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.

 

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.

Writing and philosophy

 I’ve been watching a lot of YouTube videos of Alan Moore, who’s probably best known for his graphic novels, Watchmen and V for Vendetta, both of which were turned into movies. He also wrote a Batman graphic novel, The Killing Joke, which was turned into an R rated animated movie (due to Batman having sex with Batgirl) with Mark Hamill voicing the Joker. I’m unsure if it has any fidelity to Moore’s work, which was critically acclaimed, whereas the movie received mixed reviews. I haven’t read the graphic novel, so I can’t comment.
 
On the other hand, I read Watchmen and saw the movie, which I reviewed on this blog, and thought they were both very good. I also saw V for Vendetta, starring Natalie Portman and Hugo Weaving, without having read Moore’s original. Moore also wrote a novel, Jerusalem, which I haven’t read, but is referenced frequently by Robin Ince in a video I cite below.
 
All that aside, it’s hard to know where to start with Alan Moore’s philosophy on writing, but the 8 Alan Moore quotes video is as good a place as any if you want a quick overview. For a more elaborate dialogue, there is a 3-way interview, obviously done over a video link, between Moore and Brian Catling, hosted by Robin Ince, with the online YouTube channel, How to Academy. They start off talking about imagination, but get into philosophy when all 3 of them start questioning what reality is, or if there is an objective reality at all.
 
My views on this are well known, and it’s a side-issue in the context of writing or creating imaginary worlds. Nevertheless, had I been party to the discussion, I would have simply mentioned Kant, and how he distinguishes between the ‘thing-in-itself’ and our perception of it. Implicit in that concept is the belief that there is an independent reality to our internal model of it, which is mostly created by a visual representation, but other senses, like hearing, touch and smell, also play a role. This is actually important when one gets into a discussion on fiction, but I don’t want to get ahead of myself. I just wish to make the point that we know there is an external objective reality because it can kill you. Note that a dream can’t kill you, which is a fundamental distinction between reality and a dreamscape. I make this point because I think a story, which takes place in your imagination, is like a dreamscape; so that difference carries over into fiction.
 
And on the subject of life-and-death, Moore references something he’d read on how evolution selects for ‘survivability’ not ‘truth’, though he couldn’t remember the source or the authors. However, I can, because I wrote about that too. He’s obviously referring to the joint paper written by Donald Hoffman and Chetan Prakash called Objects of Consciousness (Frontiers of Psychology, 2014). This depends on what one means by ‘truth’. If you’re talking about mathematical truths then yes, it has little to do with survivability (our modern-day dependence on technical infrastructure notwithstanding). On the other hand, if you’re talking about the accuracy of the internal model in your mind matching the objective reality external to your body, then your survivability is very much dependent on it.
 
Speaking of mathematics, Ince mentions Bertrand Russell giving up on mathematics and embracing philosophy because he failed to find a foundation that ensured its truth (my wording interpretating his interpretation). Basically, that’s correct, but it was Godel who put the spanner in the works with his famous Incompleteness Theorem, which effectively tells us that there will always exist mathematical truths that can’t be proven true. In other words, he concretely demonstrated (proved, in fact) that there is a distinction between truth and proof in mathematics. Proofs rely on axioms and all axioms have limitations in what they can prove, so you need to keep finding new axioms, and this infers that mathematics is a neverending endeavour. So it’s not the end of mathematics as we know it, but the exact opposite.
 
All of this has nothing to do with writing per se, but since they raised these issues, I felt compelled to deal with them.
 
At the core of this part of their discussion, is the unstated tenet that fiction and non-fiction are distinct, even if the boundary sometimes becomes blurred. A lot of fiction, if not all, contains factual elements. I like to cite Ian Fleming’s James Bond novels containing details like the gun Bond used (a Walther PPK) and the Bentley he drove, which had an Amherst Villiers supercharger. Bizarrely, I remember these trivial facts from a teenage obsession with all things Bond.
 
And this allows me to segue into something that Moore says towards the end of this 3-way discussion, when he talks specifically about fantasy. He says it needs to be rooted in some form of reality (my words), otherwise the reader won’t be able to imagine it at all. I’ve made this point myself, and give the example of my own novel, Elvene, which contains numerous fantasy elements, including both creatures that don’t exist on our world and technology that’s yet to be invented, if ever.
 
I’ve written about imagination before, because I argue it’s essential to free will, which is not limited to humans, though others may disagree. Imagination is a form of time travel, into the past, but more significantly, into the future. Episodic memories and imagination use the same part of the brain (so we are told); but only humans seem to have the facility to time travel into realms that don’t exist anywhere else other than the imagination. And this is why storytelling is a uniquely human activity.
 
I mentioned earlier how we create an internal world that’s effectively a simulation of the external world we interact with. In fact, my entire philosophy is rooted in the idea that we each of us have an internal and external world, which is how I can separate religion from science, because one is completely internal and the other is an epistemology of the physical universe from the cosmic scale to the infinitesimal. Mathematics is a medium that bridges them, and contributes to the Kantian notion that our perception may never completely match the objective reality. Mathematics provides models that increase our understanding while never quite completing it. Godel’s incompleteness theorem (referenced earlier) effectively limits physics as well. Totally off-topic, but philosophically important.
 
Its relevance to storytelling is that it’s a visual medium even when there are no visuals presented, which is why I contend that if we didn’t dream, stories wouldn’t work. In response to a question, Moore pointed out that, because he worked on graphic novels, he had to think about the story visually. I’ve made the point before that the best thing I ever did for my own writing was to take some screenwriting courses, because one is forced to think visually and imagine the story being projected onto a screen. In a screenplay, you can only write down what is seen and heard. In other words, you can’t write what a character is thinking. On the other hand, you can write an entire novel from inside a character’s head, and usually more than one. But if you tell a story from a character’s POV (point-of-view) you axiomatically feel what they’re feeling and see what they’re witnessing. This is the whole secret to novel-writing. It’s intrinsically visual, because we automatically create images even if the writer doesn’t provide them. So my method is to provide cues, knowing that the reader will fill in the blanks. No one specifically mentions this in the video, so it’s my contribution.
 
Something else that Moore, Catling and Ince discuss is how writing something down effectively changes the way they think. This is something I can identify with, both in fiction and non-fiction, but fiction specifically. It’s hard to explain this if you haven’t experienced it, but they spend a lot of time on it, so it’s obviously significant to them. In fiction, there needs to be a spontaneity – I’ve often compared it to playing jazz, even though I’m not a musician. So most of the time, you don’t know what you’re going to write until it appears on the screen or on paper, depending which medium you’re using. Moore says it’s like it’s in your hands instead of your head, which is certainly not true. But the act of writing, as opposed to speaking, is a different process, at least for Moore, and also for me.
 
I remember many years ago (decades) when I told someone (a dentist, actually) that I was writing a book. He said he assumed that novelists must dictate it, because he couldn’t imagine someone writing down thousands upon thousands of words. At the time, I thought his suggestion just as weird as he thought mine to be. I suspect some writers do. Philip Adams (Australian broadcaster and columnist) once confessed that he dictated everything he wrote. In my professional life, I have written reports for lawyers in contractual disputes, both in Australia and the US, for which I’ve received the odd kudos. In one instance, someone I was working with was using a cassette-like dictaphone and insisted I do the same, believing it would save time. So I did, in spite of my better judgement, and it was just terrible. Based on that one example, you’d be forgiven for thinking that I had no talent or expertise in that role. Of course, I re-wrote the whole thing, and was never asked to do it again.
 
I originally became interested in Moore’s YouTube videos because he talked about how writing affects you as a person and can also affect the world. I think to be a good writer of fiction you need to know yourself very well, and I suspect that is what he meant without actually saying it. The paradox with this is that you are always creating characters who are not you. I’ve said many times that the best fiction you write is where you’re completely detached – in a Zen state – sometimes called ‘flow’. Virtuoso musicians and top sportspersons will often make the same admission.
 
I believe having an existential philosophical approach to life is an important aspect to my writing, because it requires an authenticity that’s hard to explain. To be true to your characters you need to leave yourself out of it. Virtually all writers, including Moore, talk about treating their characters like real people, and you need to extend that to your villains if you want them to be realistic and believable, not stereotypes. Moore talks about giving multiple dimensions to his characters, which I won’t go into. Not because I don’t agree, but because I don’t over-analyse it. Characters just come to me and reveal themselves as the story unfolds; the same as they do for the reader.
 
What I’ve learned from writing fiction (which I’d self-describe as sci-fi/fantasy) – as opposed to what I didn’t know – is that, at the end of the day (or story), it’s all about relationships. Not just intimate relationships, but relationships between family members, between colleagues, between protagonists and AI, and between protagonists and antagonists. This is the fundamental grist for all stories.
 
Philosophy is arguably more closely related to writing than any other artform: there is a crossover and interdependency; because fiction deals with issues relevant to living and being.

Time again

 This is a topic I’ve written about before, many times, but I’m returning to it on this occasion because of a video I watched by Curt Jaimungal, whom I can recommend. He’s smart and interviews people who are even smarter, and he has a particular penchant for interviewing people with unorthodox ideas, but with the knowledge to support them. He also has the good sense to let them do nearly all of the talking. He rarely interjects and when he does, it’s pertinent and tends to not interrupt the flow. I’ve sometimes been annoyed by interviewers cutting someone off when they were about to say something that I was interested in hearing. I could never accuse Curt of that.
 
In this case he’s interviewing Avshalom Elitzur, whom I’ve also referenced before. He’s a bit of an iconoclast – my favourite type of person, even if I disagree with them. If I’m to be fair, I’d have to include Donald Hoffman in that category, though I’ve been a harsh critic in the past. Having said that, I’ve noticed that Donald has changed his approach over the 8 or so years I’ve been following him. As I’ve said before, it’s important to follow the people you disagree with as well as those you agree with, especially when they have knowledge or expertise that you don’t.
 
Elitzur discusses three or more topics, all related to Einstein’s theories of relativity, but mostly the special theory. He starts off by calling out (my phrase) what he considers a fundamental problem that most physicists, if not all (his phraseology) ignore, which is that time is fundamentally different to space, because time changes in a way that space does not. What’s more we all experience this, with or without a scientific theory to explain it. He gives the example of how another country (say, Japan) still exists even though you don’t experience it (assuming you’re not Japanese). If you are in Japan, make it Australia. On the other hand, another time does not exist in the same way (be it past or present), yet many physicists talk about it as if it does. I discussed this in some depth, when I tackled Sabine Hoffenfelder’s book, Existential Physics; A Scientist’s Guide to Life’s Biggest Questions.
 
Elitzur raises this at both the start and towards the end of the video, because he thinks it’s distorting how physicists perceive the world. Specifically, Einstein’s block-universe, where all directions in time exist simultaneously in the same way that all directions in space exist all at once. He mentions that Penrose challenges this and so did Paul Davies once, but not now. In fact, I challenge Davies’ position in another post I wrote after reading his book, The Demon in the Machine. Elitzur makes the point that challenging this is considered naïve but he also makes another point much more dramatically. He says that for Einstein, the ‘future cut’ in time is ‘already there’ (10.50) and consequently said, ‘…has the same degree of reality as the present cut and the past cut. Are you okay with that?’ His exact words.
 
He recounts the famous letter that Einstein wrote to the family of a good friend who had just passed away, and only 4 weeks before Einstein himself passed away (I didn’t know that before Elitzur told me), from which we have this much quoted extract: ‘The past, present and future is only a stubbornly persistent illusion.’ Davies also used this quote in his abovementioned book.
 
I’m going to talk about last what Elitzur talked about early, if not quite first, which is the famous pole-in-the-barn thought experiment. Elitzur gives a good explanation, if you haven’t come across it before, but I’ll try because I think it’s key to understanding the inherent paradox of special relativity, and also providing an explanation that reconciles with our perception of reality.
 
It's to do with Lorenz-contraction, which is that, for an observer, an object travelling transversely to their field of vision (say horizontally) shortens in the direction of travel. This is one of those Alice and Bob paradoxes, not unlike the twin paradox. Let us assume that Alice is in a space ship who goes through a tunnel with doors at both ends, so that her ship fits snugly inside with no bits hanging out (like when both are stationary). And Bob operates the doors, so that they open when Alice arrives, close when she is inside and open to allow her to leave. From Bob’s perspective, Alice’s spaceship is shorter than the tunnel, so she fits inside, no problem. Also, and this is the key point (highlighted by Elitzur): according to Bob, both doors open and close together – there is no lag.
 
The paradox is resolved by relativity theory (and the associated mathematics), because, from Alice’s perspective, the doors don’t open together but sequentially. The first door opens and then closes after she’s passed through it, and the second door opens slightly later and remains open slightly longer so that the first door closes behind her before she leaves the tunnel. In other words, both doors are closed while she’s in the tunnel, but in such a way that they’re not closed at the same time, therefore her spaceship doesn’t hit either of them. This is a direct consequence of simultaneity being different for Alice. If you find that difficult to follow, watch the video
 
I have my own unorthodox way of resolving this, because, contrary to what everyone says, I think there is a preferred frame of reference, which is provided by ‘absolute spacetime’. You can even calculate the Earth’s velocity relative to the overall spacetime of the entire universe by measuring the Doppler shift of the CMBR (cosmic microwave background radiation). This is not contentious – Penrose and Davies both give good accounts of this. It’s also related to what Tim Maudlin called, the most important experiment in physics, which is Newton spinning a bucket of water and observing the concave surface of the water due to the centrifugal force, and then asking: what is it spinning in reference to? Answer: the entire universe.
 
You might notice that when someone describes or explains the famous twin paradox, they only ever talk about the time difference – they rarely, if ever, talk about the space contraction. Personally, I don’t think space contracts in reality, but time duration does. If you take an extreme example, you could hypothetically travel across the entire galaxy in your lifetime, which means, from your perspective, the distance travelled would be whole orders of magnitude shorter. This can be resolved if it’s the ruler measuring the distance that changes and not the distance. In this case, the clock acts as a ruler. Kip Thorne has commented on this without drawing any conclusions.
 
This same logic could be applied to the spaceship and the tunnel. For Alice, it appears shorter, but she’s the one ‘measuring’ it. If one extends this logic, then I would argue that there is a ‘true simultaneity’, experienced by Bob in this case, because he is in the same frame of reference as the tunnel and the doors. I need to point out that, as far as I know, no one else agrees with me, including Elitzur. However, it’s consistent with my thought experiment about traversing the galaxy: time contracts but space doesn't.
 
I’ve raised this before, but I believe that there is an independent reality to all observers, and this is consistent with Kant’s famous dictum that there is a ‘thing-in-itself’ that we may never perceive. In other words, relativity can only tell us about what we observe, which leaves open the possibility that there is a reality that one observer has a better perception of than another. It’s possible that while ‘time passed’ is observer-dependent, space is not, but only the observer’s perception of it.
 
This is also consistent with Elitzur’s overall thesis and core argument that space and time are different. It’s also consistent with the idea that there is a frame of reference for the entire universe, which I argue is what general relativity (GR) gives us. And in fact, we observe that local frames of reference can actually travel faster than light, which is why the observable universe has a horizon: there are parts of the Universe receding from us faster than light.
 
There is another aspect of this that Elitzur doesn’t bring up, and that is that there is an edge in time for the Universe, but no boundary in space. I find it curious that, if physicists bring this up at all, they tend to gloss over it and not provide a satisfactory resolution. You see, it conflicts with the idea, inherent in the block-universe model, that there is no ‘now’.
 
Curt introduces ‘now’ towards the end of the video, but only in reference to the ‘flow’ of time that we all experience. Again, I’m a heretic in that I believe there is a universal now for the entire universe.
 
And while I don’t think it explains entanglement and non-locality in QM, it’s consistent with it. Entanglement works across space and time independently of relativistic causality, without breaking the relativistic rule that you can’t send information faster than light.
 
As it happens, there is another video by Curt with Tim Maudlin, an American philosopher of science, whom Curt introduces as ‘bringing some sober reality to this realm of quantum confusion and mysticism.’ In particular, Maudlin gives an excellent exposition of Bell’s famous theorem, and debunks the claim that it questions whether there is ‘reality’. In other words, it’s often formulated as: you can accept non-locality or you can accept reality, but you can’t have both. Just to clarify, ‘locality’ means local phenomena that obey SR (special relativity) as I’ve discussed above.
 
Maudlin argues quite cogently that you only need 2 assumptions for Bell’s theorem to make sense and neither of them break reality. The main assumption is that there is ‘statistical independence’, which he explains by giving examples of medical controlled experiments (for example, to test if tobacco causes lung cancer). It just means that random really does mean random, which gives true independence.
 
The only other assumption is that we can have non-locality, which means you can have a connection or relationship between events that is not dependent on special relativity. Numerous experiments have proven this true.
 
Maudlin challenges Sabine’s contention that Bell’s Theorem can only be explained by ‘superdeterminism’, which is another name for Einstein’s block-universe, which started this whole discussion. Sabine is so convinced by superdeterminism, she has argued that one day everyone will agree with her. This of course has implications for free will and is central to Elitzur’s argument that the future does not exist in the same way as the present or even the past, which is fixed. And that’s his point. Sabine’s and most physicist’s view on all this is that what we experience must be an illusion: there is no now, no flow of time, and no free will.

Addendum 1: I came across another video by Curt with Jacob Barandes, that came out after I posted this. Jacob is a Harvard scientist, who has done a series of videos with Curt. It's relevance to this topic is that he talks about space-time in GR and how, unlike Newtonian physics, and even SR, you can't tell which direction time and space have. And this axiomatically creates problems when you try to quantumise it (to coin a term). I think the superposition of a gravitational field creates its own problems (not discussed). He then goes on to conjecture that there should be an intermediate step in trying to derive a quantum field theory of gravity, and that is to do probabilities on gravity. He acknowledges this is a highly speculative idea.

He then goes on to talk about 'expectation values', which is the standard way physicists have tried to model QFT (quantum field theory) on to spacetime, and is called 'semi-classical gravity'. Viktor T Toth (on Quora) says about this: …it is hideously inelegant, essentially an ad-hoc averaging of the equation that is really, really ugly and is not derived from any basic principle that we know. Nevertheless, Toth argues that it 'works'. Barandes goes further and says it's based on a fallacy (watch the video if you want an elaboration). To quote Toth again: We can do quantum field theory just fine on the curved spacetime background of general relativity. What we have so far been unable to do in a convincing manner is turn gravity itself into a quantum field theory.

I tend to agree with Freeman Dyson, who contends that they are not compatible in theory or in nature. In other words, he argues that quantum gravity is a chimera. Dyson also argues that QM can't describe past events; so, if that's true, quantum gravity is attempting to describe spacetime in its future. Arguably, this is what happens the other side of the event horizon of a black hole, where space itself only exists in one's future, which leads to the singularity. 

Addendum 2: Since posting this I've watched a lot of other videos, many of them by Curt, which may become the subject of a future post. But I just wanted to reference this one with Emily Adlam, who has a view completely opposite to the one expressed in my post above. She's developed what she calls the 'Sudoku universe', or the 'all at once' universe. The analogy with Sudoku is that the outcome is already 'known' and you can start anywhere at all - there is no progression from a fixed starting point to a fixed end point. This video is 1hr 19m, and I need to point out that she knows a lot more about this subject than I do, and so does Curt. Curt had obviously read all her papers relevant to this and knew exactly what to ask her. I know that if I was to go one-on-one with her, I could never argue at her level. I intend, at some point, to write another post where I discuss points-of-view of various physicists that are all driven more by philosophy than science.

Have we forgotten what ‘mind’ means?

 There is an obvious rejoinder to this, which is, did we ever know what ‘mind’ means? Maybe that’s the real question I wanted to ask, but I think it’s better if it comes from you. The thing is that we have always thought that ‘mind’ means something, but now we are tending to think, because we have no idea where it comes from, that it has no meaning at all. In other words, if it can’t be explained by science, it has no meaning. And from that perspective, the question is perfectly valid.
 
I’ve been watching a number of videos hosted by Curt Jaimungal, whom I assume has a physics background. For a start, he’s posted a number of video interviews with a ‘Harvard scientist’ on quantum mechanics, and he provided a link (to me) of an almost 2hr video he did with Sabine Hossenfelder, and they talked like they were old friends. I found it very stimulating and I left a fairly long comment that probably no one will read.
 
Totally off-topic, but Sabine’s written a paper proposing a thought-experiment that would effectively test if QM and GR (gravity) are compatible at higher energies. She calculated the energy range and if there is no difference to the low energy experiments already conducted, it effectively rules out a quantum field for gravity (assuming I understand her correctly). I expressed my enthusiasm for a real version to be carried out, and my personal, totally unfounded prediction that it would be negative (there would be no difference).
 
But there are 2 videos that are relevant to this topic and they both involve Stephen Wolfram (who invented Mathematica). I’ve referenced him in previous posts, but always second-hand, so it was good to hear him first-hand. In another video, also hosted by Jaimungal, Wolfram has an exchange with Donald Hoffman, whom I’ve been very critical of in the past, even saying that I found it hard to take him seriously. But to be fair, I need to acknowledge that he’s willing to put his ideas out there and have them challenged by people like Stephen Wolfram (and Anil Seth in another video), which is what philosophy is all about. And the truth is that all of these people know much more about their fields than me. I’ll get to the exchange with Hoffman later.
 
I have the impression from Gregory Chaitin, in particular, that Wolfram argues that the Universe is computable; a philosophical position I’ve argued against, mainly because of chaos theory. I’ve never known Wolfram to mention chaos theory, and he certainly doesn’t in the 2 videos I reference here, and I’ve watched them a few times.
 
Jaimungal introduces the first video (with Wolfram alone) by asking him about his ‘observer theory’ and ‘what if he’s right about the discreteness of space-time’ and ‘computation underlying the fundament?’ I think it’s this last point which goes to the heart of their discussion. Wolfram introduces a term called the Ruliad, which I had to look up. I came across 2 definitions, both of which seem relevant to the discussion.
 
A concept that describes all possible computations and rule-based systems, including our physical universe, mathematics, and everything we experience.
 
A meta-structural domain that encompasses every possible rule-based system, or computational eventuality, that can describe any universe or mathematical structure.
 
Wolfram confused me when he talked about ‘computational irreducibility’, which infers that there are some things that are not computable, to which I agree. But then later he seemed to argue that everything we can know is computable, and things we don’t know now are only unknowable because we’re yet to find their computable foundation. He argues that there are ‘slices of reducible computability’ within the ‘computational irreducibility’, which is how we do mathematical physics.
 
Towards the end of the video, he talks specifically about biology, saying, ‘there is no grand theory of biology’, like we attempt in physics. He has a point. I’ve long argued that natural selection is not the whole story, and there is a mystery inherent in DNA, in as much as it’s a code whose origin and evolvement is still unknown. Paul Davies attempted to tackle this in his book, The Demon in the Machine, because it’s analogous to software code and it’s information based. This means that it could, in principle, be mathematical, which means it could lead to a biological ‘theory of everything’, which I assume is what Wolfram is claiming is lacking.
 
However, I’m getting off-track again. At the start of the video, Wolfram specifically references the Copernican revolution, because it was not just a mathematical reformulation, but it changed our entire perspective of the Universe (we are not at the centre) without changing how we experience it (we are standing still, with the sky rotating around us). At the end of the day, we have mathematical models, and some are more accurate than others, and they all have limitations – there is no all-encompassing mathematical TOE (Theory of Everything). There is no Ruliad, as per the above definitions, and Wolfram acknowledges that while apparently arguing that everything is computable.
 
I find it necessary to bring Kant into this, and his concept of the ‘thing-in-itself’ which we may never know, but only have a perception of. My argument, which I’ve never seen anyone else employ, is that mathematics is one of our instruments of perception, just like our telescopes and particle accelerators and now, our gravitational wave detectors. Our mathematical models, be they GR (general relativity), QFT or String Theory, are perceptual and conceptual tools, whose veracity are ultimately determined by empirical evidence, which means they can only be applied to things that can be measured. And I think this leads to an unstated principle that if something can’t be measured it doesn’t exist. I would put ‘mind’ in that category.
 
And this allows me to segue into the second video, involving Donald Hoffman, because he seems to argue that mind is all that there is, and it has a mathematical foundation. He put forward his argument (which I wrote about recently) that, using Markovian matrices, he’s developed probabilities that apparently predict ‘qualia’, which some argue are the fundaments of consciousness. Wolfram, unlike the rest of us, actually knows what Hoffman is talking about and immediately had a problem that his ‘mathematical model’ led to probabilities and not direct concrete predictions. Wolfram seemed to argue that it breaks the predictive chain (my terminology), but I confess I struggled to follow his argument. I would have liked to ask: what happens with QM, which can only give us probabilities? In that case, the probabilities, generated by the Born Rule, are the only link between QM and classical physics – a point made by Mark John Fernee, among others.
 
But going back to my argument invoking Kant, it’s a mathematical model and not necessarily the thing-in-itself. There is an irony here, because Kant argued that space and time are a priori in the mind, so a projection, which, as I understand it, lies at the centre of Hoffman’s entire thesis. Hoffman argues that ‘spacetime is doomed’ since Nima Arkani-Hamed and his work on amplituhedrons, because (to quote Arkani-Hamed): This is a concrete example of a way in which the physics we normally associate with space-time and quantum mechanics arises from something more basic. In other words, Arkani-Hamed has found a mathematical substructure or foundation to spacetime itself, and Hoffman claims that he’s found a way to link that same mathematical substructure to consciousness, via Markovian matrices and his probabilities.
 
Hoffman analogises spacetime to wearing a VR headset and objects in spacetime to icons on a computer desktop, which seems to infer that the Universe is a simulation, though he’s never specifically argued that. I won’t reiterate my objections to Hoffman’s fundamental idealism philosophy, but if you have a mathematical model, however it’s formulated, its veracity can only be determined empirically, meaning we need to measure something. So, what is he going to measure? Is it qualia? Is it what people report what they think?
 
No. According to Hoffman, they can do empirical tests on spacetime (so not consciousness per se) that will determine if his mathematical model of consciousness is correct, which seems a very roundabout way of doing things. From what I can gather, he’s using a mathematical model of consciousness that’s already been developed (independently) to underpin reality, and then testing it on reality, thereby implying that consciousness is an intermediate step between the mathematical model and the reality. His ambition is to demonstrate that there is a causal relationship between consciousness and reality, when most argue that it’s the other way around. I return to this point below, with Wolfram’s response.
 
Wolfram starts off in his interaction with Hoffman by defining the subjective experience of consciousness that Hoffman has mathematically modelled and asking, can he apply that to an LLM (like ChatGPT, though he doesn’t specify) and therefore show that an LLM must be conscious? Wolfram argues that such a demonstration would categorically determine the ‘success’ (his term) of Hoffman’s theory, and Hoffman agreed.
 
I won’t go into detail (watch the video) but Hoffman concludes, quite emphatically, that ‘It’s not logically possible to start with non-conscious entities and have conscious agents emerge’ (my emphasis, obviously). Wolfram immediately responded (very good-naturedly), ‘That’s not my intuition’. He then goes on to say how that’s a Leibnizian approach, which he rejected back in the 1980s. I gather that it was around that time that Wolfram adopted and solidified (for want of a better word) his philosophical position that everything is ultimately computable. So they both see mathematics as part of the ‘solution’, but in different ways and with different conclusions.
 
To return to the point I raised in my introduction, Wolfram starts off in the first video (without Hoffman), that we have adopted a position that if something can’t be explained by science, then there is no other explanation – we axiomatically rule everything else out - and he seems to argue that this is a mistake. But then he adopts a position which is the exact opposite: that everything is “computational all the way down”, including concepts like free will. He argues: “If we can accept that everything is computational all the way down, we can stop searching for that.” And by ‘that’ he means all other explanations like mysticism or QM or whatever.
 
My own position is that mathematics, consciousness and physical reality form a triumvirate similar to Roger Penrose’s view. There is an interconnection, but I’m unsure if there is a hierarchy. I’ve argued that mathematics can transcend the Universe, which is known as mathematical Platonism, a view held by many mathematicians and physicists, which I’ve written about before.
 
I’m not averse to the view that consciousness may also exist beyond the physical universe, but it’s not something that can be observed (by definition). So far, I’ve attempted to discuss ‘mind’ in a scientific context, referencing 2 scientists with different points of view, though they both emphasise the role of mathematics in positing their views.
 
Before science attempted to analyse and put mind into an ontological box, we knew it as a purely subjective experience. But we also knew that it exists in others and even other creatures. And it’s the last point that actually triggered me to write this post and not the ruminations of Wolfram and Hoffman. When I interact with another animal, I’m conscious that it has a mind, and I believe that’s what we’ve lost. If there is a collective consciousness arising from planet Earth, it’s not just humans. This is something that I’m acutely aware of, and it has even affected my fiction.
 
The thing about mind is that it stimulates empathy, and I think that’s the key to the long-term survival of, not just humanity, but the entire ecosystem we inhabit. Is there a mind beyond the Universe? We don’t know, but I would like to think there is. In another recent post, I alluded to the Hindu concept of Brahman, which appealed to Erwin Schrodinger. You’d be surprised how many famous physicists were attracted to the mystical. I can think of Pauli, Einstein, Bohr, Oppenheimer – they all thought outside the box, as we like to say.
 
Physicists have no problem mentally conceiving 6 or more dimensions in String Theory that are ‘curled up’ so miniscule we can’t observe them. But there is also the possibility that there is a dimension beyond the universe that we can’t see. Anyone familiar with Flatland by Edwin Abbott (a story about social strata as much as dimensions), would know it expounds on our inherent inability to interact with higher dimensions. It’s occurred to me that consciousness may exist in another dimension, and we might ‘feel’ it occasionally when we interact with people who have died. I have experienced this, though it proves nothing. I’m a creative and a neurotic, so such testimony can be taken with a grain of salt.
 
I’ve gone completely off-track, but I think that both Wolfram and Hoffman may be missing the point, when, like many scientists, they are attempting to incorporate the subjective experience of mind into a scientific framework. Maybe it just doesn’t fit.

Plato’s Cave & Social Media

 In a not-so-recent post, I referenced Philosophy Now Issue 165 (Dec 2024/Jan 2025), which had the theme, The Return of God. However, its cover contained a graphic and headline on a completely separate topic: Social Media & Plato’s Cave, hence the title of this post. When you turn to page 34, you come across the essay, written by Sean Radcliffe, which won him “...the 2023 Irish Young Philosopher Awards Grand Prize and Philosopher of Our Time Award. He is now studying Mathematics and Economics at Trinity College, Dublin. Where he is an active member of the University Philosophical Society.” There is a photo of him holding up both awards (in school uniform), so one assumes that 2 years ago he was still at school.
 
I wrote a response to the essay, which was published in the next issue (166), which I post below, complete with edits, which were very minor. The editor added a couple of exclamation marks: at the end of the first and last paragraphs; both of which I’ve removed. Not my style.

They published it under the heading: The Problem is the Media.

I was pleasantly surprised (as I expect were many others) when I learned that the author of Issue 165’s cover article, ‘Plato’s Cave & Social Media’, Seán Radcliffe, won the 2023 Irish Young Philosopher Award Grand Prize and Philosopher of Our Time Award for the very essay you published. Through an analogy with Plato’s Cave, Seán rightfully points out the danger of being ‘chained’ to a specific viewpoint that aligns with a political ideology or conspiracy theory. Are any of us immune? Socrates, via the Socratic dialogue immortalised by his champion Plato, transformed philosophy into a discussion governed by argument, as opposed to prescriptive dogma. In fact, I see philosophy as an antidote to dogma because it demands argument. However, if all dialogue takes place in an echo-chamber, the argument never happens.

Social media allows alternative universes that are not only different but polar opposites. To give an example that arose out of the COVID pandemic: in one universe, the vaccines were saving lives, and in an alternative universe they were bioweapons causing deaths. The 2020 US presidential election created another example of parallel universes that were direct opposites. Climate change is another. In all these cases, which universe one inhabits depends on which source of information one trusts.

Authoritarian governments are well aware that the control of information allows emotional manipulation of the populace. In social media, the most emotive and often most extreme versions of events get the most traction. Plato’s response to tyranny and populist manipulation was to recommend ‘philosopher-kings’, but no one sees that as realistic. I spent a working lifetime in engineering, and I’ve learned that no single person has all the expertise, so we need to trust the people who have the expertise we lack. A good example is the weather forecast. We’ve learned to trust it as it delivers consistently accurate short-term forecasts. But it’s an exception, because news sources are rarely agenda-free.

I can’t see political biases disappearing – in fact, they seem to be becoming more extreme, and the people with the strongest opinions see themselves as the best-informed. Even science can be politicised, as with both the COVID pandemic and with climate change. The answer is not a philosopher-king, but the institutions we already have in place that study climate science and epidemiology. We actually have the expertise; but we don’t listen to it because its proponents are not famous social media influencers.

Mathematics, consciousness, reality

 I wish to emphasise the importance of following and listening to people you disagree with. (I might write another post on the pitfalls of ‘echo-chambers’ in social media, from which I’m not immune.)
 
I’ve been following Donald Hoffman ever since I reviewed an academic paper he wrote with Chetan Prakash called Objects of Consciousness, back in November 2016, though the paper was written in 2014 (so over 10 years ago). Back then, I have to admit, I found it hard to take him seriously, especially his views on evolution, and his go-to metaphor that objective reality was analogous to desktop icons on a computer.
 
His argument is similar to the idea that we live in a computer simulation, though he’s never said that, and I don’t think he believes we do. Nevertheless, he has compared reality to wearing a VR headset, which is definitely analogous to being in a computer simulation. As I have pointed out on other posts, I contend that we do create a model of reality in our ‘heads’, which is so ‘realistic’ that we all think it is reality. The thing is that our very lives depend on it being a very accurate ‘model’, so we can interact with the external reality that does exist outside our heads. This is one of my strongest arguments against Hoffman – reality can kill you, but simulations, including the ones we have when we sleep, which we call dreams, cannot.
 
So I’ve been following Hoffman, at least on YouTube, in the 8 years since I wrote that first critique. I read an article he wrote in New Scientist on evolution (can’t remember the date), which prompted me to write a letter-to-the-Editor, which was published. And whenever I come across him on YouTube: be it in an interview, a panel discussion or straight-to-video; I always watch and listen to what he has to say. What I’ve noticed is that he’s sharpened his scalpel, if I can use that metaphor, and that he’s changed his tack, if not his philosophical position. Which brings me to the reason for writing this post.
 
A year or two ago, I wrote a comment on one of his standalone videos, challenging what he said, and it was subsequently deleted, which is his prerogative. While I was critical, I don’t think I was particularly hostile – the tone was similar to a comment I wrote today on the video that prompted this discussion (see below).
 
Hoffman’s change of tack is not to talk about evolution at all, but spacetime and how it’s no longer ‘fundamental’. This allows him to argue that ‘consciousness’ is more fundamental than spacetime, via the medium of mathematics. And that’s effectively the argument he uses in this video, which, for brevity, I’ve distilled into one succinct sentence.
 
My approach, well known to anyone who regularly follows this blog, is that consciousness and mathematics are just as fundamental to reality as the physical universe, but not in the way that Hoffman argues. I’ve adopted, for better or worse, Roger Penrose’s triumvirate, which he likes to portray in an Escher-like diagram. 

 
I wouldn’t call myself a physicalist when it comes to consciousness, for the simple reason that I don’t believe we can measure it, and despite what Hoffman (and others) often claim, I’m not convinced that it will ever succumb to a mathematical model, in the way that virtually all physical theories do.
 
I left a comment on this video, which was hosted by the ‘Essentia Foundation’, so hopefully, it’s not deleted. Here it is:
 
I agree with him about Godel’s Theorem in its seminal significance to both maths and physics, which is that they are both neverending. However, when he says that ‘reality transcends any mathematical theory’ (3.00) I agree to a point, but I’d argue that mathematics transcends the Universe (known as mathematical Platonism); so in that sense, mathematics transcends reality.
 
The other point, which he never mentions, is that mathematical models of physical phenomena can be wrong – the best example being Ptolemy’s model of the solar system. String theory may well fall into that category – at this stage, we don’t know.
 
When he discusses consciousness being mathematical (4.30): ‘If consciousness is all there is, then mathematical structure is only about consciousness’; which is a premise dressed up as a conclusion, so circular.
 
The problem I’ve always had with Donald Hoffman’s idealism philosophy is that consciousness may exist independently of the Universe; it’s not possible for us to know. But within the Universe itself, evolutionary theory tells us that consciousness came late. Now, I know that he has his own theory of evolution to counter this, but that entails an argument that’s too long to address here.
 
Regarding his argument that spacetime is not fundamental, I know about Nima Arkani-Hamed and his work on amplituhedrons, and to quote: “This is a concrete example of a way in which the physics we normally associate with space-time and quantum mechanics arises from something more basic.” But the something more basic is mathematical, not physical. It’s possible that there was something before spacetime at the very birth of the Universe, but that’s speculative. All our cosmological theories are premised on spacetime.
 
I actually don’t think consciousness can be modelled mathematically, but its neurological underpinnings can, simply because they can be measured. Consciousness itself can’t be measured, only its neurological correlates. In other words, it can’t be measured outside of a brain, which is an object dependent on the Universe’s existence and not the other way round.

Is there a cosmic purpose? Is our part in it a chimera?

 I’ve been procrastinating about writing this post for some time, because it comes closest to a ‘theory’ of Life, the Universe and Everything. ‘Theory’ in this context being a philosophical point of view, not a scientifically testable theory in the Karl Popper sense (it can’t be falsified), but using what science we currently know and interpreting it to fit a particular philosophical prejudice, which is what most scientists and philosophers do even when they don’t admit it.
 
I’ve been watching a lot of YouTube videos, some of which attempt to reconcile science and religion, which could be considered a lost cause, mainly because there is a divide going back to the Dark Ages, which the Enlightenment never bridged despite what some people might claim. One of the many videos I watched was a moderated discussion between Richard Dawkins and Jordan Peterson, which remained remarkably civil, especially considering that Peterson really did go off on flights of fancy (from my perspective), comparing so-called religious ‘truths’ with scientific ‘truths’. I thought Dawkins handled it really well, because he went to pains not to ridicule Peterson, while pointing out fundamental problems with such comparisons.
 
I’m already going off on tangents I never intended, but I raise it because Peterson makes the point that science actually arose from the Judea-Christian tradition – a point that Dawkins didn’t directly challenge, but I would have. I always see the modern scientific enterprise, if I can call it that, starting with Copernicus, Galileo and Kepler, but given particular impetus by Newton and his contemporary and rival, Leibniz. It so happens that they all lived in Europe when it was dominated by Christianity, but the real legacy they drew on was from the Ancient Greeks with a detour into Islam where it acquired Hindu influences, which many people conveniently ignore. In particular, we adopted Hindu-Arabic arithmetic, incorporating zero as a decimal place-marker, without which physics would have been stillborn.
 
Christianity did its best to stop the scientific enterprise: for example, when it threatened Galileo with the inquisition and put him under house arrest. Modern science evolved despite Christianity, not because of it. And that’s without mentioning Darwin’s problems, which still has ramifications today in the most advanced technological nation in the world.
 
A lengthy detour, but only slightly off-topic. There is a mystery at the heart of everything on the very edge of our scientific understanding of the world that I believe is best expressed by Paul Davies, but was also taken up by Stephen Hawking, of all people, towards the end of his life. I say, ‘of all people’, because Hawking was famously sceptical of the role of philosophy, yet, according to his last collaborator, Thomas Hertog, he was very interested in the so-called Big Questions, and like Davies, was attracted to John Wheeler’s idea of a cosmic-scale quantum loop that attempts to relate the end result of the Universe to its beginning.
 
Implicit in this idea is that the Universe has a purpose, which has religious connotations. So I want to make that point up front and add that there is No God Required. I agree with Davies that science neither proves nor disproves the existence of God, which is very much a personal belief, independent of any rationalisation one can make.
 
I wrote a lengthy post on Hawking’s book, The Grand Design, back in 2020 (which he cowrote with Leonard Mlodinow). I will quote from that post to highlight the point I raised 2 paragraphs ago: the link between present and past.
 
Hawking contends that the ‘alternative histories’ inherent in Feynman’s mathematical method, not only affect the future but also the past. What he is implying is that when an observation is made it determines the past as well as the future. He talks about a ‘top down’ history in lieu of a ‘bottom up’ history, which is the traditional way of looking at things. In other words, cosmological history is one of many ‘alternative histories’ (his terminology) that evolve from QM.
 
Then I quote directly from Hawking’s text:
 
This leads to a radically different view of cosmology, and the relation between cause and effect. The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us (my emphasis).
 
One can’t contemplate this without considering the nature of time. There are in fact 2 different experiences we have of time, and that has created debate among physicists as well as philosophers. The first experience is simply observational. Every event with a causal relationship that is separated by space is axiomatically also separated by time, and this is a direct consequence of the constant speed of light. If this wasn’t the case, then everything would literally happen at once. So there is an intrinsic relationship between time and light, which Einstein had the genius to see: was not just a fundamental law of the Universe; but changed perceptions of time and space for different observers. Not only that, his mathematical formulations of this inherent attribute, led him to the conclusion that time itself was fluid, dependent on an observer’s motion as well as the gravitational field in which they happened to be.
 
I’m going to make another detour because it’s important and deals with one of the least understood aspects of physics. One of the videos I watched that triggered this very essay was labelled The Single Most Important Experiment in Physics, which is the famous bucket experiment conducted by Newton, which I’ve discussed elsewhere. Without going into details, it basically demonstrates that there is a frame of reference for the entire universe, which Newton called absolute space and Einstein called absolute spacetime. Penrose also discusses the importance of this concept, because it means that all relativistic phenomena take place against a cosmic background. It’s why we can determine the Earth’s velocity with respect to the entire universe by measuring the Doppler shift against the CMBR (cosmic microwave background radiation).
 
Now, anyone with even a rudimentary knowledge of relativity theory knows that it’s not just time that’s fluid but also space. But, as Kip Thorne has pointed out, mathematically we can’t tell if it’s the space that changes in dimension or the ruler used to measure it. I’ve long contended that it’s the ruler, which can be the clock itself. We can use a clock to measure distance and if the clock changes, which relativity tell us it does, then it’s going to measure a different distance to a stationary observer. By stationary, I mean one who is travelling at a lesser speed with respect to the overall CMBR.
 
So what is the other aspect of time that we experience? It’s the very visceral sensation we all have that time ‘flows’, because we all ‘sense’ its ‘passing’. And this is the most disputed aspect of time, that many physicists tell us is an illusion, including Davies. Some, like Sabine Hossenfelder, are proponents of the ‘block universe’, first proposed by Einstein, whereby the future already exists like the past, which is why both Hossenfelder and Einstein believed in what is now called superdeterminism – everything is predetermined in advance – which is one of the reasons that Einstein didn’t like the philosophical ramifications of quantum mechanics (I’ll get to his ‘spooky action at a distance’ later).
 
Davies argues that the experience of time passing is a psychological phenomenon and the answer will be found in neuroscience, not physics. And this finally brings consciousness into the overall scheme of things. I’ve argued elsewhere that, without consciousness, the Universe has no meaning and no purpose. Since that’s the point of this dissertation, it can be summed up with an aphorism from Wheeler.
 
The Universe gave rise to consciousness and consciousness gives the Universe meaning.
 
I like to cite Schrodinger from his lectures on Mind and Matter appended to his tome, What is Life? Consciousness exists in a constant present, and I argue that it’s the only thing that does (the one possible exception is a photon of light, for which time is zero). As I keep pointing out, this is best demonstrated every time someone takes a photo: it freezes time, or more accurately, it creates an image frozen in time; meaning it’s forever in our past, but so is the event that it represents.
 
The flow of time we all experience is a logical consequence of this. In a way, Davies is right: it’s a neurological phenomenon, in as much as consciousness seems to ‘emerge’ from neuronal activity. But I’m not sure Davies would agree with me – in fact, I expect he wouldn’t.
 
Those who have some familiarity with my blog, may see a similarity between these 2 manifestations of time and my thesis on Type A time and Type B time (originally proposed by J.M.E. McTaggart, 1906); the difference between them, in both cases, being the inclusion of consciousness.
 
Now I’m going to formulate a radical idea, which is that in Type B time (the time without consciousness), the flow of time is not experienced but there are chains of causal events. And what if all the possible histories are all potentially there in the same way that future possible histories are, as dictated by Feynman’s model. And what if the one history that we ‘observe’, going all the way back to the pattern in the CMBR (our only remnant relic of the Big Bang), only became manifest when consciousness entered the Universe. And when I say ‘entered’ I mean that it arose out of a process that had evolved. Davies, and also Wheeler before him, speculated that the ‘laws’ of nature we observe have also evolved as part of the process. But what if those laws only became frozen in the past when consciousness finally became manifest. This is the backward-in-time quantum loop that Wheeler hypothesised.
 
I contend that QM can only describe the future (an idea espoused by Feynman’s collaborator, Freeman Dyson), meaning that Schrodinger’s equation can only describe the future, not the past. Once a ‘measurement’ is made, it no longer applies. Penrose explains this best, and has his own argument that the ‘collapse’ of the wave function is created by gravity. Leaving that aside, I argue that the wave function only exists in our future, which is why it’s never observed and why Schrodinger’s equation can’t be applied to events that have already happened. But what if it was consciousness that finally determined which of many past paths became the reality we observe. You can’t get more speculative than that, but it provides a mechanism for Wheeler’s ‘participatory universe’ that both Davies and Hawking found appealing.
 
I’m suggesting that the emergence of consciousness changed the way time works in the Universe, in that the past is now fixed and only the future is still open.
 
Another video I watched also contained a very radical idea, which is that spacetime is created like a web into the future (my imagery). The Universe appears to have an edge in time but not in space, and this is rarely addressed. It’s possible that space is being continually created with the Universe’s expansion – an idea explored by physicist, Richard Muller – but I think it’s more likely that the Universe is Euclidean, meaning flat, but bounded. We may never know.
 
But if the Universe has an edge in time, how does that work? I think the answer is quantum entanglement, though no one else does. Everyone agrees that entanglement is non-local, meaning it’s not restricted by the rules of relativity, and it’s not spatially dependent. I speculate that quantum entanglement is the Universe continually transitioning from a quantum state to a classical physics state. This idea is just as heretical as the one I proposed earlier, and while Einstein would call it ‘spooky action at a distance’, it makes sense, because in quantum cosmology, time mathematically disappears. And it disappears because you can’t ‘see’ the future of the Universe, even in principle.

Addendum 1: This excerpt from a panel discussion shows how this debate is unresolved even among physicists. The first speaker, Avshalom Elitzur (who is also referenced in one of the videos linked in the 2nd last paragraph of the main text) probably comes closest to expressing my viewpoint.

In effect, he describes what I expound on in my post, though I'm sure he wouldn't agree with my more radical ideas - the role of consciousness and that entanglement is intrinsically linked to the edge of time for the whole universe. However, he does say, 'In some profound way the future does not exist'. 

Addendum 2: I came across this article in New Scientist, which you might not be able to access if you're not a subscriber (I have an online subscription). Basically, the author, Karmela Padavic-Callaghan, argues that 'classical time' arises from quantum 'entanglement', citing Alessandro Coppo. To quote:

This may mean that if we perceive the passage of time, then there is some entanglement woven into the physical world. And an observer in a universe devoid of entanglement – as some theories suggest ours was at its very beginning – would have seen nothing change. Everything would be static.

The role of dissonance in art, not to mention science and mathematics

 I was given a book for a birthday present just after the turn of the century, titled A Terrible Beauty; The People and Ideas that Shaped the Modern Mind, by Peter Watson. A couple of things worth noting: it covers the history of the 20th Century, but not geo-politically as you might expect. Instead, he writes about the scientific discoveries alongside the arts and cultural innovations, and he talks about both with equal erudition, which is unusual.
 
The reason I mention this, is because I remember Watson talking about the human tendency to push something to its limits and then beyond. He gave examples in science, mathematics, art and music. A good example in mathematics is the adoption of √-1 (giving us ‘imaginary numbers’), which we are taught is impossible, then suddenly it isn’t. The thing is that it allows us to solve problems that were previously impossible in the same way that negative numbers give solutions to arithmetical subtractions that were previously unanswerable. There were no negative numbers in ancient Greece because their mathematics was driven by geometry, and the idea of a negative volume or area made no sense.
 
But in both cases: negative numbers and imaginary numbers; there is a cognitive dissonance that we have to overcome before we can gain familiarity and confidence in using them, or even understanding what they mean in the ‘real world’, which is the problem the ancient Greeks had. Most people reading this have no problem, conceptually, dealing with negative numbers, because, for a start, they’re an integral aspect of financial transactions – I suspect everyone reading this above a certain age has had experience with debt and loans.
 
On the other hand, I suspect a number of readers struggle with a conceptual appreciation of imaginary numbers. Some mathematicians will tell you that the term is a misnomer, and its origin would tend to back that up. Apparently, Rene Descartes coined the term, disparagingly, because, like the ancient Greek’s problem with negative numbers, he believed they had no relevance to the ‘real world’. And Descartes would have appreciated their usefulness in solving problems previously unsolvable, so I expect it would have been a real cognitive dissonance for him.
 
I’ve written an entire post on imaginary numbers, so I don’t want to go too far down that rabbit hole, but I think it’s a good example of what I’m trying to explicate. Imaginary numbers gave us something called complex algebra and opened up an entire new world of mathematics that is particularly useful in electrical engineering. But anyone who has studied physics in the last century is aware that, without imaginary numbers, an entire field of physics, quantum mechanics, would remain indescribable, let alone be comprehensible. The thing is that, even though most people have little or no understanding of QM, every electronic device you use depends on it. So, in their own way, imaginary numbers are just as important and essential to our lives as negative numbers are.
 
You might wonder how I deal with the cognitive dissonance that imaginary numbers induce. In QM, we have, at its most rudimentary level, something called Schrodinger’s equation, which he proposed in 1926 (“It’s not derived from anything we know,” to quote Richard Feynman) and Schrodinger quickly realised it relied on imaginary numbers – he couldn’t formulate it without them. But here’s the thing: Max Born, a contemporary of Schrodinger, formulated something we now call the Born rule that mathematically gets rid of the imaginary numbers (for the sake of brevity and clarity, I’ll omit the details) and this gives the probability of finding the object (usually an electron) in the real world. In fact, without the Born rule, Schrodinger’s equation is next-to-useless, and would have been consigned to the dustbin of history.
 
And that’s relevant, because prior to observing the particle, it’s in a superposition of states, described by Schrodinger’s equation as a wave function (Ψ), which some claim is a mathematical fiction. In other words, you need to get rid (clumsy phrasing, but accurate) of the imaginary component to make it relevant to the reality we actually see and detect. And the other thing is that once we have done that, the Schrodinger equation no longer applies – there is effectively a dichotomy between QM and classical physics (reality), which is called the 'measurement problem’. Roger Penrose gives a good account in this video interview. So, even in QM, imaginary numbers are associated with what we cannot observe.
 
That was a much longer detour than I intended, but I think it demonstrates the dissonance that seems necessary in science and mathematics, and arguably necessary for its progress; plus it’s a good example of the synergy between them that has been apparent since Newton.
 
My original intention was to talk about dissonance in music, and the trigger for this post was a YouTube video by musicologist, Rick Beato (pronounced be-arto), dissecting the Beatles song, Ticket to Ride, which he called, ‘A strange but perfect song’. In fact, he says, “It’s very strange in many ways: it’s rhythmically strange; it’s melodically strange too”. I’ll return to those specific points later. To call Beato a music nerd is an understatement, and he gives a technical breakdown that quite frankly, I can’t follow. I should point out that I’ve always had a good ‘ear’ that I inherited, and I used to sing, even though I can’t read music (neither could the Beatles). I realised quite young that I can hear things in music that others miss. Not totally relevant, but it might explain some things that I will expound upon later.
 
It's a lengthy, in-depth analysis, but if you go to 4.20-5.20, Beato actually introduces the term ‘dissonance’ after he describes how it applies. In effect, there is a dissonance between the notes that John Lennon sings and the chords he plays (on a 12-string guitar). And the thing is that we, the listener, don’t notice – someone (like Beato) has to point it out. Another quote from 15.00: “One of the reasons the Beatles songs are so memorable, is that they use really unusual dissonant notes at key points in the melody.”
 
The one thing that strikes you when you first hear Ticket to Ride is the unusual drum part. Ringo was very inventive and innovative, and became more adventurous, along with his bandmates, on later recordings. The Ticket to Ride drum part has become iconic: everyone knows it and recognises it. There is a good video where Ringo talks about it, along with another equally famous drum part he created. Beato barely mentions it, though right at the beginning, he specifically refers to the song as being ‘rhythmically strange’.
 
A couple of decades ago, can’t remember exactly when, I went and saw an entire Beatles concert put on by a rock band, augmented by orchestral strings and horn parts. It was in 2 parts with an intermission, and basically the 1st half was pre-Sergeant Pepper and the 2nd half, post. I can still remember that they opened the concert with Magical Mystery Tour and it blew me away. The thing is that they went to a lot of trouble to be faithful to the original recordings, and I realised that it was the first time I’d heard their music live, albeit with a cover band. And what immediately struck me was the unusual harmonics and rhythms they employed. Watching Beato’s detailed technical analysis puts this into context for me.
 
Going from imaginary numbers and quantum mechanics to one of The Beatles most popular songs may seem like a giant leap, but it highlights how dissonance is a universal principle for humans, and intrinsic to progression in both art and science.
 
Going back to Watson’s book that I reference in the introduction, another obvious example that he specifically talks about is Picasso’s cubism.
 
In storytelling, it may not be so obvious, and I think modern fiction has been influenced more by cinema than anything else, where the story needs to be more immediate and it needs to flow with minimal description. There is now an expectation that it puts you in the story – what we call immersion.
 
On another level, I’ve noticed a tendency on my part to create cognitive dissonance in my characters and therefore the reader. More than once, I have combined sexual desire with fear, which some may call perverse. I didn’t do this deliberately – a lot of my fiction contains elements I didn’t foresee. Maybe it says something about my own psyche, but I honestly don’t know.

Mathematics links epistemology to ontology, but it’s not that simple

A recurring theme on this blog is the relationship between mathematics and reality. It started with the Pythagoreans (in Western philosophy) and was famously elaborated upon by Plato. I also think it’s the key element of Kant’s a priori category in his marriage of analytical philosophy and empiricism, though it’s rarely articulated that way.
 
I not-so-recently wrote a post about the tendency to reify mathematical objects into physical objects, and some may validly claim that I am guilty of that. In particular, I found a passage by Freeman Dyson who warns specifically about doing that with Schrodinger’s wave function (Ψ, the Greek letter, psi, pronounced sy). The point is that psi is one of the most fundamental concepts in QM (quantum mechanics), and is famous for the fact that it has never been observed, and specifically can’t be, even in principle. This is related to the equally famous ‘measurement problem’, whereby a quantum event becomes observable, and I would say, becomes ‘classical’, as in classical physics. My argument is that this is because Ψ only exists in the future of whoever (or whatever) is going to observe it (or interact with it). By expressing it specifically in those terms (of an observer), it doesn’t contradict relativity theory, quantum entanglement notwithstanding (another topic).
 
Some argue, like Carlo Rovelli (who knows a lot more about this topic than me), that Schrodinger’s equation and the concept of a wave function has led QM astray, arguing that if we’d just stuck with Heisenberg’s matrices, there wouldn’t have been a problem. Schrodinger himself demonstrated that his wave function approach and Heisenberg’s matrix approach are mathematically equivalent. And this is why we have so many ‘interpretations’ of QM, because they can’t be mathematically delineated. It’s the same with Feynman’s QED and Schwinger’s QFT, which Dyson showed were mathematically equivalent, along with Tomanaga’s approach, which got them all a Nobel prize, except Dyson.
 
As I pointed out on another post, physics is really just mathematical models of reality, and some are more accurate and valid than others. In fact, some have turned out to be completely wrong and misleading, like Ptolemy’s Earth-centric model of the solar system. So Rovelli could be right about the wave function. Speaking of reifying mathematical entities into physical reality, I had an online discussion with Qld Uni physicist, Mark John Fernee, who takes it a lot further than I do, claiming that 3 dimensional space (or 4 dimensional spacetime) is a mathematical abstraction. Yet, I think there really are 3 dimensions of space, because the number of dimensions affects the physics in ways that would be catastrophic in another hypothetical universe (refer John Barrow’s The Constants of Nature). So it’s more than an abstraction. This was a key point of difference I had with Fernee (you can read about it here).
 
All of this is really a preamble, because I think the most demonstrable and arguably most consequential example of the link between mathematics and reality is chaos theory, and it doesn’t involve reification. Having said that, this again led to a point of disagreement between myself and Fermee, but I’ll put that to one side for the moment, so as not to confuse you.
 
A lot of people don’t know that chaos theory started out as purely mathematical, largely due to one man, Henri Poincare. The thing about physical chaotic phenomena is that they are theoretically deterministic yet unpredictable simply because the initial conditions of a specific event can’t be ‘physically’ determined. Now some physicists will tell you that this is a physical limitation of our ability to ‘measure’ the initial conditions, and infer that if we could, it would be ‘problem solved’. Only it wouldn’t, because all chaotic phenomena have a ‘horizon’ beyond which it’s impossible to make accurate predictions, which is why weather predictions can’t go reliably beyond 10 days while being very accurate over a few. Sabine Hossenfelder explains this very well.
 
But here’s the thing: it’s built into the mathematics of chaos. It’s impossible to calculate the initial conditions because you need to do the calculation to infinite decimal places. Paul Davies gives an excellent description and demonstration in his book, The Cosmic Blueprint. (this was my point-of-contention with Fernee, talking about coin-tosses).
 
As I discussed on another post, infinity is a mathematical concept that appears to have little or no relevance to reality. Perhaps the Universe is infinite in space – it isn’t in time – but if it is, we might never know. Infinity avoids empirical confirmation almost by definition. But I think chaos theory is the exception that proves the rule. The reason we can’t determine the exact initial conditions of a chaotic event, is not just physical but mathematical. As Fernee and others have pointed out, you can manipulate a coin-toss to make it totally predictable, but that just means you’ve turned a chaotic event into a non-chaotic event (after all it’s a human-made phenomenon). But most chaotic events are natural, like the orbits of the planets and biological evolution. The creation of the Earth’s moon was almost certainly a chaotic event, without which complex life would almost certainly never have evolved, so they can be profoundly consequential as well as completely unpredictable.
 

What’s inside a black hole?

 The correct answer is no one knows, but I’m going to make a wild, speculative, not fully-informed guess and suggest, possibly nothing. But first, a detour, to provide some context.
 
I came across an interview with very successful, multi-award-winning, Australian-Canadian actor, Pamela Rabe, who is best known (in Australia, at least) for her role in Wentworth (about a fictional female prison). She was interviewed by Benjamin Law in The Age Good Weekend magazine, a few weekends ago, where among many other questions, he asked, Is there a skill you wish you could acquire? She said there were so many, including singing better, speaking more languages and that she wished she was more patient. Many decades ago, I remember someone asking me a similar question, and I can still remember the answer: I said that I wish I was more intelligent, and I think that’s still true.
 
Some people might be surprised by this, and perhaps it’s a good thing I’m not, because I think I would be insufferable. Firstly, I’ve always found myself in the company of people who are much cleverer than me, right from when I started school, and right through my working life. The reason I wish I was more intelligent is that I’ve always been conscious of trying to understand things that are beyond my intellectual abilities. My aspirations don’t match my capabilities.
 
And this brings me to a discussion on black holes, which must, in some respects, represent the limits of what we know about the Universe and maybe what is even possible to know. Not surprisingly, Marcus du Sautoy spent quite a few pages discussing black holes in his excellent book, What We Cannot Know. But there is a short YouTube video by one of the world’s leading exponents on black holes, Kip Thorne, which provides a potted history. I also, not that long ago, read his excellent book, Black Holes and Time Warps; Einstein’s Outrageous Legacy (1994), which gives a very comprehensive history, in which he was not just an observer, but one of the actors.
 
It's worth watching the video because it highlights the role mathematics has played in physics, not only since Galileo, Kepler and Newton, but increasingly so in the 20th Century, following the twin revolutions of quantum mechanics and relativity theory. In fact, relativity theory predicted black holes, yet most scientists (including Einstein, initially) preferred to believe that they couldn’t exist; that Nature wouldn’t allow it.
 
We all suffer from these prejudices, including myself (and even Einstein). I discussed in a recent post how we create mathematical models in an attempt to explain things we observe. But more and more, in physics, we use mathematical models to explain things that we don’t observe, and black holes are the perfect example. If you watch the video interview with Thorne, this becomes obvious, because scientists were gradually won over by the mathematical arguments, before there was any incontrovertible physical evidence that they existed.
 
And since no one can observe what’s inside a black hole, we totally rely on mathematical models to give us a clue. Which brings me to the title of the post. The best known equation in reference to black holes in the Bekenstein-Hawking equation which give us the entropy of a black hole and predicts Hawking radiation. This is yet to be observed, but this is not surprising, as it’s virtually impossible. It’s simply not ‘hot’ enough to distinguish from the CMBR (cosmic microwave background radiation) which permeates the entire universe. 

Here is the formula:

S(BH) = kA/4(lp)^2 

Where S is the entropy of the black hole, A is the surface area of the sphere at the event horizon, and lp is the Planck length given by this formula:

√(Gh/2πc^3) 

Where G is the gravitational constant, h is Planck’s constant and c is the constant for lightspeed.

Hawking liked the idea that it’s the only equation in physics to incorporate the 4 fundamental natural constants: k, G, h and c; in one formula.

So, once again, mathematics predicts something that’s never been observed, yet most scientists believe it to be true. This led to what was called the ‘information paradox’ that all information falling into a black hole would be lost, but what intrigues me is that if a black hole can, in principle, completely evaporate by converting all its mass into radiation, then it infers that the mass is not in fact lost – it must be still there, even if we can’t see it. This means, by inference, that it can’t have disappeared down a wormhole, which is one of the scenarios conjectured.

One of the mathematical models proposed is the 'holographic principle' for black holes, for which I’ll quote directly from Wikipedia, because it specifically references what I’ve already discussed.

The holographic principle was inspired by the Bekenstein bound of black hole thermodynamics, which conjectures that the maximum entropy in any region scales with the radius squared, rather than cubed as might be expected. In the case of a black hole, the insight was that the information content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the black hole information paradox within the framework of string theory.

I know this is a long hop to make but what if the horizon not only contains the information but actually contains all the mass. In other words, what if everything is frozen at the event horizon because that’s where time ‘stops’. Most probably not true, and I don’t know enough to make a cogent argument. However, it would mean that the singularity predicted to exist at the centre of a black hole would not include its mass, but only spacetime.

Back in the 70s, I remember reading an article in Scientific American by a philosopher, who effectively argued that a black hole couldn’t exist. Now this was when their purported existence was mostly mathematical, and no one could unequivocally state that they existed physically. I admit I’m hazy about the details but, from what I can remember, he argued that it was self-referencing because it ‘swallowed itself’. Obviously, his argument was much more elaborate than that one-liner suggests. But I do remember thinking his argument flawed and I even wrote a letter to Scientific American challenging it. Basically, I think it’s a case of conflating the language used to describe a phenomenon with the physicality of it.

I only raise it now, because, as a philosopher, I’m just as ignorant of the subject as he was, so I could be completely wrong.

Addendum 1: I was of 2 minds whether to write this, but it kept bugging me - wouldn't leave me alone, so I wrote it down. I've no idea how true it might be, hence all the caveats and qualifications. It's absolutely at the limit of what we can know at this point in time. As I've said before, philosophy exists at the boundary of science and ignorance. It ultimately appealed to my aesthetics and belief in Nature’s aversion to perversity.

Addendum 2: Another reason why I'm most likely wrong is that there is a little known quirk of Newton's theory of gravity that the gravitational 'force' anywhere inside a perfectly symmetrical hollow sphere is zero. So the inside of a black hole exerting zero gravitational force would have to be the ultimate irony, which makes it highly improbable. I've no idea how that relates to the 'holographic principle' for a black hole. But I still don't think all the mass gets sucked into a singularity or down a wormhole. My conjecture is based purely on the idea that 'time' might well become 'zero' at the event horizon, though, from what I've read, no physicist thinks so. From an outsider's perspective, time dilation becomes asymptotically infinite (effective going to zero, but perhaps taking the Universe's lifetime to reach it). In this link, it begs a series of questions that seem to have no definitive answers. The alternative idea is that it's spacetime that 'falls' into a black hole, therefore taking all the mass with it.

Addendum 3: I came across this video by Tibbees (from a year ago), whom I recommend. She cites a book by Carlo Rovelli, White Holes, which is also the title of her video. Now, you can't talk about white holes without talking about black holes; they are just black holes time reversed (as she explicates). We have no evidence they actually exist, unless the Big Bang is a white hole (also mentioned). I have a lot of time for Carlo Rovelli, even though we have philosophical differences (what a surprise). Basically, he argues that, at a fundamental level, time doesn't exist, but it's introduced into the universe as a consequence of entropy (not the current topic). 

Tibbees gives a totally different perspective to my post, which is why I bring it up. Nevertheless, towards the end, she mentions that our view of a hypothetical person (she suggests Rovelli) entering a black hole is that their existence becomes assymptotically infinite. But what, if in this case, what we perceive is what actually happens. Then my scenario makes sense. No one else believes that, so it's probably incorrect.

Addendum 4: Victor T Toth, whom even Mark John Fernee defers to (on Quora), when it comes to cosmology and gravity, has said more than once, that 'the event horizon is always in your future', which infers you never reach it. This seems to contradict the prevailing view among physicists that, while that's true for another 'observer' observing 'you' (assuming you're the one falling into a black hole), from 'your' perspective you could cross the event horizon without knowing you have (see the contradiction). This is the conventional, prevailing view among physicists. To my knowledge, Toth has never addressed this apparent contradiction specifically.

However, if one follows Toth's statement to its logical conclusion, 'you' would approach the event horizon asymptotically, which is what I'm speculating. In which case, everything that falls into a black hole would accumulate at the event horizon. The thing is that gravity determines the 'true time' (τ) for a free falling object, and if τ became zero at the event horizon, then everything I've said makes sense. The thing is I really don't know enough physics to back up my conjecture with mathematics.

Addendum 5: Possibly the most important addendum to this post, in that it provides yet another plausible scenario based on what we currently know, and is rather eruditely expounded upon by someone on Quora calling himself 'The Physics Detective' (John Duffield). Of course, I've heard of the 'Firewall' explanation, without knowing if it's true or not. But I suspect no one does.

Image by W H Freeman and company, publishers of Gravitation

Addendum 6: I don't think I've ever written so many addendums to a post, which demonstrates how equivocal and unconvinced I am by my own arguments. It's symptomatic of our ignorance, and mine in particular, on this subject.

So I'm going to renege and go back to an earlier post I wrote, where I align myself with Kip Thorne, who is an actual expert on this matter.

Addendum 7: This must be a record (for the number of addendums to one post). This is another video by Curt Jaimungal posted some time after I originally wrote this (6 mths), which gives a completely different mathematical theory that effectively argues that the interior of a black hole is 'empty'. It highlights to me, just how up-in-the-air our current knowledge of black holes is. Basically, he argues that there is no singularity and that the black hole is a 'mirror'. You need to watch the video to get a grasp on what he's talking about, because I can't do it justice in this space.