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.

 

Arguments for and against human exceptionalism

 This was triggered by an article I read in Philosophy Now (Issue 171, Dec 2025 / Jan 2026) by Adam Neiblum who authored Rise of the Nones: The Importance of Freedom from Religion (Hypatia Press, 2023). I don’t normally mention the publisher, but I find it interesting that they are named after the famous female Librarian of Alexandria, Hypatia (pronounced hi-pay-shia) who was infamously killed by a Christian mob in AD 414. I’ve written about her elsewhere.
 
The article was titled, Evolution or Progress, and asks “what the difference is and why it matters”. Not really a question, though one is implied. Basically, he’s arguing that evolution is not teleological (though he doesn’t use that term). Instead, he discusses the erroneous belief that most people associate evolution with progress, which is a symptom, not just of anthropocentrism, but our religious heritage. I think these are actually 2 different things, while admitting, for many people, they are connected.
 
I want to start by challenging his premise that the association of evolution with progress is not as erroneous as it appears, depending on how one defines or describes progress. My dictionary has 2 definitions:
 
1: forward or onward movement towards a destination
 
2: development towards an improved or more advanced condition
 
By the first definition, I think he’s right, but not by the second definition. If one looks at the historical evidence, going back not just millions but billions of years: the increase in complexity and sheer diversity from the most simple cells to animals with brains, I’d argue surely applies to definition 2.
 
To emphasise my point, I’ll quote from Neiblum’s essay, who provides his own definition of progress:
 
A)    An ideal or goal – literacy, or justice, for example.
B)    A gap between this ideal and the real-world state of affairs.
C)    A process of movement – individually, collectively, or even species-wide – towards that goal or ideal.
 
We can see these are not the same ideas. Evolution is neither purposeful nor intentional, it has no ideal, aim, or end-point.
 
One can see how this aligns with my dictionary definition 1, but not definition 2.
 
To be fair to Neiblum, he does address my criticism, in as much as he acknowledges evolution results in increased complexity. But he also points out that so-called primitive lifeforms (my words, not his) like insects, crocodiles, sharks (and other so-called living fossils) still thrive. But the reason they thrive, is that they have become part of an eco-system (the same with gut bacteria, for example). Evolution never applies to a species in isolation; just look at the fact that we all can’t exist without plants processing the carbon dioxide we expire as part of the extraordinary process called photo-synthesis.
 
Neiblum then goes on to discuss the role of religion, and specifically the Christian religion, in distorting or exaggerating (again, my terms) our anthropocentrism. But I’ll return to that specific point later.
 
I would like to point out that humans are not the only examples of exceptionalism in the animal kingdom. To give just 2 examples: the peregrine falcon can literally fly through the air at 200mph (in a dive); and the sperm whale can dive down to 2-3km and stay underwater for up to 45 mins.
 
But human exceptionalism is unusual and unique in the sense that, to quote Paul Davies: ‘We can unravel the plot’. I admit I tend to get annoyed when people tend to dismiss our unique ability to comprehend the universe to the degree and extent that we’ve managed to achieve. I recently watched an excellent series titled HUMAN, presented by paleo-anthropologist, Ella Al-Shamahi, which is very extensive and comprehensive for a lay-audience, and one of the things that stood out was how ‘break-throughs’ (for want of a better term) in cognitive abilities, seem to happen virtually simultaneously in different parts of the globe; the use of written script being a good example.
 
So, our cultural evolution, has tended to happen in jumps. And, in this sense, it is synonymous with progress to which Neiblum would undoubtedly agree. In his next-to-last sentence, he states that evolution has endowed us with the unique capacity to progress (emphasis in the original) using “evidence, reason and science”.
 
Personally, I think it is our unique grasp of mathematics that has been the most salient feature in propelling our advance in knowledge and comprehension of the natural world. To quote Eugene Wigner:
 
It is difficult to avoid the impression that a miracle confronts us here… or the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.
 
This was from his famous essay, The unreasonable effectiveness of mathematics in the natural sciences. And this is arguably the only reason, as Davies asserts, ‘we can unravel the plot’.
 
In my last post, I briefly talked about language, as well as imagination. Now, I actually believe that imagination is not unique to humans, in the sense that it allows us to mentally time-travel, and I suspect other creatures can do that as well, which we see in their ability to co-operate and act towards a goal. Implicit in that ability is the capacity to imagine that goal before it’s actualised. To the extent that other creatures can do this, I contend they have free will.
 
But humans take imagination to another level, because we can mentally time-travel to worlds that don’t even exist, which we do every time we read or watch a story. And this entails that other superpower we have, which is language. To quote from my last post:

…we all think in a language, which we learn from our milieu at an extremely early age, suggesting we are ‘hardwired’ genetically to do this. Without language, our ability to grasp and manipulate abstract concepts, which is arguably a unique human capability, would not be possible. Basically, I’m arguing that language for humans goes well beyond just an ability to communicate desires and wants, though that was likely its origin.
 
And this is the thing: these abstract concepts include mathematical equations, scientific theories and engineering designs (including, by the way, the theory of evolution, which is central to this discussion). But more than this, we ‘download’ this language from generation to generation at an age when these concepts are well beyond our cognitive abilities. And it’s this unique facility that has allowed us to create entire civilisations and build the scientific enterprise that we all depend upon and take for granted (if you’re reading this).
 
I’ve spent a lot of time belabouring a point, because my arguments thus far have nothing to do with religious beliefs.
 
Religion implies that there is a purpose and we are central to that purpose. I think purpose has evolved, and I’m unsure if Neiblum would agree. I’ve argued before that the Universe appears to be pseudo-teleological or quasi-teleological in that there is no end goal, yet the very mathematical laws that we have the cognitive capacity to ‘unravel’ seem to allow for a goal, even if it’s open-ended. Possibly, I’m subconsciously influenced by my ability and passion as a storyteller, because I prefer to write a story without knowing what the ending is. I’m not the only writer who does this, though there are others who won’t start a story without knowing the ending in advance.
 
I’ve always struggled with the concept of a ‘creator’ God, which is not dissimilar to the more recent belief that we live in a simulation. In a recent episode of an Australian satirical programme called The Weekly by Charlie Pickering, one of his guests, Rhys Nicholson, did a skit on this, even citing Nick Bolstrom, who is an academic proponent, but also comparing it to the widely held belief that there is a God pulling the strings behind the scenes (metaphorically speaking). Paul Davies in his book, The Goldilocks Enigma (highly recommended) also argues that the ‘simulation hypothesis’ is just a variation on ID (Intelligent Design).
 
I also like to cite Jordan Ellenberg from his excellent book, How Not to Be Wrong; The Power of Mathematical Thinking, where, among many other contentious topics, he discusses the ‘Bayesian inference of the existence of God’, whereby he shows that the Universe being a computer simulation has at least the same probability as it has being a divine intervention.
 
The thing that has struck me about all the Gods in our combined histories is that they all have cultural origins, including the Abrahamic God, and they are all anthropomorphic. I’ve long agreed with 19th Century philosopher, Ludwig Feuerbach, that ‘God is the outward projection of man’s inner nature’. God is something internal not external, though, of course, that doesn’t rule out an external source.
 
Personally, I’m attracted to the Hindu concept of Brahman (as was Schrodinger) as a collective mind that could be the end result of consciousness rather than its progenitor. I’m not proposing this as a definitive resolution, but it would provide a goal that Neiblum considers anathema to science.
 
All that aside, I think there is another aspect to seeing ourselves as ‘exceptional’ in the animal kingdom here on Earth, because it gives us a special responsibility. We are effectively the guardians of spaceship Earth by default. However, it’s a two-edged sword: we have the unique capability to destroy it or to safeguard it. Which one we do is dependent on all of us.

John Searle (31 July, 1932 – 17 September, 2025)

 My grand-niece, giving an obituary at my mother’s funeral (a few years back), read out a rather clever poem she’d written, called ‘What’s in a dash?’ In the case of John Searle, it includes an academic career as a philosopher, who created a thought experiment that found its way outside of academia into popular discourse. It also included ignominy when he was stripped of his title as Professor Emeritus of the Philosophy of Mind and Language at the University of California, Berkeley, following accusations of sexual harassment in June 2019 (refer Wikipedia for details).
 
Just on that, we live in a time of cancel culture, but also changing social norms, which I think are largely for the better. Personally, I don’t necessarily condemn someone for sleeping with a student, depending on circumstances, though I know many find it shocking. But if they’re both legally adults and it’s consensual, I wouldn’t rush to judgement. Erwin Schrodinger, well known for his libertine views and habits, got at least one student pregnant when he was living in exile in Ireland during the war. I only know this because I read about her grandson living and working as a physicist in Australia. Apparently, he only learned of his esteemed ancestry relatively late in his life. As I said, social norms have changed.
 
And relationships in workplaces are common, including myself, though the workplace was a kitchen and not an office. Having said all that, I think being in a position of authority and coercing someone who rejected sexual advances is a sackable offence, irrespective of the environment. And according to the Wikipedia article, that was the case with Searle. Nevertheless, in the NYT obituary, they added the following:
 
After Professor Searle’s death, Jennifer Hudin, the former director of the Searle Center, stated publicly that she had faced related accusations, but that both she and Professor Searle were innocent of all charges.
 
It is worth reading her email to Colin McGinn where she disputes the outcome and how she claims that Searle was actually exonerated by the investigation, but it was subsequently overturned. Having served on a jury (for a sex-related charge, as it turns out), you literally have to work out who’s lying and who’s telling the truth; in this case, neither I nor you can do that.
 
Although it was over 3 months ago, I only learned about his death when I came across a one-page obituary in the latest issue of Philosophy Now (Issue 171, Dec 2025 / Jan 2026).
 
I won’t relate a history of his career, because others do that more comprehensively than I can, in links I’ve already provided. I read his book, MiND, a brief introduction, many years ago, probably when it was published (2004). I can still remember coming across it unexpectedly in a book shop (I hadn’t visited before or since) while I was getting work done on my car. I found it a very stimulating read. Of course, I’d heard about his famous ‘Chinese room’ thought experiment, and to quote The New York Times again:
 
According to the Stanford Encyclopedia of Philosophy, an internet reference source, the Searle thought experiment “has probably been the most widely discussed philosophical argument in cognitive science to appear since the Turing Test,” the mathematician and computer scientist Alan Turing’s 1950 procedure for determining machine intelligence.
 
While looking for obituaries online, I came across an interview he did for Philosophy Now in the Winter 1999/2000 Issue 25, so a millennium issue effectively. It gives a good overview of his philosophy that includes his ideas on language, where he coined the term, ‘speech-acts’ plus his ideas on The Construction of Social Reality (the title of a book I haven’t read). He effectively argues that these 2 fields, combined with his ideas on mind (therefore, 3 fields) are all related.
 
It was in Searle’s book, Mind, that I first came across the term, ‘intentionality’, which has a specific meaning in a philosophical context, and is related to the conscious mind’s ability to represent something externally, internally. That’s my clumsy way of explaining it, because it directly relates to my personal philosophy that we all have an internal and external world, which affects everything we do, because they are interdependent.
 
I saw an extended interview, not-so-recently, of Raymond Tallis by Robert Lawrence Kuhn on Closer to Truth, where he had a different take on it, which some might consider radical, yet is actually a good working definition: ‘Nothing is made explicit except by a creature who is conscious of it. And aware of it.’
 
In other words, there is this relationship between consciousness and reality, whereby something has no specificity (for want of a better term) until a conscious entity perceives it. I’ve made a similar point, when I’ve argued that when it comes to the question: why is there something rather than nothing? There might as well be nothing without consciousness. The Universe seems to have the inbuilt goal or destiny to be self-realisable. Paul Davies has made a similar point.
 
This is arguably related to Searle’s ideas on intentionality, because I think it’s what philosophical intentionality is all about – the mind’s ability to conjure up its own internal reality, which may or may not relate to the external reality we all inhabit. In fact, I’ve argued that evolution by natural selection is directly dependent on our ability to do this, simply because the external reality can kill us, in infinitely diverse ways.
 
Regarding Searle’s pre-occupation with intentionality, I would like to quote from another post, where I reference Searle’s book.
 
It’s not for nothing that Searle claims ‘the problem of intentionality is as great as the problem of consciousness’ – I would contend they are manifestations of the same underlying phenomena – as though one is passive and the other active. Searle wrote his book, Mind, in part, to offer explanations for these phenomena (although he added the caveat that he had only scratched the surface).
 
I argued in the same post that intentionality is really imagination, which allows us to mentally time-travel, without which, we wouldn’t be able to reconstruct the past or anticipate a future, both of which are essential for day-to-day interactions, not to mention, survival.
 
Searle would argue that intentionality is something that separates us from AI, and I would argue the same for imagination, which allows me to segue into his Chinese room thought experiment.
 
Many would argue that it’s past its use-by-date, and I even came across someone recently, calling it the ‘Chinese room fallacy’. On the other hand, with the rise of LLMs like ChatGPT, I’d say it’s prescient. Basically, Searle believed very strongly – some might say to the point of arrogance – that ‘the brain is not a computer and the mind is not software’, meaning it doesn’t run on algorithms, and I would agree. It doesn’t help that we use the word ‘language’ when talking about both computers and humans.
 
More specifically, the whole point of his Chinese room argument is that a person could answer questions addressed in Chinese and respond in Chinese (basically, inputs and outputs) without ever understanding the Chinese language, simply by blindly following a set of rules (algorithms) and manipulating symbols accordingly. Searle argued that this is basically what all computers do. The point is that it would give the impression that the person in the room understood Chinese, similarly to the way some people believe that a computer understands something the same way a human does. And this is what we’ve found with ChatGPT.
 
I’ve recently been watching a podcast series by Lex Fridman where he interviews some very clever people, including a series with mathematician, logician and philosopher, Joel David Hamkins (John Cardinal O'Hara Professor of Logic at the University of Notre Dame). I mention him, because in one of the podcasts he remarks how he finds AI not at all helpful in exploring mathematics; specifically, ChatGPT. Now, I’m not at all surprised, but maybe there are other AI tools that are specifically designed to help mathematicians. For example, mathematicians now use computers to run myriad scenarios to formulate proofs that couldn’t be achieved otherwise. But it still doesn’t mean that the computer understands what it’s doing.
 
In the Philosophy Now interview, Searle talks about language and ‘social reality’, which I’ve barely touched on, yet they are obviously related. To quote from the interview, out of context:
 
On the account that I give, social reality is a matter of what people think, and what they think is a matter of how they talk to each other, and relate to each other. So you can’t have a social reality without a language, not a human social reality without a language.
 
What he doesn’t say, at least not in this interview, is that we all think in a language, which we learn from our milieu at an extremely early age, suggesting we are ‘hardwired’ genetically to do this. Without language, our ability to grasp and manipulate abstract concepts, which is arguably a unique human capability, would not be possible. Basically, I’m arguing that language for humans goes well beyond just an ability to communicate desires and wants, though that was likely its origin.
 
In the same passage of the interview, he explains how we follow specific social protocols (though he doesn’t use that word), giving the interview itself as an example. They both know what social rules they need to follow in that particular environment. The thing is that I came across this idea when I studied social psychology and they are called ‘scripts’, which in turn, are based on ‘schema’, and these are culturally dependent. In other words, our actions and our responses, be they verbal, written or behavioural, are largely governed by social norms that we have delegated to our subconscious.
 
That maybe an oversimplification, and not doing him justice, so I recommend you read the interview for yourself.
 
Humans are not the only social animal, but we have created a cultural evolution that has overtaken our biological evolution, giving rise to the term, ‘meme’, coined by Richard Dawkins and elaborated on by others; most notably, Susan Blackmore, which I’ve discussed elsewhere. But integral to that cultural evolution is language, because, even without written script, it allows us to accumulate memories across generations in a way that no other species can, which is why we have civilisations.
 
Searle argued that he wasn’t a physicalist (or materialist), which made him clash with David Dennett, but also not a (Cartesian) dualist, which some might argue is the only alternative. Searle acknowledges that consciousness has a causal relationship with the neurons in our brain. To quote:
 
The brain is made up of all these neurons and the individual neurons…  But what happens is that neurons, through causal interactions – causal interactions, not just formal, symbolic interactions but actual causal relationships with actual neurons firing and synapses operating – cause a higher level feature of the system, namely, consciousness and intentionality.
 
I find this similar to Douglas Hoffstadter’s idea of a ‘strange loop’, which is that the causal loop goes both ways, and this relates to free will, or what someone called ‘causal consciousness’, which I claim, is related to imagination. I quote Philip Ball from his tome, The Book of Minds:
 
When we make a choice, we aren’t selecting between various possible futures, but between various imagined futures, as represented in the mind’s internal model of the world… (emphasis in the original)
 
Searle spends an entire chapter on free will in his book, Mind. I leave you with his conclusion, which might be a good place to wrap this up:
 
Even after we have resolved the most fundamental questions addressed in this book, questions such as, What is the nature of the mind? How does it relate to the rest of the physical world? How can there be such a thing as mental causation? And how can our minds have intentionality? There is still the question of whether or not we really do have freedom.

Godel and Wittgenstein; same goal, different approach

 The current issue of Philosophy Now (Issue 169, Aug/Sep 2025) has as its theme, The Sources of Knowledge Issue, with a clever graphic on the cover depicting bottles of ‘sauces’ of 4 famous philosophers in this area: Thomas Kuhn, Karl Popper, Kurt Godel and Edmund Gettier. The last one is possibly not as famous as the other 3, and I’m surprised they didn’t include Ludwig Wittgenstein, though there is at least one article featuring him inside.
 
I’ve already written a letter to the Editor over one article Challenging the Objectivity of Science by Sina Mirzaye Shirkoohi, who is a ‘PhD Candidate at the Faculty of Administrative Sciences of the University Laval in Quebec City’; and which I may feature in a future post if it gets published.
 
But this post is based on an article titled Godel, Wittgenstein & the Limits of Knowledge by Michael D McGranahan, who has a ‘BS in Geology from San Diego State and an MS in Geophysics from Stanford, with 10 years [experience] in oil and gas exploration before making a career change’, without specifying what that career change is. ‘He is a lifelong student of science, philosophy and history.’ So, on the face of it, we may have a bit in common, because I’ve also worked in oil and gas, though in a non-technical role and I have no qualifications in anything. I’ve also had a lifelong interest in science and more recently, philosophy, but I’m unsure I would call myself a student, except of the autodidactic kind, and certainly not of history. I’m probably best described as a dilettante.
 
That’s a long runup, but I like to give people their due credentials, especially when I have them at hand. McGranahan, in his own words, ‘wants to explore the convergence of Godel and Wittgenstein on the limits of knowledge’, whereas I prefer to point out the distinctions. I should say up front that I’m hardly a scholar on Wittgenstein, though I feel I’m familiar enough with his seminal ideas regarding the role of language in epistemology. It should also be pointed out that Wittgenstein was one of the most influential philosophers of the 20th Century, especially in academia.
 
I will start with a quote cited by McGranahan: “The limits of my language mean the limits of my world.”
 
I once wrote a rather pretentious list titled, My philosophy in 24 dot points, where I paraphrase Wittgenstein: We think and conceptualise in a language. Axiomatically, this limits what we can conceive and think about. This is not exactly the same as the quote given above, and it has a subtly different emphasis. In effect, I think Wittgenstein has it back-to-front, based solely on his statement, obviously out-of-context, so I might be misrepresenting him, but I think it’s the limits of our knowledge of the world, that determines the limits of our language, rather than the other way round.
 
As I pointed out in my last post, we are continually creating new language to assimilate new knowledge. So, when I say, ‘this limits what we can conceive and think about’, it’s obvious that different cultures living in different environments will develop concepts that aren’t necessarily compatible with each other and this will be reflected in their respective languages. It’s one of the reasons all languages adopt new words from other languages when people from different cultures interact.
 
Humans are unique in that we think in a language. In fact, it’s not too much of a stretch to analogise it with software, remembering software is a concept that didn’t come into common parlance until after Wittgenstein died in 1951 (though Turing died in 1954).
 
To extend that metaphor, language becomes our ‘operating language’ for ‘thinking’, and note that it happens early in one’s childhood, well before we develop an ability to comprehend complex and abstract concepts. Just on that, arguably our exposure to stories is our first encounter with abstract concepts, if by abstract we mean entities that only exist in one’s mind.
 
I have a particular view, that as far as I know, is not shared with anyone else, which is that we have a unique ability to nest concepts within concepts ad infinitum, which allows us to create mental ‘black boxes’ in our thinking. To give an example, all the sentences I’m currently writing are made of distinct words, yet each sentence has a meaning that transcends the meaning of the individual words. Then, of course, the accumulation of sentences hopefully provides a cogent argument that you can follow. The same happens in a story which is arguably even more amazing, given a novel (like Elvene) contains close to 100k words, and will take up 8hrs of your life, but probably over 2 or 3 days. So we maintain mental continuity despite breaks and interruptions.
 
Wittgenstein once made the same point (regarding words and sentences), so that specific example is not original. Where my view differs is that I contend it also reflects our understanding of the physical world, which comprises entities within entities that have different physical representations at different levels. The example I like to give is a human body made up of individual cells, which themselves contain strands of DNA that provide the code for the construction and functioning of an individual. From memory, Douglas Hoffstadter made a similar point in Godel Escher Bach, so maybe not an original idea after all.
 
Time to talk about Godel. I’m not a logician, but I don’t believe you need to be to appreciate the far-reaching consequences of his groundbreaking theorem. In fact, as McGranahan points out, there are 2 theorems: Godel’s First Incompleteness Theorem and his Second Incompleteness Theorem. And it’s best to quote McGranahan directly:
 
Godel’s First Incompleteness Theorem proves mathematically that any consistent formal mathematical system within which a certain amount of elementary arithmetic can be carried out, is incomplete – meaning, there are one or more true statements that can be made in the language of the system which can neither be proved nor disproved in the system.
 
He then states the logical conclusion of this proof:
 
This finding leads to two alternatives: Alternative #1: If a set of axioms is consistent, then it is incomplete. Alternative #2: In a consistent system, not every statement can be proved in the language of that system.
 
Godel’s Second Incompleteness Theorem is simply this: No set of axioms can prove its own consistency.
 
It’s Alternative #2 that goes to the nub of the theorem: there are and always will be mathematical ‘truths’ that can’t be proved ‘true’ using the axioms of that system. Godel said himself that such truths (true statements) might be proved by expanding the system with new axioms. In other words, you may need to discover new mathematics to uncover new proofs, and this is what we’ve found in practice, and why some conjectures take so long to prove – like hundreds of years. The implication behind this is that our search for mathematical truths is neverending, meaning that mathematics is a neverending endeavour.
 
As McGranahan succinctly puts it: So knowing something is true, and proving it, are two different things.
 
This has led Roger Penrose to argue that Godel’s Theorems demonstrate the distinction between the human mind and a computer. Because a human mind can intuit a ‘truth’ that a computer can’t prove with logic. In a sense, he’s right, which is why we have conjectures like the ones I mentioned in my last post relating to prime numbers – the twin prime conjecture, the Goldbach conjecture and Riemann’s famous hypothesis. However, they also demonstrate the relationship between Godel’s Theorem and Turing’s famous Halting Problem, which Gregory Chaitin argues are really 2 manifestations of the same problem.
 
With each of those conjectures, you can create an algorithm to find all the solutions on a computer, but you can’t run the computer to infinity, so unless it ‘stops’, you don’t know if they’re true or not. The irony is that (for each conjecture): if it stops, it’s false and if it’s true, it never stops so it’s unknown. I covered this in another post where I argued that there is a relationship between infinity and the unknowable. The obvious connection here, that no one remarks on, is that Godel’s theorems only work because mathematics is infinite. If it was finite, it would be 'complete'. I came to an understanding of Godel’s Theorem through Turing’s Halting Problem, because it was easier to understand. A machine is unable to determine if a mathematical ‘truth’ is true or not through logic alone.
 
According to McGranahan, Wittgenstein said that “Tautology and contradiction are without sense.” He then said, “Tautology and contradiction are, however, nonsensical.” This implies that ‘without sense’ and ‘nonsensical’ have different meanings, “which illustrates the very language problem of which we speak” (McGranahan using Wittgenstein’s own language style to make his point). According to McGranahan, Wittgenstein then concluded: “that mathematics (if tautology and contradiction will be allowed to stand for mathematics), is nonsense.” (Parentheses in the original)
 
According to McGranahan, “…because in his logic, mathematical formulae are not bipolar (true or false) and hence cannot form pictures and elements and objects [which is how Wittgenstein defines language], and thus cannot describe actual states of affairs, and therefore, cannot describe the world.”
 
I feel that McGranahan doesn’t really resolve this, except to say: “There would seem to be a conflict… Who is right?” I actually think that if anyone is wrong, it’s Wittgenstein, though I admit a personal prejudice, in as much as I don’t think language defines the world.
 
On the other hand, everything we’ve learned about the world since the scientific revolution has come to us through mathematics, not language, and that was just as true in Wittgenstein’s time as it is now; after all, he lived through the 2 great scientific revolutions of quantum mechanics and relativity theory, both dependent on mathematics only discovered after Newton’s revolution.
 
The limits of our knowledge of the physical world are determined by the limits of our knowledge of mathematics (known as physics). And our language, while it ‘axiomatically limits what we can conceive and think about’, can also be (and continually is) expanded to adopt new concepts.

Reality, metaphysics, infinity

 This post arose from 3 articles I read in as many days: 2 on the same specific topic; and 1 on an apparently unrelated topic. I’ll start with the last one first.
 
I’m a regular reader of Raymond Tallis’s column in Philosophy Now, called Tallis in Wonderland, and I even had correspondence with him on one occasion, where he was very generous and friendly, despite disagreements. In the latest issue of Philosophy Now (No 169, Aug/Sep 2025), the title of his 2-page essay is Pharmaco-Metaphysics? Under which it’s stated that he ‘argues against acidic assertions, and doubts DMT assertions.’ Regarding the last point, it should be pointed out that Tallis’s background is in neuroscience.
 
By way of introduction, he points out that he’s never had firsthand experience of psychedelic drugs, but admits to his drug-of-choice being Pino Grigio. He references a quote by William Blake in The Marriage of Heaven and Hell: “If the doors of perception were cleaned, then everything would appear to man as it is, Infinite.” I include this reference, albeit out-of-context, because it has an indirect connection to the other topic I alluded to earlier.
 
Just on the subject of drugs creating alternate realities, which Tallis goes into in more detail than I want to discuss here, he makes the point that the participant knows that there is a reality from which they’ve become adrift; as if they’re in a boat that has slipped its moorings, which has neither a rudder nor oars (my analogy, not Tallis’s). I immediately thought that this is exactly what happens when I dream, which is literally every night, and usually multiple times.
 
Tallis is very good at skewering arguments by extremely bright people by making a direct reference to an ordinary everyday activity that they, and the rest of us, would partake in. I will illustrate with examples, starting with the psychedelic ‘trip’ apparently creating a reality that is more ‘real’ than the one inhabited without the drug.
 
The trip takes place in an unchanged reality. Moreover, the drug has been synthesised, tested, quality-controlled, packaged, and transported in that world, and the facts about its properties have been discovered and broadcast by individuals in the grip of everyday life. It is ordinary people usually in ordinary states of mind in the ordinary world who experiment with the psychedelics that target 5HT2A receptors.
 
He's pointing out an inherent inconsistency, if not outright contradiction (contradictoriness is the term he uses), that the production and delivery of the drug takes place in a world that the recipient’s mind wants to escape from.
 
And the point relevant to the topic of this essay: It does not seem justified, therefore, to blithely regard mind-altering drugs as opening metaphysical peepholes on to fundamental reality; as heuristic devices enabling us to discover the true nature of the world. (my emphasis)
 
To give another example of philosophical contradictoriness (I’m starting to like this term), he references Berkeley:
 
Think, for instance of those who, holding a seemingly solid copy of A Treatise Concerning the Principle of Human Knowledge (1710), accept George Berkeley’s claim [made in the book] that entities exist only insofar as they are perceived. They nevertheless expect the book to be still there when they enter a room where it is stored.
 
This, of course, is similar to Donald Hoffman’s thesis, but that’s too much of a detour.
 
My favourite example that he gives, is based on a problem that I’ve had with Kant ever since I first encountered Kant.
 
[To hold] Immanuel Kant’s view that ‘material objects’ located in space and time in the way we perceive them to be, are in fact constructs of the mind – then travel by train to give a lecture on this topic at an agreed place and time. Or yet others who (to take a well-worn example) deny the reality of time, but are still confident that they had their breakfast before their lunch.
 
He then makes a point I’ve made myself, albeit in a different context.
 
More importantly, could you co-habit in the transformed reality with those to whom you are closest – those who accept without question as central to your everyday life, and who return the compliment of taking you for granted?
 
To me, all these examples differentiate a dreaming state from our real-life state, and his last point is the criterion I’ve always given that determines the difference. Even though we often meet people in our dreams with whom we have close relationships, those encounters are never shared.
 
Tallis makes a similar point:
 
Radically revisionary views, if they are to be embraced sincerely, have to be shared with others in something that goes deeper than a report from (someone else’s) experience or a philosophical text.
 
This is why I claim that God can only ever be a subjective experience that can’t be shared, because it too fits into this category.
 
I recently got involved in a discussion on Facebook in a philosophical group, about Wittgenstein’s claim that language determines the limits of what we can know, which I argue is back-to-front. We are forever creating new language for new experiences and discoveries, which is why experts develop their own lexicons, not because they want to isolate other people (though some may), but because they deal with subject-matter the rest of us don’t encounter.
 
I still haven’t mentioned the other 2 articles I read – one in New Scientist and one in Scientific American – and they both deal with infinity. Specifically, they deal with a ‘movement’ (for want of a better term) within the mathematical community to effectively get rid of infinity. I’ve discussed this before with specific reference to UNSW mathematician, Norman Wildberger. Wildberger recently gained attention by making an important breakthrough (jointly with Dean Rubine using Catalan numbers). However, for reasons given below, I have issues with his position on infinity.
 
The thing is that infinity doesn’t exist in the physical world, or if it does, it’s impossible for us to observe, virtually by definition. However, in mathematics, I’d contend that it’s impossible to avoid. Primes are called the atoms of arithmetic, and going back to Euclid (325-265BC), he proved that there are an infinite number of primes. The thing is that there are 3 outstanding conjectures involving primes: the Goldbach conjecture; the twin prime conjecture; and the Riemann Hypothesis (which is the most famous unsolved problem in mathematics at the time of writing). And they all involve infinities. If infinities are no longer ‘allowed’, does that mean that all these conjectures are ‘solved’ or does it mean, they will ‘never be solved’?
                                                                                                                    
One of the contentions raised (including by Wildberger) is that infinity has no place in computations – specifically, computations by computers. Wildberger effectively argues that mathematics that can’t be computed is not mathematics (which rules out a lot of mathematics). On the other hand, you have Gregory Chaitin who points out that there are infinitely more incomputable Real numbers than computable Real numbers. I would have thought that this had been settled, since Cantor discovered that you can have countable infinite numbers and uncountable infinite numbers; the latter being infinitely larger than the former.
 
Just today I watched a video by Curt Jaimungal interviewing Chiara Marletto on ‘Constructor Theory’, which to my limited understanding based on this extract from a larger conversation, seems to be premised on the idea that everything in the Universe can be understood if it’s run on a quantum computer. As far as I can tell, she’s not saying it is a computer simulation, but she seems to emulate Stephen Wolfram’s philosophical position that it’s ‘computation all the way down’. Both of these people know a great deal more than me, but I wonder how they deal with chaos theory, which seems to drive the entire universe at multiple levels and can’t be computed due to a dependency on infinitesimal initial conditions. It’s why the weather can’t be forecast accurately beyond 10 days (because it can’t be calculated, no matter how complex the computer modelling) and why every coin-toss is independent of its predecessor (unless you rig it).
 
Note the use of the word, ‘infinitesimal’. I argue that chaos theory is the one phenomenon where infinity meets the real world. I agree with John Polkinghorne that it allows the perfect mechanism for God to intervene in the physical world, even though I don’t believe in an interventionist God (refer Marcus du Sautoy, What We Cannot Know).
 
I think the desire to get rid of infinity is rooted in an unstated philosophical position that the only things that can exist are the things we can know. This doesn’t mean that we currently know everything – I don’t think any mathematician or physicist believes that – but that everything is potentially knowable. I have long disagreed. And this is arguably the distinction between physics and metaphysics. I will take the definition attributed to Plato: ‘That which holds that what exists lies beyond experience.’ In modern science, if not modern philosophy, there is a tendency to discount metaphysics, because, by definition, it exists beyond what we experience in the real world. You can see an allusion here to my earlier discussion on Tallis’s essay, where he juxtaposes reality as we experience it with psychedelic experiences that purportedly provide a window into an alternate reality, where ‘everything would appear to man as it is, Infinite’. Where infinity represents everything we can’t know in the world we inhabit.
 
The thing is that I see mathematics as the only evidence of metaphysics; the only connection our minds have between a metaphysical world that transcends the Universe, and the physical universe we inhabit and share with innumerable other sentient creatures, albeit on a grain of sand on an endless beach, the horizon of which we’re yet to discern.
 
So I see this transcendental, metaphysical world of endless possible dimensions as the perfect home for infinity. And without mathematics, we would have no evidence, let alone a proof, that infinity even exists.

The role of the arts. Why did it evolve? Will AI kill it?

 As I mentioned in an earlier post this month, I’m currently reading Brian Greene’s book, Until the End of Time; Mind, Matter; and Our Search for Meaning in an Evolving Universe, which covers just about everything from cosmology to evolution to consciousness, free will, mythology, religion and creativity. He spends a considerable amount of time on storytelling, compared to other art forms, partly because it allows an easy segue from language to mythology to religion.
 
One of his points of extended discussion was in trying to answer the question: why did our propensity for the arts evolve, when it has no obvious survival value? He cites people like Steven Pinker, Brian Boyd (whom I discuss at length in another post) and even Darwin, among others. I won’t elaborate on these, partly due to space, and partly because I want to put forward my own perspective, as someone who actually indulges in an artistic activity, and who could see clearly how I inherited artistic genes from one side of my family (my mother’s side). No one showed the slightest inclination towards artistic endeavour on my father’s side (including my sister). But they all excelled in sport (including my sister), and I was rubbish at sport. One can see how sporting prowess could be a side-benefit to physical survival skills like hunting, but also achieving success in combat, which humans have a propensity for, going back to antiquity.
 
Yet our artistic skills are evident going back at least 30-40,000 years, in the form of cave-art, and one can imagine that other art forms like music and storytelling have been active for a similar period. My own view is that it’s sexual selection, which Greene discusses at length, citing Darwin among others, as well as detractors, like Pinker. The thing is that other species also show sexual selection, especially among birds, which I’ve discussed before a couple of times. The best known example is the peacock’s tail, but I suspect that birdsong also plays a role, not to mention the bower bird and the lyre bird. The lyre bird is an interesting one, because they too have an extravagant tail (I’m talking about the male of the species) which surely would be a hindrance to survival, and they perform a dance and are extraordinary mimics. And the only reason one can think that this might have evolutionary value at all is because the sole purpose of those specific attributes is to attract a mate.
 
And one can see how this is analogous to behaviour in humans, where it is the male who tends to attract females with their talents in music, in particular. As Greene points out, along with others, artistic attributes are a by-product of our formidable brains, but I think these talents would be useless if we hadn’t evolved in unison a particular liking for the product of these endeavours (also discussed by Greene), which we see even in the modern world. I’m talking about the fact that music and stories both seem to be essential sources of entertainment, evident in the success of streaming services, not to mention a rich history in literature, theatre, ballet and more recently, cinema.
 
I’ve written before that there are 2 distinct forms of cognitive ability: creative and analytical; and there is neurological evidence to support this. The point is that having an analytical brain is just as important as having a creative one, otherwise scientific theories and engineering feats, for which humans seem uniquely equipped to provide, would never have happened, even going back to ancient artefacts like Stonehenge and both the Egyptian and Mayan pyramids. Note that these all happened on different continents.
 
But there are times when the analytical and creative seem to have a synergistic effect, and this is particularly evident when it comes to scientific breakthroughs – a point, unsurprisingly, not lost on Greene, who cites Einstein’s groundbreaking discoveries in relativity theory as a case-in-point.
 
One point that Greene doesn’t make is that there has been a cultural evolution that has effectively overtaken biological evolution in humans, and only in humans I would suggest. And this has been a direct consequence of our formidable brains and everything that goes along with that, but especially language.
 
I’ve made the point before that our special skill – our superpower, if you will – is the ability to nest concepts within concepts, which we do with everything, not just language, but it would have started with language, one would think. And this is significant because we all think in a language, including the ability to manipulate abstract concepts in our minds that don’t even exist in the real world. And no where is this more apparent than in the art of storytelling, where we create worlds that only exist in the imagination of someone’s mind.
 
But this cultural evolution has created civilisations and all that they entail, and survival of the fittest has nothing to do with eking out an existence in some hostile wilderness environment. These days, virtually everyone who is reading this has no idea where their food comes from. However, success is measured by different parameters than the ability to produce food, even though food production is essential. These days success is measured by one’s ability to earn money and activities that require brain-power have a higher status and higher reward than so-called low-skilled jobs. In fact, in Australia, there is a shortage of trades because, for the last 2 generations at least, the emphasis, vocationally, has been in getting kids into university courses, when it’s not necessarily the best fit for the child. This is why the professional class (including myself) are often called ‘elitist’ in the culture wars and being a tradie is sometimes seen as a stigma, even though our society is just as dependent on them as they are on professionals. I know, because I’ve spent a working lifetime in a specific environment where you need both: engineering/construction.
 
Like all my posts, I’ve gone off-track but it’s all relevant. Like Greene, I can’t be sure how or why evolution in humans was propelled, if not hi-jacked, by art, but art in all its forms is part of the human condition. A life without music, stories and visual art – often in combination – is unimaginable.
 
And this brings me to the last question in my heading. It so happens that while I was reading about this in Greene’s thought-provoking book, I was also listening to a programme on ABC Classic (an Australian radio station) called Legends, which is weekly and where the presenter, Mairi Nicolson, talks about a legend in the classical music world for an hour, providing details about their life as well as broadcasting examples of their work. In this case, she had the legend in the studio (a rare occurrence), who was Anna Goldsworthy. To quote from Wikipedia: Anna Louise Goldsworthy is an Australian classical pianist, writer, academic, playwright, and librettist, known for her 2009 memoir Piano Lessons.

But the reason I bring this up is because Anna mentioned that she attended a panel discussion on the role of AI in the arts. Anna’s own position is that she sees a role for AI, but in doing the things that humans find boring, which is what we are already seeing in manufacturing. In fact, I’ve witnessed this first-hand. Someone on the panel made the point that AI would effectively democratise art (my term, based on what I gleaned from Anna’s recall) in the sense that anyone would be able to produce a work of art and it would cease to be seen as elitist as it is now. He obviously saw this as a good thing, but I suspect many in the audience, including Anna, would have been somewhat unimpressed if not alarmed. Apparently, someone on the panel challenged that perspective but Anna seemed to think the discussion had somehow veered into a particularly dissonant aberration of the culture wars.
 
I’m one of those who would be alarmed by such a development, because it’s the ultimate portrayal of art as a consumer product, similar to the way we now perceive food. And like food, it would mean that its consumption would be completely disconnected from its production.
 
What worries me is that the person on the panel making this announcement (remember, I’m reporting this second-hand) apparently had no appreciation of the creative process and its importance in a functioning human society going back tens of thousands of years.
 
I like to quote from one of the world’s most successful and best known artists, Paul McCartney, in a talk he gave to schoolchildren (don’t know where):
 
“I don't know how to do this. You would think I do, but it's not one of these things you ever know how to do.” (my emphasis)
 
And that’s the thing: creative people can’t explain the creative process to people who have never experienced it. It feels like we have made contact with some ethereal realm. On another post, I cite Douglas Hofstadter (from his famous Pulitzer-prize winning tome, Godel, Escher, Bach: An Eternal Golden Braid) quoting Escher:
 
"While drawing I sometimes feel as if I were a spiritualist medium, controlled by the creatures I am conjuring up."
 
Many people writing a story can identify with this, including myself. But one suspects that this also happens to people exploring the abstract world of mathematics. Humans have developed a sense that there is more to the world than what we see and feel and touch, which we attempt to reveal in all art forms, and this, in turn, has led to religion. Of course, Greene spends another entire chapter on that subject, and he also recognises the connection between mind, art and the seeking of meaning beyond a mortal existence.