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 edge of time

This is a contentious idea, despite the fact that we all believe we experience it all the time. Many physicists, including ones I admire, and whom I readily admit know a lot more than me (like Sabine Hossenfelder), believe that ‘now’ is an illusion; or (in the case of Paul Davies) that it requires a neurological explanation rather than a physical one. I will go further and claim there is an edge of time for the entire universe.
 
I made the point in a previous post that if you go on YouTube, you’ll find discussions with physicists who all have their own pet theories that are at odds with virtually everyone else, and to be honest, I can’t fault them, and I’m pleased that they’re willing to share their views.
 
Well, I’m not a physicist, but this is my particular heretical viewpoint that virtually no one else agrees with, with the additional caveat that they all have more expertise than me. They will tell you that I’m stuck in 19th Century physics, but I believe I can defend myself against that simple rebut.
 
During COVID lockdown in 2021, I did a series of online courses through New Scientist, including one on The Cosmos, where one of the lecturers was Chris Impey (Distinguished Professor, Department of Astronomy, University of Arizona) who made the point that the Universe has an ‘edge in time’, but not an edge in space. He might have used the word ‘boundary’ instead of ‘edge’, which would be more appropriate for space. In fact, it’s possible that space is infinite while time is finite, which means that the concept of spacetime might have limited application, but I’m getting ahead of myself.
 
The one other person I’ve read who might (partly) agree with me is Richard Muller, who cowrote a paper with Shaun Maguire, titled Now, and the Flow of Time, as well as a book, NOW; The Physics of Time, which I’ve read more than once. Basically, the edge of time on a cosmic scale is the edge of the Big Bang (which is still happening). What I’m saying is that there is a universal ‘Now’ for the entire universe, which is one of the most heretical ideas you can hold. According to modern physics, ‘Now’ is completely subjective and dependent on the observer – there is no objective Now, which is what I challenge.
 
There is a way in which this is correct, in that different observers in different parts of the Universe see completely different things (if they’re far enough apart) and would even see different horizons for the Universe. In fact, it’s possible that an observer who is over the horizon to us will see objects we can’t see, and of course, wouldn’t see us at all. This is because objects over the horizon are travelling away from us faster than the speed of light.
 
Because the speed of light is finite, the objects that we ‘observe’ millions or billions of light years away, are commensurately that much older than we are. And it follows from this logic, that if anyone could observe Earth from these same objects, they would see it equally old compared to what we see. This means that everyone sees a different now. This leads to the logical question: how could an objective ‘now’ exist? I like to invoke Kant that we cannot know the ‘thing-in-itself’, only our perception of it.
 
And I invoke Kant when I look at relativity theory, because it’s inherently an observer-dependent theory. I would contend that all physics theories are epistemic, meaning they deal with knowledge, rather than ontic, which is what is really there. Some argue that even space and time are epistemic, not ontic, but I disagree. The dimensions of space and time determine to a large extent what sort of universe we can live in. A point made by John Barrow in his book, The Constants of Nature.
 
In a not-so-recent post, I explained the famous pole-in-the-barn paradox, where 2 different observers see different things (in fact, measure different things) yet, in both cases, there is no clash between the pole and the barn (or in the example I describe, a spaceship and a tunnel). One of my conclusions is that it’s only the time that changes for the 2 observers, and not the space. Instead, they measure a different ‘length’ or ‘distance travelled’ by using their clocks as rulers. But it also implies that one of the observers is more ‘privileged’ than the other, which seems to contradict the equivalence principle. But I can make this claim because there is a reference frame for the entire universe, which is provided by the CMBR (cosmic microwave background radiation). This is not contentious, because we can even measure our velocity relative to it by using the Doppler effect, hence our velocity relative to the entire universe.
 
But there is another famous and simple experiment that provides evidence that there is an overall frame of reference for the Universe, which philosopher of science, Tim Maudlin, called ‘the most important experiment in physics’. If you were to go to the International Space Station and spin an object, it would be subject to the same inertial forces as it would on Earth. So what’s it spinning in reference to? The spaceship, its orbit around Earth, or the entire cosmos? I’d say, the entire universe, which is obviously not spinning itself, otherwise it would have a centre. Of course, Einstein knew this, and his answer was there is no absolute time or space but absolute spacetime.
 
I raised this earlier, because, if time is finite and space infinite, the concept of absolute spacetime breaks down, at least conceptually. But space doesn’t have to be infinite to have no boundary. In fact, it’s either open and infinite or closed and finite, albeit in 3 dimensions. To provide a relatable analogy, the Earth’s surface is finite and closed, but in 2 dimensions. Marcus du Sautoy made the point that, if the Universe is spatially infinite, we might never know.
 
The other point is that you could have clocks running at different rates dependent on where they are in the Universe, yet there could still be a universal Now. This is implicit in the famous twin paradox thought experiment. I like to point out that when the twins reunite they have lived different durations of time, yet agree where they are in time together. This means you can have a universal Now for the universe while disagreeing on its age; if you lived near a massive black hole, for instance.
 
In the same way observers can travel different distances to arrive at the same destination, they can travel different time intervals as well. In fact, they would agree they’ve travelled the exact same spacetime, which is why relativity theory argues you can only talk about spacetime combined rather than space and time separately. But I argue that it’s the clock that changes and not space, where the clock is the ruler for space.

The fly-in-the-ointment is simultaneity. According to relativity theory, simultaneity is completely dependent on the observer, but again, I invoke Kant. There could be an objective simultaneity that can’t be observed. I’ve written on this before, so I’ll keep it brief, but basically, you can have a ‘true’ simultaneity, if both the observer and the events are in the same frame of reference. And you can tell if you’re not, by using the Doppler effect. Basically, the Doppler effect tells you if the source of the signals (that are apparently simultaneous) are in the same frame of reference as you. If they’re not, then they’re not simultaneous, which infers there is an objective simultaneity. Whether this applies to the entire universe is another matter.

You may be familiar with this diagram.

 

 
I want to make a couple of points that no one else does. Firstly, everything outside the past light cone is unobservable (by definition), which means relativity theory can’t be applied (in practice), yet people do (in theory). As I said earlier, relativity is epistemic and all epistemic theories (or models) have limitations. In other words, I contend that there is an ontology outside the light cones that relativity theory can’t tell us anything about (I discuss this in more detail in a post appositely titled, The impossible thought experiment).
 
Secondly, the so-called ‘hypersurface’ is a fiction, or at best, a metaphor. Yet Brian Greene, to give one example, discusses it and graphically represents it as if it’s physically real. If ‘Now’ is the edge of the Big Bang, it suffuses the entire universe (even if it’s physically infinite), which means it’s impossible to visualise.
 
Let’s talk about another epistemic theory, quantum mechanics. In fact, the ontology of QM has been an open debate for more than a century. I recently watched a discussion between Matt (from PBS Space Time) and Mithuna Yoganathan (of Looking Glass Universe), which is excellent. It turns out they’re both from Melbourne, which is where I’m writing this. I figured Mithuna was Aussie, even though she’s based in London, but I didn’t pick Matt’s accent. I have to admit he sounds more Australian in his conversation with her. Towards the end of the video, they readily admit they get very speculative (meaning philosophical) but Mithuna provides compelling arguments for the multiple worlds interpretation (MWI) of QM. Personally, I argue that MWI doesn’t address the probabilities which is intrinsic to QM. Why are some worlds more probabilistic than others? If all outcomes happen in some universe somewhere, then they all have a probability of ONE in that universe. If there are an infinite number of universes then probabilities are nonsensical.
 
If you go to 37.10m of the video where Mithuna talks about the Schrodinger equation and the ‘2 rules’, I think she gets to the nub of the problem, and at 38.10 puts it into plain English. Basically, she says that there are either 2 rules for the Universe or you need to reject the ‘measurement’ or ‘collapse’ of the wave function, which means accepting MWI (the wave function continues in another universe), which she implies without saying. She says the 2 rules makes ‘the Copenhagen interpretation untenable’. I find this interesting, because I concluded many years ago that the Universe obeys 2 sets of rules.
 
My argument is that one set of rules, determined epistemically by the Schrodinger equation, describes the future and the other set of rules, which is classical physics and is determined by what we observe, describes the past.
 
A feature of QM, which separates it from classical physics, is entanglement and non-locality. Non-locality means it doesn’t strictly obey relativity theory, yet they remain compatible (because you can’t use entanglement to transmit information faster-than-light). In fact, Schrodinger himself said that “entanglement is the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.” In other words, it obeys different rules to classical physics, with or without ‘measurement’.
 
MWI effectively argues that superposition exists in reality, albeit in parallel universes, whereas I contend that it only exists in the future. The wave function describes all of these possibilities, and via the Born rule, gives them probabilities. But when we observe it, which axiomatically puts it in the past, there is only ONE and there is no longer any superposition.
 
All physicists agree that entanglement, in principle, can apply to objects on opposite sides of the Universe. In fact, Schrodinger’s equation, in principle, can describe a wave function for the entire universe, which is why I’ve half-jokingly called it God’s equation, and have it tattooed on my arm.
 
I contend (though, as far as I know, no one agrees with me) that entanglement across the entire universe only makes sense if there is a universal Now for the entire universe. A Now that separates QM future superpositions (described by the wave function in Schrodinger’s equation) from past ‘observables’ in classical physics.

 

Addendum: this is one of the best and most erudite descriptions I've come across on entanglement and non-locality. Note how I avoided the word, 'explanation'. 

Evil arises out of complacency

 I was going to post this on Facebook and still might, but I think my blog a more apposite home.

 
Evil arises out of complacency, which is why it oftentimes only becomes obvious in hindsight, especially by those who were involved. Also, anyone can commit evil, given the circumstances, despite what we tell ourselves. When it becomes a social norm, it’s the person who resists who becomes the exception. And that’s the key to it all – it becomes normalised and we rationalise it because the subject obviously deserves it, and the perpetrator is on the side of Right (with a capital R).
 
We are witnessing its emergence in various parts of the world right now: specifically, Ukraine, Gaza and America. In the case of Ukraine, the perpetrator is Russia, who is not on ‘our side’, so it’s easy to call out. But in the case of Gaza and America, the perpetrators are traditionally our allies, so there is a tendency to turn a blind eye, and certainly not to create waves. Israel has weaponised famine in a most iniquitous fashion, because they control the aid, and even the aid is used as a weapon and a coverup for genocide and ethnic cleansing, as called out by Francesca Albanese (United Nations Special Rapporteur on the Occupied Palestinian Territories).
 
In America, people are being ‘disappeared’ off the street, which is so unbelievable that the Administration has got away with it (this obviously doesn’t happen in the epitomised free world; you must have imagined it). In both of these cases, the actions have become normalised to the point that any negative response is but a murmur. You might ask: are these acts evil? Well, genocide is usually considered a war crime, but apparently not when Israel is the aggressor. Israel knows how to leverage the West’s collective guilty conscience for the pogroms of the 20th Century. And disappearing someone might not be considered evil until it happens to a family member – that may change your perspective.
 
At the very least, Netanyahu and Trump both have cruel streaks in their psyche (as does Putin), and both of them exploit the hate felt and expressed towards outsiders and both have normalised activities that not so long ago would have been considered morally reprehensible. History may judge things differently.

Addendum: I came across this, which I think is very relevant. Professor Lyndsey Stonebridge (Professor of Humanities and Human Rights at the University of Birmingham) talks about Hannah Arendt's observation that "superfluous people are a feature of authoritarian thinking. Once you've decided that some people's lives are not as important or as valuable as others, you are already walking into trouble." Arendt, of course, was a Jewish refugee from Germany who helped refugees in Paris before escaping to America, where she made her home and reputation.

 

 

 

 

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.