The Role and Risks of Assumptions in Physical Science Modelling

About the Author

The author is an academic and practising lawyer in Australia. He has had a prior life and long-term interest in theoretical physics, astronomy, maths and philosophy.

As a lawyer, the author daily deals with the difficulties and nuances of the English language. He sees similar difficulties arising in the scientific literature in which he is interested, particularly in the form of assumptions, approximations and logical fallacies of different kinds that both infect and affect some of the relevant scientific literature.

This book is an attempt to translate his experiences gained through a life in law to these relevant areas of science and to do so by reference to many specific examples.

Dedication

This book is the product of many late nights spent reading and pondering in my study, after a day immersed in my legal career. Its motivation arose from the challenges I encountered while reading various books and journals, applying the habits and techniques I developed during my years in law.

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Allan Anforth 2024

The right of Allan Anforth to be identified as author of this work has been asserted by the author in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.

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The story, the experiences, and the words are the author’s alone.

A CIP catalogue record for this title is available from the British Library.

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Acknowledgement

The author acknowledges his debt and reliance on a plethora of authors over the centuries, some acknowledged in the book and some not.

Introduction

This book is an attempt to identify and critique the widespread use of assumption, ambiguities and approximations of various kinds in the physical sciences, and in particular, how they arise as part of the use of language.

The author is conscious of the existing body of academic literature on the topic. The literature appears in books and journals devoted to linguistics, philosophy of science, physics, astronomy and philosophy generally.

The wider debate over the role of language in scientific and philosophical publications forms the background of this book but is only traversed in outline. The reader is referred to Carol Reeves The Language of Science (2005) and M.A.K. Halliday’s book (2004) of the same title, both of which contains an excellent summary of the manner in which language is used in science. The Stanford University Encyclopaedia also contains various useful summaries as does the Oxford Companion to Philosophy.

Michael Halliday (1925–2018)

Carol Reeves

It is not possible to review all the issues raised in this literature. This book only seeks to address a subset of this these issues. To that end, the approach taken is to state relevant propositions as clearly as possible to be assessed in accordance with the ‘pub test’ with any relevant end noting. ¹ Often this test is simply expressed as the proposition being ‘self-evident’ to the author. This is not to deny that other people may have different views on these self-evident propositions and some contrary views are referred to.

The author is of the view that presenting scientific and philosophical arguments in a manner intelligible to the interested public, is a good thing to do, particularly given that it is the public that funds academic pursuits. It is also the case that public opinion is often a major factor driving politicians in their decisions on funding. This is sometimes known as ‘cooperative principle’ credited to Paul Grice².

Quotations are sometimes used in connection with propositions, not because the author believe that quoting previous writers or scholars gives the proposition any more or less credibility, but because the author wishes to avoid controversy over alleged plagiarism and because these previous writers mostly have expressed the point more elegantly than the present author can.

Part A of the book (chapters 1–7) deal with the general principles and arguments relevant to the use of language.

Part B of the book (chapters 8–10) illustrates these principles by reference to a particular set of physical models, being those models that purport to demonstrate the emergent, and non-fundamental, nature of space and time.

Part C of the book (chapters 11–14) illustrates these principles by reference to other specific well-known physical models:

The Block Model of the universe in which space and time are said to be mere illusions.

The Friedman Lemaire Robertson Walker (FLRW) cosmological model that underpins most cosmology, including theories on the Hubble expansion of the universe and the Hubble Age of the universe.

The Hubble Age of the universe.

The Lambda Cold Dark Matter Model (ΛCDM) of the universe.

Part D of the book (chapters 15) contains the author’s speculations on another possible model of the universe that provides an example of how, with relatively few changes in the assumptions made, an alternative cosmological model can emerge which is just as capable of explaining a current range of observations and phenomena, and is also capable of explaining more, including the unification of General Relativity and Quantum Field Theory.

Chapter 15 is intended to show only the sensitivity of outcome to the assumptions made and also to indulge the author’s curiosity. It is not essential to the logic of the book about the role of language in the physical sciences.

Obviously, the use of the selected examples does not purport to constitute an exhaustive list of potential examples. In a book of this size, it is also not possible to provide a detailed explanation of the selected physical theories and phenomena and to review the literature on each. For this reason, summaries are often used in Parts B and C, and the details are relegated to appendices or endnotes.

The author has attempted to move as much as possible of the detail into the appendices and endnotes and to define as many of the terms as practical in the endnotes. Ultimately, it may be that none of this material is particularly helpful to some readers. Hopefully, the interested reader can choose to read as much or little of this material as their interest and background permits.

In general, it is not the intention of this book to suggest that any 1 physical theory is ultimately right or wrong, but to illustrate where and how they are infected with assumptions, ambiguities and approximations. Further, even if the theory is infected with questionable assumptions or even with fallacious logic, it does not follow that the theory is ultimately wrong or valueless. It may simply be there are other ways of arriving at the same result without involving those questionable assumptions or fallacious logic.

Part A

Chapter 1

An Outline of the General Principles

The presence and identification of assumptions, ambiguities and approximations can be important because the truth value¹ of any physical model, or any outcome that derive from the application of that model, is only a good as its weakest link. Fallacious factual assumptions can result in entirely unphysical models of reality. Fallacious logical assumptions can do likewise but can also lead to all manner of contradictions or paradoxes, including, for example, some famous paradoxes addressed below.

Assumptions of 1 form or another have the obvious advantage of simplifying physical models whose complexity would otherwise make the modelling of little utility.² They have, however, the disadvantage of beguiling readers into believing the model and those physical conclusions derived from the modelling, are to be taken as a literal description of reality³.

The presence of assumptions gives rise to the risk of overstatement of the confidence level in the published outcome of the modelling. These outcomes are often presented to the rest of the scientific community, students and the public generally, as being established fact, or so close to it that they are beyond questioning (a ‘black box’ statement). Then, when a different assumption is made and modelled, there is a tendency to view it as necessarily wrong, because it is inconsistent with the relevant black box statement. The alternative model is viewed as almost heretical and falling within a ‘no-go zone’.⁴ See, for example, Simon Saunders (1954-) challenge to the black box postulate of the indistinguishability of particles at the quantum level.⁵

Simon Saunders

Assumptions tend to first enter the picture at the stage when scientists are engaging in the physical modelling process from which hypotheses and theories are initially developed. The modelling process is described at Chapter 6. At the core of all modelling processes are intentional⁶ exercises of the human mind, and all intentional exercises of the human mind are formulated internally, and are expressed externally, via the medium of language, including by scientists. The modelling process in Chapter 6 starts and finishes⁷ with intentional linguistic activity, and for this reason the use of language is a major, and largely unavoidable, source of assumptions and ambiguities.

This book argues that all modes of expression of the English language (and probably all languages) are inherently riddled with assumptions and ambiguities, including the specialised language used by scientists. This book is limited to the use of English because this the native language of its author and because English has become the de facto official language of science⁸ which, no doubts cause considerable problems for those scientists for whom English is not their first language.⁹ All references hereafter to ‘language’ should be read as referring to the English language, whether in thought, word or writing.

Even in the case of native English speakers, the training of scientist does not particularly equip them to understand or discern the nuances of language and its use. Maddox (1988) made this point many years ago:

Language is the next distraction. The opinion that those who practice science cannot be expected to also have a flair for knowing how sentences are constructed and strung together is held by many, but not all of those who earn their livings as researchers. The exception includes many who say that there is nothing to the use of language that cannot be picked up by reading novels on the weekend…

Naturally, it is a serious matter to assert that some, perhaps many, of those who contribute to the literature of science…are indifferent to the meaning of what they say in words…Yet the misuse of words is a common fault in the science journals.

Any scientist may assert that he or she is fully attuned to the issues raised by the use of language in their discipline and may take offence at the content of this book suggesting otherwise, but it is also possible that such reactions by scientists may betoken a level of ignorance on their part of the linguistic issues involved.

There are other intellectual disciplines that have a greater understanding of these issues, for example, philosophy, linguistics¹⁰ and law.

Language that is adapted to the particularities of the scientific subject matter, including jargon, have a use in the clarity and succinctness of communications between relevant scientists who share that specialised language; however, it also has the disadvantage of narrowing the audience and of hiding assumptions of various forms. This issue underpins the debate discussed at Chapter 7 below, concerning the duty of scientists to communicate in the common language.

Chapter 2

The Different Forms That

Assumptions Take

The present author takes it to be self-evident that assumptions exist and can be expressed in various forms. They can be:

Implicit, or

Explicit.

Assumptions can relate to:

Facts about physical reality, or

The logic applied to processes involving the assumed physical facts.

Assumptions can be made:

c. Consciously/deliberately, or

d. Unconsciously/unwittingly

Assumptions can be:

A true representation of actual reality or sound logic, or

Only a partially true or possible entirely untrue representation of actual reality or sound logic.

Explicit assumptions can be:

Acknowledged by their author, or

Left for the reader to detect for themselves¹³

Implicit assumptions can have their origin in:

The language used in the discourse.

Including specialised language within specific disciplines, and/or

Unstated factual or logical assumptions in the model of reality used.

Assumptions can be in the form of simplifying approximations which assume certain elements of a reality are sufficiently approximated by a simple model:

To which manageable dimensions and symmetries are further assumed, and

Where sometimes these approximations can actually be inconsistent with the physicals assumptions to which they relate.¹⁴

See Jacques Derrida and the role of unacknowledged assumptions – Wikipedia.↩︎

Examples are given below in the context of LQG; and also see de Olano et al (2022)↩︎

Chapter 3

Assumptions Embedded in the

Language Used

3.1 The Role of Language Generally

It is taken to be self-evident for present purposes that language (oral and written) plays a multiplicity of roles, including:

It forms the basis for the formulation of complex conscious intentional thoughts to the point that it is doubtful that anyone could clearly embody such thoughts in an intentional statement or scientific model, that they could not first clearly formulate in their thoughts;¹ that is, a person cannot talk about that which they cannot conceive.²

It is the medium for communicating to other people, including academic peers, the wider scientific community and the public. This role assumes that there exists a sufficient common language with a common vocabulary between the people involved in the communication, and,

It is the medium in which social, scientific, philosophical and other debates occur.

In the words of Michael Halliday (2005), which the present author also takes to be self-evident:

‘[language] enact the social process, our relationships with another, and it construes the human experience’ (p59).

‘Grammar transforms experience into meaning’ (p63).

Stig Stenholm (2015) succinctly summarises 1 role of language in a further self-evident statement:

‘Language is a function of reality, in which reality is the independent variable and language the dependent variable. The possible structure of being is reflected in the structure of language. Concepts are tools to represent matters of fact. Language is a picture, a map or model of reality. Language is the only tool we have to intuitively capture the possible structure of reality’ (p189).

Stig Stenholm

(1939–2007)

The highly influential 19th century philosopher Ludwig Wittgenstein³ summarised the link between language and a person’s understanding of the world, as follows:⁴

‘The limits of my language means the limits of my world.’

‘All I know is what I have words for.’

‘Whereof one cannot speak, therefore one must be silent.’

Ludwig Wittgenstein

(1889–1951)

I do not take the last quote from Wittgenstein to mean that people literally cannot talk about issues they struggle to define, although by definition they cannot talk of things they have no concept of at all. People may, for example, formulate their vague thoughts in poetic form, various physical forms such as body language, song, sign language or simply speak in a manner that recognises and accepts its inherent vagueness, often by use of metaphors⁵ and other linguistic devices that may invoke mythological or religious ideas. Some linguists argue that metaphors are central to all language⁶ and to children learning language.⁷

I also take to be self-evident that the limits of our language do not impose any limits on the scope or truth of science. Humans are still early in their evolutionary process in relation to both language and science and these two disciplines are evolving in lockstep.

Vague or poetic language, however, is not the kind of language that physicists purport to use when engaged in physically modelling or the so-called operational paradigm⁸.

Lord Kelvin put it thus:

When you can measure what you are talking about and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.

Lord Kelvin

(1824–1907)

No doubt many poets, authors, singers, philosophers and artists would not agree with Lord Kelvin.⁹

On this point, I note the previously influential views of Noam Chomsky to the effect that all languages have an underlying common grammar and all people are genetically programmed with an understanding of that grammar.¹⁰ As far as the author is aware there is no substantial body of evidence for this thesis and it is not now widely accepted.¹¹

Noam Chomsky

(1928-)

As a mode of communication, language is two directional, the speaker/writer and the hearer/reader. Assuming a speaker/writer can formulate their thoughts with sufficient clarity to express them, that expression takes the form of the spoken or written word. The hearer receives the spoken or written word, not the actual thoughts of the speaker/writer, and so the meaning that the hearer/reader takes from the communications depends in part on how the hearer/reader interprets the sounds or symbols of the spoken or written words. No sound or symbols are self-interpreting, as is obvious when a hearer/reader encounters a language with which they have no familiarity.

The interpretation taken by the hearer/reader depends on all manner of conscious and sub-conscious biases and learning, such that there is no guarantee that the meaning taken by hearer/reader is that which was intended by the speaker/writer. This fact underpins a large part of the philosophical and legal disciplines, often pejoratively referred to as ‘semantics’¹². It is why there are interminable arguments and appeals within the English legal system over the meaning of the words written on the page of a piece of legislation. It can also affect the interpretation of experimental or observational data.¹³

The interpretation also depends on the underlying psychology of the hearer/receiver of the communications¹⁴ which can include the perceived prestige of the author in a phenomenon known as the Mathew Effect.¹⁵

All conscious or intentional human activity is ultimately a value-laden exercise.

In order for effective communication to take place, the sender must intentionally transmit unambiguous messages that are received and comprehended by the intended audience. To minimise ambiguity in scientific communication, specific terms and conventions have been developed within various disciplines over time. Mastery of these terms and conventions is typically achieved through training and years of experience, with experts and academic societies contributing to the standardisation of terminology within their respective fields.

However, the constant expansion of scientific knowledge and vocabulary, driven by new discoveries and advances, creates opportunities for miscommunication even among expert peers within a single discipline, and more so across interdisciplinary or sub-disciplinary boundaries, owing to differences in training, language, and philosophical approaches. Complex interdisciplinary topics of contemporary interest, which are often of general public concern, are particularly susceptible to message distortion because they involve audiences with varied knowledge domains and levels of comprehension.

The phenomenon described by the author occurs within and between disciplines, for there are no hard boundaries between the various scientific fields—they are interrelated on micro- and macro-levels.

To misquote poet John Donne:

‘No science (or scientist) is an island entire by itself (themselves), every discovery is a piece of the universe, a part of the main.’¹⁶

Such issues underscore the thesis of this text—that is, it is important to recognise and identify the assumptions, ambiguities and approximations in the sciences which exist because they can lead to unintended consequences (not least, erroneous conclusions), and, that language plays a significant role in the creation and recognition of these assumptions, ambiguities and approximations.

3.2 The English Language Generally

There are many easy-to-read good books on the English language including Taggart and Wines (2011) and Aarts (2011). The study of the English language is usually sub-divided into ‘syntax’ and ‘semantics’. Syntax is a study of the spelling and arrangement of words, parts of speech¹⁷ and punctuation¹⁸to form a sentence, and the combination of sentences to form paragraphs and larger documents. Semantics is the study of the meaning of words and sentences. The two areas of study are not synonymous. A grammatically well-constructed sentence may still convey no meaning at all or