The infinite monkey theorem and the anthropic principle

 I was originally going to write this as an addendum to my not-so-recent post, The problem with physics, but it became obvious that it deserved a post of its own.
 
It so happens that Sabine Hossenfelder has posted a video relevant to this topic since I published that post. She cites a paper by some renowned physicists, including Lawrence Krauss, that claims a theory of everything (TOE) is impossible. Not surprisingly, Godel’s Incompleteness Theorem for mathematics forms part of their argument. In fact, the title of their paper is Quantum gravity cannot be both consistent and complete, which is a direct reference to Godel. This leads to a discussion by Sabine about what constitutes ‘truth’ in physics and the relationship between mathematical models, reality and experiments. Curiously, Australian-American, world-renowned mathematician, Terence Tao, has a similar discussion in a podcast with Lex Fridman (excellent series, btw).
 
Tao makes the point that there are 3 aspects to this, which are reality, our perception of it, and the mathematical models, and they have been converging over centuries without ever quite meeting up in a final TOE. Tao comes across as very humble, virtually egoless, yet he thinks string theory is 'out of fashion', which he has worked on, it should be pointed out. Tao self-describes himself as a ‘fox’, not a ‘hedgehog’, meaning he has diverse interests in maths, and looks for connections between various fields. A hedgehog is someone who becomes deeply knowledgeable in one field, and he has worked with such people. Tao is known for his collaborations.
 
But his 3 different but converging perspectives is consistent with my Kantian view that we may never know the thing-in-itself, only our perception of it, while such perceptions are enhanced by our mathematical interpretations. We use our mathematical models as additional, complementary tools to the physical tools, such as the LHC and the James Webb telescope.
 
Tao gives the example of the Earth appearing flat to all intents and purposes, but even the ancient Greeks were able to work out a distance to the moon orbiting us, based on observations (I don’t know the details). Over time, our mathematical theories tempered by observation, have given us a more accurate picture of the entire observable universe, which is extraordinary.
 
I’ve made the point that all our mathematical models have limitations, which makes me sceptical that a 'final' TOE will be possible, even before I’d heard of the paper that Sabine cited. But, while mathematics provides epistemological limits on what we can know, I also believe it provides ontological limits on what’s possible. The Universe obeys mathematical rules at every level we’ve observed it. The one possible exception being consciousness – I am sceptical we will ever find a mathematical model for consciousness, but that’s another topic.
 
Tao doesn’t mention the anthropic principle – at least in the videos I’ve watched – but he does at one point talk about the infinite monkey theorem, which is a real mathematical theorem and not just a thought experiment or a pop-culture meme. Basically, it says that if you have an infinite number of monkeys bashing away on typewriters they will eventually type out the complete works of Shakespeare, despite our intuitive belief that this should be impossible.
 
As Tao points out, the salient feature of this thought experiment is infinity. In his own words, ‘Infinity absolves a lot of sins’. In the real world, everything we’re aware of is finite, including the observable universe. We’ve no idea what’s beyond the horizon, and, if it’s infinite, then it may remain forever unknowable, as pointed out by Marcus du Sautoy in his excellent book, What We Cannot Know. Tao makes the point that there is a ‘finite’ limit where this extraordinary but not impossible task becomes a distinct possibility. And I would argue that this applies to the evolution of complex life, which eventually gave rise to us. An event that seems improbable, but becomes possible if the Universe is big and old enough, while remaining finite, not infinite. To me, this is another example of how mathematics determines the limits of what’s possible.

Tao has his own views on a TOE or a theory for quantum gravity, which is really what they’re talking about. I think it will require a Kuhnian revolution as I concluded in my second-to-last post, and like all resolutions, it will uncover further mysteries.

 

Sympathy and empathy; what’s the difference?

 This arose from an article I read in Philosophy Now (Issue 167, April/May 2025) by James R. Robinson, who developed his ideas while writing his MA thesis in the Netherlands. It prompted me to write a letter, which was published in the next issue (168, June/July 2025). It was given pole position, which in many periodicals would earn the appellation ‘letter of the week’ (or month or whatever). But I may be reading too much into it, because Philosophy Now group their letters by category, according to the topic they are addressing. Anyway, being first, is a first for me.
 
They made some minor edits, which I’ve kept. The gist of my argument is that there is a dependency between sympathy and empathy, where sympathy is observed in one’s behaviour, but it stems from an empathy for another person – the ability to put ourselves in their shoes. This is implied in an example (provided by Robinson) rather than stated explicitly.
 
 
In response to James R. Robinson’s ‘Empathy & Sympathy’ in Issue 167, I contend that empathy is essential to a moral philosophy, both in theory and practice. For example, it’s implicit in Confucius’s rule of reciprocity, “Don’t do to others what you wouldn’t want done to yourself” and Jesus’s Golden Rule, “Do unto others as you’d have them do unto you.” Empathy is a requisite for the implementation of either. And as both a reader and writer of fiction, I know that stories wouldn’t work without empathy. Indeed, one study revealed that reading fiction improves empathy. The tests used ‘letter box’ photos of eyes to assess the subject’s ability to read the emotion of the characters behind the eyes (New Scientist, 25 June 2008).

The dependency between empathy and sympathy is implicit in the examples Robinson provides, like the parent picking up another parent’s child from school out of empathy for the person making the request. In most of these cases there is also the implicit understanding that the favour would be returned if the boot was on the other foot. Having said that, many of us perform small favours for strangers, knowing that one day we could be the stranger.

Robinson also introduces another term, ‘passions’; but based on the examples he gives – like pain – I would call them ‘sensations’ or ‘sensory responses’. Even anger is invariably a response to something. Fiction can also create sensory responses (or passions) of all varieties (except maybe physical pain, hunger, or thirst) – which suggests empathy might play a role there as well. In other words, we can feel someone else’s emotional pain, not to mention anger, or resentment, even if the person we’re empathising with is fictional.

The opposite to compassion is surely cruelty. We have world leaders who indulge in cruelty quite openly, which suggests it’s not an impediment to success; but it also suggests that there’s a cultural element that allows it. Our ability to demonise an outgroup is the cause of most political iniquities we witness, and this would require the conscious denial of sympathy and therefore empathy, because ultimately, it requires treating them as less than human, or as not-one-of-us.

The problem with physics

 This title could be easily misconstrued, as it gives the impression that there is only one problem in physics and if we could solve that, everything would be resolved and there would be nothing left to understand or explain. Anyone familiar with this blog will know that I don’t believe that at all, so I need to unpack this before I even start.
 
And you might well ask: if I know there are a number of problems in physics, why didn’t I make that clear in the title? You see, I’ve embedded a question in the title that I want you to ask.
 
I’ve been watching a number of videos over a period of time, many of them on Curt Jaimungal’s channel, Theories of Everything, where he talks to a lot of people, much cleverer than me, some of whom have the wildest theories in science, and physics in particular. If one takes John Wheeler’s metaphor of an island of knowledge in an infinite sea of ignorance, they are all building theories on the shoreline of that island. I like to point out (as a personal ego-boost) that I came up with that metaphor before I knew Wheeler had beaten me to it.
 
To give just one example that seems totally ‘out there’, Emily Adlam proposes her ‘Sudoku universe’ where everything exists at once. She’s not alone, because it’s not dissimilar to Sabine Hossenfelder’s position, though she uses different arguments. Of course, both her and Sabine are far more knowledgeable on these topics than me, so while I disagree, I acknowledge I don’t have the chops to take them on in a proper debate. Another example is Claudia de Rahm, whom I’ve referenced before, who thinks that gravitons may have mass, which would seem to contradict the widely held belief that gravitational waves travel at the speed of light. She has discussions with Curt, that once again, are well above my level of knowledge on this topic. 

Another person he interviews is Avshalom Elitzur, who even makes statements I actually agree with. In this video, he argues that space-time is created when the wave function collapses. It’s a very unorthodox view but it’s consistent with mine and Freeman Dyson’s belief that QM (therefore the wave function) can only describe the future. However, he also has a radical idea that the ‘creation’ of space may be related to the creation of charge, because if the space is created between the particles, they repel, and if it’s created outside, they attract. I admit I have problems with this, even though it took Curt to clarify it. Richard Muller (whose book, NOW, I’ve read) also argues that space may be created along with time. Both of these ideas are consistent with the notion that the Big Bang is still in progress – both time and space are being created as the Universe expands.
 
So there are lots of problems, and the cleverest people on the planet, including many I haven’t mentioned like Roger Penrose and Sean Carroll, all have their own pet theories, all on the shoreline of Wheeler’s metaphorical island.
 
But the island metaphor provides a clue to why the problem exists, and that is that they are all just as philosophical as they are scientific. Sabine attempted to address this in 2 books she wrote: Lost in Math and Existential Physics; both of which I’ve read. But there are 2 levels to this problem when it comes to physics, which are effectively alluded to in the titles of her books. In other words, one level is philosophical and the next level is mathematical.
 
All of the people I mentioned above, along with others I haven’t mentioned, start with a philosophical position, even if they don’t use that term. And all physics theories are dependent on a mathematical model. There is also arguably a third level, which is experimental physics, and that inexorably determines whether the model, and hence the theory, is accurate.
 
But there is a catch: sometimes the experimental physics has proven the ‘theory’ correct, yet the philosophical implications are still open to debate. This is the case with quantum mechanics (QM), and has been for over a century. As Sabine pointed out in a paper she wrote, our dilemmas with QM haven’t really changed since Bohr’s and Einstein’s famous arguments over the Copenhagen interpretation, which are now almost a century old.
 
Some would argue that the most pertinent outstanding ‘problem’ in physics is the irreconcilability of gravity, or Einstein’s general theory of relativity (GR), and QM. Given the problems we have with dark matter and dark energy, which are unknown yet make up 95% of the Universe, I think we are ripe for another Kuhnian revolution in physics. And if that’s true, then we have no idea what it is.