuristic methods are used for (i) the description, analysis, and synthesis of parts of the observable universe and their transformations, and (ii) the recording and organization of the acquired knowledge into testable formalisms and methods.

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The net result of the heuristic methods is the generation of scientific knowledge, this is an irreversible process, which can be formalized as

\[ O + S \Longrightarrow O' + S' + \text{Knowledge} \]

with \( O \) denoting the scientist or scientists and S the system under study. The nature of \( S \) allows us to differentiate experimental scientists –who directly study natural systems– from theoretical scientists –who study data and formal systems–.

We have considered the general case where the state of the system after being studied by scientists differs from its original state. Contrary to a common misconception, this has nothing to do with the so-called "Heisenberg uncertainty principle" of quantum mechanics. As emphasized by Werner Karl Heisenberg: "We have to remember that what we observe is not nature in itself but nature exposed to our method of questioning" [2]. Already in formalisms such as classical thermodynamics, the modification of the state of a system due to a measurement is well-defined and is taken into account during the design of thermometers, for example.

MAIN STEPS

The net result of the heuristic methods, the production of knowledge, consists of the following main steps

\[ O_1 + S_1 \Longrightarrow O_1' + S_1' + \text{raw-data} \] \[ O_2 + \text{raw-data} \Longrightarrow O_2' + \text{raw-data} + \text{empirical-data} \] \[ O_3 + \text{empirical-data} \Longrightarrow O_3' + \text{empirical-data} + \text{hypothetical-axiom} \] \[ O_4 + \text{empirical-data} \Longrightarrow O_4' + \text{empirical-data} + \text{hypothetical-definition} \] \[ O_5 + \text{formalism} \Longrightarrow O_5' + \text{formalism} + \text{hypothetical-theorem} \]

The system \( S_1' \) resulting from observation and experimentation needs not to be the original system \( S_1 \); an extreme case is when the original system is destroyed during experimentation. In general, the original system is specifically chosen to maximize the accuracy and reliability of data acquisition process; for example, by allowing experimental control of some crucial property.

The empirical data are obtained from the raw data after applying the corresponding statistical methods and control tests. The hypothetical axioms, definitions, and theorems are tentative elements that must be tested before constituting new scientific formalisms. Notice how the hypothetical theorem has not been added to the formalism (the formalism has not changed after it was used to produce the tentative theorem).

In principle, a single scientist could perform all the steps, but today's scientific community is very specialized and empirical data is often generated by experimental scientists, whereas formalisms are developed by theoretical scientists.

TESTS

There are two main types of tests available to scientists: consistency tests and experimental tests. Consistency tests guarantee that the hypotheses are internally consistent and agree with existing formalisms [1]. Experimental tests are typical of science –in clear contrast to religion or philosophy [3]– and guarantee empirical agreement between scientific formalisms and objective reality.

If the tests fail, the hypotheses are rejected and new hypotheses must be proposed. Hypotheses that pass consistency and empirical tests are accepted and added to existent formalisms or included in a new one

\[ O_6 + \text{axiom} + \text{definition} \Longrightarrow O_6' + \text{formalism} \] \[ O_7 + \text{formalism} + \text{theorem} \Longrightarrow O_7' + \text{formalism}' \]

Many authors talk about theories and laws and some claim that laws are more universal than theories. We follow a different convention here. We focus on formalisms instead of theories for a better understanding of science. For instance, we differentiate between Lagrangian and Hamiltonian formalisms; although both formalisms give the same theory of classical mechanics, the Hamiltonian is more powerful and deep, providing fundamental contributions to statistical and quantum mechanics that would not exist if the theory of classical mechanics had been formulated solely in the initial Lagrangian formalism.

SELF-CORRECTION

The process of obtaining both raw and empirical data requires well-trained scientists, who know the inner details of the laboratory devices used. Those devices would be free of any systematic error. Calibration and repetition of the process by a different team can help uncover errors.

The process of formulating hypotheses from empirical data requires well-informed scientists, who know the previously formulated hypotheses and the result of all the tests carried out, making sure that the mistakes of the past are not repeated. This information is usually taken from a background investigation of the published literature [4,5]. Traditional presentations of the "scientific method" only consider the testing of hypotheses through new experiments; however, the first test that a new hypothesis must pass is that this hypothesis must not be at odds with available formalisms and empirical data.

In the end, despite all the precautions and tests, mistakes are made and we cannot avoid this. Fortunately, the iterative application of scientific methods provides self-correcting capabilities to science. Unfortunately, some errors remain and spread to other scientists, students, and the general public. Some of those errors have been in the scientific literature for over a century! I call them "common misconceptions" and I am preparing a book with the main misconception in the physics literature [6].

REFERENCES AND NOTES

1. Scientific knowledge is cumulative, and new theories do not contradict the old ones (or at least they should not). Contrary to what is often stated in public, quantum mechanics does not contradict general relativity. General relativity was developed for systems in which quantum effects are negligible and vice versa. Contradictions arise only when the principles of general relativity are applied directly to quantum systems or when the principles of quantum theory are applied directly to general relativistic systems, but the direct application of a theory outside its range of validity is a methodological error.
2. Physics and Philosophy: The Revolution in Modern Science 2007: HarperCollins Publishers Inc. Heisenberg, Werner.
3. And with approaches such as intelligent design and its counterexample: the Flying Spaghetti Monster. The difference between the two is that proponents of intelligent design try to pass off this concept as a scientific theory to make it more palatable to public school curriculum developers, whereas proponents of the Flying Spaghetti Monster know that theirs is not science but a parody.
4. The open science movement calls for free access to scientific literature and fights against the current closed access where information owners –including ‘not-for-profit' academic societies– transfer the scientific information to readers only after obtaining a huge amount of money, with the aggravating circumstance that the information that they store and sell was generated by others for free. This has generated paradoxes such as humble scientists without access to expensive journals where their own work is published. The open science movement is not without its problems, because it has simply transferred the costs of publication from readers to authors. The movement began with journals that charged as ‘little' as $1000 to publish a paper. Now some publishers want you to pay up to $9900 to have your work published in a flagship journal. That is around $500 per page! Academic science has gone from a situation where only the rich could read the literature to one where only the rich can publish. This is ridiculous.
5. Open science, done wrong, will compound inequities 2022: Nature 603, 363. Ross-Hellauer, Tony.
6. Common Misconceptions in Physics (book series in preparation).