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.

Kant’s 300th Birthday (22nd April)

 I wouldn’t have known this if I hadn’t read about it in Philosophy Now. I have to confess I’ve only read the first and most famous of his 3 ‘Critiques’, The Critique of Pure Reason. I have to say that I think Kant was the first philosopher I read where I realised that it’s not about trying to convince everyone you’re right (even though, that’s effectively the methodology) so much as making people think outside their own box.
 
Kant famously attempted to bridge ‘empiricism’ (a la Hume) with ‘reason’ (a la Leibniz), as both necessary in the pursuit of knowledge. In other words, you can’t rely on just one of these fundamental approaches to epistemology. He also famously categorised them as ‘post priori’ and ‘a priori’ respectively, meaning that reason or logic is knowledge gained prior or independently of observation, while empirically derived evidence is derived after an observed event (by necessity). Curiously, he categorised space and time, as a priori, meaning they were mental states. I’ve quoted this often from The Critique of Pure Reason.
 
But this space and this time, and with them all appearances, are not in themselves things; they are nothing but representations and cannot exist outside our minds.
 
I’ve always fundamentally disagreed with this, but the fact that Kant challenges our intuitively held comprehension of space and time, based on our everyday experience, makes one think more deeply about it, if one wants to present a counter-argument.
 
He’s also famous for coining the term, ‘transcendental idealism’, which is like some exotic taxonomy in the library of philosophical ideas. Again, I’ll quote from the source:

All these faculties have a transcendental (as well as an empirical) employment which concerns the form alone, and is possible apriori. 
 
By ‘all these faculties’, he’s talking about our mental faculties to use reason to understand something ‘a priori’. I concluded in an essay I wrote on this very topic, when I studied Kant, that the logical and practical realisation of ‘transcendental idealism’ is mathematics, though I doubt that’s what Kant meant. The fact is that in the intervening 200+ years, epistemology has been dominated by physics, which combines empirical evidence with mathematics in a dialectical relationship, so it’s become impossible to do one without the other. So, in a way, I think Kant foresaw this relationship before it evolved into the profound and materially successful enterprise that we call science.
 
A couple of things I didn’t know. In his early years before he gained tenure, he supplemented his meagre income by private tutoring and hustling at billiards – who would have thought.
 
He also got into trouble with newly elected king, Friedrich Wilhelm II, for his critiques on religion, when he published The General Natural History and Theory of the Heavens in 1755, arguing for a purely physical explanation of the Universe’s origins, a good 200 years before it became acceptable. In effect, he was censored, and he didn’t publish anything else on religion until after Friedrich died, whereupon he immediately made up for lost time.

Do you think Hoffman’s theories about reality and perception are true?

I’ve written about this twice before in some detail, but this was a question on Quora, I addressed last year. I include it here because it’s succinct yet provides specific, robust arguments in the negative.
 
There is a temptation to consider Hoffman a charlatan, but I think that’s a bit harsh and probably not true. The point is that he either knows what he’s arguing is virtually indefensible yet perseveres simply out of notoriety, or he really believes what he’s saying. I’m willing to give him the benefit of the doubt. I think he’s gone so far down this rabbit-hole and invested so much of his time and reputation that it would take a severe cognitive dissonance to even consider he could be wrong. And this goes for a lot of us, in many different fields. In a completely different context, just look at those who have been Trump acolytes turned critics.
 
Below is my response to the question:
 
One-word answer, No. From the very first, when I read an academic paper he co-wrote with Chetan Kaprash, titled Objects of Consciousness (Frontiers in Psychology, 17 June 2014), I have found it very difficult to take him seriously. And everything I’ve read and seen since, only makes me more sceptical.

Hoffman’s ideas are consistent with the belief that we live in a computer simulation, though he’s never made that claim. Nevertheless, his go-to analogy for ‘objects’ we consider to be ‘real’ is the desktop icons on your computer. He talks about the ‘spacetime perceptual interface of H. Sapiens’ as a direct reference to a computer desktop, but it only exists in our minds. In fact, what he describes is what one would experience if one were to use a VR headset. But there is another everyday occurrence where we experience this phenomenon and it’s known as dreaming. Dreams are totally solipsistic, and you’ll notice they often defy reality without us giving them a second thought – until we wake up.

So, how do you know you’re not in a dream? Well, for one, we have no common collective memories with anyone we meet. Secondly, interactions and experiences we have in a dream, that would kill us in real life, don’t. Have you ever fallen from a great height in a dream? I have, many times.

And this is the main contention I have with Hoffman: reality can kill you. He readily admitted in a YouTube video that he wouldn’t step in front of a moving train. He tells us to take the train "seriously but not literally", after all it’s only a desktop icon. But, in his own words, if you put a desktop icon in the desktop bin it will have ‘consequences’. So, walking in front of a moving train is akin to putting the desktop icon of yourself in the bin. A good metaphor perhaps, but hardly a scientifically viable explanation of why you would die.

There are so many arguments one can use against Hoffman, that it’s hard to know where to start, or stop. His most outrageous claim is that ‘space and time doesn’t exist unperceived’, which means that all of history, including cosmological history only exists in the mind. Therefore, not only could we have not evolved, but neither could the planets, solar system and galaxies. In fact, the light we see from distant galaxies, not to mention the CMBR (the earliest observable event in the Universe), doesn’t exist unless someone’s looking at it.

Finally, you can set up a camera to take an image of an object (like a wild cat at night) without any conscious object in sight, except maybe the creature it took a photo of. But then, how did the camera only exist when the animal who didn’t see it, created it with its own consciousness?
 

Addendum:

Following my publishing this post, I watched a later, fairly recent video by Hoffman where he gives further reasons for his beliefs. In particular, he states that physics has shown that space and time are no longer fundamental, which is quite a claim. He cites the work of Nima Arkani-Hamed who has used a mathematical object called amplituhedrons to accurately predict the amplitudes of gluons in particle physics. I’ve read about this before in a book by Graham Farmelo (The Universe Speaks in Numbers; How Modern Maths Reveals Nature’s Deepest Secrets). Farmelo tells us that Arkani-Hamed is an American born Iranian, at the Princeton Institute for Advanced Study. To quote Arkani-Hamed directly from Farmelo's book:
 
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.
 
And this appears to be the point that Hoffman has latched onto, which he’s extrapolated to say that space and time are not fundamental. Whereas I drew a slightly different conclusion. In my discussion of Farmelo’s book, I made the following point:


The ‘something more basic’ is only known mathematically, as opposed to physically. I found this a most compelling tale and a history lesson in how mathematics appears to be intrinsically linked to the minutia of atomic physics.
 
I followed this with another reference to Arkani-Hamed.



In the same context, Arkani-Hamed says that ‘the mathematics of whole numbers in scattering-amplitude theory chimes… with the ancient Greeks' dream: to connect all nature with whole numbers.’
 
But, as I pointed out both here and in my last post, mathematical abstractions providing descriptions of natural phenomena are not in themselves physical. I see them as a code that allows us to fathom nature’s deepest secrets, which I believe Arkani-Hamed has contributed to.
 
Hoffman’s most salient point is that we need to go beyond time and space to find something more fundamental. In effect, he’s saying we need to go outside the Universe, and he might even be right, but that does not negate the pertinent, empirically based and widely held belief that space and time are arguably the most fundamental parameters within the Universe. If he’s saying that consciousness possibly exists beyond, therefore outside the Universe, I won’t argue with that, because we don’t know.
 
Hoffman has created mathematical models of consciousness, which I admit I haven’t read or seen, and he argues that those mathematical models lead to the same mathematical objects (abstractions) that Arkani-Hamed and others have used to describe fundamental physics. Therefore, consciousness creates the objects that the mathematics describes. That’s a very long bow to draw, to use a well-worn euphemism.
 

What does physics really tell us about reality?

 A little while ago I got into another discussion with Mark John Fernee (see previous post), but this time dealing with the relationship between ontology and epistemology as determined by physics. It came about in reference to a paper in Physics Today that someone cited, by N. David Nermin, a retired Professor of physics in Ithaca, New York, titled What’s bad about this habit. In particular, he talked about our tendency to ‘reify’ mathematically determined theories into reality. It helps if we have some definitions, which Fernee conveniently provided that were both succinct and precise.

Epistemology - concerning knowledge.

Ontology - concerning reality.

Reify - to think of an idea as real.

It so happens that around the same time I read an article in New Scientist (25 Mar 2024, pp.32-5) Strange but true? by philosopher, Eric Schwitzgebel, which covers similar territory. The title tells you little, but it’s really about how modern theories in physics don’t really tell us what reality is; instead giving us a range of possibilities to choose from.

I will start with Nermin, who spends the first page talking about quantum mechanics (QM), as it’s the most obvious candidate for a mathematical theory that gets reified by almost everyone who encounters it. This selected quote gives a good feel for what he’s talking about.

When I was a graduate student learning quantum field theory, I had a friend who was enchanted by the revelation that quantum fields were the real stuff that makes up the world. He reified quantum fields. But I hope you will agree that you are not a continuous field of operators on an infinite-dimensional Hilbert space. Nor, for that matter, is the page you are reading or the chair you are sitting in. Quantum fields are useful mathematical tools. They enable us to calculate things.

I found another quote by Freeman Dyson (2014), who makes a similar point to Nermin about the wave function (Ψ).

Unfortunately, people writing about quantum mechanics often use the phrase "collapse of the wave-function" to describe what happens when an object is observed. This phrase gives a misleading idea that the wave-function itself is a physical object. A physical object can collapse when it bumps into an obstacle. But a wave-function cannot be a physical object. A wave-function is a description of a probability, and a probability is a statement of ignorance. Ignorance is not a physical object, and neither is a wave-function. When new knowledge displaces ignorance, the wave-function does not collapse; it merely becomes irrelevant.

But Nermin goes on to challenge even the reality of space and time. Arguing that it is a mathematical abstraction. 

What about spacetime itself? Is that real? Spacetime is a (3+1) dimensional mathematical continuum. Even if you are a mathematical Platonist, I would urge you to consider that this continuum is nothing more than an extremely effective way to represent relations between distinct events.

He then goes on to explain that ‘an event… can be represented as a mathematical point in spacetime.’

He elaborates how this has become so reified into ordinary language that we’re no longer aware that it is an abstraction.

So spacetime is an abstract four-dimensional mathematical continuum of points that approximately represent phenomena whose spatial and temporal extension we find it useful or necessary to ignore. The device of spacetime has been so powerful that we often reify that abstract bookkeeping structure, saying that we inhabit a world that is such a four (or, for some of us, ten) dimensional continuum. The reification of abstract time and space is built into the very languages we speak, making it easy to miss the intellectual sleight of hand.

And this is where I start to have issues with his overall thesis, whereas Fernee said, ‘I completely concur with what he has written, and it is well articulated.’ 

When I challenged Fernee specifically on Nermin’s points about space-time, Fernee argued:

His contention was that even events in space-time are an abstraction. We all assume the existence of an objective reality, and I don't know of anyone who would seriously challenge that idea. Yet our descriptions are abstractions. All we ask of them is that they are consistent, describe the observed phenomena, and can be used to make predictions.

I would make an interesting observation on this very point, that distinguishes an AI’s apparent perspective of space and time compared to ours. Even using the word, ‘apparent’, infers there is a difference that we don’t think about.

I’ve made the point in other posts, including one on Kant, that we create a model of space and time in our heads which we use to interact with the physical space and time that exists outside our heads, and so do all living creatures with eyes, ears and touch. In fact, the model is so realistic that we think it is the external reality.

When we throw or catch a ball on the sporting field, we know that our brains don’t work out the quadratic equations that determine where it’s going to land. But imagine an AI controlled artillery device, which would make those calculations and use a 3-dimensional grid to determine where its ordinance was going to hit. Likewise, imagine an AI controlled drone using GPS co-ordinates – in other words, a mathematical abstraction of space and time – to navigate its way to a target. And that demonstrates the fundamental difference that I think Nermin is trying to delineate. The point is that, from our perspective, there is no difference.

This quote gives a clearer description of Nermin’s philosophical point of view.

Space and time and spacetime are not properties of the world we live in but concepts we have invented to help us organize classical events. Notions like dimension or interval, or curvature or geodesics, are properties not of the world we live in but of the abstract geometric constructions we have invented to help us organize events. As Einstein once again put it, “Space and time are modes by which we think, not conditions under which we live.”

Whereas I’d argue that they are both, and the mathematics tells us things about the ‘properties of the world [universe]’ which we can’t directly perceive with our senses – like ‘geodesics’ and the ‘curvature’ of spacetime. Yet they can be measured as well as calculated, which is why we know GR (Einstein’s general theory of relativity) works.

My approach to understanding physics, which may be misguided and would definitely be the wrong approach according to Nermin and Fernee, is to try and visualise the concepts that the maths describes. The concept of a geodesic is a good example. I’ve elaborated on this in another post, but I can remember doing Newtonian-based physics in high school, where gravity made no sense to me. I couldn’t understand why the force of gravity seemed to be self-adjusting so that the acceleration (g) was the same for all objects, irrespective of their mass.

It was only many years later, when I understood the concept of a geodesic using the principle of least action, that it all made sense. The objects don’t experience a force per se, but travel along the path of least action which is also the path of maximum relativistic time. (I’ve described this phenomenon elsewhere.) The point is that, in GR, mass is not in the equations (unlike Newton’s mathematical representation) and the force we all experience is from whatever it is that stops us falling, which could be a chair you’re sitting on or the Earth.

So, the abstract ‘geodesic’ explains what Newton couldn’t, even though Newton gave us the right answers for most purposes.

And this leads me to extend the discussion to include the New Scientist article. The author, Eric Schwitzgebel, ponders 3 areas of scientific inquiry: quantum mechanics (are there many worlds?); consciousness (is it innate in all matter?) and computer simulations (do we live in one?). I’ll address them in reverse order, because that’s easiest.

As Paul Davies pointed out in The Goldilocks Enigma, the so-called computer-simulation hypothesis is a variant on Intelligent Design. If you don’t believe in ID, you shouldn’t believe that the universe is a computer simulation, because some entity had to design it and produce the code.

'Is consciousness innate?' is the same as pansychism, as Schwitzgebel concurs, and I’d say there is no evidence for it, so not worth arguing about. Basically, I don’t want to waste time on these 2 questions, and, to be fair, Schwitzgebel’s not saying he’s an advocate for either of them.

Which brings me to QM, and that’s relevant. Schwitzbegel makes the point that all the scientific interpretations have bizarre or non-common-sensical qualities, of which MWI (many worlds interpretation) is just one. Its relevance to this discussion is that they are all reifications that are independent of the mathematics, because the mathematics doesn’t discern between them. And this gets to the nub of the issue for me. Most physicists would agree that physics, in a nutshell, is about creating mathematical models that are then tested by experimentation and observation, often using extremely high-tech, not-to-mention behemoth instruments, like the LHC and the James Webb telescope.

It needs to be pointed out that, without exception, all these mathematical models have limitations and, historically, some have led us astray. The most obvious being Ptolemy’s model of the solar system involving epicycles. String theory, with its 10 dimensions and 10^500 possible universes, is a potential modern-day contender, but we don’t really know.

Nevertheless, as I explained with my brief discourse on geodesics (above), there are occasions when the mathematics provides an insight we would otherwise be ignorant of.

Basically, I think what Schwitzgebel is really touching on is the boundary between philosophy and science, which I believe has always existed and is an essential dynamic, despite the fact that many scientists are dismissive of its role.

Returning to Nermin, it’s worth quoting his final passage.

Quantum mechanics has brought home to us the necessity of separating that irreducibly real experience from the remarkable, beautiful, and highly abstract super-structure we have found to tie it all together.

The ‘real experience’ includes the flow of time; the universality of now which requires memory for us to know it exists; the subjective experience of free will. All of these are considered ‘illusions’ by many scientists, not least Sabine Hossenfelder in her excellent book, Existential Physics. I tend to agree with another physicist, Richard Muller, that what this tells us is that there is a problem with our theories and not our reality.

In an attempt to reify QM with reality, I like the notion proposed by Freeman Dyson that it’s a mathematical model that describes the future. As he points out, it gives us probabilities, and it provides a logical reason why Feynman’s abstraction of an infinite number of ‘paths’ are never observed.

Curiously, Fernee provides tacit support for the idea that the so-called ‘measurement’ or ‘observation’ provides an ‘abstract’ distinction between past and future in physics, though he doesn’t use those specific words.

In quantum mechanics, the measurement hypothesis, which includes the collapse of the wave function, is an irreversible process. As we perceive the world through measurements, time will naturally seem irreversible to us.

Very similar to something Davies said in another context:

The very act of measurement breaks the time symmetry of quantum mechanics in a process sometimes described as the collapse of the wave function…. the rewind button is destroyed as soon as that measurement is made.

Lastly, I would like to mention magnetism, because, according to SR, it’s mathematically dependent on a moving electric charge. Only it’s not always, as this video explicates. You can get a magnetic field from electric spin, which is an abstraction, as no one suggests that electrons do physically spin, even though they produce measurable magnetic moments.

What most people don’t know is that our most common experience of a magnetic field, which is a bar magnet, is created purely by electron spin and not moving electrons.

Does simultaneity have any meaning?

 Someone on Quora asked me a question about simultaneity with respect to Einstein’s special theory of relativity (SR), so I referenced a 30min video of a lecture on the subject, which I’ve cited before on this blog. It not only provides a qualitative explanation or description, but also provides the calculations which demonstrate the subjectivity of simultaneity as seen by different observers.
 
Below I’ve copied exactly what I posted on Quora, including the imbedded video. I’ll truncate the question to make things simpler. The questioner (Piet Venter) asked if there is experimental evidence, which I ignored, partly because I don’t know if there is, but also because it’s mathematically well understood and it’s a logical consequence of SR. Afterwards, I’ll discuss the philosophical ramifications.
 
Does the train embankment thought experiment of Einstein really demonstrate relativity of simultaneity?
 
Actually, there’s a very good YouTube video, which explains this much better than I can. It’s a lecture on the special theory of relativity (SR) and you might find the mathematics a bit daunting, but it’s worth persevering with. He gives the perspective from both a ‘stationary’ observer and a ‘moving’ observer. Note that he also allows for space-contraction for the ‘moving’ case to arrive at the correct answer.

 
To be specific, he uses the Bob and Alice scenario with Bob in a spaceship, so Bob’s ‘stationary’ with respect to the light signals, while he’s ‘moving’ with respect to Alice. What I find interesting is that from Bob’s perspective, he sees what I call a ‘true simultaneity’ (though no one uses that term) because everything is in the same frame of reference for Bob. The lecturer explains both their perspectives qualitatively in the first 6 mins, before he gets into the calculations.
 
When he does the calculations, Bob sees no difference in the signals, while Alice does. This infers that Bob has a special status as an observer compared to Alice. This is consistent with the calculations if you watch the whole video. The other point that no one mentions, is that Alice can tell that the signal on Bob’s ship is moving with respect to her reference-frame because of the Doppler shift of the light, whereas Bob sees no Doppler shift.

 
I commit a heresy by talking about a ‘true simultaneity’, while physicists will tell you there’s no such thing. But even the lecturer in the video makes the point that, according to Bob, he sees the two events recorded by his ‘clocks’ as happening at the same time, because everything is stationary in his frame of reference. Even though his frame of reference is moving relative to others, including Alice, and also compared to anyone on Earth, presumably (since he’s in a spaceship).
 
I contend that Bob has a special status and this is reflected in the mathematics. So is this a special case or can we generalise this to other events? People will argue that a core tenet of Einstein’s relativity is that there are no observers with a ‘special status’. But actually, the core tenet, as iterated by the lecturer in the video, is that the speed of light is the same for all observers, irrespective of their frame of reference. This means that even if an observer is falling into a black hole at the speed of light, they would still see any radiation travelling at the speed of light relative to them. So relativity creates paradoxes, and I gave a plausible resolution to that particular paradox in a recent post, as did David Finkelstein in 1958. (The ‘special status’ is that Bob is in the same frame of reference, his spaceship, as the light source and the 2 resultant events.)
 
In another even more recent post, I cited Kip Thorne explaining how, when one looks at the curvature of spacetime, one gets the same results if spacetime is flat and it’s the ruler that distorts. If one goes back to the Bob and Alice thought experiment in the video, Alice sees (or measures) a distortion, in as much as the front clock in Bob’s spaceship ‘lags’ his rear clock, where for Bob they are the same. This is because, from Alice’s perspective, the light signal takes longer to reach the front because it’s travelling away from her (from Bob’s perspective, it’s stationary). On the other hand, the rear clock is travelling towards the light signal (from her perspective).
 
When I was first trying to get my head around relativity, I took an unusual and novel approach. Because we are dealing with light waves, it occurred to me that both observers would ‘see’ the same number of waves, but the waves would be longer or shorter, which also determines the time and distance that they measure, because waves have wavelength (corresponding to distance) and frequency (corresponding to time).
 
If I apply this visualisation trick to Alice’s perception, then the waves going to the front clock must get longer and the waves going to the rear must get shorter, if they are to agree with the number of waves that Bob ‘sees’, whereby from his perspective, there’s no change in wavelength or frequency. And if the number of waves correspond to a ‘ruler’, then Alice’s ruler becomes distorted while Bob’s doesn’t. So she ‘measures’ a longer distance to the front from the light source than the rear, and because it takes longer for the light to reach the front clock, then it ‘lags’ (relative to Bob’s recording) according to her observation, using her own clocks (refer video).
 
So, does this mean that there is a universal simultaneity that we can all agree on? No, it doesn’t. For a start, using the thought experiment in the video, Bob is travelling relative to a frame of reference, which is the spacetime of the Universe. In fact, if there is a gravitational gradient in his space ship then that would be enough to put his clocks out of sync, so his frame of reference is idealised.
 
But I would make the point that not all observations of simultaneity are equal. While observers in different locations in the Universe would see the same events happening in different sequences; for events having a causal relationship, then all observers would see the same sequence, irrespective of their frame of reference. Since everything that happens is causally related to past events, then everything exists in a sequence that is unchangeable. It’s just that there is no observer who can see all causal sequences – it’s impossible. This brings me back to Kant, whom I reference in my last post, that there is an epistemological gap between what we can observe and what really is. If there is a hypothetical ‘universal now’ for the entire universe, no single observer within the universe can see it. Current wisdom is that it doesn’t exist, but I contend that, if it does, we can’t know.

What would Kant say?

Even though this is a philosophy blog, my knowledge of Western philosophy is far from comprehensive. I’ve read some of the classic texts, like Aristotle’s Nicomachean Ethics, Descartes Meditations, Hume’s A treatise of Human Nature, Kant’s Critique of Pure Reason; all a long time ago. I’ve read extracts from Plato, as well as Sartre’s Existentialism is a Humanism and Mill’s Utilitarianism. As you can imagine, I only recollect fragments, since I haven’t revisited them in years.
 
Nevertheless, there are a few essays on this blog that go back to the time when I did. One of those is an essay on Kant, which I retitled, Is Kant relevant to the modern world? Not so long ago, I wrote a post that proposed Kant as an unwitting bridge between Plato and modern physics. I say, ‘unwitting’, because, as far as I know, Kant never referenced a connection to Plato, and it’s quite possible that I’m the only person who has. Basically, I contend that the Platonic realm, which is still alive and well in mathematics, is a good candidate for Kant’s transcendental idealism, while acknowledging Kant meant something else. Specifically, Kant argued that time and space, like sensory experiences of colour, taste and sound, only exist in the mind.
 
Here is a good video, which explains Kant’s viewpoint better than me. If you watch it to the end, you’ll find the guy who plays Devil’s advocate to the guy expounding on Kant’s views makes the most compelling arguments (they’re both animated icons).

But there’s a couple of points they don’t make which I do. We ‘sense’ time and space in the same way we sense light, sound and smell to create a model inside our heads that attempts to match the world outside our heads, so we can interact with it without getting killed. In fact, our modelling of time and space is arguably more important than any other aspect of it.
 
I’ve always had a mixed, even contradictory, appreciation of Kant. I consider his insight that we may never know the things-in-themselves to be his greatest contribution to epistemology, and was arguably affirmed by 20th Century physics. Both relativity and quantum mechanics (QM) have demonstrated that what we observe does not necessarily reflect reality. Specifically, different observers can see and even measure different parameters of the same event. This is especially true when relativistic effects come into play.
 
In relativity, different observers not only disagree on time and space durations, but they can’t agree on simultaneity. As the Kant advocate in the video points out, surely this is evidence that space and time only exist in the mind, as Kant originally proposed. The Devil’s advocate resorts to an argument of 'continuity', meaning that without time as a property independent of the mind, objects and phenomena (like a candle burning) couldn’t continue to happen without an observer present.
 
But I would argue that Einstein’s general theory of relativity, which tells us that different observers can measure different durations of space and time (I’ll come back to this later), also tells us that the entire universe requires a framework of space and time for the objects to exist at all. In other words, GR tells us, mathematically, that there is an interdependence between the gravitational field that permeates and determines the motion of objects throughout the entire universe, and the spacetime metric those same objects inhabit. In fact, they are literally on opposite sides of the same equation.
 
And this brings me to the other point that I think is missing in the video’s discussion. Towards the end, the Devil’s advocate introduces ‘the veil of perception’ and argues:
 
We can only perceive the world indirectly; we have no idea what the world is beyond this veil… How can we then theorise about the world beyond our perceptions? …Kant basically claims that things-in-themselves exist but we do not know and cannot know anything about these things-in-themselves… This far-reaching world starts to feel like a fantasy.
 
But every physicist has an answer to this, because 20th Century physics has taken us further into this so-called ‘fantasy’ than Kant could possibly have imagined, even though it appears to be a neverending endeavour. And it’s specifically mathematics that has provided the means, which the 2 Socratic-dialogue icons have ignored. Which is why I contend that it’s mathematical Platonism that has replaced Kant’s transcendental idealism. It’s rendered by the mind yet it models reality better than anything else we have available. It’s the only means we have available to take us behind ‘the veil of perception’ and reveal the things-in-themselves.
 
And this leads me to a related point that was actually the trigger for me writing this in the first place.
 
In my last post, I mentioned I’m currently reading Kip A. Thorne’s book, Black Holes and Time Warps; Einstein’s Outrageous Legacy (1994). It’s an excellent book on many levels, because it not only gives a comprehensive history, involving both Western and Soviet science, it also provides insights and explanations most of us are unfamiliar with.
 
To give an example that’s relevant to this post, Thorne explains how making measurements at the extreme curvature of spacetime near the event horizon of a black hole, gives the exact same answer whether it’s the spacetime that distorts while the ‘rulers’ remain unchanged, or it’s the rulers that change while it’s the spacetime that remains ‘flat’. We can’t tell the difference. And this effectively confirms Kant’s thesis that we can never know the things-in-themselves.
 
To quote Thorne:
 
What is the genuine truth? Is spacetime really flat, or is it really curved? To a physicist like me this is an uninteresting question because it has no physical consequences (my emphasis). Both viewpoints, curved spacetime and flat, give the same predictions for any measurements performed with perfect rulers and clocks… (Earlier he defines ‘perfect rulers and clocks’ as being derived at the atomic scale)
 
Ian Miller (a physicist who used to be active on Quora) once made the point, regarding space-contraction, that it’s the ruler that deforms and not the space. And I’ve made the point myself that a clock can effectively be a ruler, because a clock that runs slower measures a shorter distance for a given velocity, compared to another so-called stationary observer who will measure the same distance as longer. This happens in the twin paradox thought experiment, though it’s rarely mentioned (even by me).