If everything is belief, what is reality?

This arose from a video I watched of Curt Jaimungal’s where he takes Neil deGrasse Tyson to task for saying: “Don’t say I believe anything.” Curt then says (to the viewer, not Neil): “Your wincing is justified.” But we don’t know the context, and maybe Neil was saying that in response to a specific issue, where he was possibly being told what he ‘believed’. If that’s the case, it’s different to Curt’s inference that Neil doesn’t believe anything at all.

Having said that, there is another video where Curt criticises Neil's position concerning the role of philosophy, where Neil takes the position a lot of physicists do, that there is no role for philosophy in science, whereas I argue that theoretical physicists practice philosophy even if they don’t know it (Curt makes exactly the same point). 

However, I have an issue with Curt’s position, when he elaborates (in the first video) that we only have varying degrees of belief, implying there is nothing we can say that is true with complete certainty. I’ve taken issue with this before with people less qualified than Curt. I’m one of those who makes a distinction between things I know and things I believe, between facts and theory. I think this distinction is important, otherwise everything is up for grabs. And, in a way, this is already happening, when Donald Hoffman argues that there is no objective reality. For example, “There is no objective moon or spacetime that exists even when unperceived… 

It’s a consequence of my go-to metaphor that there is an island of knowledge surrounded by a sea of ignorance, where science is the island and philosophy is the shoreline, and they interact and inform each other. As John Wheeler pointed out, as the island grows, so does the shoreline, therefore the interaction will never stop. This in itself is a philosophical position, consequently a belief.  

It's obvious to me that scientists have beliefs, and I have no dispute with Curt over that particular point, which is what he spends the first few minutes of his video elaborating on, using philosophical quotes like, “Most contemporary philosophers characterize belief as a propositional attitude.” (Emphasis in the original.) Meaning, in effect, it can be updated later when one finds new evidence, as Curt explicitly points out. In other words, it’s conditional, which I expect all scientists agree is the case for all scientific theories. This is a logical consequence arising from there being no theory that can explain all phenomena – they all have limitations. Therefore, all scientists have beliefs about phenomena that a particular theory can’t explain.

But my point is that this doesn’t rule out facts and truths that an existing theory covers, based on empirical evidence. And this was Neil’s point in another video, where he claims that empirical evidence will always overrule philosophy, and I agree. In the same way that empirical evidence will overrule a scientific conjecture or hypothesis, which is basically the scientific method in a nutshell.

I wrote a comment on Curt’s post, where I referenced Bell’s Theorem, and how Alain Aspect demonstrated (by experiment) that it proved Einstein wrong about entanglement (refer my post discussing Brian Greene’s interview with him). Basically, I contend that Aspect demonstrated something that was true (quantum entanglement), therefore, I claim it’s no longer a belief, but something we know. But that has since led to other beliefs that physicists and philosophers of science argue over. For instance, Sabine Hossenfelder argues it’s evidence of superdeterminism, not non-locality (as Aspect would argue).

So I contend there is a dialectic between science and philosophy, between facts and theory. In the same comment, I argued there are mathematical truths like there being an infinite number of primes, which I contend transcends belief. Many argue that this is still a belief (including, possibly, Curt) but my response is that, where you have something that can be either true or false, and it’s demonstrated to be true, it becomes a fact and no longer a belief. Another example I give, is that the Earth goes around the Sun or it doesn’t – it’s either true or false – and if it’s true, it’s a fact, therefore something I claim to know.

Now, you might argue this is a belief, based on what others have told me, which is correct. But here’s the thing: look at the alternative, which is that the sun goes around the Earth, which was believed for millennia, and a classic case of a propositional belief being updated with new evidence. The new evidence is not just astronomical data but a deeper understanding of reality and the nature of gravity in particular. So it’s similar to the example I gave of Alain Aspect, where empirical evidence provides facts.

In the case of our theories on gravity (first Newton’s, then Einstein’s), they not only provide an explanation for the Earth’s orbit around the Sun, but a lot of other phenomena that were previously inexplicable or even unknown - black holes, anyone? Curt would argue that it’s still a belief, only with a very high degree of confidence. But if I go back to my metaphor: it’s become part of the island of knowledge, and I can’t see it being cut adrift back into the sea of ignorance.

My other point is that this knowledge, or fact, or truth, then becomes the basis for new beliefs, otherwise I can’t see how science can progress. Curt would argue that this in itself is a belief, because it’s a philosophical position (see below), and I can’t argue with that. So, even claiming there are truths in mathematics, for example, is a philosophical position, therefore a belief. Does this lead to a contradiction? I don’t think believing in truths axiomatically means there are no truths, which is an even greater contradiction.

After watching the video a second time, I wrote another comment on Curt’s post, where I attempt to address this point:

Towards the end, Curt provides a counter viewpoint that scientific theories are contingent, which most, if not all, scientists would agree. However, my point is that a scientific theory needs to contain some 'truths' otherwise it's useless. I don't believe there are no 'truths' in the world; just that they all have applicable limitations. I'm talking about 'truth' in an epistemological sense; something we know, even though it started out as a belief. I don't believe in epistemological relativism. Obviously, that's a philosophical position, so axiomatically, a belief.

But, leaving aside scientific beliefs and truths, and whether the latter even exist, there is another extreme viewpoint that Curt addresses, where he quotes Bas van Fraassen:

“I believe many things, I believe I had a father, that I wrote a book, that we are still in America, and not on a flying saucer… Could I be wrong? Are there circumstances under which I would correctly give up some of these beliefs? Certainly.”

(I could make exactly the same assertions, except I live in Australia.)

And the ‘circumstances’ are, when I am dreaming, but to question one’s reality to that extent (when awake), I would argue, lies on the road to madness. We would normally expect, if someone genuinely questioned these ‘facts’, they would need psychiatric help. In other words, taking extreme examples of where truth could be questioned opens a Pandora’s box, usually known as insanity.

But what if the whole pack of cards comes crashing down, and we learn that we live in a simulation? As more than a few people claim, therefore believe. I don’t see how that changes the reality I deal with every day, which can literally be a matter of life and death. That’s my litmus test for reality – it can kill me.

And this brings me back to Donald Hoffman, who doesn’t believe we live in a simulation, but nevertheless believes everything we see and interact with is a fabrication of the mind. He even argues that the 3 dimensional space we ‘perceive’ is in fact, 2 dimensional, despite all the evidence to the contrary, and despite the fact that it would be impossible for one to live in a 2D world in the same way that one can live in a 3D world – we would fall apart, for a start.

I wish to give an example of something I ‘know,’ which is utterly trivial, yet transcends belief. I know that I can’t breathe without air. But here’s the thing: air exists in space and time, whether perceived or not. I don’t ‘believe’ it ceases to exist when I stop interacting with it, or when I take off my ‘headset of my own making’ (to cite Hoffman). Does that mean, if I could ‘take my headset off’, I’d stop breathing? Even when we are dreaming, experiencing a simulacrum of ‘our own making’, we continue to breath, because the external reality continues to exist, even while unperceived.

 

Addendum: This is one of those posts where I keep going over arguments in my mind. So, in response to Bas van Fraassen, one could argue that you don’t know if you’re a brain-in-a-vat, which is a well known philosophical conundrum, even though I don’t know of a philosopher who actually believes that. Nevertheless, there have been a number of sci-fi movies involving characters having false memories. Ones that come to mind are Ghost in the Shell, Dark City, City of Lost Children and even Blade Runner. There is also the Hyperion series by Dan Simmons dealing with people having their brains jacked, not dissimilar to the Matrix movies.

However, in real life we can verify our memories with physical records and through our interactions with others who have had the same experience. This is how I claim we know if something we remembered was a dream or not. So yes, we can have false memories, though usually not about what country we live in or whether we have a father, or if I’m the author of this blog.

In my childhood, there are 2 events that stood out and were bizarre enough to make me wonder if they were just a dream or not. Remember, in my original post, I explicitly reference dreaming as the ‘circumstances’ that Bas van Fraassen mentions as exceptions where his beliefs could be wrong.

One of the events was a fight between my parents that never happened, so it must have been a vivid dream. The other was an event that occurred when I was 7 or 8 years old, and were sounds that came out of the walls of the room I was lying in, while I was sick in bed. This is a very strong candidate for a dream except my father was a witness, and was even able to recall it decades later.

 

Should you believe me?

Note how prefacing the question with ‘why’ would change its focus if not its intent. I’ll return to this point at the end. I was originally going to write a post on time travel and UFOs, but I got sidetracked in my 'research'. In particular, I watched a talk given by famous sceptic, Michael Shermer (executive director of The Skeptics Society) and I remember reading his column in Scientific American in the 70s or 80s when I was a regular reader. He’s only slightly younger than me.

 

He gives a number of challenges in his talk, which are insightful in themselves, and I would gladly take them up. Basically, he’s making the point that when you challenge someone to explain why they believe something, they mostly can’t. He gives the examples of climate change and evolution, which he says are positions based on political beliefs rather than whether or not they understand the science behind them. I fall into this category, even though I’ve read books and accounts on these topics that most people wouldn’t bother, despite holding very passionate views on them.

 

Regarding evolutionary theory, I’d recommend Nick Lane’s excellent book, Life Ascending; The Ten Great Inventions of Evolution, which I’ve written about before. But I have another argument, which I’ve also presented before. Since Darwin and Wallace independently proposed their theories of evolution by natural selection over 160 years ago (1859 to be precise), we’ve made extraordinary discoveries that they could never have dreamed about, specifically in palaeontology and genetics. But here’s the thing: all the evidence discovered in the interim is not neutral; what has proven them right could just as readily have proven them wrong.

 

Regarding anthropomorphic climate change, I know of the role of greenhouse gases like carbon dioxide (CO2) and methane, without knowing the details, and I know that ultimately it’s caused by the difference in heat that can escape our atmosphere and the heat that’s trapped, which can’t be measured directly. However, NASA has data that is publicly available on their website, which combines historical ice-core data with atmospheric data collected at Mauna Loa in Hawaii, and they show how the 2 sources of data are complementary and seamlessly connected.

 

But I have a subsidiary argument, which is that we need to trust the expertise of people who work in climatology, because the rest of us don’t have it. I learned this from spending over 4 decades in engineering, where I constantly relied on expertise by people in various fields from structural and civil engineering to architecture to mechanical and electrical engineering to process engineering to software design and automation. The problem is, with the internet, you can always find an ‘expert’ to provide the evidence that supports your view, which was very prominently exhibited during the not-so-recent COVID pandemic.

 

But, in the case of climate change, nearly all the arguments I’ve come across (that question it) are that it’s a hoax and/or a global conspiracy to keep climatologists in a job. I admit I don’t take those arguments seriously. However, there is someone I know who was a geologist and had spent a very successful career in mining, who put up a technical argument based on the tonnes of CO2 in the atmosphere and how, as a percentage, it contradicted the official reporting, including that provided by NASA. NASA’s data is in ppm (parts per million), and I pointed out that to convert the weight into ppm you had to allow for the molecular weight of CO2, which brings it back in line with the reported results. He knew I was right and he didn't respond. But as Shermer would have pointed out, he was on the Right of politics and I’m on the Left, which axiomatically creates the divide. I’ve long argued that climate change should never have been politicised. But having said that, you’ll find people on the other side of the argument who will say exactly the same thing.

 

Shermer added a couple of other challenges to demonstrate how much we don’t know or take for granted. He asked, ‘Can you explain how a zipper works?’ No, but I can draw a diagram. Engineers often draw a picture when explaining something. He also asked, ‘Can you draw a bicycle?’ and explained how many people get it wrong. Well, actually, I can. I stopped the video to prove it to myself, though I had to raise the handlebars when I finished it. Mind you, I started drawing before I could write.

 

However, Shermer made me question myself, which is why I’m writing this post. You see I write about topics where I’m not an expert, specifically physics and cosmology. I’m not even a proper philosopher – I don’t even have a degree let alone a PhD. My only defence is that I’m well read and pay attention to people who know a lot more than me, even if I disagree with them. And what I’ve found from watching panel discussions on YouTube is that even experts can’t agree.

 

To give an example, I watched a panel discussion between 2 prominent philosophers of science and a theoretical physicist: Tim Maudlin, Hilary Lawson and Sabine Hossenfelder respectively; on whether there are particles or fields. Tim Maudlin appeared to be the odd one out, yet I found I was more in agreement with him, which might just be a reflection of my own ignorance. Basically, he argued that the ‘field’ in quantum mechanics is the wavefunction of the particle which doesn’t even exist in spacetime (it exists in Hilbert space with potentially infinite dimensions) and can’t be measured. It’s possible that Lawson and Hossenfelder were talking about something different – I don’t know enough to comment – but Hossenfelder said you can have different mathematical models that describe the same phenomenon. Maudlin quoted John Bell as saying we effectively don’t have a particle until it creates a spot on a screen or a photographic emulsion. Which is why I think it exists in the past and the wavefunction exists in the future, compatible with Freeman Dyson’s viewpoint.

 

Speaking of Bell, I watched another video with Neil deGrasse Tyson talking to Jana Levin about entanglement which is one of the best discussions I’ve seen on the topic. The point that I think needs to be emphasised is that entanglement introduces instantaneity, which to me, only makes sense if there is a universal 'now'. Tyson focused the discussion on the ramifications for cryptology, where they both agreed that it can’t be used to send a message faster-than-light, though I do it in my science fiction (I readily acknowledge I break the known laws of physics in my sci-fi).

 

I think there is an inherent contradiction or conundrum in physics and cosmology that the Universe has an edge in time but not space, whereas relativity theory tells us there is only spacetime (they are not separate) and ‘now’ is a purely subjective experience – there is no universal, objective now. This has led to physicists arguing that our experience of time ‘flowing’ is an illusion. Paul Davies believes that this experience will ultimately be 'explained by neuroscience, not physics'. Sabine Hossenfelder argues that there is no ‘now’ – it’s an illusion. Everyone knows that I greatly admire both of these scientists, both of whom know a lot more than me, yet I also think that postulating something that’s so outside our everyday experience, requires better explanations than we currently have. To me, it’s a sign that there is something wrong with our current theories rather than a sign that we all suffer from the same illusion that there is a past, present and future.

 

Getting back to Shermer and the role of expertise (though he doesn’t mention it, but I do): what I’ve found is that if you watch a discussion on a topic like evolution or climate change, especially when it’s combative, and you have someone present who is more knowledgeable and more experienced, they will invariably win the argument. And to extend that to my position, I imagine that if I was to have a discussion with Sabine, she would win hands down, and I would have to defer to her greater expertise, while not necessarily agreeing with her.

 

I once wrote a post where I critiqued her position on determinism and free will. It so happened I referenced this post to someone I met online, and to my surprise they said it was ‘very balanced’. I didn’t think it was balanced at all, given my prejudices, but I took it as a compliment.

 

So, addressing the question at the head of this post, the answer is, No. You shouldn’t simply believe what I say or argue; instead, you should do your own research and draw your own conclusions.

The Case Against Reality by Donald D. Hoffman

As I’ve pointed out before, YouTube has allowed scientists and philosophers of all stripes to promote pet theories that they know they can’t pursue academically with the same freedom. In fact, I’ve heard comments from people like Gregory Chaitin and Sabine Hossenfelder, who feel that the innate conservatism in academia is hindering progress in research and exploring new ideas.

 

Donald Hoffman is possibly an exception given his credentials: ‘Professor of Cognitive Sciences at the University of California, Irvine… [He] is the author of over one hundred scholarly articles on various aspects of human perception and cognition. He received a Distinguished Scientific Award of the American Psychological Association for early career research into visual perception, the Rustum Roy Award of the Chopra Foundation and the Troland Research Award of the US National Academy of Sciences.’

 

All of the above I’ve lifted verbatim from the About The Author section to his book, The Case Against Reality (2019). The copy I have is Penguin paperback (2020). The subtitle is How evolution hid the truth from our eyes. I first came across Hoffman 10 years ago (2016), when someone sent me a link to an academic paper he cowrote with Chetan Prakash called Objects of Consciousness, which I reviewed back then.

 

All of this gives Hoffman enormous credibility, without even mentioning that he had direct communication with Francis Crick before the latter died. His book is obviously aimed at people like myself, who have an interest in science but are not academic, with the intention of convincing us that his ideas are unassailable. But the truth is that by the time I reached the end of his book, I was more convinced that he was wrong than when I started. Now that’s a huge admission given the extraordinary gap in our credentials not to mention the limitations of my knowledge in neuroscience.

 

I wrote a post some time ago, where I talked about how important beliefs are in the development of science. What I’ve learned from watching various science experts on YouTube, who have, what one might call, ‘fringe ideas’, is that they form a very strong belief and then look for the evidence to support it. I include myself in this, even though I’m not a scientist. My fringe idea is that there is a universal now, and I think this is consistent with relativity theory, even though everyone will tell you that I’m wrong. The one thing going in my favour is that the Universe appears to have an edge in time and a finite age, which runs contrary to the orthodox view that there is no objective now. From what I’ve seen and read, physicists gloss over this conundrum, including Brian Greene in his excellent book, The Fabric of the Cosmos.

 

A better example is cosmologist Claudia de Rahm, who is one of the very few scientists (perhaps the only one with the necessary expertise) who thinks that gravitons could have mass. The point is that we don’t even know if gravitons exist, and she readily acknowledges, that if they do exist, they might be impossible to detect.

 

So I can’t criticise Hoffman simply because his ideas are ‘out there’; it’s not uncommon among scientists, including famous ones like Sir Roger Penrose.

 

This is a lengthy preamble, but I want to make one other point, before I get into the nitty gritty of his arguments. I wrote a post once on how I believe science works, which, in a nutshell, builds on what we already know, even when we have so-called revolutions in science. Ever since the scientific revolutions of Copernicus, Galileo, Kepler, and of course, Newton and Leibniz, our theories have extended science rather than outright replaced what went before. Claudia de Rahm (cited above) in answer to an audience question I watched online, made the explicit point that whatever new discoveries we make, they have to explain what we already know, so we don’t just throw everything in the rubbish bin (to use her turn-of-phrase).

 

Many people don’t know that one of Einstein’s self-imposed constraints on his General Theory of Relativity (GR) was that it had to agree mathematically with Newton’s theory of gravity when relativistic effects were negligible. Likewise, quantum mechanics (QM) hasn’t so much replaced classical physics, as added to it and possibly underpins it. UK based Aussie physicist, Mithuna Yoganathan (from the Looking Glass Universe YouTube channel) has made the point that she’s attracted to the many worlds interpretation (MWI) of QM because she can’t accept that the Universe obeys 2 sets of rules: for quantum mechanics and classical physics. The fact that she even mentions it suggests to me that it’s quite plausible, in which case, QM adds new physics without completely overturning the old.

 

The reason I’ve spent so much time on this detour is that, according to Hoffman, we need to reinvent virtually all the physics of the past 4-500 years, as well as evolutionary theory.

 

In fact, Hoffman states that “ITP asserts that one theory of objective reality – that it consists of physical objects in spacetime – is false.” (p.82) Einstein’s GR, mentioned earlier, is one such theory and currently underpins the latest cosmological model, specifically ΛCDM. ITP is Hoffman’s ‘Interface Theory of Perception’ which he analogises with a desktop interface on a computer, and to extend the analogy, the ‘objects’ we perceive are like ‘icons on the desktop’, so not ‘real’. I’ll return to this point later, given its significance to his argument.

 

After reading his book, I have many philosophical differences with Hoffman, but there is one point in particular, which is central to his entire thesis, where I’d argue the evidence contradicts him. I’m calling it the ‘principle of object permanence’. I admit I made that up, but it’s something that I argue evolution by natural selection selected for, because it’s a principle we not only take for granted but is cognitively found in babies and other animals. In other words, it’s the fundamental belief that an object still exists when we can’t see it. I will give an example of its ‘evolutionary value’ shortly, but it’s the direct opposite of what Hoffman believes. And I mention its evolutionary value because key to Hoffman’s theory is that evolution by natural selection supports his position and not mine.

 

He calls his theorem FBT, ‘Fitness-Beats-Truth’, which effectively means that evolution selects for fitness, not truth, while being somewhat hand-wavy about what those terms mean and how they can be quantified. The one example he provides in his book is a graphic representation. In fact, all his ‘evidence’ is based on computer modelling according to the examples he gives. He combines FBT with ITP (already mentioned), asserting they prove that he’s right: object permanence does not exist (as I defined it above).

 

I’m not going to try and prove his FBT or ITP wrong; I’m going to show why I believe the principle of object permanence is a necessary belief for evolutionary fitness. Now Hoffman would agree that the perception of object permanence affects evolutionary fitness but that doesn’t mean it’s real. However, I contend that it can make the difference between life and death, which does make it real.

 

I will give an example I read about once, involving crows not humans, which I assume really happened. Actually, it involved crows and humans, but it’s the cognitive ability of the crow that’s tested. A human with a gun set a trap for a crow using bait, then went into hiding until the crow took the bait. The crow, however saw the man go into hiding, and believing in object permanence waited patiently till the man left. Then the man got a companion, and this time the crow waited until both of them left. So they repeated the exercise using 3 gunmen and this time after 2 left, the crow thought it was safe, only it wasn’t. The exercise proved that the crow couldn’t count past 2. But you can see how a belief in object permanence can be critical to survival.

 

Now Hoffman has an answer to this, because it’s comparable to being hit by a car or being killed by any so-called object in his ‘interface’ (hence the name, ITP). He would say you need to take the car ‘seriously but not literally’. I admit I have a problem with that statement: I take the car ‘seriously’ because it can kill me but I don’t take it ‘literally’ because it’s not ‘real’. Hoffman keeps comparing this to someone playing Grand Theft Auto on a computer, because we live in an ‘interface’ not spacetime and there are no objects, only ‘icons’, including your own body. He later argues we don’t live in a computer simulation, which I’ll return to.

 

For examples of truth that evolution didn’t select for, he mentions oxygen and ultraviolet light causing sunburn. His point is that in both cases we don’t need to know about oxygen in order to know that the ability to breathe air confers fitness or know about ultraviolet light to know that keeping our skin covered against prolonged exposure to sunlight also confers fitness. By these examples, truth means explanations, to which I’d agree: evolution doesn’t select for explanations and I wrote about that elsewhere, while also discussing Hoffman. Note how sunlight and air exist externally to us.

 

Returning to my principle of object permanence, Hoffman cites Einstein’s famous retort to Bohr, ‘Do you think the moon ceases to exist when you’re not watching?’ It turns out that Hoffman does: “There is no objective moon or spacetime that exists even when unperceived…” (p.198)

 

I would like to know how that affects the tides occurring all around the world, although, according to Hoffman, there is no ‘around the world’, because there is no 3-dimensional space, and there is no cause and effect. He also claims that DNA and chromosomes don’t exist unperceived which turns evolutionary theory on its head. I discussed that in my original post on Hoffman. It reinforces my earlier point that Hoffman’s theory requires all of science to be replaced, including evolutionary theory as well as cosmology. He doesn’t explain how DNA and chromosomes can only exist when observed, yet underpin evolutionary theory as we currently know and understand it. He also claims the same for neurons in the brain, meaning consciousness creates them rather than the converse, which is the consensus of virtually all neuroscientists. Hoffman acknowledges this fundamental disagreement.

 

He spends a lot of time discussing optical illusions in considerable detail as supporting evidence that what we perceive is not real. I agree with him that our sensory experiences, like colour, sound and smell are all totally subjective and that other animals’ sensory experiences can be completely different to ours. We know that some animals can see colours we can’t and vice versa, and some can hear sounds that we can’t. But here’s the thing: colours are created by reflected light from an external source, and sounds are caused by vibrations transmitted through a medium, like air, and we’re evolutionarily adapted to pick them up and transform them into sensory experiences. To use his terms, the ‘fitness’ is our sensory experience and the ‘truth’ is our explanation of their external origins. So, yes, we evolved for fitness, not a scientific understanding called truth, but that doesn’t rule out object permanence (as described above) nor their location in space and time.

 

For the sake of brevity, I can’t address all his points but there is one other I find particularly contentious, and that is the idea that 3 dimensions of space are redundant, and we only need 2. Hoffman cites the cosmological holographic principle, which is basically the idea that all the (quantum) information inside a black hole is available holographically on the surface of its event horizon, which, it needs to be pointed out, is a sphere. Some argue that our entire universe could be modelled on the same principle, that everything in it could be a hologram projected from a 2-dimensional horizon. Hoffman argues that since all the information can be contained in 2 dimensions the third dimension of space that we ‘perceive’ is redundant and is used for ‘error-correction’. Aside from this being highly speculative physics, Hoffman overlooks the fact that the 2-dimensional surface of an event horizon on a sphere can only exist in 3-dimensional space; a hollow sphere in 2 dimensions becomes a circle.

 

But there is more: the inverse square law for gravity, which is in both Newton’s and Einstein’s theories, is a direct consequence of space being 3-dimensional. John Barrow gives the best account I’ve come across in his excellent book, The Constants of Nature. Given Hoffman’s access to academia, I’d recommend he talk to Barrow, or at least, read his book. Hoffman quotes Arkani-Hamed in a 2014 lecture at the Perimeter Institute: “Almost all of us believe that spacetime doesn’t exist; that spacetime is doomed, and has to be replaced by some more primitive building blocks.” (p.114) Now, I’m obviously not familiar with Arkani-Hamed’s work, but Graham Farmelo (The Universe Speaks in Numbers) also quotes Arkani-Hamed in a different context, which is the success of mathematical objects called amplituhedrons in predicting the amplitude of gluons in particle physics. Note this has an experimental physics basis, and is not just theoretical.

 

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. (my emphasis)

 

Now, I know that some physicists are speculating that spacetime might be an emergent property from something deeper (as inferred in the above quote from Arkani-Hamed), but that’s not the same as saying it doesn’t exist. If, on the other hand, Arkani-Hamed really believes that ‘spacetime doesn’t exist’, then he needs to replace the highly successful GR with something else. He also needs to explain the cosmological history based on the observable CMBR (cosmic microwave background radiation) that is the remnant of the Big Bang (13.8 billion years ago). I don’t know how you can have a cosmological history without spacetime. Hoffman challenges this by arguing for a ‘top-down cosmology’, that starts with an observer, but that’s another topic for another time.

 

In fact, Hoffman argues that conscious agents generate spacetime and all the physics we currently know, including quantum mechanics.

 

Conscious realism must ground a theory of quantum gravity, explain the emergence of our spacetime interface, and its objects, explain the appearance of Darwinian evolution within that interface, and explain the evolutionary emergence of human psychology. (pp.198-9)

 

We must show how conscious agents generate spacetime, objects, physical dynamics and evolutionary dynamics. We must get back quantum theory and general relativity, and generalisations of these theories that are mathematically precise. (p.184-5)

 

Hoffman does this by creating a mathematical model of consciousness that apparently generates all of what we call objective reality. He reveals this in an appendix, titled, Precisely; The Right to Be Wrong. He doesn’t make it clear who has ‘the right to be wrong’: himself or the rest of us. It’s very obtuse mathematics, in the form of logic rather than equations, but basically, he creates a mathematical formula for ‘conscious agents’, and then, using ‘Markovian dynamics’, effectively derives spacetime. I don’t pretend I can follow it. He concludes by saying: “…perhaps a dynamic evolution of conscious agents toward small-world networks may appear in spacetime as the dynamics of gravity.” (p.205) I think the words, ‘perhaps’ and ‘may’, do a lot of heavy-lifting. To provide context, Hoffman argues that it’s networks of ‘conscious agents’, not individuals, that generate the world we call reality.

 

Earlier this year, I attended a 2hr stage presentation by Prof Brian Cox, which was very esoteric, discussing wormholes, black holes and other cosmological exotica, but he never mentioned that ‘spacetime is doomed’; so that’s the orthodox view.

 

In summary, I have 2 fundamental contentions with Hoffman, without even considering his ideas on evolution. Anyone who has lost an object (like car keys) knows they still exist unobserved, including Hoffman, I suspect. He will rationalise that he takes them ’seriously but not literally’. However, that explains nothing, unless you’re in a video game (refer below). My argument is that evolution confers fitness on perceiving ‘object permanence’ because it’s a matter of life-and-death, as per my crow story.

 

My second contention is that we live in 3D not 2D. To demonstrate, draw an animal, any animal, on paper, so it’s flat and you can cut it out. Then draw an alimentary canal from its mouth to its anus. If you then cut it out, it falls apart into 2 pieces. This is as good a reason as any why we don’t live in a 2D universe. Hoffman mentions, in passing, while discussing something else, that he can’t visualise 4D, and there’s a good reason for that: we don’t need to; even though we can represent any finite dimensional world mathematically. The reason we can only visualise 3D and less, is because we live in a 3D world.

 

Hoffman finishes his main text (before the Appendix) with this:

 

Spacetime is your virtual reality, a headset of your own making. The objects you see are your inventions. You create them with a glance and destroy them with a blink. You have worn this headset all your life. What happens when you take it off? (p.202)

 

Despite claiming that he doesn’t believe we live in a computer simulation, his description of ‘reality’ is indistinguishable from one. This is demonstrated by calling objects and even his own body, ‘icons’, and that he believes the world is 2D like a screen, which we erroneously perceive as 3D (according to him), because it increases our evolutionary fitness.

 

He reinforces that view here: “The interface theory of perception contends that there is a screen – an interface – between us and objective reality.” (p.191, my emphasis)

 

Later he talks about spirituality, which I won’t elaborate on, except to say that the idea that consciousness can escape its physical constraints, as opposed to creating them, is not ruled out or ruled in.

Addendum: I admit to indulging in a fantasy of ‘talking’ to Donald Hoffman, so we could have a Socratic conversation.

Mathematics, language and reality

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

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

 

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

 

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

 

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

 

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

 

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