Axioms

An axiom is a statement that is accepted as true without proof. Axioms serve as the foundational principles or assumptions upon which other statements are built. Given that these statements are accepted without proof, it is possible to build a system of thought (or belief) that actually lacks foundations in any true sense.

Most people, encountering the idea of axioms, may have done so when studying geometry at the school. Famously, Euclidean geometry is built on axioms. (Sometimes these are referred to as his five axioms also there is often debate over the fifth - see below. I will simply list the five below.)

Euclid's axioms are:

The Axiom of Line Segment The Axiom of Extension The Axiom of Circle The Axiom of Right Angles The Parallel Postulate

Instead of suggesting that subjects like geometry and mathematics are well suited to being built on sets of rules, it would probably be more accurate to say that geometry and mathematics are the products of sets of rules. In a sense, they are sets of rules ‘personified’.

I have never heard of the idea of axioms being applied to anatomy or biology. These subjects are not devoid of rules but they do not play a prominent role. Are there any statements in anatomy or biology, accepted as true without proof? So, for each of these subjects, I asked AI whether there were any axioms. The results given by ChatGPT are pasted below.

My intention was to find out what AI might find out about how these subjects were being portrayed. Unlike Euclidean geometry, there has been no deliberate attempt to determine and state the basic tenets of anatomy or biology.

(NB Axiom and tenet are words for which much te same dictionary definition is given. Because of its geometrical and mathematical connections ‘axiom’, I suggest, has more rigid, logical connotations, whereas ‘tenet’ does not. So, at least, what might these be for anatomy and biology.)

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AI prompts and responses

A: Are there any axioms in anatomy?

Q: In anatomy, axioms are fundamental principles or truths that serve as the foundation for understanding the structure and function of the human body. While anatomy is primarily an empirical science based on observation and experimentation, certain principles are considered axiomatic due to their universal applicability and reliability. These axioms guide anatomical study and provide a framework for interpreting anatomical structures and relationships.

Some commonly recognized axioms in anatomy include:

1. Structural hierarchy: The human body is organized into levels of structural complexity, from atoms and molecules to cells, tissues, organs, and organ systems.
2. Form follows function: The structure of an anatomical component is closely related to its function. This principle, attributed to the American architect Louis Sullivan, is equally applicable in anatomy, where the form of a biological structure is intricately linked to its physiological role.
3. Bilateral symmetry: Many structures in the human body exhibit bilateral symmetry, meaning they have mirror-image counterparts on the left and right sides. This symmetry is particularly evident in paired organs such as the kidneys and lungs.
4. Hierarchy of organization: Anatomical structures can be organized into hierarchical systems, with each level building upon the previous one. For example, tissues are composed of cells, and organs are composed of tissues.
5. Anatomical position: The standard reference position for describing anatomical structures is the anatomical position, in which the body is standing erect, facing forward, with arms at the sides and palms facing forward. This position provides a consistent frame of reference for describing the location and orientation of anatomical structures.
6. Homeostasis: The body maintains a state of dynamic equilibrium, known as homeostasis, through regulatory mechanisms that control internal conditions such as temperature, pH, and nutrient levels. Homeostasis is essential for the proper functioning of cells, tissues, and organ systems.

These axioms, among others, provide a conceptual framework for anatomical study and help anatomists make sense of the complex organization of the human body. They facilitate communication and understanding among healthcare professionals, researchers, and educators in the field of anatomy.

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A: Are there any axioms in biology?

Q: In biology, axioms are fundamental principles or truths that serve as the foundation for understanding living organisms and their interactions with their environment. These axioms provide a framework for biological research, education, and the application of biological knowledge across various fields. While biology encompasses a vast array of disciplines and subfields, several overarching axioms are widely recognized:

1. Cell theory: This foundational principle states that all living organisms are composed of one or more cells, and that the cell is the basic unit of structure and function in living organisms. Cell theory is central to understanding the organization and functioning of all living organisms.
2. Theory of evolution by natural selection: Proposed by Charles Darwin, this theory asserts that species evolve over time through the process of natural selection, whereby organisms with traits that confer advantages in their environment are more likely to survive and reproduce. Evolution by natural selection is considered the central unifying principle of biology.
3. Unity of biochemistry: Living organisms share a common biochemistry, with similar metabolic pathways, genetic codes, and molecular structures. This principle underscores the unity of life and the evolutionary relatedness of all living organisms.
4. Hierarchical organization: Biological systems are organized into hierarchical levels of complexity, from molecules and cells to tissues, organs, organisms, populations, and ecosystems. This hierarchical organization reflects the nested structure of biological systems and the interactions among levels of organization.
5. Homeostasis: Living organisms maintain internal stability and balance through regulatory mechanisms that adjust physiological processes in response to internal and external changes. Homeostasis is essential for the survival and proper functioning of organisms in diverse environments.
6. Continuity of life: Living organisms reproduce, passing on genetic information to subsequent generations. This continuity of life ensures the perpetuation of species and the ongoing evolution of life on Earth.
7. Interdependence of organisms: Living organisms are interconnected within ecosystems, where they interact with one another and with their environment. This interdependence underlies ecological relationships, such as predator-prey interactions, symbiosis, and nutrient cycling.

These axioms, among others, provide a conceptual framework for understanding the diversity, complexity, and interconnectedness of life on Earth. They guide biological research, education, and the application of biological knowledge in fields ranging from medicine and agriculture to conservation and biotechnology.

End of AI responses

A Too Static Anatomy

I was a little surprised one afternoon during a dissecting class by what a colleague said as he mused out loud. He was wondering why it was that arteries closer to the heart had more elastic tissue in their walls than those further away which had more muscle fibres in their walls. It was clear from what he was saying that he thought that some sort of predetermined pattern was laid down deliberately in embryo. His was a quite static view. He did not take into account the pressure differences within the arterial tree and the different stimulatory effects these might have on the cells in the arterial walls. One might envisage, a higher pressure (closer to the heart) stimulating greater elastic fibre production at the expense of muscle fibres - and vice versa.

I was told by a medical student in one such dissecting class that, in coronary bypass surgery, grafted veins become like arteries after the operation due to the arterial pressures they experience. I have not been able to find convincing support for this assertion, although there is evidence that their walls do thicken in response to these pressures. I cannot find evidence that grafted veins become arteries per se. However, the fact that they do change illustrates the dynamic nature of the structures of the body and how we should be careful never to overlook that fact.

Visualising Thinking

I have been wondering what to do with the following diagram. It depicts how our thinking must be given different forms in order to test our ideas. In my experience, students collect data and perform statistical tests without considering carefully what they are really doing. They often follow what somebody else has done successfully, confident that ‘if it worked for them, it’ll work for me’. In brief (and often without realising it), they begin with an idea, turn it into a numerical model upon which numerical/statistical tests can be performed and then convert back into terms applicable to the original idea. This is what this diagram portrays.

My liking for this diagram comes from its similarity to a diagram I came across as a student. Instead of 20 detailed steps, it gave the four corner of a square. The problem was how to go from a research question Q to its answer A in the absence of a direct path between them? Both Q and A take a verbal form. The solution was to convert the verbal question Q into a numerical form Q’ upon which statistical tests could be performed so as to reach answer A’. That answer, also being in a numerical form, was simply converted back into a verbal form: the answer A. Thus, we can go from Q to A indirectly via Q’ and A’.

I should apologise if I infringe anybody’s copyright by reproducing the top diagram. If I ever had a note about the source of this diagram, I have lost it. I have tried to find the source; I have even tried Google Lens - but to no avail.

I am somebody, the copyright of whose work has been ‘violated’ on more than one occasion. (For example, see my Anatomical Wordbook at Anna's Archive. The copy at Open Library/Internet Archive seems to be no longer available.) I do not mind. I want to share my thought as freely as possible. (Hence my website: ~sjlewis.)

What science is about...

I do not often - if ever - cite quotations from living persons. There is clearly a certain finality about utterances from those who can utter no more. (And who can no longer change their minds about what they have said.) However, here I make an exception having come across the following from the physicist Carlo Rovelli (b. 1956), in my notes:

This is what science is about: exploring new ways of conceptualising the world.

As usual, the quotations I cite are those with which I heartily agree. This time, in doing so, I am sure to be recontextualising. As a physicist, Rovelli is exploring new ways of conceptualising the physical world - and probably the whole universe. (Sometimes physicists have used ‘world’ as shorthand for ‘universe’.)

As a human biologist, I consider myself to be exploring new ways of conceptualising what I consider to be the most interesting thing in the universe: ourselves as physical - and conscious, self-reflecting - entities.

Any science that explores new ways of conceptualising its objects of interest is doing more nuts-and-bolts, mechanistic science. It is trying to go beyond the obvious and understand the meaning of things.