An excursion into the absurd with Camus as a guide

Someone lent me a book on Camus, titled Albert Camus and the literature of revolt. It was written by John Cruikshank, ‘the first professor of French at the University of Sussex; founding the French studies department at that institution in 1962’ (Wikipedia). It was first published in 1959, but I believe the edition I had was the ‘third Galaxy printing, 1963’, even though the copyright says 1960 just to confuse everyone.

 

Camus died 4 Jan 1960, but the author references him consistently as still alive, which is what you’d expect if it was written in 1959. It’s a very dense read, even for an academic. I’m not exaggerating when I say I found Kant’s Critique of Pure Reason an easier read (mind you, that was over 25 years ago).

 

I read 2 of Camus’ novels in high school (in the 1960s): The Plague (in English) and L’Etranger (in French). The Plague had quite an effect on my fertile brain at the age of 16, because it challenged a short lifetime’s indoctrination in Christianity. To be fair, I was already challenging the concept of God I had been raised on, so I think my mind was ripe. I’ve read it twice since, which says a lot. I saw the recent movie, The Stranger, based on the novel, L’Etranger, and I have to say I thought it was very well done, even down to the use of black-and-white visuals to capture the period, and found it very true to my memory of it.

 

Camus is famous for his philosophical position on the absurd, which is effectively the subject of Cruickshank’s tome over 224 densely worded pages. Having said that, I believe Camus’ position is often misrepresented and Cruikshank appears to agree, so a large portion of his text deals with disabusing us of the widely held belief that Camus’ entire philosophical position was that life is absurd and we have no choice but to accept it. Many cite his treatment of the Myth of Sisyphus as evidence of this position (refer next paragraph). In reality, Camus seems to have spent his entire intellectual life looking for a resolution to the absurd condition, but I’m getting ahead of myself.

 

For those who don’t know, The Myth of Sisyphus is Camus’ literary essay on a Greek mythology concerning the punishment given to Sisyphus: ‘who was condemned to repeat forever the same meaningless task of pushing a boulder up a mountain, only to see it roll down again just as it nears the top. The essay concludes, "The struggle itself towards the heights is enough to fill a man's heart. One must imagine Sisyphus happy."’ (Wikipedia)

 

Also, according to Wikipedia, ‘The absurd lies in the juxtaposition between the fundamental human need to attribute meaning to life and the "unreasonable silence" of the universe in response.’ As an aside, many scientists seem to take this position by default. In fact, Paul Davies, whom I often cite on this blog, refers to this position by most scientists as the ‘absurd universe’ without any hint of irony. In response, Davies argues that humanity is in the privileged position of being able to ‘unravel the plot’ (his phrase), but that’s perhaps too much of a diversion for this post, though I may return to it later

 

I have my own thoughts on the myth of Sisyphus in that it’s like a time loop, which of course, is not what Camus had in mind. In fact, I think the Marvel movie, Dr Strange (starring Benedict Cumberbatch) alludes to the myth towards the end, when Dr Strange traps his nemesis in a time loop – a point I make in my online review. The thing about a time loop is that you’d have no memory of the previous loop, in the same way that, if you were reincarnated, you’d have no memories of your previous incarnation. And, logically, that’s the only way one could deal with eternity.

 

I remember as quite a young child (pre-teens) lying in bed one night trying to grasp the concept of infinity or eternity and you literally look into the abyss. You realise how impossible it is to conceive – it’s a mind-fuck in the real sense of the term. In other words, we are not meant to comprehend it – it’s literally beyond our conception let alone perception. I’ve long argued that only in mathematics, does infinity have a home – in fact, it’s built into its foundations, despite the efforts of many to get rid of it.

 

So, with that in mind, the myth of Sisyphus is another way to look at eternity and show that it’s truly absurd to a human consciousness. It renders eternity into an activity that we can comprehend and viscerally feel. I know that’s not the absurdity that Camus had in mind, but that’s my take-home lesson. The truth is that we couldn’t live with immortality even if it was offered.

 

A detour. Now back to the main theme: Camus’ attempt to deal with the intrinsic absurdity of life without resorting to metaphysics. Early in his book, Cruikshank discusses a quote from The Myth of Sisyphus that brings Camus’ preoccupation with the absurd into focus.

 

“There is only one really serious philosophical problem, and that is suicide.”

 

In fact, Cruikshank discusses this at length, but basically Camus is asking us: if life is absurd, why not end it? In conclusion, Camus contends that suicide is not an escape from the absurd but giving into it, and it’s hard not to agree with him. But this begs another question: how does one live with the absurd if that’s all the universe has to offer.

 

Camus argued that we need to revolt but seemed to struggle with how that can be achieved without revolution, especially when revolutions invariably involve violence. One suspects this is a major reason for Camus rejecting Marxist communism, which led to a falling out with his contemporary French philosopher and writer, Jean-Paul Sartre. Anyone who has read Marx and Engel’s treatise on communism will know that revolution is a key step in its inception.

 

Right towards the end of Cruikshank’s book, when he discusses Camus’ plays, there is a very lucid and insightful analysis of his play, Les Justes, which is about the plotting and assassination of the Grand-Duke Sergei Alexandrovich (referred to as Grand-Duke Serge). Camus had this to say about its historical veracity:

 

However strange some situations in this play may appear they are nevertheless historically true… All my characters really existed and behaved in the way I describe. I have simply tried to give probability to what was already true.

 

Cruickshank makes the point that, in his view, this play is far superior to others Camus wrote in the depiction of the characters and the tensions between them. The reason I feel it’s worth discussing is because it seems to address the inherent tension between idealism and terrorism, personified by 2 of the main characters, that seems to arise ineluctably when people combine political ambition with violent means.

 

There is another quote by Camus in a completely different context, which I feel is relevant:

 

"But practically, I know men and recognise them by their behaviour, by the totality of their deeds, by the consequences caused in life by their presence."

 

Camus was involved in the French resistance, and would have observed the best and worst in men, as did my father in a German POW camp. They both would have appreciated better than most of us how our moral compass can become distorted in a war environment. Both Camus, based on his writings and stated beliefs, and my father, based on what little he was willing to tell me, were very principled in the face of brutal conflict. One could argue that war is the absolute epitome of the absurd, yet men can sometimes find something abstract to hang onto so that they survive, not only physically but mentally.

 

Camus rejected existentialism, according to his own testimony, yet the one strand that runs through the novels I read and the one movie I saw, Far From Men (based on a short story) is the protagonists’ authenticity, though I suspect Camus would have loathed that term. Cruickshank repeatedly makes the point that Camus was a product of 2 environments: European France and Mediterranean Algiers. In both, I suspect, he felt an outsider and that’s a recurring theme in the fiction I am familiar with.

 

I will end by going off on a completely different tack, as is my wont. Early in his text, Cruikshank said something that caught my attention, which was an allusion to ‘truth’. This is the quote out of context:

 

Camus claims that reason is powerless and he offers no comparable alternative to truth.

 

Now, one assumes that Camus is talking about metaphysical truth or the absolute truths that religious texts claim they provide. After all, I believe this is Camus’ biggest bone of contention: that metaphysics in the form of so-called religious truths can’t deliver us from our absurd condition.

 

However, I have a counter argument. The obvious answer to me is mathematics. What’s more, I claim that mathematical truths transcend the universe therefore are metaphysical. There are 2 dictionary definitions of ‘metaphysical’, both relevant to mathematics in my Platonist view.

 

1.     Based on abstract reasoning

2.     Transcending physical matter or the laws of nature

 

Here’s the thing: given that the Universe follows mathematical rules that transcend the universe, at both its deepest level and its cosmological scale, how can it be intrinsically absurd? What would be absurd, is a universe without consciousness. It’s our very presence that makes the Universe not absurd, and I feel that’s what Camus missed, though it was staring him in the face.

 

Since I started writing fiction, I realised that nearly all fiction is about relationships. There are exceptions – Hemingway’s The Old Man and the Sea springs to mind. The subtext of all the fiction I’ve written is about relationships and companionship; and all that entails, including separation, betrayal and redemption. It’s in relationships that we find meaning in this short interval of existence, with or without metaphysical purpose.

Mathematics, language and reality

I recently read an online article with Quanta Magazine, titled How Writing Changes Mathematical Thought, featuring David E Dunning, ‘a historian of mathematics at the Smithsonian’s National Museum of American History’, who was interviewed by John Pavlus.

 

In particular, Dunning pointed out how the notation we use affects the way we explore mathematics and even comprehend it. The most significant innovation was the introduction of Hindu-Arabic numerals, along with its corresponding arithmetic, which we owe to Fibonacci (of Fibonacci numbers fame) in the 12^th Century. Tibees gives a good summary in this short video. The thing is that we would really struggle to do modern mathematics using Roman numerals, and it would be impossible for computers.

 

Dunning gives the example of the difference between Newton’s and Leibniz’s notation for calculus and how “Leibniz’s calculus got used a lot more in continental Europe, and it just grew and was fertile in a way that Newton’s wasn’t.” Which is why we all use Leibniz’s notation today.

 

But there is a more fundamental point, I believe, that Dunning doesn’t discuss. And that is the Wittgensteinian (new word) principle that the language we use limits what we can think about, because we all think in a language. And also, it’s the language of mathematics that I believe resolves the argument going back to Plato and Aristotle, whether mathematics is invented or discovered. On that last point, we invent the language but the relationships that the language describes are discovered. I contend there is a tendency to conflate the language of mathematics with mathematical formulations, because we learn them in tandem.

 

I pointed out in a much earlier post that there is also a tendency to treat mathematics as just another language, like the ones we think in, which takes the conflation I mention above to another level. The fact is that we still use the language we think in to describe mathematical notation and relationships. In other words, we absorb the language we use to do mathematics into our thinking language as a subset thereof. And this brings me back to Wittgenstein’s point, because we keep expanding our language to capture new concepts and ideas, otherwise we cognitively stagnate. And I see mathematical language as such an expansion, otherwise we can’t understand the concepts it’s describing. And perhaps this is why so many people struggle with mathematics in school, but that’s another topic.

 

One of Pavlus’s questions was: Why don’t we teach people to do math with, say, a more pictorial or visual kind of notation?

 

This is what led Dunning to talk about Newton’s and Leibniz’s respective calculus notation, but it got me thinking in a different direction.

 

Specifically, how we are visual creatures, and how I try to visualise mathematical concepts as much as possible. A graph can tell you so much more than the written equation can, and makes some concepts very easy to grasp. The best example that most people would be familiar with is a sine wave. You can see where the wave is zero and where it’s 1 and -1, and everything in between, and how it cycles in periods of 2π radians. It also shows just by looking at the graph how the cosine of an angle is 90 degrees (π/2 radians) out of phase with the corresponding sine wave, just by depicting them on the same graph.

 

Another example most of us are familiar with is a parabola being the graphical representation of a quadratic equation. The zeros (or square roots) are where the graph crosses the x axis, which can’t be greater than 2, so can have 2 square roots. However, you can have one square root if the parabola kisses the x axis and no roots if it doesn’t touch it. Though we all know we can have imaginary roots (√-1), but you need another graph which includes an imaginary axis along with the real axis.

 

In fact, complex algebra is a lot easier to understand if it’s depicted graphically. I’m a little annoyed that it wasn’t taught to me that way when I first encountered it. By depicting it on an Argand diagram, where the imaginary (i) axis replaces the y axis in a Cartesian diagram, and using polar co-ordinates, you can see how multiplication requires adding the angles, and multiplying a complex number by i means rotating everything anticlockwise by 90 degrees.

 

Even esoteric topics like Riemann’s hypothesis becomes amenable to comprehension by mortals when it’s demonstrated graphically, as this video demonstrates quite effectively.

 

Calculus is taught using graphs: the tangent of a curve being found by differentiation and the area under a curve being found by integration. Why one is the inverse function of the other, I’m not sure anyone can tell you. Differential calculus allows one to grasp the concept of instantaneity, which doesn’t physically exist, but it’s an idealism that is more than useful. Likewise, it’s almost incomprehensible that an infinite number of infinitesimal strips can give you a finite area under a curve, but it works. Calculus is like magic.

 

But I extend this visualisation into physics, where everything is depicted in the language of mathematics.

 

I never understood Einstein’s General Theory of Relativity (GR), which is a theory of gravity, until I grasped the concept of a geodesic, which can be visualised. And I can thank Richard Feynman for explaining it relatively succinctly, including mathematical formulations, in his excellent book, Six Not-So-Easy Pieces. A geodesic is the shortest distance between 2 points, and on a sphere, it’s always a great circle. Intercontinental aircraft fly along geodesics for that very reason, though they appear curved when the map is projected onto a flat surface.

 

But here’s the thing, as pointed out by Feynman: “In a uniform gravitational field the trajectory with maximum proper time for a fixed elapsed time is a parabola.” I’ll describe what he means by ‘maximum proper time’ in a moment, because that’s the key to understanding it. But we all learned that a projectile travels through the air following a parabolic curve in high school physics, without knowing anything about GR. We did it using Newton’s equations. But Einstein gives us the same result, assuming the object is not travelling at relativistic speeds.

 

And here’s why, again quoting Feynman: An object always moves from one place to another so that a clock carried on it gives a longer time than any other trajectory (italics in the original). In his words, The time measured by a moving clock is called its “proper time” (τ). In free fall, the trajectory makes the proper time of an object a maximum. And that’s what’s called a geodesic in GR.

 

And that paragraph allowed me to finally comprehend General Relativity. Any deviation of an object from free fall in a gravitational field (from its geodesic), and remember there is a gravitational field everywhere in the Universe, means its clock will slow down which is what SR (special theory of relativity) tells us. I’ve always believed that SR is dependent on GR and not the other way round, and Feynman indirectly confirmed this for me.

 

But visualisations can be misleading, and I think the wavefunction (Ψ) in Schrodinger’s equation is a case-in-point, because it’s not a physical wave. It exists in Hilbert space which, in principle, can have infinite dimensions. There is another way of expressing the same quantum mechanical (QM) phenomena and that is with Heisenberg’s matrix formulation. In fact, Heisenberg’s formulation preceded Schrodinger’s but they are mathematically equivalent. And this brings me back to Dunning’s point that the language we mathematically express something in, will give an intuitively different picture.

 

I recently read an article on Heisenberg’s revolutionary discoveries in Philosophy Now (Issue 172, Feb/Mar 2026, by Dr Kanan Purkayastha), which made the point that ‘Heisenberg attempted to calculate the behaviour of electrons around atoms using quantities we can observe’, so basically an epistemological approach. On the other hand, Schrodinger started with a principle postulated by De Broglie that an electron’s momentum could be formulated as a wave, similar to a photon, which I would call an ontological approach. Philip Ball in his book, Beyond Weird, made a similar point: that Heisenberg’s matrix approach is ‘epistemic’ and Schrodinger’s wave function approach is ‘ontic’ (his terms).

 

Many people originally thought that the famous Heisenberg Uncertainty Principle was an epistemological one, including Einstein, who said it was “just an expression of the limits of what can be determined by measurements. Or in philosophers’ terms, the nature of uncertainty would be an epistemic one.”

 

However, it falls out of Schrodinger’s equation by using a Fourier transform, so it is a mathematical restraint, not just a physical one. Schrodinger’s wavefunction also entails superposition and entanglement, which led Schrodinger to state that entanglement is the defining feature of quantum mechanics, meaning it’s what separates it from classical physics. The other thing about Schrodinger’s equation is that it can only give us probabilities, and following an observation, it no longer applies. This leads me to argue that the wavefunction exists in the future; as far as I know, an idea not shared by anyone else except Freeman Dyson (who is no longer with us).

 

Probabilities were the subject of a recent post, but the thing is we only apply probabilities to things that are yet to happen. After something has happened its probability is no longer relevant; it effectively becomes 1. And this is what happens in QM, as described above. To quote from another online article by Phys Org:

The results showed that the photon's physical presence was distributed across both paths simultaneously, demonstrating that the particle is truly delocalized until a detector forces it into a single location.

 

This is identical to a description provided by Alain Aspect that I reported in a not-so-recent post. But, as Freeman Dyson explains, it corresponds to a change in perspective by the observer from the future to the past, which occurs at the time of ‘detection’.

 

I’d like to make a point about the fact that probabilities exist, not only in QM but classical physics – after all, the entire gambling industry is based on probabilities. I contend that it means the Universe is not deterministic. Simplistic, yes, but I can’t think of a better argument. It’s also my argument against claims of so-called prophecy. You either believe in free will or you believe in prophecy, but you can’t believe in both.

 

I could imagine having a discussion (argument) with a physicist on this issue, where they claim that probabilities are a statistical outcome, as a consequence of what we cannot know. Therefore, the outcome of a coin toss, for example, could be deterministic and the probability is a consequence of our ignorance, not the event. In fact, I had this discussion (over coin tosses) with physicist, Mark John Fernee (Qld Uni). Chaos theory mathematically ensures it can never be known definitively, which is an epistemological argument. However, I argue that chaos occurs ontologically as well, and that the entire universe’s evolvement is dependent on this principle.

 

Just as in the case with Heisenberg’s Uncertainty Principle and people thinking it was a consequence of what we can't physically measure, many physicists argue that chaos theory is a consequence of our limitations of observation. However, I argue that in both cases, the limitation is built into the mathematics, which makes it a feature of the Universe.

 

So, I’ve gone way off track, but while we need a language to understand and express the mathematics we discover, nature is already determined by the rules that mathematics dictates.

 

Epistemology, ontology and the mathematical connection between them

It’s been a philosophical obsession of mine to try and understand the deep connection between mathematics, sentience and the physical universe. A recent video, an online article and a New Scientist article have all contributed to my reappraisal of these apparently disparate yet seemingly interdependent phenomena. The last post I wrote also triggered a reassessment, where I brought up the inherent tension and interrelationship between ontology and epistemology. I contend (though I didn’t spell it out in that post) that there is a loop between epistemology and ontology, which hopefully will become clear during this discourse.

 

I’ll start with the New Scientist article, (7 March 2026, pp.31-40), which is really a collection of articles by different writers, and elaborates on different responses to recent data from DESI (Dark Energy Spectroscopy Instrument). DESI suggests that the lambda constant (Λ), part of the ΛCDM (Lambda Cold Dark Matter) model of the Universe, may not be constant after all. Λ represents the cosmological constant, originally formulated by Einstein, then dropped by Einstein, then reinstated posthumously when more accurate measurements of the Universe’s expansion, and indeed acceleration, required its insertion (as an adjunct to Einstein’s equation for General Relativity, GR). That’s a nutshell exposition, but the consequences are explained in the next paragraph.

 

If Λ does remain constant the Universe will accelerate to a point where virtually everything currently observable will disappear over the horizon (yes, there is a horizon for the entire universe). However, DESI suggests that may not happen if Λ decreases in value as the Universe ages. The jury is still out, as they say.

 

By ‘responses’ to DESI, I mean theories, which are in essence, mathematical models, and that’s what I want to focus on. This is a case where measurements, therefore empirical data, have led to existing theories being put under strain, and therefore new models or theories are being formulated. For those familiar with Thomas Khun’s seminal tome, The Structure of Scientific Revolutions, this is arguably an example of a ‘scientific revolution’ in progress. Kuhn argued that advances in science have occurred in ‘revolutions’, not in gradual increments as commonly believed. He coined the term, ’paradigm shift’, to describe this epistemological phenomenon. What’s more, he argues this ‘shift’ inexorably arises when new data no longer agrees with an existing theory.

 

However, others might argue that the paradigm shift precedes the data confirming it. But I think it’s a combination. To give some well know historical examples. We have the Copernicus revolution overturning the longstanding Ptolemy model of the Universe without a massive change in known data. In fact, Stephen Hawking argued in his book, The Grand Design, that both theories fitted the observations of the day.

 

Of course, Galileo famously followed up on Copernicus at great personal risk, and one of his arguments centred around the fact that he could observe moons around Jupiter using a new-fangled device called a telescope. Then Kepler used the extensive observational data collected by Tycho Brahe to mathematically demonstrate that planets orbit in ellipses, not circles. It’s hard for us to imagine in the 21^st Century just how big a revolutionary idea that was. It’s a case where mathematics provided a key role in formulating his thesis, and that has become increasingly pertinent ever since.

 

Then Newton went further, using his newly discovered (or invented) mathematical tool called calculus to determine that the orbits of the planets were determined by gravity, which also kept him bound to Earth. Who would have thought that the same phenomenon that keeps you on Earth also keeps the moon in orbit and the very planets in orbit around the sun? That’s a huge leap – a ‘paradigm shift’ of enormous consequence.

 

And the story continues with Einstein, building on Newton and Maxwell, where he formulated mathematical formulae to describe phenomena yet to be observed as well as explain phenomena that had been observed yet hitherto had remained inexplicable. Around the same time, Planck used empirical data to arrive at a constant (h), now called Planck’s constant, which Planck originally considered to be just a mathematical trick to get the right answer. It was Einstein who realised its true significance when he used it to explain the photo-electric effect. By the way, another constant, c (the speed of light) actually falls out of Maxwell’s equations, and it was Einstein’s genius to realise this was a ‘law’ of the Universe and not just a mathematical accident.

 

So scientific discoveries, in physics specifically, require a synergistic relationship between mathematics and empirical data that goes both ways.

 

Now I want to discuss the other side of my obsession, which is the relationship between mathematics and sentience – specifically, human sentience – as we have the ability to comprehend mathematics that goes well beyond any evolutionary requirement to merely survive. I recently wrote a post about human exceptionalism, where I mention that ‘our unique grasp of mathematics has been the most salient feature in propelling our advance in knowledge and comprehension of the natural world.’

 

And this leads me to a Curt Jaimungal video I watched recently, where he interviews David Blessis, who is French (going by his accent), and who is apparently a mathematician and possibly a philosopher of mathematics, given the nature of the discussion. He makes a statement, which I found quite profound, despite its lack of esoteric language, or possibly because of it, in answer to Curt’s question, how would he define mathematics?

 

‘My definition of mathematics is imagining things and pretending they really exist.’

 

As a succinct description of mathematical Platonism, it’s hard to go past it. Though I think he was having a dig at Platonism, rather than extolling it as a viable philosophical position.

 

He goes on to call it a ‘side-effect’, after invoking what he calls the ‘logic side of mathematics’, which is how we validate its truth (my expression, not his). To quote Blessis again:

 

‘And the logic side is the core technique to produce that side-effect.’

 

So, while I quote Blessis, I have a different perspective, which I’m sure he wouldn’t agree with. My own view is that mathematics already exists in a purely abstract realm, independently of us and the Universe, which we access using logic.

 

He goes on to introduce a term, ‘meaning-making’, which is what humans do with mathematics that is not evident in its logic.

 

‘There is something about mathematics that cannot be explained by formal logic.’

 

This goes to the heart of Godel’s famous Incompleteness Theorem, though Blessis never mentions it (at least not in this video), which intrinsically differentiates ‘proof’ from ‘truth’. It’s a point that Penrose raises again and again: that humans are able to divine a mathematical truth in a way that a machine never will. And I agree, because I don’t think AI will ever actually ‘understand’ things the way we do, despite increasingly giving the impression that they do. So it would seem that Blessis, Penrose and myself are on the same page, when he distinguishes ‘meaning’ from ‘logic’.

 

He goes on to provide an example when he discusses Andrew Wiles famous proof of Fermat’s Last Theorem. In his initial publication of his proof, a fatal flaw was found, and Wiles went away to ‘fix his proof’, as Blessis puts it. Then he asks: ‘What does it mean to fix a proof?’ The inference being that a proof is not enough. If you can ‘fix’ a proof, then is any proof valid? He doesn’t specifically ask this, but I got the impression that is what he meant.

 

There has to be ‘meaning’, according to Blessis, but again, I have a different perspective. To me, the fact that Wiles had to ‘fix’ his proof, is evidence that there is an objective ‘truth’, which exists before the proof is found. I’ve posited in a much earlier post that if you haven’t solved a puzzle, does that mean there's no solution until you have? This is consistent with my earlier point that mathematics exists independently of us; but, without logic, we can’t access it.

 

Blessis also talks about axioms, and many people would argue that because the mathematics we render is dependent on axioms, it is therefore dependent on us. He discusses set theory, which I won’t go into because I don’t know enough about it; only that it’s considered foundational to formal mathematics. And the thing is that formal mathematics is dependent on axioms and it is formal mathematics that lies at the heart of Godel’s Incompleteness Theorem. But here’s the thing: according to Godel, we discover new mathematical truths by expanding our axioms, and that is what has happened in practice. The best example is the discovery (I’ll use that term) of non-Euclidean geometry by adopting curvature. The introduction of new axioms or ‘operations’ that were once forbidden under an existing formalism allows one to find solutions to problems that were previously considered unsolvable. The square root of -1 being the best exemplar I can think of.

 

So the relationship between humans and mathematics is that we create a language in the form of numbers and systems of numbers (base arithmetic) along with operations like addition, multiplication and their inverse functions, among more complex ones like calculus and trigonometry, which then allow us to navigate an abstract landscape that keeps revealing new secrets. But alongside that, we have developed an epistemology called physics that appears to uncover a suite of mathematical rules or laws that underpin the Universe at all levels of our comprehension.

 

I haven’t mentioned the online article (from Quanta Magazine), which is an exposition on the work of Astrid Eichhorn, a physicist at Heidelberg University in Germany, who is exploring, in her own words, ‘a conservative theory of quantum gravity’, which she calls ‘asymptotic safety’. I won’t elaborate, but its relevance to this discussion, is that she’s using mathematics to explore new models of reality (my expression) that may solve existing conundrums or ones yet to be found. Specifically, she’s looking at a ‘fractal space-time’, which, as the author (Charlie Wood) says, ‘sounds pretty out there.’

 

I’m not advocating her theory or any of the ones I read about in New Scientist; I just want to point out that we implicitly believe that any theory or model of reality must be mathematical.

 

So mathematics provides us with the link between epistemology and ontology that I opened this discussion with. And implicit in this belief is another belief that it pre-exists the universe that it not only describes, but to some extent, rules.

 

As I said in my last post: A mathematical epistemology can only be verified with numbers. We need to take measurements, which is what DESI is doing, to give a current, ongoing example. But all our mathematical models of reality have limitations – there are no exceptions. I think this will always be true, and in the same way that Godel’s Incompleteness Theorem ‘proved’ that our formal knowledge of mathematics can never be complete; likewise, I think our epistemology of the physical Universe will also remain incomplete. So in the same way that mathematics appears to have secrets that may never be revealed, so does the Universe we inhabit, at all scales.