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.

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.
 

How scale demonstrates that mathematics is intrinsically entailed in the Universe

 I momentarily contemplated another title: Is the Planck limit an epistemology or an ontology? Because that’s basically the topic of a YouTube video that’s the trigger for this post. I wrote a post some time ago where I discussed whether the Universe is continuous or discrete, and basically concluded that it was continuous. Based on what I’ve learned from this video, I might well change my position. But I should point out that my former opposition was based more on the idea that it could be quantised into ‘bits’ of information, whereas now I’m willing to acknowledge that it could be granular at the Planck scale, which I’ll elaborate on towards the end. I still don’t think that the underlying reality of the Universe is in ‘bits’ of information, therefore potentially created and operated by a computer.
 
Earlier this year, I discussed the problem of reification of mathematics so I want to avoid that if possible. By reification, I mean making a mathematical entity reality. Basically, physics works by formulating mathematical models that we then compare to reality through observations. But as Freeman Dyson pointed out, the wave function (Ψ), for example, is a mathematical entity and not a physical entity, which is sometimes debated. The fact is that if it does exist physically, it’s never observed, and my contention is that it ‘exists’ in the future; a view that is consistent with Dyson’s own philosophical viewpoint that QM can only describe the future and not the past.
 
And this brings me to the video, which has nothing to say about wave functions or reified mathematical entities, but uses high school mathematics to explore such esoteric and exotic topics as black holes and quantum gravity. There is one step involving integral calculus, which is about as esoteric as the maths becomes, and if you allow that 1/∞ = 0, it leads to the formula for the escape velocity from any astronomical body (including Earth). Note that the escape velocity literally allows an object to escape a gravitational field to infinity (∞). And the escape velocity for a black hole is c (the speed of light).
 
All the other mathematics is basic algebra using some basic physics equations, like Newton’s equation for gravity, Planck’s equation for energy, Heisenberg’s Uncertainty Principle using Planck’s Constant (h), Einstein’s famous equation for the equivalence of energy and mass, and the equation for the Coulomb Force between 2 point electric charges (electrons). There is also the equation for the Schwarzschild radius of a black hole, which is far easier to derive than you might imagine (despite the fact that Schwarzschild originally derived it from Einstein’s field equations).
 
Back in May 2019, I wrote a post on the Universe’s natural units, which involves the fundamental natural constants, h, c and G. This was originally done by Planck himself, which I describe in that post, while providing a link to a more detailed exposition. In the video (embedded below), the narrator takes a completely different path to deriving the same Planck units before describing a method that Planck himself would have used. In so doing, he explains how at the Planck level, space and time are not only impossible to observe, even in principle, but may well be impossible to remain continuous in reality. You need to watch the video, as he explains it far better than I can, just using high school mathematics.
 
Regarding the title I chose for this post, Roger Penrose’s Conformal Cyclic Cosmology (CCC) model of the Universe, exploits the fact that a universe without matter (just radiation) is scale invariant, which is essential for the ‘conformal’ part of his theory. However, that all changes when one includes matter. I’ve argued in other posts that different forces become dominant at different scales, from the cosmological to the subatomic. The point made in this video is that at the Planck scale all the forces, including gravity, become comparable. Now, as I pointed out at the beginning, physics is about applying mathematical models and comparing them to reality. We can’t, and quite possibly never will, be able to observe reality at the Planck scale, yet the mathematics tells us that it’s where all the physics we currently know is compatible. It tells me that not only is the physics of the Universe scale-dependent, but it's also mathematically dependent (because scale is inherently mathematical). In essence, the Universe’s dynamics are determined by mathematical parameters at all scales, including the Planck scale.
 
Note that the mathematical relationships in the video use ~ not = which means that they are approximate, not exact. But this doesn’t detract from the significance that 2 different approaches arrive at the same conclusion, which is that the Planck scale coincides with the origin of the Universe incorporating all forces equivalently.
 
 
Addendum: I should point out that Viktor T Toth, who knows a great deal more about this than me, argues that there is, in fact, no limit to what we can measure in principle. Even the narrator in the video frames his conclusion cautiously and with caveats. In other words, we are in the realm of speculative physics. Nevertheless, I find it interesting to contemplate where the maths leads us.

When truth becomes a casualty, democracy is put at risk

 You may know of Raimond Gaita as the author of Romulus, My Father, a memoir of his childhood, as the only child of postwar European parents growing up in rural Australia. It was turned into a movie directed by Richard Roxborough (his directorial debut) and starring Eric Bana. What you may not know is that Raimond Gaita is also a professor of philosophy who happens to live in the same metropolis as me, albeit in different suburbs.
 
I borrowed his latest tome, Justice and Hope; Essays, Lectures and Other Writings, from my local library (published last year, 2023), and have barely made a dent in the 33 essays, unequally divided into 6 parts. So far, I’ve read the 5 essays in Part 1: An Unconditional Love of the World, and just the first essay of Part 2: Truth and Judgement, which is titled rather provocatively, The Intelligentsia in the Age of Trump. Each essay heading includes the year it was written, and the essay on the Trump phenomenon (my term, not his) was written in 2017, so after Trump’s election but well before his ignominious attempt to retain power following his election defeat in 2020. And, of course, he now has more stature and influence than ever, having just won the Presidential nomination from the Republican Party for the 2024 election, which is only months away as I write.
 
Gaita doesn’t write like an academic in that he uses plain language and is not afraid to include personal anecdotes if he thinks they’re relevant, and doesn’t pretend that he’s nonpartisan in his political views. The first 5 essays regarding ‘an unconditional love of the world’ all deal with other writers and postwar intellects, all concerned with the inhumane conditions that many people suffered, and some managed to survive, during World War 2. This is confronting and completely unvarnished testimony, much darker and rawer than anything I’ve come across in the world of fiction, as if no writer’s imagination could possibly capture the absolute lowest and worst aspects of humanity.
 
None of us really know how we would react in those conditions. Sometimes in dreams we may get a hint. I’ve sometimes considered dreams as experiments that our minds play on us to test our moral fortitude. I know from my father’s experiences in WW2, both in the theatre of war and as a POW, that one’s moral compass can be bent out of shape. He told me of how he once threatened to kill someone who was stealing from wounded who were under his care. The fact that the person he threatened was English and the wounded were Arabs says a lot, as my father held the same racial prejudices as most of his generation. But I suspect he’d witnessed so much unnecessary death and destruction on such a massive scale that the life of a petty, opportunistic thief seemed worthless indeed. When he returned, he had a recurring dream where there was someone outside the house and he feared to confront them. And then on one occasion he did and killed them barehanded. His telling of this tale (when I was much older, of course) reminded me of Luke Skywalker meeting and killing his Jungian shadow in The Empire Strikes Back. My father could be a fearsome presence in those early years of my life – he had demons and they affected us all.
 
Another one of my tangents, but Gaita’s ruminations on the worst of humanity perpetrated by a nation with a rich and rightly exalted history makes one realise that we should not take anything for granted. I’ve long believed that anyone can commit evil given the right circumstances. We all live under this thin veneer that only exists because we mostly have everything we need and are generally surrounded by people who have no real axe to grind and who don’t see our existence as a threat to their own wellbeing.
 
I recently saw the movie, Civil War, starring Kirsten Dunst, who plays a journalist covering a hypothetical conflict in America, consequential to an authoritarian government taking control of the White House. The aspect that I found most believable was how the rule of law no longer seemed to apply, and people had become completely tribal whereupon one’s neighbour could become one’s enemy. I’ve seen documentaries on conflicts in Rwanda and the former Yugoslavia where this has happened – neighbours become mortal enemies, virtually overnight, because they suddenly find themselves on opposite sides of a tribal divide. I found the movie quite scary because it showed what happens when the veneer of civility we take for granted is not just lifted, but disappears.
 
On the first page of his essay on Trump, Gaita sets the tone and the context that resulted in Brexit on one side of the Atlantic and Trump’s Republican nomination on the other.
 
Before Donald Trump became the Republican nominee, Brexit forced many among the left-liberal intelligentsia to ask why they had not realised that resentment, anger and even hatred could go so deep as they did in parts of the electorate.
 
I think the root cause of all these dissatisfactions and resentments that lead to political upheavals that no one sees coming is trenchant inequality. I remember my father telling me when I was a child that the conflict in Ireland wasn’t between 2 religious groups but about wealth and inequality. I suspect he was right, even though it seems equally simplistic.
 
In all these divisions that we’ve seen, including in Australia, is the perception that people living in rural areas are being left out of the political process and not getting their fair share of representation, and consequentially everything else that follows from that, which results in what might be called a falling ‘standard of living’. The fallout from the GFC, which was global, exacerbated these differences, both perceived and real, and conservative politicians took advantage. They depicted the Left as ‘elitist’, which is alluded to in the title of Gaita’s essay, and is ‘code’ for ignorant and arrogant. This happened in Australia and I suspect in other Western democracies as well, like the UK and America.
 
Gaita expresses better than most how Trump has changed politics in America, if no where else, by going outside the bounds of normal accepted behaviour for a world leader. In effect, he’s changed the social norms that one associates with a person holding that position.
 
To illustrate my point, I’ll provide selected quotes, albeit out of context.
 
To call Trump a radically unconventional politician is like calling the mafia unconventional debt collectors; it is to fail to understand how important are the conventions, often unspoken, that enables decency in politics. Trump has poured a can of excrement over those conventions.
 
He has this to say about Trump’s ‘alternative facts’ not only espoused by him, but his most loyal followers.

In linking reiterated accusations of fake news to elites, Trump and his accomplices intended to undermine the conceptual and epistemic space that makes conversations between citizens possible.
 
It is hardly possible to exaggerate the seriousness of this. The most powerful democracy on Earth, the nation that considers itself and is often considered by others to be the leader of ‘the free world’, has a president who attacks unrelentingly the conversational space that can exist only because it is based on a common understanding – the space in which citizens can confidently ask one another what facts support their opinions. If they can’t ask that of one another, if they can’t agree on when something counts as having been established as fact, then the value of democracy is diminished.
 
He then goes on to cite J.D. Vance’s (recently nominated as Trump’s running VP), Hillbilly Elegy, where ‘he tells us… that Obama is not an American, that he was “born in some far-flung corner of the world”, that he has ties to Islamic extremism…’ and much worse.
 
Regarding some of Trump’s worse excesses during his 2016 campaign like getting the crowd to shout “Lock her up!” (his political opponent at the time) Gaita makes this point:
 
At the time, a CNN reporter said that his opponents did not take him seriously, but they did take him literally, whereas his supporters took him seriously but not literally. It was repeated many times… he would be reigned in by the Republicans in the House and the Senate and by trusted institutions. [But] He hasn’t changed in office.
 
It’s worth contemplating what this means if he wins Office again in 2024. He’s made it quite clear he’s out for revenge, and he’s also now been given effective immunity from prosecution by the Supreme Court if he seeks revenge through the Justice Department while he’s in Office. There is also the infamous Project 2025 which has the totally unhidden agenda to get rid of the so-called ‘deep state’ and replace public servants with Trump acolytes, not unlike a dictatorship. Did I just use that word?
 
Trump has achieved something I’ve never witnessed before, which Gaita doesn’t mention, though I have the benefit of an additional 7 years hindsight. What I’m referring to is that Trump has created an alternative universe, and from the commentary I’ve read on forums like Quora and elsewhere, you either live in one universe or the other – it’s impossible to claim you inhabit both. In other words, Trump has created an unbridgeable divide, which can’t be reconciled politically or intellectually. In one universe, Biden stole the 2020 POTUS election from Trump, and in another universe, Trump attempted to overturn the election and failed.
 
This is the depth of division that Trump has created in his country, and you have to ask: How far will people go to defend their version of the truth?
 
It was less than a century ago that fascism threatened the entire world order and created the most extensive conflict witnessed by humankind. I don’t think it’s an exaggeration to say that we are on the potential brink of creating a new brand of authoritarianism in the country epitomised by the slogan, ‘the free world’.

Daniel C Dennett (28 March 1942 - 19 April 2024)

 I only learned about Dennett’s passing in the latest issue of Philosophy Now (Issue 162, June/July 2024), where Daniel Hutto (Professor of Philosophical Psychology at the University of Wollongong) wrote a 3-page obituary. Not that long ago, I watched an interview with him, following the publication of his last book, I’ve Been Thinking, which, from what I gathered, is basically a memoir, as well as an insight into his philosophical musings. (I haven’t read it, but that’s the impression I got from the interview.)
 
I should point out that I have fundamental philosophical differences with Dennett, but he’s not someone you can ignore. I must confess I’ve only read one of his books (decades ago), Freedom Evolves (2006), though I’ve read enough of his interviews and commentary to be familiar with his fundamental philosophical views. It’s something of a failing on my part that I haven’t read his most famous tome, Consciousness Explained (1991). Paul Davies once nominated it among his top 5 books, along with Douglas Hofstadter’s Godel Escher Bach. But then he gave a tongue-in-cheek compliment by quipping, ‘Some have said that he explained consciousness away.’
 
Speaking of Hofstadter, he and Dennett co-published a book, The Mind’s I, which is really a collection of essays by different authors, upon which Dennett and Hofstadter commented. I wrote a short review covering only a small selection of said essays on this blog back in 2009.
 
Dennett wasn’t afraid to tackle the big philosophical issues, in particular, anything relating to consciousness. He was unusual for a philosopher in that he took more than a passing interest in science, and appreciated the discourse that axiomatically arises between the 2 disciplines, while many others (on both sides) emphasise the tension that seems to arise and often morphs into antagonism.
 
What I found illuminating in one of his YouTube videos was how Dennett’s views of the world hadn’t really changed that much over time (mind you, neither have mine), and it got me thinking that it reinforces an idea I’ve long held, but was once iterated by Nietzsche, that our original impulses are intuitive or emotive and then we rationalise them with argument. I can’t help but feel that this is what Dennett did, though he did it extremely well.
 
I like the quote at the head of Hutto’s obituary: “The secret of happiness is: Find something more important than you are and dedicate your life to it.”

 

More on radical ideas

 As you can tell from the title, this post carries on from the last one, because I got a bit bogged down on one issue, when I really wanted to discuss more. One of the things that prompted me was watching a 1hr presentation by cosmologist, Claudia de Rahm, whom I’ve mentioned before, when I had the pleasure of listening to an on-line lecture she gave, care of New Scientist, during the COVID lockdown.
 
Claudia’s particular field of study is gravity, and, by her own admission, she has a ‘crazy idea’. Now here’s the thing: I meet a lot of people on Quora and in the blogosphere, who like me, live (in a virtual sense) on the fringes of knowledge rather than as academic or professional participants. And what I find is that they often have an almost zealous confidence in their ideas. To give one example, I recently came across someone who argued quite adamantly that the Universe is static, not expanding, and has even written a book on the subject. This is contrary to virtually everyone else I’m aware of who works in the field of cosmology and astrophysics. And I can’t help but compare this to Claudia de Rahm who is well aware that her idea is ‘crazy’, even though she’s fully qualified to argue it.
 
In other words, it’s a case of the more you know about a subject, the less you claim to know, because experts are more aware of their limitations than non-experts. I should point out, in case you didn’t already know, I’m not one of the experts.
 
Specifically, Claudia’s crazy idea is that not only are there gravitational waves, but gravitons and that gravitons have an extremely tiny amount of mass, which would alter the effect of gravity at very long range. I should say that at present, the evidence is against her, because if she’s right, gravity waves would travel not at the speed of light, as predicted by Einstein, but ever-so-slightly less than light.
 
Freeman Dyson, by the way, has argued that if gravitons do exist, they would be impossible to detect, but if Claudia is right, then they would be.
 
In her talk, Claudia also discusses the vacuum energy, which according to particle physics, should be 28 orders of magnitude greater than the relativistic effect of ‘dark energy’. She calls it ‘the biggest discrepancy in the entire history of science’. This suggests that there is something rotten in the state of theoretical physics, along with the fact, that what we can physically observe, only accounts for 5% of the Universe.
 
It should be pointed out that at the end of the 19th Century no one saw or predicted the 2 revolutions in physics that were just around the corner – relativity theory and quantum mechanics. They were an example of what Thomas Kuhn called The Structure of Scientific Revolutions (the title of his book expounding on this). And I’d suggest that these current empirical aberrations in cosmology are harbingers of the next Kuhnian revolution.
 
Roger Penrose, whom I’ve referenced a number of times on this blog, is someone else with some ‘crazy’ ideas compared to the status quo, for which I admire him even if I don’t agree with him. One of Penrose’s hobby horses is his own particular inference from Godel’s Incompleteness Theorem, which he learned as a graduate (under Steen, at Cambridge) and which he discusses in this video. He argues that it provides evidence that humans don’t think like computers. If one takes the example of Riemann’s Hypothesis (really a conjecture) we know that a computer can’t tell us if it’s true or not (my example, not Penrose’s).* However, most mathematicians believe it is true, and it would be an enormous shock if it was proven untrue, or a contra-example was found by a computer. This is the case with other conjectures that have been proven true, like Fermat’s Last Theorem and Poincare’s conjecture. Penrose’s point, if I understand him correctly, is that it takes a human mind and not a computer to make this leap into the unknown and grasp a ‘truth’ out of the aether.
 
Anyone who has engaged in some artistic endeavour can identify with this, even if it’s not mathematical truths they are seeking but the key to unravelling a plot in a story.
 
Penrose makes the point in the video that he’s a ‘visual’ person, which he thinks is unusual in his field. Penrose is an excellent artist, by the way, and does all his own graphics. This is something else I can identify with, as I was quite precocious as a very young child at drawing (I could draw in perspective, though no one taught me) even though it never went anywhere.
 
Finally, some crazy ideas of my own. I’ve pointed out on other posts that I have a predilection (for want of a better term) for Kant’s philosophical proposition that we can never know the ‘thing-in-itself’ but only a perception of it.
 
With this in mind, I contend that this philosophical premise not only applies to what we can physically detect via instruments, but what we theoretically infer from the mathematics we use to explore nature. As heretical an idea as it may seem, I argue that mathematics is yet another 'instrument' we use to probe the secrets of the Universe. Quantum mechanics and relativity theory being the most obvious.
 
As I’ve tried to expound on other posts, relativity theory is observer-dependent, in as much as different observers will both measure and calculate different values of time and space, dependent on their specific frame of reference. I believe this is a pertinent example of Kant’s proposition that the thing-in-itself escapes our perception. In particular, physicists (including Penrose) will tell you that events that are ostensibly simultaneous to us (in a galaxy far, far away) will be perceived as both past and future by 2 observers who are simply crossing a street in opposite directions. I’ve written about this elsewhere as ‘the impossible thought experiment’.
 
The fact is that relativity theory rules out the event being observed at all. In other words, simultaneous events can’t be observed (according to relativity). For this reason, virtually all physicists will tell you that simultaneity is an illusion – there is no universal now.
 
But here’s the thing: if there is an edge in either space or time, it can only be observed from outside the Universe. Relativity theory, logically enough, can only tell us what we can observe from within the Universe.
 
But to extend this crazy idea, what’s stopping the Universe existing within a higher dimension that we can’t perceive. Imagine being a fish and you spend your entire existence in a massive body of water, which is your entire universe. But then one day you are plucked out of that environment and you suddenly become aware that there is another, even bigger universe that exists right alongside yours.
 
There is a tendency for us to think that everything that exists we can learn and know about – it’s what separates us from every other living thing on the planet. But perhaps there are other dimensions, or even worlds, that lie forever beyond our comprehension.

*Footnote: Actually, Penrose in his book, The Emperor’s New Mind, discusses this in depth and at length over a number of chapters. He makes the point that Turing’s ‘proof’ that it’s impossible to predict whether a machine attempting to compute all the Riemann zeros (for example) will stop, is a practical demonstration of the difference between ‘truth’ and ‘proof’ (as Godel’s Incompleteness Theorem tell us). Quite simply, if the theorem is true, the computer will never stop, so it can never be proven algorithmically. It can only be proven (or disproven) if one goes ‘outside the [current] rules’ to use Penrose’s own nomenclature.

Radical ideas

 It’s hard to think of anyone I admire in physics and philosophy who doesn’t have at least one radical idea. Even Richard Feynman, who avoided hyperbole and embraced doubt as part of his credo: "I’d rather have doubt and be uncertain, than be certain and wrong."
 
But then you have this quote from his good friend and collaborator, Freeman Dyson:


Thirty-one years ago, Dick Feynman told me about his ‘sum over histories’ version of quantum mechanics. ‘The electron does anything it likes’, he said. ‘It goes in any direction at any speed, forward and backward in time, however it likes, and then you add up the amplitudes and it gives you the wave-function.’ I said, ‘You’re crazy.’ But he wasn’t.
 
In fact, his crazy idea led him to a Nobel Prize. That exception aside, most radical ideas are either still-born or yet to bear fruit, and that includes mine. No, I don’t compare myself to Feynman – I’m not even a physicist - and the truth is I’m unsure if I even have an original idea to begin with, be they radical or otherwise. I just read a lot of books by people much smarter than me, and cobble together a philosophical approach that I hope is consistent, even if sometimes unconventional. My only consolation is that I’m not alone. Most, if not all, the people smarter than me, also hold unconventional ideas.
 
Recently, I re-read Robert M. Pirsig’s iconoclastic book, Zen and the Art of Motorcycle Maintenance, which I originally read in the late 70s or early 80s, so within a decade of its publication (1974). It wasn’t how I remembered it, not that I remembered much at all, except it had a huge impact on a lot of people who would never normally read a book that was mostly about philosophy, albeit disguised as a road-trip. I think it keyed into a zeitgeist at the time, where people were questioning everything. You might say that was more the 60s than the 70s, but it was nearly all written in the late 60s, so yes, the same zeitgeist, for those of us who lived through it.
 
Its relevance to this post is that Pirsig had some radical ideas of his own – at least, radical to me and to virtually anyone with a science background. I’ll give you a flavour with some selective quotes. But first some context: the story’s protagonist, whom we assume is Pirsig himself, telling the story in first-person, is having a discussion with his fellow travellers, a husband and wife, who have their own motorcycle (Pirsig is travelling with his teenage son as pillion), so there are 2 motorcycles and 4 companions for at least part of the journey.
 
Pirsig refers to a time (in Western culture) when ghosts were considered a normal part of life. But then introduces his iconoclastic idea that we have our own ghosts.
 
Modern man has his own ghosts and spirits too, you know.
The laws of physics and logic… the number system… the principle of algebraic substitution. These are ghosts. We just believe in them so thoroughly they seem real.
 
Then he specifically cites the law of gravity, saying provocatively:
 
The law of gravity and gravity itself did not exist before Isaac Newton. No other conclusion makes sense.
And what that means, is that the law of gravity exists nowhere except in people’s heads! It’s a ghost! We are all of us very arrogant and conceited about running down other people’s ghosts but just as ignorant and barbaric and superstitious about our own.
Why does everybody believe in the law of gravity then?
Mass hypnosis. In a very orthodox form known as “education”.
 
He then goes from the specific to the general:
 
Laws of nature are human inventions, like ghosts. Laws of logic, of mathematics are also human inventions, like ghosts. The whole blessed thing is a human invention, including the idea it isn’t a human invention. (His emphasis)
 
And this is philosophy in action: someone challenges one of your deeply held beliefs, which forces you to defend it. Of course, I’ve argued the exact opposite, claiming that ‘in the beginning there was logic’. And it occurred to me right then, that this in itself, is a radical idea, and possibly one that no one else holds. So, one person’s radical idea can be the antithesis of someone else’s radical idea.
 
Then there is this, which I believe holds the key to our disparate points of view:
 
We believe the disembodied 'words' of Sir Isaac Newton were sitting in the middle of nowhere billions of years before he was born and that magically he discovered these words. They were always there, even when they applied to nothing. Gradually the world came into being and then they applied to it. In fact, those words themselves were what formed the world. (again, his emphasis)
 
Note his emphasis on 'words', as if they alone make some phenomenon physically manifest.
 
My response: don’t confuse or conflate the language one uses to describe some physical entity, phenomena or manifestation with what it describes. The natural laws, including gravity, are mathematical in nature, obeying sometimes obtuse and esoteric mathematical relationships, which we have uncovered over eons of time, which doesn’t mean they only came into existence when we discovered them and created the language to describe them. Mathematical notation only exists in the mind, correct, including the number system we adopt, but the mathematical relationships that notation describes, exist independently of mind in the same way that nature’s laws do.
 
John Barrow, cosmologist and Fellow of the Royal Society, made the following point about the mathematical ‘laws’ we formulated to describe the first moments of the Universe’s genesis (Pi in the Sky, 1992).
 
Specifically, he says our mathematical theories describing the first three minutes of the Universe predict specific ratios of the earliest ‘heavier’ elements: deuterium, 2 isotopes of helium and lithium, which are 1/1000, 1/1000, 22 and 1/100,000,000 respectively; with the remaining (roughly 78%) being hydrogen. And this has been confirmed by astronomical observations. He then makes the following salient point:



It confirms that the mathematical notions that we employ here and now apply to the state of the Universe during the first three minutes of its expansion history at which time there existed no mathematicians… This offers strong support for the belief that the mathematical properties that are necessary to arrive at a detailed understanding of events during those first few minutes of the early Universe exist independently of the presence of minds to appreciate them.
 
As you can see this effectively repudiates Pirsig’s argument; but to be fair to Pirsig, Barrow wrote this almost 2 decades after Pirsig’s book.
 
In the same vein, Pirsig then goes on to discuss Poincare’s Foundations of Science (which I haven’t read), specifically talking about Euclid’s famous fifth postulate concerning parallel lines never meeting, and how it created problems because it couldn’t be derived from more basic axioms and yet didn’t, of itself, function as an axiom. Euclid himself was aware of this, and never used it as an axiom to prove any of his theorems.
 
It was only in the 19th Century, with the advent of Riemann and other non-Euclidean geometries on curved surfaces that this was resolved. According to Pirsig, it led Poincare to question the very nature of axioms.
 
Are they synthetic a priori judgements, as Kant said? That is, do they exist as a fixed part of man’s consciousness, independently of experience and uncreated by experience? Poincare thought not…
Should we therefore conclude that the axioms of geometry are experimental verities? Poincare didn’t think that was so either…
Poincare concluded that the axioms of geometry are conventions, our choice among all possible conventions is guided by experimental facts, but it remains free and is limited only by the necessity of avoiding all contradiction.
 
I have my own view on this, but it’s worth seeing where Pirsig goes with it:
 
Then, having identified the nature of geometric axioms, [Poincare] turned to the question, Is Euclidean geometry true or is Riemann geometry true?
He answered, The question has no meaning.
[One might] as well as ask whether the metric system is true and the avoirdupois system is false; whether Cartesian coordinates are true and polar coordinates are false. One geometry can not be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.
 
I think this is a false analogy, because the adoption of a system of measurement (i.e. units) and even the adoption of which base arithmetic one uses (decimal, binary, hexadecimal being the most common) are all conventions.
 
So why wouldn’t I say the same about axioms? Pirsig and Poincare are right in as much that both Euclidean and Riemann geometry are true because they’re dependent on the topology that one is describing. They are both used to describe physical phenomena. In fact, in a twist that Pirsig probably wasn’t aware of, Einstein used Riemann geometry to describe gravity in a way that Newton could never have envisaged, because Newton only had Euclidean geometry at his disposal. Einstein formulated a mathematical expression of gravity that is dependent on the geometry of spacetime, and has been empirically verified to explain phenomena that Newton couldn’t. Of course, there are also limits to what Einstein’s equations can explain, so there are more mathematical laws still to uncover.
 
But where Pirsig states that we adopt the axiom that is convenient, I contend that we adopt the axiom that is necessary, because axioms inherently expand the area of mathematics we are investigating. This is a consequence of Godel’s Incompleteness Theorem that states there are limits to what any axiom-based, consistent, formal system of mathematics can prove to be true. Godel himself pointed out that that the resolution lies in expanding the system by adopting further axioms. The expansion of Euclidean to non-Euclidean geometry is a case in point. The example I like to give is the adoption of √-1 = i, which gave us complex algebra and the means to mathematically describe quantum mechanics. In both cases, the axioms allowed us to solve problems that had hitherto been impossible to solve. So it’s not just a convenience but a necessity.
 
I know I’ve belaboured a point, but both of these: non-Euclidean geometry and complex algebra; were at one time radical ideas in the mathematical world that ultimately led to radical ideas: general relativity and quantum mechanics; in the scientific world. Are they ghosts? Perhaps ghost is an apt metaphor, given that they appear timeless and have outlived their discoverers, not to mention the rest of us. Most physicists and mathematicians tacitly believe that they not only continue to exist beyond us, but existed prior to us, and possibly the Universe itself.
 
I will briefly mention another radical idea, which I borrowed from Schrodinger but drew conclusions that he didn’t formulate. That consciousness exists in a constant present, and hence creates the psychological experience of the flow of time, because everything else becomes the past as soon as it happens. I contend that only consciousness provides a reference point for past, present and future that we all take for granted.

It all started with Euclid

 I’ve mentioned Euclid before, but this rumination was triggered by a post on Quora that someone wrote about Plato, where they argued, along with another contributor, that Plato is possibly overrated because he got a lot of things wrong, which is true. Nevertheless, as I’ve pointed out in other posts, his Academy was effectively the origin of Western philosophy, science and mathematics. It was actually based on the Pythagorean quadrivium of geometry, arithmetic, astronomy and music.
 
But Plato was also a student and devoted follower of Socrates and the mentor of Aristotle, who in turn mentored Alexander the Great. So Plato was a pivotal historical figure and without his writings, we probably wouldn’t know anything about Socrates. In the same way that, without Paul, we probably wouldn’t know anything about Jesus. (I’m sure a lot of people would find that debatable, but, if so, it’s a debate for another post.)
 
Anyway, I mentioned Euclid in my own comment (on Quora), who was the Librarian at Alexandria around 300BC, and thus a product of Plato’s school of thought. Euclid wrote The Elements, which I contend is arguably the most important book written in the history of humankind – more important than any religious text, including the Bible, Homer’s Iliad and the Mahabharata, which, I admit, is quite a claim. It's generally acknowledged as the most copied text in the secular world. In fact, according to Wikipedia:
 
It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing in 1482.
 
Euclid was revolutionary in one very significant way: he was able to demonstrate what ‘truth’ was, using pure logic, albeit in a very abstract and narrow field of inquiry, which is mathematics.
 
Before then, and in other cultures, truth was transient and subjective and often prescribed by the gods. But Euclid changed all that, and forever. I find it extraordinary that I was examined on Euclid’s theorems in high school in the 20th Century.
 
And this mathematical insight has become, millennia later, a key ingredient (for want of a better term) in the hunt for truths in the physical world. In the 20th Century, in what has become known as the Golden Age of Physics, the marriage between mathematics and scientific inquiry at all scales, from the cosmic to the infinitesimal, has uncovered deeply held secrets of nature that the Pythagoreans, and Euclid for that matter, could never have dreamed of. Look no further than quantum mechanics (QM) and the General Theory of Relativity (GR). Between these 2 iconic developments, they underpin every theory we currently have in physics, and they both rely on mathematics that was pivotal in the development of the theories from the outset. In other words, without the mathematics of complex algebra and Riemann geometry respectively, these theories would have been stillborn.
 
I like to quote Richard Feynman from his book, The Character of Physical Law, in a chapter titled, The Relation of Mathematics to Physics:
 
…what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics... Why? I have not the slightest idea. It is only my purpose to tell you about this fact.
 
The strange thing about physics is that for the fundamental laws we still need mathematics.
 
Physicists cannot make a conversation in any other language. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. She offers her information only in one form.
 
And this has only become more evident since Feynman wrote those words.
 
There was another revolution in the 20th Century, involving Alan Turing, Alonso Church and Kurt Godel; this time involving mathematics itself. Basically, each of these independently demonstrated that some mathematical truths were elusive to proof. Some mathematical conjectures could not be proved within the mathematical system from which they arose. The most famous example would be Riemann’s Hypothesis, involving primes. But the Goldbach conjecture (also involving primes) and the conjecture of twin primes also fit into this category. While most mathematicians believe them to be true, they are yet to be proven. I won’t elaborate on them, as they can easily be looked up.
 
But there is more: according to Gregory Chaitin, there are infinitely more incomputable Real numbers than computable Real numbers, which means that most of mathematics is inaccessible to logic.
 
So, when I say it all started with Euclid, I mean all the technology and infrastructure that we take for granted; and which allows me to write this so that virtually anyone anywhere in the world can read it; only exists because Euclid was able to derive ‘truths’ that stood for centuries and ultimately led to this.

Logic rules

I’ve written on this topic before, but a question on Quora made me revisit it.
 
Self-referencing can lead to contradiction or to illumination. It was a recurring theme in Douglas Hofstadter’s Godel Escher Bach, and it’s key to Godel’s famous Incompleteness Theorem, which has far-reaching ramifications for mathematics if not epistemology generally. We can never know everything there is to know, which effectively means there will always be known unknowns and unknown unknowns, with possibly infinitely more of the latter than the former.
 
I recently came across a question on Quora: Will a philosopher typically say that their belief that the phenomenal world "abides by all the laws of logic" is an entailment of those laws being tautologies? Or would they rather consider that belief to be an assumption made outside of logic?

If you’re like me, you might struggle with even understanding this question. But it seems to me to be a question about self-referencing. In other words, my understanding is that it’s postulating, albeit as a question, that a belief in logic requires logic. The alternative being ‘the belief is an assumption made outside of logic’. It’s made more confusing by suggesting that the belief is a tautology because it’s self-referencing.
 
I avoided all that, by claiming that logic is fundamental even to the extent that it transcends the Universe, so not a ‘belief’ as such. And you will say that even making that statement is a belief. My response is that logic exists independently of us or any belief system. Basically, I’m arguing that logic is fundamental in that its rules govern the so-called laws of the Universe, which are independent of our cognisance of them. Therefore, independent of whether we believe in them or not.
 
I’ve said on previous occasions that logic should be a verb, because it’s something we do, and not just humans, but other creatures, and even machines. But that can’t be completely true if it really does transcend the Universe. My main argument is hypothetical in that, if there is a hypothetical God, then said God also has to obey the rules of logic. God can’t tell us the last digit of pi (it doesn’t exist) and he can’t make a prime number non-prime or vice versa, because they are determined by pure logic, not divine fiat.
 
And now, of course, I’ve introduced mathematics into the equation (pun intended) because mathematics and logic are inseparable, as probably best demonstrated by Godel’s famous theorem. It was Euclid (circa 300BC) who introduced the concept of proof into mathematics, and a lynch pin of many mathematical proofs is the fundamental principle of logic that you can’t have a contradiction, including Euclid’s own relatively simple proof that there are an infinity of primes. Back to Godel (or forward 2,300 years, to be more accurate), and he effectively proved that there is a distinction between 'proof' and 'truth' in mathematics, in as much as there will always be mathematical truths that can’t be proven true within a given axiom based, consistent, mathematical system. In practical terms, you need to keep extending the ‘system’ to formulate more truths into proofs.
 
It's not a surprise that the ‘laws of the Universe’ that I alluded to above, seem to obey mathematical ‘rules', and in fact, it’s only because of our prodigious abilities to mine the mathematical landscape that we understand the Universe (at every observable scale) to the extent that we do, including scales that were unimaginable even a century ago.
 
I’ve spoken before about Penrose’s 3 Worlds: Physical, Mental and Platonic; which represent the Universe, consciousness and mathematics respectively. What links them all is logic. The Universe is riddled with paradoxes, yet even paradoxes obey logic, and the deeper we look into the Universe’s secrets the more advanced mathematics we need, just to describe it, let alone understand it. And logic is the means by which humans access mathematics, which closes the loop.
 

 Addendum: I'd forgotten that I wrote a similar post almost 5 years ago, where, unsurprisingly, I came to much the same conclusion. However, there's no reference to God, and I provide a specific example.