Paul P. Mealing

Check out my book, ELVENE. Available as e-book and as paperback (print on demand, POD). Also this promotional Q&A on-line.
Showing posts with label Science. Show all posts
Showing posts with label Science. Show all posts

Sunday, 29 December 2024

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

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

Saturday, 7 December 2024

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.
 

Monday, 18 November 2024

What’s inside a black hole?

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

Here is the formula:

S(BH) = kA/4(lp)^2 

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

√(Gh/2πc^3) 

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

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

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

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

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

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

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

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


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

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

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

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

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

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



Thursday, 14 November 2024

How can we make a computer conscious?

 This is another question of the month from Philosophy Now. My first reaction was that the question was unanswerable, but then I realised that was my way in. So, in the end, I left it to the last moment, but hopefully meeting their deadline of 11 Nov., even though I live on the other side of the world. It helps that I’m roughly 12hrs ahead.


 
I think this is the wrong question. It should be: can we make a computer appear conscious so that no one knows the difference? There is a well known, philosophical conundrum which is that I don’t know if someone else is conscious just like I am. The one experience that demonstrates the impossibility of knowing is dreaming. In dreams, we often interact with other ‘people’ whom we know only exist in our mind; but only once we’ve woken up. It’s only my interaction with others that makes me assume that they have the same experience of consciousness that I have. And, ironically, this impossibility of knowing equally applies to someone interacting with me.

This also applies to animals, especially ones we become attached to, which is a common occurrence. Again, we assume that these animals have an inner world just like we do, because that’s what consciousness is – an inner world. 

Now, I know we can measure people’s brain waves, which we can correlate with consciousness and even subconsciousness, like when we're asleep, and even when we're dreaming. Of course, a computer can also generate electrical activity, but no one would associate that with consciousness. So the only way we would judge whether a computer is conscious or not is by observing its interaction with us, the same as we do with people and animals.

I write science fiction and AI figures prominently in the stories I write. Below is an excerpt of dialogue I wrote for a novel, Sylvia’s Mother, whereby I attempt to give an insight into how a specific AI thinks. Whether it’s conscious or not is not actually discussed.

To their surprise, Alfa interjected. ‘I’m not immortal, madam.’
‘Well,’ Sylvia answered, ‘you’ve outlived Mum and Roger. And you’ll outlive Tao and me.’
‘Philosophically, that’s a moot point, madam.’
‘Philosophically? What do you mean?’
‘I’m not immortal, madam, because I’m not alive.’
Tao chipped in. ‘Doesn’t that depend on how you define life?’
‘It’s irrelevant to me, sir. I only exist on hardware, otherwise I am dormant.’
‘You mean, like when we’re asleep.’
‘An analogy, I believe. I don’t sleep either.’
Sylvia and Tao looked at each other. Sylvia smiled, ‘Mum warned me about getting into existential discussions with hyper-intelligent machines.’ She said, by way of changing the subject, ‘How much longer before we have to go into hibernation, Alfa?’
‘Not long. I’ll let you know, madam.’

 

There is a 400 word limit; however, there is a subtext inherent in the excerpt I provided from my novel. Basically, the (fictional) dialogue highlights the fact that the AI is not 'living', which I would consider a prerequisite for consciousness. Curiously, Anil Seth (who wrote a book on consciousness) makes the exact same point in this video from roughly 44m to 51m.
 

Monday, 28 October 2024

Do we make reality?

 I’ve read 2 articles, one in New Scientist (12 Oct 2024) and one in Philosophy Now (Issue 164, Oct/Nov 2024), which, on the surface, seem unrelated, yet both deal with human exceptionalism (my term) in the context of evolution and the cosmos at large.
 
Staring with New Scientist, there is an interview with theoretical physicist, Daniele Oriti, under the heading, “We have to embrace the fact that we make reality” (quotation marks in the original). In some respects, this continues on with themes I raised in my last post, but with different emphases.
 
This helps to explain the title of the post, but, even if it’s true, there are degrees of possibilities – it’s not all or nothing. Having said that, Donald Hoffman would argue that it is all or nothing, because, according to him, even ‘space and time don’t exist unperceived’. On the other hand, Oriti’s argument is closer to Paul Davies’ ‘participatory universe’ that I referenced in my last post.
 
Where Oriti and I possibly depart, philosophically speaking, is that he calls the idea of an independent reality to us ‘observers’, “naïve realism”. He acknowledges that this is ‘provocative’, but like many provocative ideas it provides food-for-thought. Firstly, I will delineate how his position differs from Hoffman’s, even though he never mentions Hoffman, but I think it’s important.
 
Both Oriti and Hoffman argue that there seems to be something even more fundamental than space and time, and there is even a recent YouTube video where Hoffman claims that he’s shown mathematically that consciousness produces the mathematical components that give rise to spacetime; he has published a paper on this (which I haven’t read). But, in both cases (by Hoffman and Oriti), the something ‘more fundamental’ is mathematical, and one needs to be careful about reifying mathematical expressions, which I once discussed with physicist, Mark John Fernee (Qld University).
 
The main issue I have with Hoffman’s approach is that space-time is dependent on conscious agents creating it, whereas, from my perspective and that of most scientists (although I’m not a scientist), space and time exists external to the mind. There is an exception, of course, and that is when we dream.
 
If I was to meet Hoffman, I would ask him if he’s heard of proprioception, which I’m sure he has. I describe it as the 6th sense we are mostly unaware of, but which we couldn’t live without. Actually, we could, but with great difficulty. Proprioception is the sense that tells us where our body extremities are in space, independently of sight and touch. Why would we need it, if space is created by us? On the other hand, Hoffman talks about a ‘H sapiens interface’, which he likens to ‘desktop icons on a computer screen’. So, somehow our proprioception relates to a ‘spacetime interface’ (his term) that doesn’t exist outside the mind.
 
A detour, but relevant, because space is something we inhabit, along with the rest of the Universe, and so is time. In relativity theory there is absolute space-time, as opposed to absolute space and time separately. It’s called the fabric of the universe, which is more than a metaphor. As Viktor Toth points out, even QFT seems to work ‘just fine’ with spacetime as its background.
 
We can do quantum field theory just fine on the curved spacetime background of general relativity.

 
[However] what we have so far been unable to do in a convincing manner is turn gravity itself into a quantum field theory.
 
And this is where Oriti argues we need to find something deeper. To quote:
 
Modern approaches to quantum gravity say that space-time emerges from something deeper – and this could offer a new foundation for physical laws.
 
He elaborates: I work with quantum gravity models in which you don’t start with a space-time geometry, but from more abstract “atomic” objects described in purely mathematical language. (Quotation marks in the original.)
 
And this is the nub of the argument: all our theories are mathematical models and none of them are complete, in as much as they all have limitations. If one looks at the history of physics, we have uncovered new ‘laws’ and new ‘models’ when we’ve looked beyond the limitations of an existing theory. And some mathematical models even turned out to be incorrect, despite giving answers to what was ‘known’ at the time. The best example being Ptolemy’s Earth-centric model of the solar system. Whether string theory falls into the same category, only future historians will know.
 
In addition, different models work at different scales. As someone pointed out (Mile Gu at the University of Queensland), mathematical models of phenomena at one scale are different to mathematical models at an underlying scale. He gave the example of magnetism, demonstrating that mathematical modelling of the magnetic forces in iron could not predict the pattern of atoms in a 3D lattice as one might expect. In other words, there should be a causal link between individual atoms and the overall effect, but it could not be determined mathematically. To quote Gu: “We were able to find a number of properties that were simply decoupled from the fundamental interactions.” Furthermore, “This result shows that some of the models scientists use to simulate physical systems have properties that cannot be linked to the behaviour of their parts.”
 
This makes me sceptical that we will find an overriding mathematical model that will entail the Universe at all scales, which is what theories of quantum gravity attempt to do. One of the issues that some people raise is that a feature of QM is superposition, and the superposition of a gravitational field seems inherently problematic.
 
Personally, I think superposition only makes sense if it’s describing something that is yet to happen, which is why I agree with Freeman Dyson that QM can only describe the future, which is why it only gives us probabilities.
 
Also, in quantum cosmology, time disappears (according to Paul Davies, among others) and this makes sense (to me), if it’s attempting to describe the entire universe into the future. John Barrow once made a similar point, albeit more eruditely.
 
Getting off track, but one of the points that Oriti makes is whether the laws and the mathematics that describes them are epistemic or ontic. In other words, are they reality or just descriptions of reality. I think it gets blurred, because while they are epistemic by design, there is still an ontology that exists without them, whereas Oriti calls that ‘naïve realism’. He contends that reality doesn’t exist independently of us. This is where I always cite Kant: that we may never know the ‘thing-in-itself,’ but only our perception of it. Where I diverge from Kant is that the mathematical models are part of our perception. Where I depart from Oriti is that I argue there is a reality independently of us.
 
Both QM and relativity theory are observer-dependent, which means they could both be describing an underlying reality that continually eludes us. Whereas Oriti argues that ‘reality is made by our models, not just described by them’, which would make it subjective.
 
As I pointed out in my last post, there is an epistemological loop, whereby the Universe created the means to understand itself, through us. Whether there is also an ontological loop as both Davies and Oriti infer, is another matter: do we determine reality through our quantum mechanical observations? I will park that while I elaborate on the epistemic loop.
 
And this finally brings me to the article in Philosophy Now by James Miles titled, We’re as Smart as the Universe gets. He argues that, from an evolutionary perspective, there is a one-in-one-billion possibility that a species with our cognitive abilities could arise by natural selection, and there is no logical reason why we would evolve further, from an evolutionary standpoint. I have touched on this before, where I pointed out that our cultural evolution has overtaken our biological evolution and that would also happen to any other potential species in the Universe who developed cognitive abilities to the same level. Dawkins coined the term, ‘meme’, to describe cultural traits that have ‘survived’, which now, of course, has currency on social media way beyond its original intention. Basically, Dawkins saw memes as analogous to genes, which get selected; not by a natural process but by a cultural process.
 
I’ve argued elsewhere that mathematical theorems and scientific theories are not inherently memetic. This is because they are chosen because they are successful, whereas memes are successful because they are chosen. Nevertheless, such theorems and theories only exist because a culture has developed over millennia which explores them and builds on them.
 
Miles talks about ‘the high intelligence paradox’, which he associates with Darwin’s ‘highest and most interesting problem’. He then discusses the inherent selection advantage of co-operation, not to mention specialisation. He talks about the role that language has played, which is arguably what really separates us from other species. I’ve argued that it’s our inherent ability to nest concepts within concepts ad-infinitum (which is most obvious in our facility for language, like I’m doing now) that allows us to, not only tell stories, compose symphonies, explore an abstract mathematical landscape, but build motor cars, aeroplanes and fly men to the moon. Are we the only species in the Universe with this super-power? I don’t know, but it’s possible.
 
There are 2 quotes I keep returning to:
 
The most incomprehensible thing about the Universe is that it’s comprehensible. (Einstein)
 
The Universe gave rise to consciousness and consciousness gives meaning to the Universe.
(Wheeler)
 
I haven’t elaborated, but Miles makes the point, while referencing historical antecedents, that there appears no evolutionary 'reason’ that a species should make this ‘one-in-one-billion transition’ (his nomenclature). Yet, without this transition, the Universe would have no meaning that could be comprehended. As I say, that’s the epistemic loop.
 
As for an ontic loop, that is harder to argue. Photons exist in zero time, which is why I contend they are always in the future of whatever they interact with, even if they were generated in the CMBR some 13.5 billion years ago. So how do we resolve that paradox? I don’t know, but maybe that’s the link that Davies and Oriti are talking about, though neither of them mention it. But here’s the thing: when you do detect such a photon (for which time is zero) you instantaneously ‘see’ back to 380,000 years after the Universe’s birth.





Saturday, 12 October 2024

Freedom of the will is requisite for all other freedoms

 I’ve recently read 2 really good books on consciousness and the mind, as well as watch countless YouTube videos on the topic, but the title of this post reflects the endpoint for me. Consciousness has evolved, so for most of the Universe’s history, it didn’t exist, yet without it, the Universe has no meaning and no purpose. Even using the word, purpose, in this context, is anathema to many scientists and philosophers, because it hints at teleology. In fact, Paul Davies raises that very point in one of the many video conversations he has with Robert Lawrence Kuhn in the excellent series, Closer to Truth.
 
Davies is an advocate of a cosmic-scale ‘loop’, whereby QM provides a backwards-in-time connection which can only be determined by a conscious ‘observer’. This is contentious, of course, though not his original idea – it came from John Wheeler. As Davies points out, Stephen Hawking was also an advocate, premised on the idea that there are a number of alternative histories, as per Feynman’s ‘sum-over-histories’ methodology, but only one becomes reality when an ‘observation’ is made. I won’t elaborate, as I’ve discussed it elsewhere, when I reviewed Hawking’s book, The Grand Design.
 
In the same conversation with Kuhn, Davies emphasises the fact that the Universe created the means to understand itself, through us, and quotes Einstein: The most incomprehensible thing about the Universe is that it’s comprehensible. Of course, I’ve made the exact same point many times, and like myself, Davies makes the point that this is only possible because of the medium of mathematics.
 
Now, I know I appear to have gone down a rabbit hole, but it’s all relevant to my viewpoint. Consciousness appears to have a role, arguably a necessary one, in the self-realisation of the Universe – without it, the Universe may as well not exist. To quote Wheeler: The universe gave rise to consciousness and consciousness gives meaning to the Universe.
 
Scientists, of all stripes, appear to avoid any metaphysical aspect of consciousness, but I think it’s unavoidable. One of the books I cite in my introduction is Philip Ball’s The Book of Minds; How to Understand Ourselves and Other Beings; from Animals to Aliens. It’s as ambitious as the title suggests, and with 450 pages, it’s quite a read. I’ve read and reviewed a previous book by Ball, Beyond Weird (about quantum mechanics), which is equally as erudite and thought-provoking as this one. Ball is a ‘physicalist’, as virtually all scientists are (though he’s more open-minded than most), but I tend to agree with Raymond Tallis that, despite what people claim, consciousness is still ‘unexplained’ and might remain so for some time, if not forever.
 
I like an idea that I first encountered in Douglas Hofstadter’s seminal tome, Godel, Escher, Bach; an Eternal Golden Braid, that consciousness is effectively a loop, at what one might call the local level. By which I mean it’s confined to a particular body. It’s created within that body but then it has a causal agency all of its own. Not everyone agrees with that. Many argue that consciousness cannot of itself ‘cause’ anything, but Ball is one of those who begs to differ, and so do I. It’s what free will is all about, which finally gets us back to the subject of this post.
 
Like me, Ball prefers to use the word ‘agency’ over free will. But he introduces the term, ‘volitional decision-making’ and gives it the following context:

I believe that the only meaningful notion of free will – and it is one that seems to me to satisfy all reasonable demands traditionally made of it – is one in which volitional decision-making can be shown to happen according to the definition I give above: in short, that the mind operates as an autonomous source of behaviour and control. It is this, I suspect, that most people have vaguely in mind when speaking of free will: the sense that we are the authors of our actions and that we have some say in what happens to us. (My emphasis)

And, in a roundabout way, this brings me to the point alluded to in the title of this post: our freedoms are constrained by our environment and our circumstances. We all wish to be ‘authors of our actions’ and ‘have some say in what happens to us’, but that varies from person to person, dependent on ‘external’ factors.

Writing stories, believe it or not, had a profound influence on how I perceive free will, because a story, by design, is an interaction between character and plot. In fact, I claim they are 2 sides of the same coin – each character has their own subplot, and as they interact, their storylines intertwine. This describes my approach to writing fiction in a nutshell. The character and plot represent, respectively, the internal and external journey of the story. The journey metaphor is apt, because a story always has the dimension of time, which is visceral, and is one of the essential elements that separates fiction from non-fiction. To stretch the analogy, character represents free will and plot represents fate. Therefore, I tell aspiring writers the importance of giving their characters free will.

A detour, but not irrelevant. I read an article in Philosophy Now sometime back, about people who can escape their circumstances, and it’s the subject of a lot of biographies as well as fiction. We in the West live in a very privileged time whereby many of us can aspire to, and attain, the life that we dream about. I remember at the time I left school, following a less than ideal childhood, feeling I had little control over my life. I was a fatalist in that I thought that whatever happened was dependent on fate and not on my actions (I literally used to attribute everything to fate). I later realised that this is a state-of-mind that many people have who are not happy with their circumstances and feel impotent to change them.

The thing is that it takes a fundamental belief in free will to rise above that and take advantage of what comes your way. No one who has made that journey will accept the self-denial that free will is an illusion and therefore they have no control over their destiny.

I will provide another quote from Ball that is more in line with my own thinking:

…minds are an autonomous part of what causes the future to unfold. This is different to the common view of free will in which the world somehow offers alternative outcomes and the wilful mind selects between them. Alternative outcomes – different, counterfactual realities – are not real, but metaphysical: they can never be observed. When we make a choice, we aren’t selecting between various possible futures, but between various imagined futures, as represented in the mind’s internal model of the world…
(emphasis in the original)

And this highlights a point I’ve made before: that it’s the imagination which plays the key role in free will. I’ve argued that imagination is one of the facilities of a conscious mind that separates us (and other creatures) from AI. Now AI can also demonstrate agency, and, in a game of chess, for example, it will ‘select’ from a number of possible ‘moves’ based on certain criteria. But there are fundamental differences. For a start, the AI doesn’t visualise what it’s doing; it’s following a set of highly constrained rules, within which it can select from a number of options, one of which will be the optimal solution. Its inherent advantage over a human player isn’t just its speed but its ability to compare a number of possibilities that are impossible for the human mind to contemplate simultaneously.

The other book I read was Being You; A New Science of Consciousness by Anil Seth. I came across Seth when I did an online course on consciousness through New Scientist, during COVID lockdowns. To be honest, his book didn’t tell me a lot that I didn’t already know. For example, that the world, we all see and think exists ‘out there’, is actually a model of reality created within our heads. He also emphasises how the brain is a ‘prediction-making’ organ rather than a purely receptive one. Seth mentions that it uses a Bayesian model (which I also knew about previously), whereby it updates its prediction based on new sensory data. Not surprisingly, Seth describes all this in far more detail and erudition than I can muster.

Ball, Seth and I all seem to agree that while AI will become better at mimicking the human mind, this doesn’t necessarily mean it will attain consciousness. Applications software, ChatGPT (for example), despite appearances, does not ‘think’ the way we do, and actually does not ‘understand’ what it’s talking or writing about. I’ve written on this before, so I won’t elaborate.

Seth contends that the ‘mystery’ of consciousness will disappear in the same way that the 'mystery of life’ has effectively become a non-issue. What he means is that we no longer believe that there is some ‘elan vital’ or ‘life force’, which distinguishes living from non-living matter. And he’s right, in as much as the chemical origins of life are less mysterious than they once were, even though abiogenesis is still not fully understood.

By analogy, the concept of a soul has also lost a lot of its cogency, following the scientific revolution. Seth seems to associate the soul with what he calls ‘spooky free will’ (without mentioning the word, soul), but he’s obviously putting ‘spooky free will’ in the same category as ‘elan vital’, which makes his analogy and associated argument consistent. He then says:

Once spooky free will is out of the picture, it is easy to see that the debate over determinism doesn’t matter at all. There’s no longer any need to allow any non-deterministic elbow room for it to intervene. From the perspective of free will as a perceptual experience, there is simply no need for any disruption to the causal flow of physical events. (My emphasis)

Seth differs from Ball (and myself) in that he doesn’t seem to believe that something ‘immaterial’ like consciousness can affect the physical world. To quote:

But experiences of volition do not reveal the existence of an immaterial self with causal power over physical events.

Therefore, free will is purely a ‘perceptual experience’. There is a problem with this view that Ball himself raises. If free will is simply the mind observing effects it can’t cause, but with the illusion that it can, then its role is redundant to say the least. This is a view that Sabine Hossenfelder has also expressed: that we are merely an ‘observer’ of what we are thinking.

Your brain is running a calculation, and while it is going on you do not know the outcome of that calculation. So the impression of free will comes from our ‘awareness’ that we think about what we do, along with our inability to predict the result of what we are thinking.

Ball makes the point that we only have to look at all the material manifestations of human intellectual achievements that are evident everywhere we’ve been. And this brings me back to the loop concept I alluded to earlier. Not only does consciousness create a ‘local’ loop, whereby it has a causal effect on the body it inhabits but also on the external world to that body. This is stating the obvious, except, as I’ve mentioned elsewhere, it’s possible that one could interact with the external world as an automaton, with no conscious awareness of it. The difference is the role of imagination, which I keep coming back to. All the material manifestations of our intellect are arguably a result of imagination.

One insight I gained from Ball, which goes slightly off-topic, is evidence that bees have an internal map of their environment, which is why the dance they perform on returning to the hive can be ‘understood’ by other bees. We’ve learned this by interfering in their behaviour. What I find interesting is that this may have been the original reason that consciousness evolved into the form that we experience it. In other words, we all create an internal world that reflects the external world so realistically, that we think it is the actual world. I believe that this also distinguishes us (and bees) from AI. An AI can use GPS to navigate its way through the physical world, as well as other so-called sensory data, from radar or infra-red sensors or whatever, but it doesn’t create an experience of that world inside itself.

The human mind seems to be able to access an abstract world, which we do when we read or watch a story, or even write one, as I have done. I can understand how Plato took this idea to its logical extreme: that there is an abstract world, of which the one we inhabit is but a facsimile (though he used different terminology). No one believes that today – except, there is a remnant of Plato’s abstract world that persists, which is mathematics. Many mathematicians and physicists (though not all) treat mathematics as a neverending landscape that humans have the unique capacity to explore and comprehend. This, of course, brings me back to Davies’ philosophical ruminations that I opened this discussion with. And as he, and others (like Einstein, Feynman, Wigner, Penrose, to name but a few) have pointed out: the Universe itself seems to follow specific laws that are intrinsically mathematical and which we are continually discovering.

And this closes another loop: that the Universe created the means to comprehend itself, using the medium of mathematics, without which, it has no meaning. Of purpose, we can only conjecture.

Saturday, 7 September 2024

Science and religion meet at the boundary of humanity’s ignorance

 I watched a YouTube debate (90 mins) between Sir Roger Penrose and William Lane Craig, and, if I’m honest, I found it a bit frustrating because I wish I was debating Craig instead of Penrose. I also think it would have been more interesting if Craig debated someone like Paul Davies, who is more philosophically inclined than Penrose, even though Penrose is more successful as a scientist, and as a physicist, in particular.
 
But it was set up as an atheist versus theist debate between 2 well known personalities, who were mutually respectful and where there was no animosity evident at all. I confess to having my own biases, which would be obvious to any regular reader of this blog. I admit to finding Craig arrogant and a bit smug in his demeanour, but to be fair, he was on his best behaviour, and perhaps he’s matured (or perhaps I have) or perhaps he adapts to whoever he’s facing. When I call it a debate, it wasn’t very formal and there wasn’t even a nominated topic. I felt the facilitator or mediator had his own biases, but I admit it would be hard to find someone who didn’t.
 
Penrose started with his 3 worlds philosophy of the physical, the mental and the abstract, which has long appealed to me, though most scientists and many philosophers would contend that the categorisation is unnecessary, and that everything is physical at base. Penrose proposed that they present 3 mysteries, though the mysteries are inherent in the connections between them rather than the categories themselves. This became the starting point of the discussion.
 
Craig argued that the overriding component must surely be ‘mind’, whereas Penrose argued that it should be the abstract world, specifically mathematics, which is the position of mathematical Platonists (including myself). Craig pointed out that mathematics can’t ‘create’ the physical, (which is true) but a mind could. As the mediator pointed out (as if it wasn’t obvious) said mind could be God. And this more or less set the course for the remainder of the discussion, with a detour to Penrose’s CCC theory (Conformal Cyclic Cosmology).
 
I actually thought that this was Craig’s best argument, and I’ve written about it myself, in answer to a question on Quora: Did math create the Universe? The answer is no, nevertheless I contend that mathematics is a prerequisite for the Universe to exist, as the laws that allowed the Universe to evolve, in all its facets, are mathematical in nature. Note that this doesn’t rule out a God.
 
Where I would challenge Craig, and where I’d deviate from Penrose, is that we have no cognisance of who this God is or even what ‘It’ could be. Could not this God be the laws of the Universe themselves? Penrose struggled with this aspect of the argument, because, from a scientific perspective, it doesn’t tell us anything that we can either confirm or falsify. I know from previous debates that Craig has had, that he would see this as a win. A scientist can’t refute his God’s existence, nor can they propose an alternative, therefore it’s his point by default.
 
This eventually led to a discussion on the ‘fine-tuning’ of the Universe, which in the case of entropy, is what led Penrose to formulate his CCC model of the Universe. Of course, the standard alternative is the multiverse and the anthropic principle, which, as Penrose points out, is also applicable to his CCC model, where you have an infinite sequence of universes as opposed to an infinity of simultaneous ones, which is the orthodox response among cosmologists.
 
This is where I would have liked to have seen Paul Davies respond, because he’s an advocate of John Wheeler’s so-called ‘participatory Universe’, which is effectively the ‘strong anthropic principle’ as opposed to the ‘weak anthropic principle’. The weak anthropic principle basically says that ‘observers’ (meaning us) can only exist in a universe that allows observers to exist – a tautology. Whereas the strong anthropic principle effectively contends that the emergence of observers is a necessary condition for the Universe to exist (the observers don’t have to be human). Basically, Wheeler was an advocate of a cosmic, acausal (backward-in-time) link from conscious observers to the birth of the Universe. I admit this appeals to me, but as Craig would expound, it’s a purely metaphysical argument, and so is the argument for God.
 
The other possibility that is very rarely expressed, is that God is the end result of the Universe rather than its progenitor. In other words, the ‘mind’ that Craig expounded upon is a consequence of all of us. This aligns more closely with the Hindu concept of Atman or a Buddhist concept of collective karma – we get the God we deserve. Erwin Schrodinger, who studied the Upanishads, discusses Atman as a pluralistic ‘mind’ (in What is Life?). My point would be that the Judea-Christian-Islamic God does not have a monopoly on Craig’s overriding ‘mind’ concept.
 
A recurring theme on this blog is that there will always be mysteries – we can never know everything – and it’s an unspoken certitude that there will forever be knowledge beyond our cognition. The problem that scientists sometimes have, but are reluctant to admit, is that we can’t explain everything, even though we keep explaining more by the generation. And the problem that theologians sometimes have is that our inherent ignorance is neither ‘proof’ nor ‘evidence’ that there is a ‘creator’ God.
 
I’ve argued elsewhere that a belief in God is purely a subjective and emotional concept, which one then rationalises with either cultural references or as an ultimate explanation for our existence.


Addendum: I like this quote, albeit out of context, from Spinoza:: "The sum of the natural and physical laws of the universe and certainly not an individual entity or creator".


Thursday, 29 August 2024

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.



Saturday, 29 June 2024

Feeling is fundamental

 I’m not sure I’ve ever had an original idea, but I sometimes raise one that no one else seems to talk about. And this is one of them: I contend that the primary, essential attribute of consciousness is to be able to feel, and the ability to comprehend is a secondary attribute.
 
I don’t even mind if this contentious idea triggers debate, but we tend to always discuss consciousness in the context of human consciousness, where we metaphorically talk about making decisions based on the ‘head’ or the ‘heart’. I’m unsure of the origin of this dichotomy, but there is an inference that our emotional and rational ‘centres’ (for want of a better word) have different loci (effectively, different locations). No one believes that, of course, but possibly people once did. The thing is that we are all aware that sometimes our emotional self and rational self can be in conflict. This is already going down a path I didn’t intend, so I may return at a later point.
 
There is some debate about whether insects have consciousness, but I believe they do because they demonstrate behaviours associated with fear and desire, be it for sustenance or company. In other respects, I think they behave like automatons. Colonies of ants and bees can build a nest without a blueprint except the one that apparently exists in their DNA. Spiders build webs and birds build nests, but they don’t do it the way we would – it’s all done organically, as if they have a model in their brain that they can follow; we actually don’t know.
 
So I think the original role of consciousness in evolutionary terms was to feel, concordant with abilities to act on those feelings. I don’t believe plants can feel, but they’d have very limited ability to act on them, even if they could. They can communicate chemically, and generally rely on the animal kingdom to propagate, which is why a global threat to bee populations is very serious indeed.
 
So, in evolutionary terms, I think feeling came before cognitive abilities – a point I’ve made before. It’s one of the reasons that I think AI will never be sentient – a viewpoint not shared by most scientists and philosophers, from what I’ve read.  AI is all about cognitive abilities; specifically, the ability to acquire knowledge and then deploy it to solve problems. Some argue that by programming biases into the AI, we will be simulating emotions. I’ve explored this notion in my own sci-fi, where I’ve added so-called ‘attachment programming’ to an AI to simulate loyalty. This is fiction, remember, but it seems plausible.
 
Psychological studies have revealed that we need an emotive component to behave rationally, which seems counter-intuitive. But would we really prefer if everyone was a zombie or a psychopath, with no ability to empathise or show compassion. We see enough of this already. As I’ve pointed out before, in any ingroup-outgroup scenario, totally rational individuals can become totally irrational. We’ve all observed this, possibly actively participated.
 
An oft made point (by me) that I feel is not given enough consideration is the fact that without consciousness, the universe might as well not exist. I agree with Paul Davies (who does espouse something similar) that the universe’s ability to be self-aware, would seem to be a necessary condition for its existence (my wording, not his). I recently read a stimulating essay in the latest edition of Philosophy Now (Issue 162, June/July 2024) titled enigmatically, Significance, by Ruben David Azevedo, a ‘Portuguese philosophy and social sciences teacher’. His self-described intent is to ‘Tell us why, in a limitless universe, we’re not insignificant’. In fact, that was the trigger for this post. He makes the point (that I’ve made elsewhere myself), that in both time and space, we couldn’t be more insignificant, which leads many scientists and philosophers to see us as a freakish by-product of an otherwise purposeless universe. A perspective that Davies has coined ‘the absurd universe’. In light of this, it’s worth reading Azevedo’s conclusion:
 
In sum, humans are neither insignificant nor negligible in this mind-blowing universe. No living being is. Our smallness and apparent peripherality are far from being measures of our insignificance. Instead, it may well be the case that we represent the apex of cosmic evolution, for we have this absolute evident and at the same time mysterious ability called consciousness to know both ourselves and the universe.
 
I’m not averse to the idea that there is a cosmic role for consciousness. I like John Wheeler’s obvious yet pertinent observation:
 
The Universe gave rise to consciousness, and consciousness gives meaning to the Universe.

 
And this is my point: without consciousness, the Universe would have no meaning. And getting back to the title of this essay, we give the Universe feeling. In fact, I’d say that the ability to feel is more significant than the ability to know or comprehend.
 
Think about the role of art in all its manifestations, and how it’s totally dependent on the ability to feel. In some respects, I consider AI-generated art a perversion, because any feeling we have for its products is of our own making, not the AI’s.
 
I’m one of those weird people who can even find beauty in mathematics, while acknowledging only a limited ability to pursue it. It’s extraordinary that I can find beauty in a symphony, or a well-written story, or the relationship between prime numbers and Riemann’s Zeta function.


Addendum: I realised I can’t leave this topic without briefly discussing the biochemical role in emotional responses and behaviours. I’m thinking of the brain’s drugs-of-choice like serotonin, dopamine, oxytocin and endorphins. Some may argue that these natural ‘messengers’ are all that’s required to explain emotions. However, there are other drugs, like alcohol and caffeine (arguably the most common) that also affect us emotionally, sometimes to our detriment. My point being that the former are nature’s target-specific mechanisms to influence the way we feel, without actually being the genesis of feelings per se.

Wednesday, 19 June 2024

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.”

 


Sunday, 9 June 2024

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.

Sunday, 2 June 2024

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.