Natural laws; a misnomer?

I’ve referenced Raymond Tallis before, and I have to say up front that I have a lot of respect for his obvious erudition and the breadth of his intellectual discourse. He is an author and regular columnist in Philosophy Now, with a background in neuroscience. I always read his column, because he’s erudite and provocative. In Issue 144 (June/July 2021) he wrote an essay titled, The Laws of Nature. He didn’t use the term ‘misnomer’ anywhere, but that was the gist of his argument.

Tallis and I have a fundamental disagreement concerning the philosophy of science; and physics, in particular. This will become obvious as I expound on his article. He starts by pointing out how the word ‘law’ has theological connotations, as well as cultural ones. It’s a word normally associated with humanmade rules or edicts, which are necessary just so we can live together. An obvious one is what side of the road to drive on, otherwise we would have carnage and road-rage would be the least of our worries.

 

Science evolved out of a religious epistemology (I know that’s an oxymoron), but the pioneers of physics, like Galileo, Kepler and Newton, were all religious people and, from their perspective, they were uncovering ‘God’s laws’. This even extended to Einstein, who often referred to ‘God’ in a metaphorical sense, and saw himself and his contemporary physicists as uncovering the ‘Old One’s Secrets’. Even Stephen Hawking, a self-declared atheist, coined the phrase, ‘The Mind of God’.

 

So I agree with Tallis on this point that the use of the word, law, in this context, is misleading and carries the baggage of an earlier time, going back to the ancient Greeks (and other cultures) that human affairs were contingent on the whims of the Gods.

 

So Tallis searched around for an alternative term, and came up with ‘habits’, whilst admitting that it’s not ideal and that ‘it will have to punch above its usual weight’. But I think Tallis chose the word because, in human terms, ‘habit’ means something we acquire out of familiarity, and may or may not be the best method, or approach, to a specific situation. The idea that nature follows ‘habits’ implies there is no rhyme or reason behind their efficacy or apparent success. Even the word, success, is loaded, yet I think it subverts his point, because they are ‘successful’ in the sense that they ultimately produced a lifeform that can cognise them (more on that below).

 

Tallis makes the point that in nature ‘things just happen’, and the ‘laws’ are our attempt to ‘explain’ them. But, extending this line of thought, he suggests that actually we invent laws to ‘describe’ what nature does, which is why ‘habits’ is a better term.

 

The expectation of finding an explanation of nature’s regularity is the result of extrapolating to the whole of things the belief that every individual thing happens for a reason – that nothing ‘just happens’.

 

The word ‘regularity’ is apt and is one that physicists often use, because that is what we have learned about nature on all scales, and it is why it is predictable to the degree that it is. There is, of course, a missing element in all this, and that is the role of mathematics. I’m not surprised that Tallis doesn’t mention the word (even once as best I can tell), because he believes that physicists have a tendency to ‘mistake the map for the territory’ when they invoke mathematics as having a pivotal role in our epistemology. In another essay, he once argued that the only reason mathematics has a place in physics is because we need to measure things, or quantify them, in order to make predictions that can be verified. However, the very laws (or habits) that are the subject of his essay, are completely dependent on mathematics to be comprehensible at all.

 

In closing, Tallis makes a very good argument: there is a gap between the ‘habits’ that nature follows and the humanmade ‘laws’ in our science that we use to describe these habits. He makes the point that we are forever trying to close this gap as we discover more about nature’s habits. And he’s right, because it appears that, no matter how much we learn, there are always more of nature’s secrets to decipher. Every theory we’ve devised thus far has limits and we’ve even reached a point where our theory for the very large appears irreconcilable, mathematically, with our theory for the very small. But the point I’d make is that mathematics not only gives us our best description of reality, it also delineates the limitations of any particular theory. Consequently, I contend there will always be a gap.

 

Physicists say that the best we can do is provide a model and that model is always mathematical. Hawking made this point in his book, The Grand Design. So the model describes the laws, or habits, to the extent that we understand them at the time, and that it gets updated as we learn more.

 

Tallis mentions the well-known example of Newton’s ‘laws’ being surpassed by Einstein’s. But here’s the thing: the ‘inverse square law’ still applies and that’s not surprising, as it’s dependent on the Universe existing in 3 spatial dimensions. So we not only have a ‘law’ that carries over, but we have an explanation for it. But here’s another thing: the 3 spatial dimensions in combination with the single dimension of time is probably the only combination of dimensions that would allow for a universe to be habitable. Cosmologist and Fellow of the Royal Society, John D Barrow, expounds on this in some detail in his book, The Constants of Nature. (As a side note, planets can only remain in stable orbits over astronomical time periods in 3 dimensions of space.) So where I depart philosophically from Tallis, is that there are fundamental parameters in the Universe’s very structure that determine the consequences of something existing that can understand that structure. 

 

Nevertheless, I agree with Tallis to the extent that I think the term, law, is a misnomer, and I think a better word is ‘principle’. If one goes back to Einstein’s theory of gravity replacing Newton’s, it introduces a fundamental principle called the 'principle of least action', which I think was pointed out by Emmy Noether, not Einstein. As it turns out, the principle of least action also ‘explains’ or ‘describes’ optical refraction, as well as forming the basis of Richard Feynman’s path integral method for QED (quantum electrodynamics). The principle of least action, naturally, has a mathematical formulation called the Lagrangian.

 

Speaking of Emmy Noether, she derived a famous mathematical theorem (called Noether’s theorem) that is a fundamental ‘principle’ in physics, describing the intrinsic relationship between symmetries and conservation laws. It’s hard to avoid the term, law, in this context because it appears to be truly fundamental based on everything we know.

 

So, is this a case of confusing the map with the terrain? Maybe. The Universe doesn’t exist in numbers – it exists as a process constrained by critical parameters, all of which can only be deciphered by mathematics. To give just one example: Planck’s constant, h, determines the size of atoms which form the basis of everything you see and touch.

Other relevant posts: the-lagrangian-possibly-most.html

                                   the-universes-natural-units_9.html

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.

 

Why is there something rather than nothing (in 400 words)

This is another ‘Question of the Month’ from Philosophy Now (Issue 123, December 2017 / January 2018). My 8^th submission, with 6 from 7 previously published. I think this is my best yet, so I’ll be disappointed if it doesn’t get a guernsey. It depends on the other submissions – after all, it’s a competition and they only select 12 or less.

I’ve written on this topic before in a more lengthy post, but enforced brevity and succinctness sharpens one’s focus.



This is arguably the most fundamental question in philosophy. I once heard a respected philosopher (in a debate) say it was the ‘wrong question’, without proffering a ‘right question’. I thought this was a cop-out, not to mention a not-so-subtle evasion. But there are two major aspects to this question, and most attempted answers only address one. We inhabit a universe we believe to be around 14 billion years old, and proto-human consciousness only existed about 6 million years ago, with homo sapiens arriving on the scene only very recently – roughly 200,000 years ago. But here’s the thing: without a conscious entity to perceive the Universe, there might as well be nothing.

Einstein famously said: “The most incomprehensible thing about the Universe is that it’s comprehensible.” Many scientists, if not most, believe that the Universe and our status within it is a freak accident. Paul Davies in his erudite book, The Goldilocks Enigma, calls this interpretation, the ‘absurd universe’. The standard scientific answer to this enigma is that there are a multitude, possibly an infinite number of universes. If this is the case, then there are an infinite number of you and me. The multiverse hypothesis says that all possibilities are equally valid, which doesn’t explain anything, except to say that the freak accident of our existence can only be understood within an endless sea of all possible existences.

A number of physicists and cosmologists have pointed out that there are constants pertaining to fundamental physical laws that permit complex life forms to evolve. Even small variances in these numbers, either up or down, could have made the Universe lifeless. And as cosmologist, John Barrow, has pointed out, the Universe needs to be of the mind-boggling scale we observe to allow time for complex life - meaning us - to evolve. In light of these deductions, Brandon Carter coined and defined two anthropic principles. The weak anthropic principle says that only a universe that contains observers can be observed (which is a tautology). The strong anthropic principle says that only a universe that permits observers to emerge can exist. To be self-realised, a universe requires consciousness, otherwise it’s effectively non-existent; in the same way that a lost manuscript by Shakespeare would be non-existent.



Postscript: I must say that I find it a touch ironic that the most popular 'scientific' answer to this question is that there is an infinite amount of everything. Which may be right, yet we may never know.

Addendum: This was published in Issue 125, April/May 2018 of Philosophy Now. To give due credit, they did some useful edits (to the sequence of presentation rather than the content), most of which I've adopted.

How and why beliefs matter in science

I was going to call this: What is reality? because there is so much disagreement about what constitutes reality in physics and philosophy. In some respects I've addressed that specifically in not-so-recent posts like, What sorts of things exist and how? and My 2 sided philosophy. New Scientist puts out booklets that contain articles published in their magazine (periodicals) on particular themes and two that I have are on quantum mechanics and cosmology. Both of these areas are at the frontiers of physics and therefore bump up against metaphysics and/or philosophy. So this post is intended to be a discussion of people's beliefs and my beliefs in particular, and how those beliefs affect our perspective(s) on science and reality. It needs to be pointed out that sometimes people argue metaphysical ideas as if they are scientific theories, when, strictly speaking, they're not. They will discuss their particular point of view as if it can't be challenged because (according to them) science has proved them right. I will provide examples as I progress.

Before I start, I need to mention a well-written book with a similar title: Why Beliefs Matter; Reflections on the Nature of Science by E. Brian Davies (Professor of Mathematics at Kings College London and a Fellow of the Royal Society); which I discussed back in February 2011 (twice).

When I studied philosophy at a tertiary institution (which I never completed, I might add), one of the lecturers made a salient point which has stayed with me ever since: there are things you know and things you believe, and what you believe should be contingent on what you know and not the other way round. So, for the sake of consistency, I need to define what I mean by ‘things I know’. Scientific discoveries and theories that have been demonstrated valid through evidence, I call ‘things I know’, whereas philosophical ruminations I would call ‘things I believe’. So, for example, I would contend that evolution is something 'I know' because 150 years of accumulated evidence in a variety of disciplines tells me so, even though I’ve not made any of those discoveries myself nor ever contributed intellectually or otherwise to the discipline of evolutionary biology. It needs to be pointed out that the evidence that demonstrates evolution to be valid could equally demonstrate it to be false – the evidence is not neutral.

Because quantum mechanics and relativity theories both challenge our intuitive ideas of how the world works, they provide grist for philosophical and metaphysical interpretations, some of which border on the absurd. Whether I fit into that category or not, I leave for the reader to draw their own conclusions.

I will start with Einstein’s theories of relativity because they have become the basis of all cosmological theories developed over the last century. It was 100 years on November 2015 that he published his seminal paper on the General Theory of Relativity (the Special Theory of Relativity was published 10 years earlier in 1905). In fact, I attempted an exposition on the General Theory to mark the centenary of its birth. This is one of the ‘things I know’ because the sat-nav in your car, or on your phone, utilises both of these theories to provide accurate locations. Of course, there have been innumerable experiments that have proven Einstein’s theories correct in the 100 years that have past since their inception, so there’s no argument concerning their validity. However, there were beliefs held by Einstein, as a direct consequence of his theory, that have since been proven wrong. A mathematical consequence of his theory was to express time as a 4th dimension along with the 3 dimensions of space, which led to the concept of spacetime. Whereas space and time dimensions can change depending on an observer’s frame of reference and velocity, the combined dimension of spacetime remains unchanged.

One of Einstein’s beliefs was that time is a fixed dimension just like space, so the future is just as fixed as the past. In other words, Einstein believed in a strict determinism, which rules out free will. This strongly held belief led Einstein to dispute one of the fundamental tenets of quantum mechanics: that it was random and its outcomes could only be predicted by probabilities. So how can I claim that Einstein’s specific belief in this instance has been proven wrong? It’s generally acknowledged by physicists that quantum mechanics is one of the most successful theories, if not the most successful theory, in the history of science. And indeterminism is an intrinsic attribute of QM brought about by the collapse of the wave function, called its decoherence (which I’ll elaborate on later). In fact, this has led to a range of widely held beliefs, which I’ve discussed elsewhere.

Only a month ago I wrote a post challenging the beliefs of a correspondent to Philosophy Now, who effectively argued that there is no time without consciousness. And a year ago (Nov 2016), I wrote a post challenging a paper written by a couple of academics in California that consciousness brings objects into ‘reality’ including spacetime, which is ‘impermanent’. And more recently, I came across an article in another Philosophy Now magazine (Issue 93, Nov/Dec 2012) called On ‘Known-To-Be-False’ Materialist Philosophies of Mind by Graham Smetham, a Buddhist philosopher. Yes, that’s the full title with ‘On Known-To-Be-False’ highlighted in red. Smethan argues that materialists (who argue that mind is a consequence of ‘materials’ like neurons and synapses in the brain) are using obsolete classical physics. To quote ‘…the belief in the existence of solid material stuff which exists completely independent of mind is now about as scientifically acceptable as the phlogiston theory of heat.’ The context of this proclamation was the discovery of the Higgs boson at the Large Hadron Collider, which effectively demonstrates that ‘Mass, and so matter, are derived aspects of an insubstantial process of reality.’ (Italics in the original.) Basically, Smethan adheres to an extreme interpretation of the Copenhagen interpretation of QM that ‘things’ only come into existence when observed by a conscious entity.

All three of these abovementioned ‘beliefs’ - argued as virtually indisputable - border on solipsism, which is the philosophical premise that everything you see and observe is the product of your mind. The problem with solipsism is that there can only be ONE observer, and everyone else is a product of that observer’s observations. To get around this, they would argue that mind came first, and all other minds are a consequence thereof, rather than a consequence of individual brains. Basically, they all argue that we have the causal process in reverse. Consciousness has not arisen out of an evolutionary process that itself arose from a cosmological process, but the entire cosmological process arose from mind, of which we are all a part.

There is a way, however, in which Smethan could be right, which he alludes to in his ‘Conclusions’. John Wheeler, who famously coined the term, black hole, has argued that we and the Universe are the consequence of a cosmic scale quantum time loop. The point is that QM allows for backwards in time possibilities that have been demonstrated experimentally. In the famous double slit experiment, it’s well known that ‘detecting’ which slit a photon will go through destroys the interference pattern that occurs when it goes through both. In other words, when we try and determine which slit a photon will go through it stops being a wave and becomes a particle. Only waves can produce interference, which infers that the photon goes through both slits simultaneously. Wheeler conjectured that if we ‘looked at’ the photon after it had gone through the slit(s) but before it hit the screen, it would have the same effect. This infers that the ‘detection’ works backwards in time. He was proven correct when the technology eventually caught up with his thought experiment.

There is something compelling about the idea that the Universe saw us coming, which would make it teleological and would support the so-called Strong Anthropic Principle. Paul Davies has argued cogently for the Strong Anthropic Principle without calling it by that name. In his book, The Goldilocks Enigma, he looks at all current scenarios and ‘beliefs’ concerning the nature of the Universe, and he concludes that ‘I have suggested that only self-consistent loops capable of understanding themselves can create themselves, so that only universes with (at least the potential for) life and mind really exist.’  This ‘belief’ is logically consistent with Wheeler’s ‘belief’ and it’s no coincident that Davies dedicated the book to Wheeler, whom he saw as a mentor.

In an earlier book, The Mind of God, Davies expresses the same view in subtly different words:

I belong to the group of scientists who do not subscribe to a conventional religion but nevertheless deny that the universe is a purposeless accident… I have come to the point of view that mind – i.e., conscious awareness of the world – is not a meaningless and incidental quirk of nature, but an absolute fundamental facet of reality. That is not to say that we are the purpose for which the universe exists. Far from it. I do, however, believe that we human beings are built into the scheme of things in a very basic way.

I’ve written about this on other posts, and I’ve concluded that the Universe is pseudo-teleological in as much as the natural laws that it obeys allow for complex intelligent life to evolve without a blueprint or a final goal evident. Both QM and chaos theory make a deterministic universe virtually impossible - I will elaborate on this later.

Richard Feynman, who is arguably the most famous physicist in the post-Einstein era was mentored by Wheeler, and took Wheeler’s backwards in time idea and incorporated it into his Nobel Prize winning theory, QED (quantum electrodynamics).

Robbert Dijkgraaf, who is a professor at the Princeton Institute for Advanced Study and calls himself a mathematical physicist, describes in a not-too-esoteric lecture (on string theory) how Richard Feynman, in his Nobel Prize acceptance speech, told the world how he got this idea from Wheeler. Apparently Wheeler rang him up and said, ‘I know why all the electrons are exactly the same. It’s because they are all the same electron.’ So Feynman logically asked him how this could be and Wheeler responded: ‘Because the same electron simply repeats over time.’ If you go to the 19min mark of Dijkgraaf’s lecture, he explains it with images. What Dijkgraaf doesn’t explain is that an anti-particle (which is a positron in the case of an electron) going forward in time is mathematically equivalent to a particle (electron) going backwards in time. In an interview, I saw with Feynman, he said the ‘same electron’ idea he left alone but the ‘backwards in time’ idea he took from Wheeler.

And since we’re talking about time, I would like to reference a podcast someone alerted me to where scientists and philosophers explain how time has been effectively explained away in physics. While this is partly true, I found the discussion a little disingenuous, if not misleading, because they didn’t provide the context nor explain the significance of time in both relativity theory and QM.

To provide context, Carlo Rovelli, who has written a couple of popular science books (recently translated into English) has stated that at a fundamental level in physics, time disappears mathematically. And Paul Davies, whom I referenced above, has also written in The Goldilocks Enigma: [The] vanishing of time for the entire universe becomes very explicit in quantum cosmology, where the time variable simply drops out of the quantum description. To be more specific, John Wheeler and Bryce De-Witt, in the late 1960s, rewrote Einstein’s field equations for general relativity (gravity) in the same form as electromagnetism and time simply disappeared, which became known as the Wheeler-DeWitt equation.

And yet: Einstein’s very successful theories of relativity incorporate time as a 4th dimension into spacetime, which provides the effective structure of the Universe, even if it can be warped by gravity. And one of the most important and seminal equations in QM is the time dependent Schrodinger equation. What’s more, the wave function, which is the centrepiece of the equation, is incorporated into Feynman’s QED where its phase is time variant (as it is in Schrodinger’s original).

For me, this paradox simply underlines my ‘belief’ that time is the fundamental parameter that makes the marriage of general relativity with QM a stumbling block. I’ve written a number of posts on ‘time’ over a number of years, some of which I’ve plundered for this post. In one of the New Scientist articles I referenced at the start of this post, Anil Ananthaswamy explains how the wave function of Schrodinger’s equation, whilst it evolves in time, ‘…time is itself not part of the Hilbert space where everything else physical sits, but somehow exists outside of it.’ (Hilbert space is the ‘abstract’ space that Schrodinger’s wave function inhabits.) ‘When we measure the evolution of a quantum state, it is to the beat of an external timepiece of unknown provenance.’  My ‘belief’, which I’ve expressed elsewhere, is that time doesn’t exist in QM (in the sense that Ananthaswamy describes above). I came to this conclusion even before I read Ananthaswamy’s article because it would explain superposition, which is a well known phenomenon in QM.

What’s more, the ‘external timepiece’ could be provided by gravity, since gravity determines the rates of clocks, even to the extent that clocks stop when they reach the event horizon of a black hole. I find this a compelling idea, and compelling ideas have a tendency to become beliefs.

And getting to the nub of the title of this post, it’s beliefs that drive science or scientific breakthroughs. Basically, scientists follow a belief until it’s validated or it’s proven wrong.

I mentioned Carlo Rovelli earlier, who is a proponent of loop quantum gravity theory, and one of his books I’ve read is Reality Is Not What It Seems: The Journey to Quantum Gravity, which is essentially a brief and erudite history of physics going back to the Ancient Greeks. Curiously, he’s dismissive of Schrodinger’s equation, which he relegates to a footnote, and argues that the wave function is a mathematical fiction which has conceptually led people astray from a true understanding of QM. He argues that Heisenberg’s matrix formulation is conceptually superior because there is nothing in between observations – the wave function and Hilbert space simply don’t exist.

In his historical account of QM, Rovelli goes straight from Heisenberg to Dirac’s equation as if Schrodinger played no significant role. In fact, Dirac derived his eponymous equation from Schrodinger's, and therefore contains its own (fictional) wave function. Heisenberg and Schrodinger were rivals, philosophically, professionally and politically (during WW2, Heisenberg worked on the atomic bomb project for the Nazis while Schrodinger went into exile in Ireland). Max Born contributed to both Heisenberg’s matrix formulation and Schrodinger’s wave interpretation (by determining how to derive probabilities from Schrodinger’s eponymous equation). Even though Heisenberg eschewed Schrodinger’s wave function, Schrodinger was able to demonstrate that they were mathematically equivalent once Born’s rule was applied to his equation (by squaring the modulus of the wave function which removes the imaginary component). Dirac applied Einstein’s special theory of relativity to Schrodinger’s equation which provides negative energies (as Schrodinger himself had discovered and abandoned). But Dirac predicted that the negative energies could be interpreted as antiparticle electrons (positrons) and was later proven correct.

Obviously, Rovelli is far more knowledgeable on this topic than me, yet we have different ‘beliefs’, as do many other physicists. Jim Al-Khalili, a physicist at the University of Surrey, has written one of the best introductory books on QM I’ve read, called Quantum: A Guide for the Perplexed. Unlike Rovelli, the wave function is key to his exposition and Schrodinger’s equation is the only equation in the entire book, which he calls 'the most important equation in physics'.

At the time I read Rovelli’s book, I also read Roger Penrose’s latest tome, Fashion Faith and Fantasy in the New Physics of the Universe. I’ve long been a fan of Penrose and we share some ‘beliefs’, though I don’t necessarily share his ‘belief’ of a cyclic universe. Penrose can be delightfully edifying or maddeningly esoteric. This book, however, I found quite accessible, and he put the more challenging aspects of his exposition in an appendix.

I didn’t realise before that Penrose does most of his own illustrations, which are surprisingly good quality for someone not known for his artistic talents. On the back cover is an illustration (credited to Penrose) of a mermaid sitting on a rock with a seashore landscape in the background and the underwater world in the foreground, including the mermaid’s tail. I know from reading the book that this is a metaphor for Penrose’s own ‘beliefs’ regarding QM. The underwater world represents the quantum universe and the seashore represents the classical world of physics, with the water’s surface representing the wave function collapse or decoherence that delineates the two. From what I’ve read and know on this subject, most physicists ignore this dichotomy whereas I ‘believe’ there are 2 worlds that interact and the so-called collapse of Schrodinger’s wave function is the mathematical representation of that interaction.

Penrose ‘believes’ that gravity causes this decoherence and reading one of the New Scientist articles I mentioned, decoherence occurs when superposition can no longer exist. The reason that superposition doesn’t occur on a macro scale, according to Penrose, is that if you get enough particles together they create a gravitational field which in itself can’t be superimposed. It’s well known that clock rates change in a gravitational field, even from your head to your toe. If you have a superposition (of 2) separated far enough then their different clock rates determined by Planck’s hf (or atomically) will cause a decoherence so the particle suddenly becomes 1 in the so-called classical physical world.

In another New Scientist article, Yakir Aharonov, at Chapman University, Orange, California, asked the fundamental question some 50 years ago: ‘Does time in quantum mechanics have to flow from the past to the present? The answer, at least mathematically, is no.’ Aharonov along with a colleague, Jeff Tollaksen, has been performing experiments to attempt to demonstrate this. I won’t elaborate, but, of course, some argue that the experiments, whilst compelling, can be interpreted in other ways. But Aharonov says the mathematical interpretation of time symmetry is 'very elegant'.

However, the decoherence, which I argue is the interface between the QM and classical physics world, creates a time asymmetry that we are all familiar with: the past is fixed yet the future is open-ended. Once decoherence occurs, the time symmetry that Aharonov ‘believes’ becomes time assymetrical. Schrodinger once pointed out (according to John Gribbin’s biography) that the Born rule, which multiplies the complex component of the wave function by its conjugate to remove the imaginary component and provide a probability, is effectively the same as solving the equation both forwards and backwards in time. As Arthur I Miller points out in Graham Farmelo’s book, It Must Be Beautful: ‘Born’s aim was nothing less striking than to associate Schrodinger’s wave function with the presence of matter.’ In other words, it was Born’s great insight that gave us a mathematical means to go from the quantum world to the classical world by transforming Schrodinger’s equation into probabilities.

It should be pointed out that Schrodinger’s equation was purely suppositional. As Feynman once pointed out: ‘No one knows where Schrodinger’s equation came from. It came out of Schrodinger’s head. It can’t be derived from anything we know.’ I’ve jokingly called Schrodinger’s equation God’s equation because it attempts to predict the future via probabilities, and, statistically, it’s proven very accurate.

So what about the mathematical prediction that time disappears in quantum cosmology. I don’t know enough to answer that, but I’ve always found the Hartle-Hawking model of the Universe somewhat compelling. They argue, mathematically, that the time dimension may have originally been a 4th 'spatial' dimension (expressed through complex algebra, therefore imaginary) and this implies that in the beginning there was no time. Now, people will say: How can you have a beginning without time? I don’t know, but I admit that the idea appeals to me.

Is time symmetrical at a macro level, without QM? It’s been argued that Newtonian physics allows for time reversal and it’s only entropy that provides a direction in time. Entropy’s time direction is usually explained by the example of dropping an egg on the floor. If you were to run a film (or video) backwards of the event with the egg coming together and rising from the floor, everyone would know it’s impossible. But entropy doesn’t really provide a direction for time because it’s based on probabilities. To give another example, if you open a bottle of perfume in a room the perfume molecules quickly disperse to all corners of the room, they don’t congregate in one corner. There is an infinitesimal probability that they could all end up in one corner but there is a much higher probability, that increases with time, that they will disperse everywhere.

However, time asymmetry on a macro scale (without QM) is caused by chaos theory. Chaos theory is described as deterministic but unpredictable, which sounds like a contradiction, but it’s dependent on initial conditions; which is why weather forecasts are only predictable short term. A slight change has long term effects, but short term is predictable. This even applies to the orbits of the planets, which, despite appearances, are mathematically chaotic. It’s Earth's position in its orbit that's unpredictable (in the order of 150 million km over 100 million years).

I think that one of the more insightful posts I’ve written for this blog was called What is now? However, one issue I didn’t really address was: Is there a universal now? Towards the end of that post I explained how Einstein’s special theory of relativity made simultaneity impossible to be agreed upon by different observers, pending their relative velocities and positions in spacetime. Einstein concluded that there was no universal 'now' because everyone’s ‘time’ was different.

However, as we’ve already seen, Einstein was not infallible. One of the New Scientist articles I read challenges this particular aspect of Einstein’s relativity. Certainly, people who are in the same ‘frame of reference’ (occupy the same dimensional point of spacetime) would agree on ‘now’. Rovelli, whom I cited earlier, has argued that ‘now’ is the edge of the Big Bang. In my previous post, I made the point that we talk about an ‘age of the Universe’ which infers a universal now and I tend to agree with Rovelli: it’s the edge of the Big Bang which is everywhere in the Universe, including where you are currently standing or sitting. And entanglement, which is a feature of QM that doesn’t exist in classical physics, also infers a universal now. Science fiction writers, like myself, adopt a universal now even though we know we can’t physically send a signal anywhere in the Universe faster than the speed of light. But this contradiction (between relativity and QM) led to a renowned debate between Einstein and Niels Bohr, where Einstein famously called entanglement: ‘spooky action at a distance’. To cut a century long story short, every experiment, which has tested entanglement over relativity, has shown that QM triumphs.

This is a post with no conclusions, just a collection of ‘beliefs’, so I’ll finish with a joke provided by Robbert Dijkgraaf in his aforementioned video (at the 45 min mark).

What’s the difference between a physicist and a mathematician?
A physicist studies the laws that God chose nature to obey.
A mathematician studies the laws that God has to obey.

My 2 sided philosophy

In a way, this gets incorporated into Roger Penrose's 3 world philosophy that I discussed last year, but the core principle of my world view, that turns up again and again in my musings, can be best understood as a philosophy in 2 parts, if not 2 worlds. I'm not an academic, so don't expect me to formalise this as I suspect one is meant to, but there is a principle involved here that I wish to make more fundamental than I have done in the past.

This has been prompted, not surprisingly, by various things I’ve read recently, in particular in Philosophy Now (Issues 117 & 118) and a letter I wrote to the Editor of said magazine, which re-iterated some of the ideas that I expressed in my post on Penrose’s 3 Worlds, referenced above.

A great deal of my personal philosophy stems from the view that there are effectively 2 worlds for each and every one of us: an inner world and an outer world; and the confluence and interaction of these 2 aspects of reality pretty well determine how we live our lives, how we navigate relationships and how we effectively determine our destiny.

I’ve even used this dichotomous philosophical principle as a premise for how I write fiction. Basically, a story should include an inner journey and an outer journey where the outer journey is the plot and the inner journey is the character. In fact, writing fiction reinforced my philosophical point of view, when I realised it’s totally analogous to real life. The outer journey is fate and the inner journey is free will. The 2 are complementary rather than contradictory, but the complementarity is even more obvious when one thinks of it in terms of consciousness and the physical world. To illustrate my point, I will insert an edited version of the letter (I referenced above) to the Editor of Philosophy Now.

This is in reference to an essay by Nick Inman, titled “Nowhere Men” (published in Issue 117).

One doesn’t need to argue for a ‘soul’ or a ‘spirit’ to appreciate that some aspects of Inman’s argument have validity without religious connotations. In particular, there are 2 aspects of one’s self, whereby one aspect is subjective and uniquely known only to ‘You’, and another aspect is objective and known to everyone you interact with. But I think the most pertinent point he makes is that it is only through intelligent conscious entities, like us, that the Universe has any meaning at all. In answer to the oft asked question: Why is there something rather than nothing? Without consciousness there might as well be nothing. When you cease to be conscious there is nothing for You. Because consciousness is so ubiquitous and taken-for-granted in our everyday lives, we tend not to consider its essential role in providing reality. In other words, we need both an objective world and subjective consciousness for reality to become manifest.

As you can see, this is almost an ontological manifesto, which suggests that the existence of the Universe and the emergence of intelligent beings are entwined in ways which we prefer to ignore or dismiss. The scientific answer to this is that there is a multiverse of possibly infinite universes, the vast majority of which cannot sustain life. I’ve discussed this elsewhere, but the multiverse is an epistemological dead end in that it explains everything and nothing, which, ironically, is its appeal. We don’t know if there is a metaphysical purpose to our existence, and I’m not arguing that there is; I’m simply pointing out that reality requires both an objective world, called the Universe, and a subjective consciousness, epitomised by our existence.

It is for this reason that the so-called strong anthropic principle (as opposed to the weak principle) has long appealed to me. Neither of the anthropic principles, I should point out, are scientific principles; they are more like metaphysical premises that can’t be proven or falsified, given our current knowledge. I’m currently reading a highly ambitious and lengthy book by John Hands called Cosmo Sapiens; Human Evolution from the Origin of the Universe. It’s a comprehensive survey and review of the latest scientific theories concerning cosmology, biological evolution and the emergence of humanity. Not surprisingly, he briefly discusses Brandon Carter’s weak and strong anthropic principles plus John Barrow’s and Frank Tipler’s book-length dissertation on the subject. Effectively, the weak anthropic principle states that the Universe allows conscious intelligent agents to arise because we’re in it, which Hands points out is a tautology – a point I’ve made myself on this blog. The strong anthropic principle effectively states that the Universe specifically allows intelligent agents to exist otherwise it wouldn’t exist itself. It’s not stated that way, but that’s a reasonable interpretation, and, as you can see, it leans heavily towards teleology, which I’ve also discussed elsewhere. On that point, if one believes in teleology then it’s hard not to conclude that the Universe is deterministic, which means there is no free will. Einstein believed this so strongly that he couldn’t accept the inherent indeterminism displayed by quantum mechanics and therefore believed that the theory was incomplete and hid an underlying deterministic Universe that we're yet to discover.

Personally, I believe in free will and a non-deterministic Universe, which creates a paradox for the strong anthropic principle. I resolve this paradox by arguing for a pseudo-teleological Universe, whereby the Universe has all the laws of physics and parameters to allow conscious entities to evolve without determining what they will be in advance. I’ve argued this in a post on the fine-tuned Universe, and elsewhere.

I’m not arguing a religious reason for our existence, though, of course, I don’t know if such a reason exists, and I would argue that neither does anyone else, though many people claim they do. I’m arguing what the evidence tells me. We are the consequence of a lengthy and convoluted evolution that we are still struggling to understand and explain, even down to the molecular level. The Universe has laws and parameters that are ‘finely tuned’ for the emergence of complex intelligent life and we are the evidence. Without consciousness the Universe would have no meaning at all, which is why the strong anthropic principle is apposite if not scientific. Our existence is the only thing that gives the Universe meaning and we are the only entities (that we know of) that have the cognitive capacity to probe that meaning, which we do through science, I should point out, not religion.

Now, anyone who read my post on Penrose’s 3 worlds, knows it consisted of the Universe, Mind and Mathematics. So where does mathematics fit into my 2 sided philosophy? Mathematics, as most of us know it and use it, is a bridge between the Universe and the Mind, specifically the human mind. And it’s a bridge that has provided more insights and more meaning than any other we’ve discovered. In fact, the limits of our knowledge of mathematics arguably determines the limits of our knowledge of the Universe, certainly in the last century and since the times of Galileo and Newton. A few years ago, following in the footsteps of John Barrow, I wrote a post called Mathematics as religion. Religion, in its many cultural manifestations, often claims to have access to transcendental truth. Well, I contend that mathematics is our only depository of universal transcendental truths and Godel’s Incompleteness Theorem effectively tells us that it’s infinite, so it’s a never-ending endeavour. By corollary, it follows that there are and always will be mathematical truths that we don’t know.

Last week’s New Scientist (4 Feb 2017) cover story was ‘The Essence of Reality’, which was an attempt to understand what truly underpins the Universe beyond space and time. Some argue that the answer is information, essentially quantum information, which of course is mathematical. The point is, notwithstanding whether that question can ever be answered, quantum mechanics, which is a little over a century old, remains our most successful scientific theory to date, and can only be understood and interpreted through the medium of mathematics.


Footnote: Brandon Carter’s definitions of his 2 anthropic principles.

The weak principle: ‘that what we can expect to observe must be restricted by the condition necessary for our presence as observers.’

The strong principle: ‘that the universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers with it at some stage.’

Physics, mathematics, the Universe - is Reason its raison d'être?

I’ve just read Paul Davies’ The Mind of God: Science & The Search for Ultimate Meaning, published in 1992, so a couple of decades old now. He wrote this as a follow-up to God and the New Physics, which I read some years ago. This book is more philosophical and tends to deal with cosmology and the laws of physics – it’s as much about epistemology and the history of science as about the science itself. Despite its age, it’s still very relevant, especially in regard to the relationship between science and religion and science and mathematics, both of which he discusses in some depth.

Davies is currently at The University of Arizona (along with Lawrence Krauss, who wrote A Universe from Nothing, amongst others), but at the time he wrote The Mind of God, Davies was living and working in Australia, where he wrote a number of books over a couple of decades. He was born and educated in England, so he’s lived on 3 continents.

Davies is often quoted out of context by Christian fundamentalists, giving the impression that he supports their views, but anyone who reads his books knows that’s far from the truth. When he first arrived in America, he was sometimes criticised on blogs for ‘promoting his own version of religion’, usually by people who had heard of him but never actually read him. From my experience of reading on the internet, religion is a sensitive topic in America on both sides of the religious divide, so unless your views are black or white you can be criticised by both sides. It’s worth noting that I’ve heard or read Richard Dawkins reference Davies on more than a few occasions, always with respect, even though Davies is not atheistic.

Davies declares his philosophical position very early on, which is definitely at odds with the generally held scientific point of view regarding where we stand in the scheme of things:

I belong to the group of scientists who do not subscribe to a conventional religion but nevertheless deny that the universe is a purposeless accident… I have come to the point of view that mind – i.e., conscious awareness of the world – is not a meaningless and incidental quirk of nature, but an absolute fundamental facet of reality. That is not to say that we are the purpose for which the universe exists. Far from it. I do, however, believe that we human beings are built into the scheme of things in a very basic way.

In a fashion, this is a formulation of the Strong Anthropic Principle, which most scientists, I expect, would eschew, but it’s one that I find appealing, much for the same reasons given by Davies. The Universe is such a complex phenomenon, its evolvement (thus far) culminating in the emergence of an intelligence able to fathom its own secrets at extreme scales of magnitude in both space and time. I’ve alluded to this ‘mystery’ in previous posts, so Davies’ philosophy appeals to me personally, and his book, in part, attempts to tackle this very topic.

Amongst other things, he gives a potted history of science from the ancients (especially the Greeks, but other cultures as well) and how it has largely replaced religion as the means to understand natural phenomena at all levels. This has resulted in a ‘God-of-the-Gaps’, where, epistemologically, scientific investigations and discoveries have gradually pushed God out of the picture. He also discusses the implications of a God existing outside of space and time actually creating a ‘beginning’. The idea of a God setting everything in motion (via the Big Bang) and then watching his creation evolve over billions of years like a wound up watch (Davies’ analogy) is no more appealing than the idea of a God who has to make adjustments or rewind it occasionally, to extend the metaphor.

In discussing how the scientific enterprise evolved, in particular how we search for the cause of events, reminded me of my own attraction to science from a very early age. Children are forever asking ‘why’ and ‘how’ questions – we have a natural inclination to wonder how things work – and by the time I’d reached my teens, I’d realised that science was the best means to pursue this.

Davies gives an example of Newton coming up with mathematical laws to explain gravity that not only provided a method to calculate projectiles on Earth but also the orbits of planets in the solar system. Brian Cox in a documentary on Gravity, wrote the equation down on a piece of paper, borrowing a pen from his cameraman, to demonstrate how simple it is. But Newton couldn’t explain why everything didn’t simply collapse in on itself and evoked God as the explanation for keeping the clockwork universe functioning. So Newton’s explanation of gravity, albeit a work of genius, didn’t go far enough.

Einstein then came up with his theory that gravity was a consequence of the curvature of space-time caused by mass, but, as Cox points out in his documentary, Einstein’s explanation doesn’t go far enough either, and there are still aspects of gravity we don’t understand, at the quantum level and in black holes where the laws of physics as we know them break down. As an aside, it’s the centenary year of Einstein publishing his General Theory of Relativity and I’ve just finished reading a book (The Road to Relativity by Hanoch Gutfreund and Jurgen Renn) which goes through the original manuscript page by page explaining Einstein’s creative process.

But back to Newton’s theory, I remember, in high school, trying to understand why acceleration in a gravitational field was the same irrespective of the mass of the body, and I could only resort to the mathematics to give me an answer, which didn’t seem satisfactory. I can also remember watching a light plane in flight over our house and seeing it side-slipping in the wind. In other words, the direction of the nose was slightly offset to its direction of travel to counter a side wind. I remember imagining the vectors at play and realising that I could work them out with basic trigonometry. It made me wonder for the first time, why did mathematics provide an answer and an explanation – what was the link between mathematics, a product of the mind, and a mechanical event, a consequence of the physical world?

I’ve written quite a lot on the topic of mathematics and its relationship to the laws of nature; Davies goes into this in some depth. It is worth quoting him on the subject, especially in regard to the often stated scepticism that the laws of nature only exist in our minds.

Sometimes it is argued that laws of nature, which are attempts to capture [nature’s] regularities systematically, are imposed on the world by our minds in order to make sense of it… I believe any suggestion that the laws of nature are similar projections of the human mind [to seeing animals in the constellations, for example] is absurd. The existence of regularities in nature are a mathematical objective fact… Without this assumption that the regularities are real, science is reduced to a meaningless charade.

He adds the caveat that the laws as written are ‘human inventions, but inventions designed to reflect, albeit imperfectly, actually existing properties of nature.’ Every scientist knows that our rendition of nature’s laws have inherent limitations, despite their accuracy and success, but quite often they provide new insights that we didn’t expect. Well known examples are Maxwell’s equations predicting electromagnetic waves and the constant speed of light, and Dirac’s equation predicting anti-matter. Most famously, Einstein’s special theory of relativity predicted the equivalence of energy and mass, which was demonstrated with the detonation of the atomic bomb. All these predictions were an unexpected consequence of the mathematics.

Referring back to Gutfreund’s and Renn’s book on Einstein’s search for a theory of gravity that went beyond Newton but was consistent with Newton, Einstein knew he had to find a mathematical description that not only fulfilled all his criteria regarding relativistic space-time and the equivalence of inertial and gravitational mass, but would also provide testable predictions like the bending of light near massive stellar objects (stars) and the precession of mercury’s orbit around the sun. We all know that Riemann’s non-Euclidian geometry gave him the mathematical formulation he needed and it’s been extraordinarily successful thus far, despite the limitations I mentioned earlier.

Davies covers quite a lot in his discussion on mathematics, including a very good exposition on Godel’s Incompleteness Theorem, Turing’s proof of infinite incomputable numbers, John Conway’s game of life with cellular automata and Von Neuman’s detailed investigation of self-replicating machines, which effectively foreshadowed the mechanics of biological life before DNA was discovered.

In the middle of all this, Davies makes an extraordinary claim, based on reasoning by Oxford mathematical physicist David Deutsch (the most vocal advocate for the many worlds interpretation of quantum mechanics and a leader in quantum computer development). Effectively, Deutsch argues that mathematics works in the real world (including electronic calculators and computers) not because of logic but because the physical world (via the laws of physics) is amenable to basic arithmetic: addition, subtraction etc. In other words, he’s basically saying that we only have mathematics because there are objects in our world that we can count. In effect, this is exactly what Davies says.

This is not the extraordinary claim. The extraordinary claim is that there may exist universes where mathematics, as we know it, doesn’t work, because there are no discrete objects. Davies extrapolates this to say that a problem that is incomputable with our mathematics may be computable with alternative mathematics that, I assume, is not based on counting. I have to confess I have issues with this.

To start from scratch, mathematics starts with numbers, which we all become acquainted with from an early age by counting objects. It’s a small step to get addition from counting but quite a large step to then abstract it from the real world, so the numbers only exist in our heads. Multiplication is simply adding something a number of times and subtraction is simply taking away something that was added so you get back to where you started. The same is true for division where you divide something you multiplied to go backwards in your calculation. In other words, subtraction and division are just the reverse operations for addition and multiplication respectively. Then you replace some of the numbers by letters as ‘unknowns’ and you suddenly have algebra. Now you’re doing mathematics.

The point I’d make, in reference to Davies’ claim, is that mathematics without numbers is not mathematics. And numbers may be to a different base or use different symbols, but they will all produce the same mathematics. I agree with Deutsch that mathematics is intrinsic to our world – none of us would do mathematics if it wasn’t. But I find the notion that there could hypothetically exist worlds where mathematics is not relevant or is not dependent on number, absurd, to use one of Davies’ favourite utterances.

Earlier in the book, Davies expresses scepticism at the idea that the laws of nature could arise with the universe – that they didn’t exist beforehand. In other words, he’s effectively arguing that they are transcendent. Since the laws are firmly based in mathematics, it’s hard to argue that the laws are transcendent but the mathematics is not.

I have enormous respect for Davies, and I wonder if I’m misrepresenting him. But this is what he said, albeit out of context:

Imagine a world in which the laws of physics were very different, possibly so different that discreet objects did not exist. Some of the mathematical operations that are computable in our world would not be so in this world, and vice versa.

Speaking of mathematical transcendence, he devotes almost an entire chapter to the underlying mystery of mathematics’ role in explicating natural phenomena through physics, with particular reference to mathematical Platonists like Kurt Godel, Eugene Wigner and Roger Penrose. But it’s a quote from Richard Feynman, who was not a Platonist as far as I know, that sums up the theme.

When you discover these things, you get the feeling that they were true before you found them. So you get the idea that somehow they existed somewhere… Well, in the case of physics we have double trouble. We come across these mathematical interrelationships but they apply to the universe, so the problem of where they are is doubly confusing… Those are philosophical questions that I don’t know how to answer.

Interestingly, in his later book, The Goldilocks Enigma (2006), Davies distances himself from mathematical Platonism and seems to espouse John Wheeler’s view that both the mathematics and the laws of nature emerged ‘higgledy-piggledy’ and are not transcendent. He also tackles the inherent conflict between the Strong Anthropic Principle, which he seems to support, and a non-teleological universe, which science virtually demands, but I’ll address that later.

Back to The Mind of God, he discusses in depth one of the paradigms of our age that the Universe can be totally understood by algorithms leading to the possibility that the Universe we live in is a Matrix-like computer simulation. Again, referring to The Goldilocks Enigma, he discounts this view as a variation on Intelligent Design. Towards the end of Mind of God, he discusses metaphysical, even mystical possibilities, but not as a replacement for science.

But one interesting point he makes, that I’ve never heard of before, was proposed by James Hartle and Murray Gellmann, who claim:

…that the existence of an approximately classical world, in which well-defined material objects exist in space, and in which there is a well-defined concept of time, requires special cosmic initial conditions.

In other words, they’re saying that the Universe would be a purely quantum world with everything in superpositional states (nothing would be fixed in space and time) were it not for ‘the special quantum state in which the universe originated.’ James Hartle developed with Stephen Hawking the Hawking-Hartle model of the Universe where time evolved out of a 4th dimension in a quantum big bang. It may be that Hartle’s and Gellmann’s conjecture is dependent on the veracity of that particular model. The link between the two ideas is only alluded to by Davies.

Apropos to the book’s title, Davies spends an entire chapter on ‘God’ arguments, in particular cosmological and ontological arguments that require a level of philosophical nous that, frankly, I don’t possess. Having said that, it became obvious to me that arguments for God are more dependent on subjective ‘feelings’ than rational requirements. After lengthy discussions on ‘necessary being’ and a ‘contingent universe’, and the tension if not outright contradiction the two ideas pose, Davies pretty well sums up the situation with this:

What seems to come through such analyses loud and clear is the fundamental incompatibility of a completely timeless, unchanging, necessary God with the notion of creativity in nature, with a universe that can change and evolve and bring forth the genuinely new…

In light of this, the only ‘God’ that makes sense to me is one that evolves like ‘Its’ creation and, in effect, is a consequence of it rather than its progenitor.

One of the points that Davies makes is how the Universe is not strictly deterministic or teleological, yet it allows for self-organisation and the evolvement of complexity; in essence, a freedom of evolvement without dictating it. I would call this pseudo-teleological and is completely consistent with both quantum and chaotic events, which dominate all natural phenomena from cosmological origins to the biological evolution of life.

This brings one back to the quote from Davies at the beginning of this discussion that the universe is not a meaningless accident. Inherent in the idea of meaningfulness is the necessary emergence of consciousness and its role as the prime source of reason. If not for reason the Universe would have no cognisance of its own existence and it would be truly ‘purposeless’ in every way. It is for this reason that people believe in God, in whatever guise they find him (or her, as the case may be). Because we can find reason in living our lives and use reason to understand the Universe, the idea that the Universe itself has no reason is difficult to reconcile.