Paul P. Mealing

Check out my book, ELVENE. Available as e-book and as paperback (print on demand, POD). 2 Reviews: here. Also this promotional Q&A on-line.

Tuesday, 19 January 2016

Is this the God equation?

Yes, this is a bit tongue-in-cheek, but like most things tongue-in-cheek it just might contain an element of truth. I’m not a cosmologist or even a physicist, so this is just me being playful yet serious in as much as anyone can be philosophically serious about the origins of Everything, otherwise known as the Universe.

Now I must make a qualification, lest people think I’m leading them down the garden path. When people think of ‘God’s equation’, they most likely think of some succinct equation or set of equations (like Maxwell’s equations) from which everything we know about the Universe can be derived mathematically. For many people this is a desired outcome, founded on the belief that one day we will have a TOE (Theory Of Everything) – itself a misnomer – which will incorporate all the known laws of the Universe in one succinct theory. Specifically, said theory will unite the Electromagnetic force, the so-called Weak force, the so-called Strong force and Gravity as all being derived from a common ‘field’. Personally, I think that’s a chimera, but I’d be happy to be proven wrong. Many physicists believe some version of String Theory or M Theory will eventually give us that goal. I should point out that the Weak force has already been united with the Electromagnetic force.

So what do I mean by the sobriquet, God’s equation? Last week I watched a lecture by Allan Adams as part of MIT Open Courseware (8.04, Spring 2013) titled Lecture 6: Time Evolution and the Schrodinger Equation, in which Adams made a number of pertinent points that led me to consider that perhaps Schrodinger’s Equation (SE) deserved such a title. Firstly, I need to point out that Adams himself makes no such claim, and I don’t expect many others would concur.

Many of you may already know that I wrote a post on Schrodinger’s Equation nearly 5 years ago and it has become, by far, the most popular post I’ve written. Of course Schrodinger’s Equation is not the last word in quantum mechanics –more like a starting point. By incorporating relativity we have Dirac’s equation, which predicted anti-matter – in fact, it’s a direct consequence of relativity and SE. In fact, Schrodinger himself, followed by Klein-Gordon, also had a go at it and rejected it because it gave answers with negative energy. But Richard Feynman (and independently, Ernst Stuckelberg) pointed out that this was mathematically equivalent to ordinary particles travelling backwards in time. Backwards in time, is not an impossibility in the quantum world, and Feynman even incorporated it into his famous QED (Quantum Electro-Dynamics) which won him a joint Nobel Prize with Julian Schwinger and Sin-Itiro Tomonaga in 1965. QED, by the way, incorporates SE (just read Feynman’s book on the subject).

This allows me to segue back into Adams’ lecture, which, as the title suggests, discusses the role of time in SE and quantum mechanics generally. You see ‘time’ is a bit of an enigma in QM.

Adams’ lecture, in his own words, is to provide a ‘grounding’ so he doesn’t go into details (mathematically) and this suited me. Nevertheless, he throws terms around like eigenstates, operators and wave functions, so familiarity with these terms would be essential to following him. Of those terms, the only one I will use is wave function, because it is the key to SE and arguably the key to all of QM.

Right at the start of the lecture (his Point 1), Adams makes the salient point that the Wave function, Ψ, contains ‘everything you need to know about the system’. Only a little further into his lecture (his Point 6) he asserts that SE is ‘not derived, it’s posited’. Yet it’s completely ‘deterministic’ and experimentally accurate. Now (as discussed by some of the students in the comments) to say it’s ‘deterministic’ is a touch misleading given that it only gives us probabilities which are empirically accurate (more on that later). But it’s a remarkable find that Schrodinger formulated a mathematical expression based on a hunch that all quantum objects, be they light or matter, should obey a wave function.

But it’s at the 50-55min stage (of his 1hr 22min lecture) that Adams delivers his most salient point when he explains so-called ‘stationary states’. Basically, they’re called stationary states because time remains invariant (doesn’t change) for SE which is what gives us ‘superposition’. As Adams points out, the only thing that changes in time in SE is the phase of the wave function, which allows us to derive the probability of finding the particle in ‘classical’ space and time. Classical space and time is the real physical world that we are all familiar with. Now this is what QM is all about, so I will elaborate.

Adams effectively confirmed for me something I had already deduced: superposition (the weird QM property that something can exist simultaneously in various positions prior to being ‘observed’) is a direct consequence of time being invariant or existing ‘outside’ of QM (which is how it’s usually explained). Now Adams makes the specific point that these ‘stationary states’ only exist in QM and never exist in the ‘Real’ world that we all experience. We never experience superposition in ‘classical physics’ (which is the scientific pseudonym for ‘real world’). This highlights for me that QM and the physical world are complementary, not just versions of each other. And this is incorporated in SE, because, as Adams shows on his blackboard, superposition can be derived from SE, and when we make a measurement or observation, superposition and SE both disappear. In other words, the quantum state and the classical state do not co-exist: either you have a wave function in Hilbert space or you have a physical interaction called a ‘wave collapse’ or, as Adams prefers to call it, ‘decoherence’. (Hilbert space is a theoretical space of possibly infinite dimensions where the wave function theoretically exists in its superpositional manifestation.)

Adams calls the so-called Copenhagen interpretation of QM the “Cop Out” interpretation which he wrote on the board and underlined. He prefers ‘decoherence’ which is how he describes the interaction of the QM wave function with the physical world. My own view is that the QM wave function represents all the future possibilities, only one of which will be realised. Therefore the wave function is a description of the future yet to exist, except as probabilities; hence the God equation.

As I’ve expounded in previous posts, the most popular interpretation at present seems to be the so-called ‘many worlds’ interpretation where all superpositional states exist in parallel universes. The most vigorous advocate of this view is David Deutsch, who wrote about it in a not-so-recent issue of New Scientist (3 Oct 2015, pp.30-31). I also reviewed his book, Fabric of Reality, in September 2012. In New Scientist, Deutsch advocated for a non-probabilistic version of QM, because he knows that reconciling the many worlds interpretation with probabilities is troublesome, especially if there are an infinite number of them. However, without probabilities, SE becomes totally ineffective in making predictions about the real world. It was Max Born who postulated the ingenious innovation of squaring the modulus of the wave function (actually multiplying it with its complex conjugate, as I explain here) which provides the probabilities that make SE relevant to the physical world.

As I’ve explained elsewhere, the world is fundamentally indeterministic due to asymmetries in time caused by both QM and chaos theory. Events become irreversible after QM decoherence, and also in chaos theory because the initial conditions are indeterminable. Now Deutsch argues that chaos theory can be explained by his many worlds view of QM, and mathematician, Ian Stewart, suggests that maybe QM can be explained by chaos theory as I expound here. Both these men are intellectual giants compared to me, yet I think they’re both wrong. As I’ve explained above, I think that the quantum world and the classical world are complementary. The logical extension of Deutch’s view, by his own admission, requires the elimination of probabilities, making SE ineffectual. And Stewart’s circuitous argument to explain QM probabilities with chaos theory eliminates superposition, for which we have indirect empirical evidence.

If I’m right in stating that QM and classical physics are complementary (and Adams seems to make the same point, albeit not so explicitly) then a TOE may be impossible.

Tuesday, 12 January 2016

How to write a story so it reads like a movie in your head

I’ve written about writing a few times now, including Writing’s 3 Essential Skills (Jul. 2013) and How to Create an Imaginary, Believable World (Aug. 2010), the last one being a particularly popular post. Also, I taught a creative writing course in 2009 and have given a couple of talks on the subject, but never intentionally to provide advice on how to make a story read like a movie in your head.

This post has arisen from a conversation I had when I realised I had effectively taught myself how to do this. It’s not something that I deliberately set out to do but I believe I achieved it inadvertently and comments from some readers appear to confirm this. At YABooksCentral, a teenage reviewer has made the point specifically, and many others have said that my book (Elvene) would make a good movie, including a filmmaker. Many have said that they ‘could see everything’ in their mind’s eye.

Very early in my writing career (though it’s never been my day job) I took some screenwriting courses and even wrote a screenplay. I found that this subconsciously influenced my prose writing in ways that I never foresaw and that I will now explain. The formatting of a screenplay doesn’t lend itself to fluidity, with separate headings for every scene and dialogue in blocks interspersed with occasional brief descriptive passages. Yet a well written screenplay lets you see the movie in your mind’s eye and you should write it as you’d imagine it appearing on a screen. However, contrary to what you might think, this is not the way to write a novel. Do not write a novel as if watching a movie. Have I confused you? Well, bear this in mind and hopefully it will all make sense before the end.

Significantly, a screenplay needs to be written in ‘real time’, which means descriptions are minimalistic and exposition non-existent (although screenwriters routinely smuggle exposition into their dialogue). Also, all the characterisation is in the dialogue and the action – you don’t need physical descriptions of a character, including their attire, unless it’s significant; just gender, generic age and ethnicity (if it’s important). It was this minimalistic approach that I subconsciously imported into my prose fiction.

There is one major difference between writing a screenplay and writing a novel and the two subsequent methods require different states of mind. In writing a screenplay you can only write what is seen and heard on the screen, whereas a novel can be written entirely (though not necessarily) from inside a character’s head. I hope this clarifies the point I made earlier. Now, as someone once pointed out to me (fellow blogger, Eli Horowitz) movies can take you into a character’s head through voiceover, flashbacks and dream sequences. But, even so, the screenplay would only record what is seen and heard on the screen, and these are exceptions, not the norm. Whereas, in a novel, getting inside a character’s head is the norm.

To finally address the question implicit in my heading, there are really only 2 ‘tricks’ for want of a better term: write the story in real time and always from some character’s point of view. Even description can be given through a character’s eyes, and the reader subconsciously becomes an actor. By inhabiting a character’s mind, the reader becomes fully immersed in the story.

Now I need to say something about scenes, because, contrary to popular belief, scenes are the smallest component of a story, not words or sentences or paragraphs. It’s best to think of the words on the page like the notes on a musical score. When you listen to a piece of music, the written score is irrelevant, and, even if you read the score, you wouldn’t hear the music anyway (unless, perhaps, if you’re a musician or a composer). Similarly, the story takes place in the reader’s mind where the words on the page conjure up images and emotions without conscious effort.

In a screenplay a scene has a specific definition, defined by a change in location or time. I use the same definition when writing prose. There are subtle methods for expanding and contracting time psychologically in a movie, and those can also be applied to prose fiction. I’ve made the point before that the language of story is the language of dreams, and in dreams, as in stories, sudden changes in location and time are not aberrant. In fact, I would argue that if we didn’t dream, stories wouldn’t work because our minds would continuously and subconsciously struggle with the logic.


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Tuesday, 5 January 2016

Free will revisited

I’ve written quite a lot on this in the past, so one may wonder what I could add.

I’ve just read Mark Balaguer’s book, Free Will, which I won when Philosophy Now published my answer to their Question of the Month in their last issue (No 111, December 2015). It’s the fourth time I’ve won a book from them (out of 5 submissions).

It’s a well written book, not overly long or over-technical in a philosophical sense, so very readable whilst being well argued. Balaguer makes it clear from the outset where he stands on this issue, by continually referring to those who argue against free will as ‘the enemies of free will’. Whilst this makes him sound combative, the tone of his arguments are measured and not antagonistic. In his conclusion, he makes the important distinction that in ‘blocking’ arguments against free will, he’s not proving that free will exists.

He makes the distinction between what he calls Hume-style free will and Non-predetermined free will (NDP), which is a term I believe he’s coined for himself. Hume-style free will, is otherwise known as ‘compatibilism’, which means it’s compatible with determinism. In other words, even if everything in the world is deterministic from the Big Bang onwards, it doesn’t rule out you having free will. I know it sounds like a contradiction, but I think it’s to do with the fact that a completely deterministic universe doesn’t conflict with the subjective sense we all have of having free will. As I’ve expressed in numerous posts on this blog, I think there is ample evidence that the completely deterministic universe is a furphy, so compatibilism is not relevant as far as I’m concerned.

Balaguer also coins another term, ‘torn decision’, which he effectively uses as a litmus test for free will. In a glossary in the back he gives a definition which I’ve truncated:

A torn decision is a conscious decision in which you have multiple options and you’re torn as to which option is best.

He gives the example of choosing between chocolate or strawberry flavoured ice cream and not making a decision until you’re forced to, so you make it while you’re still ‘torn’. This is the example he keeps coming back to throughout the book.

In recent times, experiments in neuro-science have provided what some people believe are ‘slam-dunk’ arguments against free will, because scientists have been able to predict with 60% accuracy what decision a subject will make seconds before they make it, simply by measuring neuron activity in certain parts of the brain. Balaguer provides the most cogent arguments I’ve come across challenging these contentions. In particular, the Haynes studies, which showed neuron activity up to 10 seconds prior to the conscious decision. Balaguer points out that the neuron activity for these studies occurs in the PC and BA10 areas of the brain, which are associated with the ‘generation of plans’ and the ‘storage of plans’ respectively. He makes the point (in greater elaboration than I do here) that we should not be surprised if we subconsciously use our ‘planning’ areas of the brain whilst trying to make ‘torn decisions’. The other experiment and their counterparts, known as the Libet studies (since the 1960s) showed neuron activity half a second prior to conscious decision-making and was termed the ‘readiness potential’.  Balaguer argues that there is ‘no evidence’ that the readiness potential causes the decision. Even so, it could be argued that, like the Haynes studies, it is subconscious activity happening prior to the conscious decision.

It is readily known (as Balaguer explicates) that much of our thinking is subconscious. We all have the experience of solving a problem subconsciously so it comes to us spontaneously when we don’t expect it to. And anyone who has pursued some artistic endeavour (like writing fiction) knows that a lot of it is subconscious so that the story and its characters appear on the page with seemingly divine-like spontaneity.

Backtracking to so-called Hume-style free will, it does have a relevance if one considers that our ‘wants’ - what we wish to do - are determined by our desires and needs. We assume that most of the animal kingdom behave on this principle. Few people (including Balaguer) discuss other sentient creatures when they discuss free will, yet I’ve long believed that consciousness and free will go hand-in-hand. In other words, I really can’t see the point of consciousness without free will. If everything is determined subconsciously, without the need to think, then why have we evolved to think?

But humans take thinking to a new level compared to every other species on the planet, so that we introspect and cogitate and reason and internally debate our way to many a decision.

Back in Feb., 2009, I reviewed Douglas Hofstadter’s Pulitzer prize winning book, Godel, Escher, Bach where, among other topics, I discussed consciousness, as that’s one of the themes of his book. Hofstadter coins the term ‘strange loop’. This is what I wrote back then:

By strange loop, Hofstadter means that we can effectively look at all the levels of our thinking except the ground level, which is our neurons. In between we have symbols, which is language, which we can discuss and analyse in a dispassionate way, just like I’m doing now. I can talk about my own thoughts and ideas as if they weren’t mine at all. Consciousness, in Hofstadter’s model (for want of a better word) is the top level, and neurons are the hardware level. In between we have the software (symbols) which is effectively language.

I was quick to point out that ‘software’ in this context is a metaphor – I don’t believe that language is really software, even though we ‘download’ it from generation to generation and it is indispensable to human reasoning, which we call thinking.

The point I’d make is that this is a 2 way process: the neurons are essential to thoughts, yet our thoughts I expect can affect neurons. I believe there is evidence that we can and do rewire our brains simply by exercising our mental faculties, even in later years, and surely exercising consciously is the very definition of will.