Does infinity and the unknowable go hand in glove?

A recurring theme on my blog has been the limits of what we can know. So Marcus du Sautoy’s book, What We Cannot Know, fits the bill. I acquired it after I saw him give a talk at the Royal Institute on the subject, promoting the book, which is entertaining and enlightening in and of itself. I’ve previously read his The Music of the Primes and Finding Moonshine, both of which are very erudite and stimulating. He’s made a few TV programmes as well.

Previously, I’ve written blog posts based on books by Bryan Magee (Ultimate Questions) and Noson S. Yanofsky (The Outer Limits of Reason; What Science, Mathematics, and Logic CANNOT Tell Us). Yanofsky is a Professor in computer science, while Magee was a Professor of Philosophy (later a broadcaster and Member of British Parliament). I have to admit that Yanofsky’s book appealed to me more, because it’s more science based. Magee’s book was very erudite and provocative; my one criticism being that he seemed almost dismissive of the role that mathematics plays in the limits of what we can know. He specifically states that “...rationality requires us to renounce the pursuit of proof in favour of the pursuit of progress.” (My emphasis). However, pursuit of proof is exactly what mathematicians do, and, what’s more, they do it consistently and successfully, even though there is a famous proof that says there are limits to what we can prove (Godel’s Incompleteness Theorem).

Marcus du Sautoy is a mathematician, and a very good communicator as well, as can be evidenced on some of his YouTube videos, including some with Numberphile. But his book is not limited to mathematics. In fact, he discusses pretty much all the fields of our knowledge which appear to incorporate limits, which he metaphorically calls ‘Edges’. These include, chaos theory, quantum mechanics, consciousness, the Universe, and of course, mathematics itself. One is tempted to compare his book with Yanofsky’s, as they are both very erudite and educational, whilst taking different approaches. But I won’t, except to say they are both worth reading.

One aspect of du Sautoy’s book, which is unusual, yet instructive, is that he consulted other experts in their respective fields, including John Polkinghorne, John Barrow, Kristof Koch and Robert May. May, in particular, did pioneering work in chaos theory on animal populations in the 1970s. An ex-pat Australian, he’s now a member of the House of Lords, which is where du Sautoy had lunch with him. All these interlocutors were very stimulating and worthy additional contributors to their respective topics.

Very early on (p.10, in fact) du Sautoy mentions a famous misprediction by French philosopher, Auguste Compte, in 1835, about the stars: “We shall never be able to study, by any method, their chemical composition or their mineralogical structure.” Yet, less than a century later, it was being done by spectroscopy as a virtually standard practice, which in turn led to the knowledge that the Universe was expanding consistently in all directions. Throughout the book, du Sautoy reminds us of Compte’s prediction, when it appears that there are some things we will never know. He also quotes Donald Rumsfeld on the very next page:

There are known knowns; these are things that we know that we know. We also know there are known unknowns, that is to say, we know there are some things we do not know. But there are also unknown unknowns, the ones we don’t know we don’t know.

At the time, people tended to treat Rumsfeld’s statement as a bit of a joke and a piece of political legerdemain, given its context: weapons of mass destruction. However, in the field of science, it’s perfectly correct: there are hierarchies of knowledge, and when one looks back, historically, there have always been unknown unknowns, and, therefore, it’s a safe bet they will exist in the future as well. In other words, our future discoveries are dependent on secrets the Universe has yet to reveal to us mere mortals.

Towards the end of his book, du Sautoy gets more philosophical, which is not surprising, and he makes a point that I’ve not seen or heard before. He argues that some things about the Universe, like time, and the possibility of a multiverse, might remain unknown without physically getting outside the Universe, which is impossible. This, of course, raises the issue of God. Augustine, among others, has argued that God exists outside the Universe, and therefore, outside time. Paul Davies made the same point in his book, The Mind of God, with specific reference to Augustine.

Du Sautoy, who is a self-declared atheist, contends that God represents what we cannot know, which is consistent with the idea that some things we cannot know, can only be known from outside the Universe. But du Sautoy makes the point that there is something that exists outside the Universe that we know and that is mathematics. He, therefore, makes the tongue-in-cheek suggestion that maybe we can replace God with mathematics. Curiously, John Barrow made the same mischievous suggestion in one of his books – probably, Pi in the Sky. According to du Sautoy, Barrow is a Christian, which surprised me as much as du Sautoy, given that you would never know it from his writings. While on the subject of God, John Polkinghorne is a well known theologian as well as a physicist. Again, according to du Sautoy, Polkinghorne contends that God could intervene in the Universe via chaos theory. I once made the same point, although I also said I didn’t believe in an interventionist God, as that leads to people claiming they know God’s will, and that leads to all sorts of acts done in God’s name, and we all know how that usually ends. The problem with believing in an interventionist God is that it axiomatically leads to people believing they can influence said God.

Getting back to the subject at hand, du Sautoy says:

If there was no universe, no matter, no space, nothing. I think there would still be mathematics. Mathematics does not require the physical world to exist.

Following on from du Sautoy’s book, I started re-reading Eli Maor’s book, e: the story of a number, which incidentally covers the history of calculus going back to the ancient Greeks and Archimedes, in particular. The Greeks had a problem in that they couldn’t acknowledge infinity – it was taboo. Maor believes that Archimedes must have known the concept of infinity because he appreciated how an iterative process could converge to a value, but he wasn’t allowed to say so. Even in the modern day, there are mathematicians who wish to be rid of the concept of infinity, yet it’s intrinsic to mathematics everywhere you look.

This is relevant because the very nature of infinity tells us that there will always be truths beyond our kin. You can use a Turing machine (a computer) to calculate all the zeros in Riemann’s hypothesis and, if it’s true, it will never stop. Now, du Sautoy makes an interesting observation about this (which he expounds upon in this video, if you want it firsthand) that it’s possible that Riemann’s hypothesis is unknowable. In fact, there’s a small collection of conjectures associated with prime numbers that fall into this category (the Goldbach conjecture and the twin-prime conjecture being another 2). But here’s the thing: if one can prove that the Riemann hypothesis is unknowable, then it must be true. This is because, if it was untrue, there would have to be at least one result that didn’t fit the hypothesis, which would make it ‘knowable’.

The unknowable possibility is a direct consequence of Godel’s Incompleteness Theorem. To quote du Sautoy:

Godel proved mathematically that within any axiomatic system framework for number theory that was free of contradictions there were true statements about numbers that could not be proved within that framework – a mathematical proof that mathematics has its limitations. (My empasis).

I highlighted that passage because I left it out when proposing a definition to someone on Quora, and as a consequence, my interlocutor tried to argue that my definition was incorrect. Basically, I was saying that within any axiomatic system of mathematics there are ‘truths’ that can’t be proven. That’s Godel’s famous theorem in essence and in practice. However, one can find proofs, in principle, by using new axioms outside that particular system. And we see this in practice. The axiom that geometry can be non-Euclidean created new proofs, and the introduction of √-1 created new mathematics, called complex algebra, that gave solutions to previously unsolvable problems.

Towards the end of his book, du Sautoy references a little known and obscure point made by the renowned logician Alonso Church, called the ‘paradox of unknowability’, which proves that unless you know it all, there will always be truths that are by their very nature unknowable.

In effect, Church has extended Godel’s theorem to the physical world. Du Sautoy gives the example of all the dice that are lost in his house. There is either an even number of them or an odd number. One of these is true, but it is unknowable unless he can find them all. A more universal example is whether the Universe is infinite or finite. One of these is true but it’s currently unknowable and may be for all time. Du Sautoy makes the point that if we learn it’s finite then it becomes knowable, but if it’s infinite it may remain forever unknowable. This is similar to the Riemann hypothesis being knowable or unknowable. If it’s false then the Turing machine stops, which makes it finite, but, if it’s true, it is both infinite and unknowable, based on that thought experiment. It was only at this point in my essay that I came up with its title. I’ve expressed it as a question, but it’s really a conclusion.

If we go back to Archimedes and his struggle with the infinite, we can see that probably for most of humankind’s history, the infinite was considered outside the mortal realm. In other words, it was the realm of God. In fact, du Sautoy quotes Descartes: God is the only thing I positively conceive as infinite.

I’ve long contended that mathematics is the only ‘realm’ (for want of a better word) where infinity is completely at home. In Maor’s book, at one point, he discusses the difference between applied mathematics and pure mathematics, and it occurred to me that this distinction could explain the perennial argument about whether mathematics is invented or discovered. But the plethora of infinities, which is also intrinsic to unknowable ‘truths’, as outlined above, infers that there will always be mathematical ‘things’ waiting to be discovered. What’s more, the ‘marriage’ between theoretical physics and pure mathematics has never been more productive.

Addendum 1: After writing this, I re-watched an interview with Norman Wildberger on the subject of infinity and Real numbers. Wildberger is an Australian mathematician with ‘unorthodox’ views on the foundations of mathematics, as he explains in the video.

Wildberger is not a crank: he’s an academic mathematician, who has unusual philosophical ideas on mathematics. He makes the valid point that computers can only work with finite numbers (meaning numbers with a finite decimal extension), and that is the criterion he uses to determine whether something mathematical is ‘real’. He says he doesn’t believe in Real numbers, as they are defined, because they are infinitely uncomputable.

In effect, he argues they have no place in the physical world, but I disagree. In chaos theory, the reason chaotic phenomena are unpredictable is because you have to calculate the initial conditions to infinite decimal places, which is impossible. This is both mathematical and physical evidence that some things are ‘unknowable’.

Addendum 2: Sabine Hossenfelder argues that infinity is only 'real' in the mathematical world. She contends that in physics, it's not 'real', because it's not 'measurable'. She gives a good exposition in this YouTube video.

Dame Diana Rigg (20 Jul 1938 – 10 Sep 2020)

It’s very rare for me to publish 2 posts in 2 days, and possibly unprecedented to publish 3 in less than a week. However, I couldn’t let this pass, for a number of reasons. Arguably, Dame Diana Rigg has had little to do with philosophy but quite a lot to do with culture and, of course, storytelling, which is a topic close to my heart.

In one of the many tributes that came out, there is an embedded video (c/- BBC Archives, 1997), where she talks about acting in a way that most of us don’t perceive it. She says, in effect, that an audience comes to a theatre (or a cinema) because they want to ‘believe’, and an actor has to give them (or honour) that ‘belief’. (I use the word, honour, she didn’t.)

This is not dissimilar to the ‘suspension of disbelief’ that writers attempt to draw from their readers. I’ve watched quite a few of Diana Rigg’s interviews, given over the decades, and I’m always struck by her obvious intelligence, not to mention her wit and goodwill.

 

I confess to being somewhat smitten by her character, Emma Peel, as a teenager. It was from watching her that I learned one falls for the character and not the actor playing her. Seeing her in another role, I was at first surprised, then logically reconciled, that she could readily play someone else less appealing.

 

Emma Peel was a role before its time in which the female could have the same hero status as her male partner. She explained, in one of the interviews I saw, that the role had originally been written for a man and they didn’t have time to rewrite it. So it occurred by accident. Originally, it was Honor Blackman, as Cathy Gale (who also passed away this year). But it was Diana Rigg as Emma Peel who seemed to be the perfect foil for Steed (Patrick Macnee). No one else filled those shoes with quite the same charm.

 

It was a quirky show, as only the British seem to be able to pull off: Steed in his vintage Bentley and Mrs Peel in her Lotus Elan, which I desired almost as much as her character.

 

The show time-travelled without a tardis, combining elements of fantasy and sci-fi that influenced my own writing. I suspect there is a bit of Emma Peel in Elvene, though I’ve never really analysed it.

Does history progress? If so, to what?

This is another Question of the Month from Philosophy Now. The last two I submitted weren’t published, but I really don’t mind as the answers they did publish were generally better than mine. Normally, with a question like this, you know what you want to say before you start. In other words, you know what your conclusion is. But, in this case, I had no idea.

 

At first, I wasn’t going to answer, because I thought the question was a bit obtuse. However, I couldn’t help myself. I started by analysing the question and then just followed the logic.

 

 

I found a dissonance to this question, because ‘history’, by definition, is about the past and ‘progress’ infers projection into the future. In fact, a dictionary definition of history tells us it’s “the study of past events, particularly in human affairs”. And a dictionary definition of progress is “forward or onward movement to a destination”. If one puts the two together, there is an inference that history has a ‘destination’, which is also implicit in the question.

 

I’ve never studied history per se, but if one studies the evolution of ideas in any field, be it science, philosophy, arts, literature or music, one can’t fail to confront the history of human ideas, in all their scope and diversity, and all the richness that has arisen out of that, imbued in culture as well as the material and social consequences of civilisations.

 

There are two questions, one dependent on the other, so we need to address the first one first. If one uses metrics like health, wealth, living conditions, peace, then there appears to be progress over the long term. But if one looks closer, this progress is uneven, even unequal, and one wonders if the future will be even more unequal than the present, as technologies become more available and affordable to some societies than others.

 

Progress infers change, and the 20^th Century saw more change than in the entire previous history of humankind. I expect the 21^st Century will see more change still, which, like the 20^th Century, will be largely unpredictable. This leads to the second question, which I’ll rephrase to make more germane to my discussion: what is the ‘destination’ and do we have control over it?

 

Humans, both as individuals and collectives, like to believe that they control their destiny. I would argue that, collectively, we are currently at a cross roads, which is evidenced by the political polarisation we see everywhere in the Western world.

 

But this cross roads has social and material consequences for the future. It’s epitomised by the debate over climate change, which is a litmus test for whether we control our destiny or not. It not only requires political will, but the consensus of a global community, and not just the scientific community. If we do nothing, it will paradoxically have a bigger impact than taking action. But there is hope: the emerging generation appears more predisposed than the current one.

Secrets to good writing

I wrote this, because it came up on Quora as a question, What makes good writing?

I should say up front that there are a lot of much better writers than me, most of whom write for television, in various countries, but Europe, UK, America, Australia and New Zealand are the ones I’m most familiar with.

 

I should also point out that you can be ‘good’ at something without being ‘known’, so to speak. Not all ‘good’ cricketers play for Australia and not all ‘good’ footballers play in the national league. I have a friend who has won awards in theatre, yet she’s never made any money out of it; it’s strictly amateur theatre. She was even invited (as part of a group) to partake in a ‘theatre festival’ in Monaco a couple of years ago. Luckily, the group qualified for a government grant so they could participate.

 

Within this context, I call myself a good writer, based partly on feedback and partly on comparing myself to other writers I’ve read. I’ve written about this before, but I’ll keep it simple; almost dot points.

 

Firstly, good writing always tells the story from some character’s point of view (POV) and it doesn’t have to be the same character throughout the story. In fact, you can change POV even within the same scene or within dialogue, but it’s less confusing if you stay in one.

 

You take the reader inside a character’s mind, so they subconsciously become an actor. It’s why the reader is constantly putting themselves in the character’s situation and reacting accordingly.

 

Which brings me to the second point about identifying good writing. It can make the reader cry or laugh or feel angry or scared – in fact, feel any human emotion.

 

Thirdly, good writing makes the reader want to keep returning to the story. There are 2 ways you can do this. The most obvious and easiest way is to create suspense – put someone in jeopardy – which is why crime fiction is so popular.

 

The second way is to make the reader invest in the character(s)’ destiny. They like the characters so much that they keep returning to their journey. This is harder to do, but ultimately more satisfying. Sometimes, you can incorporate both into the same story.

A story should flow, and there is one way that virtually guarantees this. When I attended a screenwriting course (some decades ago), I was told that a scene should either provide information about the story or information about a character or move the story forward. In practice, I found that if I did the last one, the other 2 took care of themselves.

Another ‘trick’ from screenwriting is to write in ‘real time’ with minimal description, which effectively allows the story to unfold like a movie inside the reader’s head.

 

A story is like a journey, and a journey needs a map. A map is a sequence of plot points that are filled in with scenes that become the story.

None of the above are contentious, but my next point is. I contend that good writing is transparent or invisible. By this I mean that readers, by and large, don’t notice good writing, they only notice bad writing. If you watch a movie, the writing is completely invisible. No one consciously comments on good screenwriting; they always comment on the good acting or the good filmmaking, neither of which would exist without a good script.

 

How is this analogous to prose writing? The story takes place in the reader’s imagination, not on the page. Therefore, the writing should be easy-to-read and it should flow, following a subliminal rhythm; and most importantly, the reader should never be thrown out of the story. Writing that says, ‘look at me, see how clever I am’, is the antithesis of this. I concede, not everyone agrees.

 

I’ve said before that if we didn’t dream, stories wouldn’t work. Dream language is the language of stories, and they can both affect us the same way. I remember when I was a kid, movies could affect me just as dramatically as dreams. When reading a story, we inhabit its world in our imagination, conjuring up imagery without conscious effort.

 

 

Example:

 

The world got closer until it eventually took up almost all their vision. Their craft seemed to level out as if it was skimming the surface, but at an ultra-high altitude. As they got lower the dark overhead was replaced by a cobalt-blue and then they passed through clouds and they could see they were travelling across an ocean with waves tipped by froth, and then eventually they approached a shoreline and they seemed to slow down as a long beach stretched like a ribbon from horizon to horizon. Beyond the beach there were hills and mountains, which they accelerated over until they came to flat grassy plains, and in the distance they saw some dots on the ground, which became a village of people and horses and huts that poked into the air like upside down cones.

Did the Universe see us coming?

 I recently read The Grand Design by Stephen Hawking (2010), co-authored by Leonard Mlodinow, who gets ‘second billing’ (with much smaller font) on the cover, so one is unsure what his contribution was. Having said that, other titles listed by Mlodinow (Euclid’s Window and Feynman’s Rainbow) make me want to search him out. But the prose style does appear to be quintessential Hawking, with liberal lashings of one-liners that we’ve come to know him for. Also, I think one can confidently assume that everything in the book has Hawking’s imprimatur.

 

I found this book so thought-provoking that, on finishing it, I went back to the beginning, so I could re-read his earlier chapters in the context of his later ones. On the very first page he says, rather provocatively, ‘philosophy is dead’. He then spends the rest of the book giving his account of ‘life, the universe and everything’ (which, in one of his early quips, ‘is not 42’). He ends the first chapter (introduction, really) with 3 questions:

 

1)    Why is there something rather than nothing?

2)    Why do we exist?

3)    Why this particular set of laws and not some other?

It’s hard to get more philosophical than this.

 

I haven’t read everything he’s written, but I’m familiar with his ideas and achievements, as well as some of his philosophy and personal prejudices. ‘Prejudice’ is a word that is usually used pejoratively, but I use it in the same sense I use it on myself, regarding my ‘pet’ theories or beliefs. For example, one of my prejudices (contrary to accepted philosophical wisdom) is that AI will not achieve consciousness.

 

Nevertheless, Hawking expresses some ideas that I would not have expected of him. His chapter titled, What is Reality? is where he first challenges the accepted wisdom of the general populace. He argues, rather convincingly, that there are only ‘models of reality’, including the ones we all create inside our heads. He doesn’t say there is no objective reality, but he says that, if we have 2 or more ‘models of reality’ that agree with the evidence, then one cannot say that one is ‘more true’ than another.

 

For example, he says, ‘although it is not uncommon for people to say that Copernicus proved Ptolemy wrong, that is not true’. He elaborates: ‘one can use either picture as a model of the universe, for our observations of the heavens can be explained by assuming either the earth or the sun is at rest’.

 

However, as I’ve pointed out in other posts, either the Sun goes around the Earth or the Earth goes around the Sun. It has to be one or the other, so one of those models is wrong.

 

He argues that we only ‘believe’ there is an ‘objective reality’ because it’s the easiest model to live with. For example, we don’t know whether an object disappears or not when go into another room, nevertheless he cites Hume, ‘who wrote that although we have no rational grounds for believing in an objective reality, we also have no choice but to act as if it’s true’.

 

I’ve written about this before. It’s a well known conundrum (in philosophy) that you don’t know if you’re a ‘brain-in-a-vat’. But I don’t know of a single philosopher who thinks that they are. The proof is in dreams. We all have dreams that we can’t distinguish from reality until we wake up. Hawking also referenced dreams as an example of a ‘reality’ that doesn’t exist objectively. So dreams are completely solipsistic to the extent that all our senses will play along, including taste.

 

Considering Hawking’s confessed aversion to philosophy, this is all very Kantian. We can never know the thing-in-itself. Kant even argued that time and space are a priori constructs of the mind. And if we return to the ‘model of reality’ that exists in your mind: if it didn’t accurately reflect the external objective reality outside your mind, the consequences would be fatal. To me, this is evidence that there is an objective reality independent of one’s mind - it can kill you. However, if you die in a dream, you just wake up.

 

Of course, this all leads to subatomic physics, where the only models of reality are mathematical. But even in this realm, we rely on predictions made by these models to determine if they reflect an objective reality that we can’t see. To return to Kant, the thing-in-itself is dependent on the scale at which we ‘observe’ it. So, at the subatomic scale, our observations may be tracks of particles captured in images, not what we see with the naked eye. The same can be said on the cosmic scale; observations dependent on instruments that may not even be stationed on Earth.

 

To get a different perspective, I recently read an article on ‘reality’ written by Roger Penrose (New Scientist, 16 May 2020) which was updated from one he wrote in 2006. Penrose has no problem with an ‘objective independent reality’, and he goes to some lengths (with examples) to show the extraordinary agreement between our mathematical models and physical reality. 

 

Our mathematical models of physical reality are far from complete, but they provide us with schemes that model reality with great precision – a precision enormously exceeding that of any description free of mathematics.

 

(It should be pointed out that Penrose and Hawking won a joint prize in physics for their work in cosmology.)

 

But Penrose gets to the nub of the issue when he says, ‘...the “reality” that quantum theory seems to be telling us to believe in is so far removed from what we are used to that many quantum theorists would tell us to abandon the very notion of reality’. But then he says in the spirit of an internal dialogue, ‘Where does quantum non-reality leave off and the physical reality that we actually experience begin to take over? Present day quantum theory has no satisfactory answer to this question’. (I try to answer this below.)

 

Hawking spends an entire chapter on this subject, called Alternative Histories. For me, this was the most revealing chapter in his book. He discusses at length Richard Feynman’s ‘sum over histories’ methodology, called QED or quantum electrodynamics. I say methodology instead of theory, because it’s a mathematical method that has proved extraordinarily accurate in concordance with Penrose’s claim above. Feynman compared it to measuring the distance between New York and Seattle (from memory) to within the width dimension of a human hair.

 

Basically, as Hawking expounds, in Feynman’s theory, a quantum particle can take every path imaginable (in the famous double-slit experiment, say) and then he adds them altogether, but because they’re waves, most of them cancel each other out. This leads to the principle of superposition, where a particle can be in 2 places or 2 states at once. However, as soon as it’s ‘observed’ or ‘measured’ it becomes one particle in one state. In fact, according to standard quantum theory, it’s possible for a single photon to be split into 2 paths and be ‘observed’ to interfere with itself, as described in this video. (I've edited this after Wes Hansen from Quora challenged it). I've added a couple of Wes's comments in an addendum below. Personally, I believe 'superposition' is part of the QM description of the future, as alluded to by Freeman Dyson (see  below). So I don't think superposition really occurs.

 

Hawking contends that the ‘alternative histories’ inherent in Feynman’s mathematical method, not only affect the future but also the past. What he is implying is that when an observation is made it determines the past as well as the future. He talks about a ‘top down’ history in lieu of a ‘bottom up’ history, which is the traditional way of looking at things. In other words, cosmological history is one of many ‘alternative histories’ (his terminology) that evolve from QM.

 

This leads to a radically different view of cosmology, and the relation between cause and effect. The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us (my emphasis).

 

As it happens, John Wheeler made the exact same contention, and proposed that it could happen on a cosmic scale when we observed light from a distant quasar being ‘gravitationally lensed’ by an intervening galaxy or black hole (refer Davies paper, linked below). Hawking makes specific reference to Wheeler’s conjecture at the end of his chapter. It should be pointed out that Wheeler was a mentor to Feynman, and Feynman even referenced Wheeler’s influence in his Nobel Prize acceptance speech.

 

A contemporary champion of Wheeler’s ideas is Paul Davies, and he even dedicates his book, The Goldilocks Enigma, to Wheeler.

 

Davies wrote a paper which is available on-line, where he describes Wheeler’s idea as the “…participatory universe” in which observers—minds, if you like—are inextricably tied to the concretization of the physical universe emerging from quantum fuzziness over cosmological durations.

 

In the same paper, Davies references and attaches an essay by Freeman Dyson, where he says, “Dyson concludes that a quantum description cannot be applied to past events.”

 

And this leads me back to Penrose’s question: how do we get the ‘reality’ we are familiar with from the mathematically modelled quantum world that strains our credulousness? If Dyson is correct, and the past can only be described by classical physics then QM only describes the future. So how does one reconcile this with Hawking’s alternative histories?

 

I’ve argued elsewhere that the path from the infinitely many paths of Feynman’s theory, is only revealed when an ‘observation’ is made, which is consistent with Hawking’s point, quoted above. But it’s worth quoting Dyson, as well, because Dyson argues that the observer is not the trigger.

 

... the “role of the observer” in quantum mechanics is solely to make the distinction between past and future...

 

What really happens is that the quantum-mechanical description of an event ceases to be meaningful as the observer changes the point of reference from before the event to after it. We do not need a human observer to make quantum mechanics work. All we need is a point of reference, to separate past from future, to separate what has happened from what may happen, to separate facts from probabilities.

 

But, as I’ve pointed out in other posts, consciousness exists in a constant present. The time for ‘us’ is always ‘now’, so the ‘point of reference’, that is key to Dyson’s argument, correlates with the ‘now’ of a conscious observer.

 

We know that ‘decoherence’ is not necessarily dependent on an observer, but dependent on the wave function interacting with ‘classical physics’ objects, like a laboratory apparatus or any ‘macro’ object. Dyson’s distinction between past and future makes sense in this context. Having said that, the interaction could still determine the ‘history’ of the quantum event (like a photon), even it traversed the entire Universe, as in the cosmic background radiation (for example).

 

In Hawking’s subsequent chapters, including one titled, Choosing Our Universe, he invokes the anthropic principle. In fact, there are 2 anthropic principles called the ‘weak’ and the ‘strong’. As Hawking points out, the weak anthropic principle is trivial, because, as I’ve pointed out, it’s a tautology: Only universes that produce observers can be observed.

 

On the other hand, the strong anthropic principle (which Hawking invokes) effectively says, Only universes that produce observers can ‘exist’. One can see that this is consistent with Davies’ ‘participatory universe’.

 

Hawking doesn’t say anything about a ‘participatory universe’, but goes into some detail about the fine-tuning of our universe for life, in particular the ‘miracle’ of how carbon can exist (predicted by Fred Hoyle). There are many such ‘flukes’ in our universe, including the cosmological constant, which Hawking also discusses at some length.

 

Hawking also explains how an entire universe could come into being out of ‘nothing’ because the ‘negative’ gravitational energy cancels all the ‘positive’ matter and radiation energy that we observe (I assume this also includes dark energy and dark matter). Dark energy is really the cosmological constant. Its effect increases with the age of the Universe, because, as the Universe expands, gravitational attraction over cosmological distances decreases while ‘dark energy’ (which repulses) doesn’t. Dark matter explains the stable rotation of galaxies, without which, they’d fly apart.

 

Hawking also describes the Hartle-Hawking model of cosmology (without mentioning James Hartle) whereby he argues that in a QM only universe (at its birth), time was actually a 4^th spatial dimension. He calls this the ‘no-boundary’ universe, because, as John Barrow once quipped, ‘Once upon a time, there was no time’. I admit that this ‘model’ appeals to me, because in quantum cosmology, time disappears mathematically.

 

Hawking’s philosophical view is the orthodox one that, if there is a multiverse, then the anthropic principle (weak or strong) ensures that there must be a universe where we can exist. I think there are very good arguments for the multiverse (the cosmological variety, not the QM multiple worlds variety) but I have a prejudice against an infinity of them because then there would be an infinity of me.

 

Hawking is a well known atheist, so, not surprisingly, he provides good arguments against the God hypothesis. There could be a demiurge, but if there is, there is no reason to believe it coincides with any of the Gods of mythology. Every God I know of has cultural ties and that includes the Abrahamic God.

 

For someone who claims that ‘philosophy is dead’, Hawking’s book is surprisingly philosophical and thought-provoking, as all good philosophy should be. In his conclusions, he argues strongly for ‘M theory’, believing it will provide the theory(s) of everything that physicists strive for. M theory, as Hawking acknowledges, requires ‘supersymmetry’, and from what I know and read, there is little or no evidence of it thus far. But I agree with Socrates that every mystery resolved only uncovers more mysteries, which history, thus far, has confirmed over and over.

 

My views have evolved and, along with the ‘strong anthropic principle’, I’m becoming increasingly attracted to Wheeler’s ‘participatory universe’, because the more of its secrets we learn, the more it appears as if ‘the Universe saw us coming’, to paraphrase Freeman Dyson.

Addendum (23Apr2021): Wes Hansen, whom I met on Quora, and who has strong views on this topic, told me outright that he's not a fan of Hawking or Feynman. Not surprisingly, he challenged some of my views and I'm not in a position to say if he's right or wrong. Here are some of his comments:

You know, I would add, the problem with the whole “we create history by observation” thing is, it takes a whole lot of history for light to travel to us from distant galaxies, so it leads to a logical fallacy. Consider:

Suppose we create the past with our observations, then prior to observation the galaxies in the Hubble Deep Fields did not exist. Then where does the light come from? You see, we are actually seeing those galaxies as they existed long ago, some over 10 billion years ago.

We have never observed a single photon interfering with itself, quite the opposite actually: Ian Miller's answer to Can a particle really be in several places at the same time in the subatomic world, or is this just modern mysticism?. This is precisely why I cannot tolerate Hawking or Feynman, it’s absolute nonsense!

Regarding his last point, I think Ian Miller has a point. I don't always agree with Miller, but he has more knowledge on this topic than me. I argue that the superposition, which we infer from the interference pattern, is in the future. The idea of a single photon taking 2 paths and interfering with itself is deduced solely from the interference pattern (see linked video in main text). My view is that superposition doesn't really happen - it's part of the QM description of the future. I admit that I effectively contradicted myself, and I've made an edit to the original post to correct that.

 

Not losing the plot, and even how to find it

As I’ve pointed out in previous posts, the most difficult part of writing for me is plotting. The characters come relatively easy, though there is always the danger that they can be too much alike. I’ve noticed from my own reading that some authors produce a limited range of characters, not unlike some actors. Whether I fall into that category is for others to judge. 

But my characters do vary in age and gender and include AI entities (like androids). Ideally, a character reveals more of themselves as the story unfolds and even changes or grows. One should not do this deliberately – it’s best to just let it happen – try not to interfere is the intention if not always the result.

I’ve also pointed out previously that whether to outline or not is a personal preference, and sometimes a contentious one. As I keep saying, you need to find what works for you, and for me it took trial and error.

In my last post on this topic, I compared plotting to planning a project, because that is what I did professionally. On a project you have milestones that become ‘goals’ and there is invariably a suite of often diverse activities required to come together at the right time. In effect, making sure everything aligns was what my job was all about.

When it comes to plotting, we have ‘plot points’, which are analogous to milestones but not really the same thing. And this is relevant to whether one ‘outlines’ or not. A very good example is given in the movie, Their Finest (excellent movie), which is a film within a film and has a screenwriter as the protagonist. The writers have a board where they pin up the plot points and then join them up with scenes, which is what they write.

On the other hand, a lot of highly successful writers will tell you that they never outline at all, and there is a good reason for that. Spontaneity is what all artists strive for – it’s the very essence of creativity. I’ve remarked myself, that the best motivation to write a specific scene is the same as the reader’s: to find out what happens next. As a writer, you know that if you are surprised then so will your readers be.

Logically, if you don’t have an outline, you axiomatically don’t know what happens next, and the spontaneity that you strive for, is all but guaranteed. So what do I do? I do something in between. I learned early on that I need a plot point to aim at, and whether I know what lies beyond that plot point is not essential.

I found a method that works for me, and any writer needs to find a method that works for them. I keep a notebook, where I’ll ‘sketch’ what-ifs, which I’ll often do when I don’t know what the next plot point is. But once I’ve found it, and I always recognise it when I see it, I know I can go back to my story-in-progress. But that particular plot point should be far enough in the future that I can extemporise, and other plot points will occur spontaneously in the interim.

Backstory is often an important part of plot development. J.K. Rowling created a very complex backstory that was only revealed in the last 2 books of her Harry Potter series. George Lucas created such an extensive backstory for Star Wars, he was able to make 3 prequels out of it.

So, whether you outline or not may be dependent on how much you already know about your characters before you start.