The fine-tuned Universe

I’ve discussed this before in relation to John D. Barrow’s revelations concerning the fine structure constant, amongst other things, in his excellent book, The Constants of Nature. A recent episode of Catalyst, called Custom Universe also raised this issue, plus the latest issue of New Scientist (6 June 2015, pp.37-39) explaining the extraordinary fine difference in mass between neutrons and protons (that can’t be explained with our current knowledge of physics) and, in particular, the consequences of small variations to that difference.

In other words, the stability of atoms, including the prototype atom, hydrogen, is dependent on the neutron being slightly heavier than the proton by 0.14% (the neutron is 939.6 Mev and the proton is 938.3 Mev). Making the difference much bigger would result in more complex atoms becoming impossible to create and much smaller would have converted all hydrogen atoms into inert helium, therefore no fusion in stars and no other atoms. Smaller still or making protons heavier than neutrons would have resulted in protons decaying into neutrons and therefore no atoms at all.

This is just one of many examples of fine-tuning in our universe that makes the evolution of complex life forms, and therefore intelligent life, possible. And, of course, we still don’t know why matter outweighed anti-matter in the early stages of the universe by 1 billion and 1 to 1 billion, otherwise the universe would be just radiation and nothing else.

The standard answer to this is the multiverse, which postulates that there exists up to an infinite number of alternative universes, and, logically, we must exist in the one universe that allows intelligent life, like us, to evolve. Brian Cox (in Human Universe) uses the analogy of a lottery. When we buy a lottery ticket the chances of winning is some astronomical number, and in our individual lifetimes, very few of us ever win. However, as Cox points out, someone wins every time, and that’s the same with the multiverse. We win because we are in it and all the others that don’t win are unknown and unknowable because no consciousness can evolve in them to find out. This is known as the weak Anthropic Principle, which I’ve discussed elsewhere.

What many people don’t realise is that if there is an infinite number of universes then there must be an infinite number of you and me, because, in an infinite amount of space and time, anything that can happen once must happen an infinite number of times – a mathematical truism.

But many see the multiverse as a cop-out, because it explains everything and nothing. It says all things are possible therefore we are possible, problem solved. It provides an answer with no explanation. And, at its extreme interpretation, it says that everything is possible an infinite number of times.

Max Tegmark advocates this extreme interpretation in his book, Our Mathematical Universe, where he postulates up to 4 levels of multiverses, including the quantum multiverse. In fact, Tegmark conjured up a thought experiment, whereby if you die you just find yourself in an alternative quantum universe, and therefore you are effectively immortal. To take this to its logical conclusion, there must exist a universe where everyone lives forever, therefore we all eventually find Heaven, or at least, its mathematically plausible equivalent.

Equally relevant to this topic, is the issue of biological evolution, and I’ve just finished reading an excellent book on this subject, Life Ascending; The Ten Great Inventions of Evolution by Nick Lane. Now many people (including Richard Dawkins, I imagine) will take issue with the word ‘invention’ and ‘evolution’ appearing in the same sentence, let alone on the cover of a book. But I doubt Dawkins would take issue with any of the material between the covers, even in the places where his name is cited. Lane, of course, is aware of some people’s sensitivity to the word ‘invention’ in this context, and is quick to explain he’s not referring to a ‘creator’ but to the extraordinary inventiveness inherent in the process of natural selection. In the same way, and for the same reasons, I have no problem in appropriating the word ‘design’ when discussing evolution because natural selection is nature’s design methodology and its more significant ‘inventions’ are the subject of the book, hence the totally apposite title.

Lane structures the book into 10 chapters that cover his ‘ten inventions’: 1) The Origin of Life; 2) DNA; 3) Photosynthesis; 4)The Complex Cell; 5) Sex; 6) Movement; 7) Sight; 8) Hot Blood; 9)Consciousness; 10) Death.

I have to say that this is the best book on evolution that I’ve read, not least because Lane has such a commanding knowledge of his subject and a very accessible style of prose. Lane is a biochemist by training and it’s his ability to explain what happens at a molecular level that gives the book so much intellectual weight. He appears up to date on all the latest discoveries and provides historical context everywhere; so we learn how theories have developed, sometimes stalled, sometimes been disproved and sometimes yet to be confirmed. Anyone who studies science, at whatever level, appreciates that we never know everything and we never will, but that we are constantly uncovering newly discovered nature’s secrets that would astound the likes of Darwin and his contemporaries with their depth and ingenuity.

All the chapters contain information that I wasn’t aware of previously, but the first two chapters are probably the most revelatory and the most enthralling. One suspects that it’s at this level that Lane is most intrigued and therefore most knowledgeable on all the latest developments. I won’t go into details, but he provides the best arguments I’ve come across on how life, at its simplest form, may have evolved from pure chemistry. In light of the title of this post, I was struck on more than one occasion on how just the right elements or combination of factors arose to produce the forebears of life as we now know it.

This is all good grist for those who believe we have a special destiny, and that there is the ‘hand’ of some immaterial force behind it all. The other extreme is to be dismissive of this view as ‘weak-minded’ and ‘unintelligent’, yet I find the idea that our existence is an accident that should never have happened equally absurd and, dare-I-say-it, unintelligent. My own view, that I’ve expressed elsewhere, is that the Universe is brim-full of purpose yet that purpose has evolved with no plan or blueprint in sight, no pre-destined goal, just a set of laws that have allowed it all to happen.

If there is a ‘creator’, then ‘he’, ‘she’ or ‘it’ works in a very strange fashion, certainly not in the manner that creationists and ID advocates would have us believe, because the ‘design’ has been done piece-meal with many wrong turns, much trial and error and many catastrophes on a grand scale, of which we could easily become one ourselves. In comparison to the epic story of life, we are like mayflies, existing for less than a day, thus far – it’s a sobering thought.

In regard to the ridiculous debate on religion versus science, it is worth quoting Lane himself from the last paragraph of his book.

I think the picture painted here in this book is true. Life most surely evolved, along the lines described here. That is not dogma, but evidence tested in reality and corrected accordingly. Whether this grand picture is compatible with faith in God, I do not know. For some people, intimately acquainted with evolution, it is; for others, it is not.

Addendum: This is a YouTube interview with physicist, Leonard Susskind, who discusses the fine-tuned universe on Closer to Truth, which appears to be a series of interviews with well known scientists and philosophers giving us their interpretation of philosophical cum scientific conundrums.

Susskind, not surprisingly, delivers a very compelling argument for the multi-verse, or, as he calls it, the mega-verse, and, in so doing, references String or M Theory as supporting this view. Personally, I'm a bit of a sceptic of String theory and its many variations, as it reminds me of Ptolemy's epicycles, but I may well be proven wrong in the near or far future. Only time will tell.

But what struck me as I listened to Lenny's argument, was that, even if it's true, it still means that our universe is very special, amongst all the possibilities. However, as I pointed out in my main post, if there are an infinite number of universes then it's not special at all.

The Introspective Cosmos

I haven’t written anything meaty for a while, and I’m worried I might lose my touch. Besides, I feel the need to stimulate my brain and, hopefully, yours in the process.

Just before Christmas, I read an excellent book by Noson S. Yanofsky, titled: The Outer Limits of Reason; What Science, Mathematics, and Logic CANNOT Tell Us. Yanofsky is Professor in the Department of Computer and Information Science at Brooklyn College and The Graduate Center of the City of University of New York. He is also co-author of Quantum Computing for Computer Scientists (which I haven’t read).

Yanofsky’s book (the one I read) covers a range of topics, including classical and quantum physics, chaos theory, determinism, free will, Godel’s Incompleteness Theorem, the P-NP problem, the anthropic principle and a whole lot more. The point is that he is well versed in all these areas, yet he’s very easy to read. His fundamental point, delineated in the title, is that it is impossible for us to know everything. And there will always be more that we don’t know compared to what we do know. Anyone with a remote interest in epistemology should read this book. He really does explain the limits of our knowledge, both theoretically and practically. At the end of each section he gives a synopsis of ‘further reading’, not just a list. I found the book so compelling, I even read all the ‘Notes’ in the appendix (something I rarely do).

Along the way, he explains things like countable infinities and uncountable infinities and why it is important to make the distinction. He also explains the difference between computing problems that are simply incomputable and computing problems that are computable but would take more time than the Universe allows, even if the computer was a quantum computer.

He discusses, in depth, philosophical issues like the limitations of mathematical Platonism, and provides compelling arguments that the mathematics we use to describe physical phenomena invariably have limitations that the physical phenomena don’t. In other words, no mathematical equation, no matter its efficacy, can cover all physical contingencies. The physical world is invariably more complex than the mathematics we use to interpret it, and a lot of the mathematical tools we use deal with large scale averages rather than individual entities – like the universal gas equation versus individual molecules.

He points out that there is no ‘fire in the equations’ (as does Lee Smolin in Time Reborn, which I’ve also read recently) meaning mathematics can describe physical phenomena but can’t create them. My own view is that mathematics is a code that only an intelligence like ours can uncover. As anyone who reads my blog knows, I believe mathematics is largely discovered, not invented. Marcus du Sautoy presented a TV programme called The Code, which exemplifies this view. But this code is somehow intrinsic in nature in that the Universe obeys laws and the laws not only require mathematics to quantify them but, without mathematics, we would not know their existence except, possibly, at a very rudimentary and uninformed level.

Yanofsky discusses Eugene Wigner’s famous declaration concerning ‘The Unreasonable Effectivenessof Mathematics’ and concludes that it arises from the fact that we use mathematics to probe the physical world, and that, in fact, leaving physics aside, there is a ‘paucity of mathematics in general science’. But in the next paragraph, Yanofsky says this:

The answers to Wigner’s unreasonable effectiveness leads to much deeper questions. Rather than asking why the laws of physics follow mathematics, ask why there are any laws at all.

In the same vein, Yanofsky gives a personal anecdote of a student asking him why complex numbers work for quantum mechanics. He answers that ‘…the universe does not function using complex numbers, Newton’s formula, or any other law of nature. Rather, the universe works the way it does. It is humans who use the tools they have to understand the world.’ And this is completely true as far as it goes, yet I would say that complex numbers are part of ‘the code’ required to understand one of the deepest and fundamental mysteries of the Universe.

Yanofsky’s fundamental question, quoted above, ‘why are there any laws at all?’ leads him to discuss the very structure of the universe, the emergence of life and, finally, our place in it. In fact he lists this as 3 questions:

1: Why is there any structure at all in the universe?

2: Why is the structure that exists capable of sustaining life?

3: Why did this life-sustaining structure generate a creature with enough intelligence to understand the structure?

I’ve long maintained that the last question represents the universe’s greatest enigma. There is something analogous here between us as individuals and the cosmos itself. We are each an organism with a brain that creates something we call consciousness that allows us to reflect on ourselves, individually. And the Universe created, via an extraordinary convoluted process, the ability to reflect on itself, its origins and its possible meaning.

Not surprisingly, Yanofsky doesn’t give any religious answers to this but, instead, seems to draw heavily on Paul Davies (whom he acknowledges generously at the end of the chapter) in providing various possible answers to these questions, including John Wheeler’s controversial thesis that the universe, via a cosmic scale quantum loop, has this particular life and intelligence generating structure simply because we’re in it. I’ve discussed these issues before, without coming to any definitive conclusion, so I won’t pursue them any further here.

In his notes on this chapter, Yanofsky makes this point:

Perhaps we can say that the universe is against having intelligent life and that the chances of having intelligent life are, say, 0.0000001 percent. We, therefore, only see intelligent life in 0.0000001 percent of the universe.

This reminds me of John Barrow’s point, in one of his many books, that the reason the universe is so old, and so big, is because that’s how long it takes to create complex life, and, because the universe is uniformly expanding, age and size are commensurate.

So Yanofsky’s is a deep and informative book on many levels, putting in perspective not only our place in the universe but the infinite knowledge we will never know. Towards the end he provides a table that summarises the points he delineates throughout the book in detail:

Solvable computer problems                             Unsolvable computer problems

Describable phenomena                                    Indescribable phenomena

Algebraic numbers                                            Transcendent numbers

(Provable) mathematical statements                 Mathematical facts

Finally, he makes the point that, in our everyday lives, we make decisions based primarily on emotions not reason. We seemed to have transcended our biological and evolutionary requirements when we turned to mathematics and logic to comprehend phenomena hidden from our senses and attempted to understand the origin and structure of the universe itself.

Why is there something rather than nothing?

Jim Holt has written an entire book on this subject, titled Why Does the World Exist? An Existential Detective Story. Holt is a philosopher and frequent contributor to The New Yorker, the New York Times and the London Review of Books, according to the blurb on the inner title page. He’s also very knowledgeable in mathematics and physics, and has the intellectual credentials to gain access to some of the world’s most eminent thinkers, like David Deutsch, Richard Swinburne, Steven Weinberg, Roger Penrose and the late John Updike, amongst others. I’m stating the obvious when I say that he is both cleverer and better read than me.

The above-referenced, often-quoted existential question is generally attributed to Gottfried Leibniz, in the early 18^th Century and towards the end of his life, in his treatise on the “Principle of Sufficient Reason”, which, according to Holt, ‘…says, in essence, that there is an explanation for every fact, an answer to every question.’ Given the time in which he lived, it’s not surprising that Leibniz’s answer was ‘God’.  Whilst Leibniz acknowledged the physical world is contingent, God, on the other hand, is a ‘necessary being’.

For some people (like Richard Swinburne), this is still the only relevant and pertinent answer, but considering Holt makes this point on page 21 of a 280 page book, it’s obviously an historical starting point and not a conclusion. He goes on to discuss Hume’s and Kant’s responses but I’ll digress. In Feb. 2011, I wrote a post on metaphysics, where I point out that there is no reason for God to exist if we didn’t exist, so I think the logic is back to front. As I’ve argued elsewhere (March 2012), the argument for a God existing independently of humanity is a non sequitur. This is not something I’ll dwell on – I’m just putting the argument for God into perspective and don’t intend to reference it again.

Sorry, I’ll take that back. In Nov 2011, I got into an argument with Emanuel Rutten on his blog, after he claimed that he had proven that God ‘necessarily exists’ using modal logic. Interestingly, Holt, who understands modal logic better than me, raises this same issue. Holt references Alvin Platinga’s argument, which he describes as ‘dauntingly technical’. In a nutshell: because of God’s ‘maximal greatness’, if one concedes he can exist in one possible world, he must necessarily exist in all possible worlds because ‘maximal greatness’ must exist in all possible worlds. Apparently, this was the basis of Godel’s argument (by logic) for the existence of God. But Holt contends that the argument can just as easily be reversed by claiming that there exists a possible world where ‘maximal greatness’ is absent’. And ‘if God is absent from any possible world, he is absent from all possible worlds…’ (italics in the original). Rutten, by the way, tried to have it both ways: a personal God necessarily exists, but a non-personal God must necessarily not exist. If you don’t believe me, check out the argument thread on his own blog which I link from my own post, Trying to define God (Nov. 2011).

Holt starts off with a brief history lesson, and just when you think: what else can he possibly say on the subject? he takes us on a globe-trotting journey, engaging some truly Olympian intellects. As the book progressed I found the topic more engaging and more thought-provoking. At the very least, Holt makes you think, as all good philosophy should. Holt acknowledges an influence and respect for Thomas Nagel, whom he didn’t speak with, but ‘…a philosopher I have always revered for his originality, depth and integrity.’

I found the most interesting person Holt interviewed to be David Deutsch, who is best known as an advocate for Hugh Everett’s ‘many worlds’ interpretation of quantum mechanics. Holt had expected a frosty response from Deutsch, based on a review he’d written on Deutsch’s book, The Fabric of Reality, for the Wall Street Journal where he’d used the famous description given to Lord Byron: “mad, bad and dangerous to know”. But he left Deutsch’s company with quite a different impression, where ‘…he had revealed a real sweetness of character and intellectual generosity.’

I didn’t know this, but Deutsch had extended Turing’s proof of a universal computer to a quantum version, whereby  ‘…in principle, it could simulate any physically possible environment. It was the ultimate “virtual reality” machine.’ In fact, Deutsch had presented his proof to Richard Feynman just before his death in 1988, who got up, as Deutsch was writing it on a blackboard, took the chalk off him and finished it off. Holt found out, from his conversation with Deutsch, that he didn’t believe we live in a ‘quantum computer simulation’.

Deutsch outlined his philosophy in The Fabric of Reality, according to Holt (I haven’t read it):

Life and thought, [Deutsch] declared, determine the very warp and woof of the quantum multiverse… knowledge-bearing structures – embodied in physical minds – arise from evolutionary processes that ensure they are nearly identical across different universes. From the perspective of the quantum multiverse as a whole, mind is a pervasive ordering principle, like a giant crystal.

When Holt asked Deutsch ‘Why is there a “fabric of reality” at all?’ he said “[it] could only be answered by finding a more encompassing fabric of which the physical multiverse was a part. But there is no ultimate answer.” He said “I would start with the principle of comprehensibility.”

He gave the example of a quasar in the universe and a model of the quasar in someone’s brain “…yet they embody the same mathematical relationships.” For Deutsch, it’s the comprehensibility of the universe (in particular, its mathematical comprehensibility) that provides a basis for the ‘fabric of reality’. I’ll return to this point later.

The most insightful aspect of Holt’s discourse with Deutsch was his differentiation between explanation by laws and explanation of specifics. For example, Newton’s theory of gravitation gave laws to explain what Kepler could only explain by specifics: the orbits of planets in the solar system. Likewise, Darwin and Wallace’s theory of natural selection gave a law for evolutionary speciation rather than an explanation for every individual species. Despite his affinity for ‘comprehensibility’, Deutsch also claimed: “No, none of the laws of physics can possibly answer the question of why the multiverse is there.”

It needs to be pointed out that Deutsch’s quantum multiverse is not the same as the multiverse propagated by an ‘eternally-inflating universe’. Apparently, Leonard Susskind has argued that “the two may really be the same thing”, but Steven Weinberg, in conversation with Holt, thinks they’re “completely perpendicular”.

Holt’s conversation with Penrose held few surprises for me. In particular, Penrose described his 3 worlds philosophy: the Platonic (mathematical) world, the physical world and the mental world. I’ve expounded on this in previous posts, including the one on metaphysics I mentioned earlier but also when I reviewed Mario Livio’s book, Is God a Mathematician? (March 2009).

Penrose argues that mathematics is part of our mental world (in fact, the most complex and advanced part) whilst our mental world is produced by the most advanced and complex part of the physical world (our brains). But Penrose is a mathematical Platonist, and conjectures that the universe is effectively a product of the Platonic world, which creates an existential circle when you contemplate all three. Holt found Penrose’s ideas too ‘mystical’ and suggests that he was perhaps more Pythagorean than Platonist. However, I couldn’t help but see a connection with Deutsch’s ‘comprehensibility’ philosophy. The mathematical model in the brain (of a quasar, for example) having the same ‘mathematical relationships’ as the quasar itself. Epistemologically, mathematics is the bridge between our comprehensibility and the machinations of the universe.

One thing that struck me right from the start of Holt’s book, yet he doesn’t address till the very end, is the fact that without consciousness there might as well be nothing. Nothingness is what happens when we die, and what existed before we were born. It’s consciousness that determines the difference between ‘something’ and ‘nothing’. Schrodinger, in What is Life? made the observation that consciousness exists in a continuous present. Possibly, it’s the only thing that does. After all, we know that photons don’t. As Raymond Tallis keeps reminding us, without consciousness, there is no past, present or future. It also means that without memory we would not experience consciousness. So some states of unconsciousness could simply mean that we are not creating any memories.

Another interesting personality in Holt’s engagements was Derek Parfit, who contemplated a hypothetical ‘selector’ to choose a universe. Both Holt and Parfit concluded, through pure logic, using ‘simplicity’ as the criterion, that there would be no selector and ‘lots of generic possibilities’ which would lead to a ‘thoroughly mediocre universe’. I’ve short-circuited the argument for brevity, but, contrary to Holt’s and Parfit’s conclusion, I would contend that it doesn’t fit the evidence. Our universe is far from mediocre if it’s produced life and consciousness. The ‘selector’, it should be pointed out, could be a condition like ‘goodness’ or ‘fullness’. But, after reading their discussion, I concluded that the logical ‘selector’ is the anthropic principle, because that’s what we’ve got: a universe that’s comprehensible containing conscious entities that comprehend it.

P.S. I wrote a post on The Anthropic Principle last month.

Addendum 1: In reference to the anthropic principle, the abovementioned post specifies a ‘weak’ version and a ‘strong’ version, but it’s perhaps best understood as a ‘passive’ version and an ‘active’ version. To combine both posts, I would argue that the fundamental ontological question in my title, raises an obvious, fundamental ontological fact that I expound upon in the second last paragraph: ‘without consciousness, there might as well be nothing.’ This leads me to be an advocate for the ‘strong’ version of the anthropic principle. I’m not saying that something can’t exist without consciousness, as it obviously can and has, but, without consciousness, it’s irrelevant.

Addendum 2 (18 Nov. 2012): Four months ago I wrote a comment in response to someone recommending Robert Amneus's book, The Origin of the Universe; Case Closed (only available as an e-book, apparently).

In particular, Amneus is correct in asserting that if you have an infinitely large universe with infinite time, then anything that could happen will happen an infinite number of times, which explains how the most improbable events can become, not only possible, but actual. So mathematically, given enough space and time, anything that can happen will happen. I would contend that this is as good an answer to the question in my heading as you are likely to get.

The Anthropic Principle

I’ve been procrastinating over this topic for some time, probably a whole year, such is the epistemological depth hidden behind its title; plus it has religious as well as scientific overtones. So I recently re-read John D. Barrow’s The Constants of Nature with this specific topic in mind. I’ve only read 3 of Barrow’s books, though his bibliography is extensive, and the anthropic principle is never far from the surface of his writing.

To put it into context, Barrow co-wrote a book titled, The Anthropic Cosmological Principle, with Frank J. Tipler in 1986, that covers the subject in enormous depth, both technically and historically. But it’s a dense read and The Constants of Nature, written in 2002, is not only more accessible but possibly more germane because it delineates the role of constants, dimensions and time in making the universe ultimately livable. I discussed Barrow’s The Book of Universes in May 2011, which, amongst other things, explains why the universe has to be so large and so old if life is to exist at all. In March this year, I also discussed the role of ‘chaos’ in the evolution of the universe and life, which leads me (at least) to contend that the universe is purpose-built for life to emerge (but I’m getting ahead of myself).

We have the unique ability (amongst species on this planet) to not only contemplate the origins of our existence, but to ruminate on the origins of the universe itself. Therefore it’s both humbling, and more than a little disconcerting, to learn that the universe is possibly even more unique than we are. This, in effect, is the subject of Barrow’s book.

Towards the end of the 19^th Century, an Irish physicist, George Johnstone, attempted to come up with a set of ‘units’ based on known physical constants like c (the speed of light), e (the charge on an electron) and G (Newton’s gravitational constant). At the start of the 20^th Century, Max Planck did the same, adding h (Planck’s quantum constant) to the mix. The problem was that these constants either produced very large numbers or very small ones, but they pointed the way to understanding the universe in terms of ‘Nature’s constants’.

Around the same time, Einstein developed his theory of relativity, which was effectively an extension of the Copernican principle that no observer has a special frame of reference compared to anyone else. Specifically, the constant, c, is constant irrespective of an observer’s position or velocity. In correspondence with Ilse Rosenthal-Schneider (1891-1990), Einstein expressed a wish that there would be dimensionless constants that arose from theory. In other words, Einstein wanted to believe that nature’s constants were not only absolute but absolutely no other value.  In his own words,  he wanted to know if “God had any choice in making the world”. In some respects this sums up Barrow’s book, because nature’s constants do, to a great extent, determine whether the universe could be life-producing.

On page 167 of the paperback edition (Vintage Books), Barrow produces a graph that shows the narrow region allowed by the electromagnetic coupling constant, α, and the mass ratio of an electron to a proton, β, for a habitable universe with stars and self-reproducible molecules. Not surprisingly, our universe is effectively in the middle of the region. On page 168, he produces another graph of α against the strong coupling constant, α_s, that allows the carbon atom to be stable. In this case, the region is extraordinarily small (in both graphs, the scales are logarithmic).

I was surprised to learn that Immanuel Kant was possibly the first to appreciate the relationship between Newton’s theory of gravity being an inverse square law and the 3 dimensions of space. He concluded that the universe was 3D because of the inverse square law, whereas, in fact, we would conclude the converse. Paul Ehrenfest (1890 – 1933), who was a friend of Einstein, extended Kant’s insight when he theorised that stable planetary orbits were only possible in 3 dimensions (refer my post, This is so COOL, May 2012). But Ehrenfest made another revelation when he realised that 3 dimensional waves were special. In even dimensions, different parts of a ‘wavy disturbance’ travel at different speeds, and, whilst waves in odd dimensions have disturbances all travelling at the same speed, they become increasingly distorted in dimensions other than 3. On page 222, Barrow produces another graph demonstrating that only a universe with 3 dimensions of space and one of time, can produce a universe that is neither unpredictable, unstable nor too simple.

But the most intriguing and informative chapter in his book concerns research performed by himself, John Webb, Mike Murphy, Victor Flambaum, Vladimir Dzuba, Chris Churchill, Michael Drinkwater, Jason Prochaska and Art Wolfe that the fine structure constant (α) may have been a different value in the far distant past by the miniscule amount of 0.5 x 10^-5, which equates to 5 x 10^-16 per year. Barrow speculates that there are fundamentally 3 ages to the universe, which he calls the radiation age, the cold dark matter age and the vacuum energy age or curvature age (being negative curvature) and we are at the start of the third age. He simplifies this as the radiation era, the dust era and the curvature era. He contends that the fine structure constant increased in the dust era but is constant in the curvature era. Likewise, he believes that the gravitational constant, G, has decreased in the dust era but remains constant in the curvature era. He contends: ‘The vacuum energy and the curvature are the brake-pads of the Universe that turn off variations in the constants of Nature.’

Towards the end of the book, he contemplates the idea of the multiverse, and unlike other discussions on the topic, points out how many variations one can have. Do you just have different constants or do you have different dimensions, of both space and/or time? If you have every possible universe then you can have an infinite number, which means that there are an infinite number of every universe, including ours. He made this point in The Book of Universes as well.

I’ve barely scratched the surface of Barrow’s book, which, over 300 pages, provides ample discussion on all of the above topics plus more. But I can’t leave the subject without providing a definition of both the weak anthropic principle and the strong anthropic principle as given by Brandon Carter.

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.’

The weak principle is effectively a tautology: only a universe that could produce observers could actually be observed. The strong principle is a stronger contention and is an existential one. Note that the ‘observers’ need not be human, and, given the sheer expanse of the universe, it is plausible that other ‘intelligent’ life-forms could exist that could also comprehend the universe. Having said that, Tipler and Barrow, in The Anthropic Cosmological Principle, contended that the consensus amongst evolutionary biologists was that the evolution of human-like intelligent beings elsewhere in the universe was unlikely.

Whilst this was written in 1986, Nick Lane (first Provost Venture Research Fellow at University College London) has done research on the origin of life, (funded by Leverhulme Trust) and reported in New Scientist (23 June 2012, pp.33-37) that complex life was a ‘once in four billion years of evolution… freak accident’.  Lane provides a compelling argument, based on evidence and the energy requirements for cellular life, that simple life is plausibly widespread in the universe but complex life (requiring mitochondria) ‘…seems to hinge on a single fluke event – the acquisition of one simple cell by another.’ As he points out: ‘All the complex life on Earth – animals, plants, fungi and so on – are eukaryotes, and they all evolved from the same ancestor.’

I’ve said before that the greatest mystery of the universe is that it created the means to understand itself. We just happen to be the means, and, yes, that makes us special, whether we like it or not. Another species could have evolved to the same degree and may do over many more billions of years and may have elsewhere in the universe, though Nick Lane’s research suggests that this is less likely than is widely believed.

The universe, and life on Earth, could have evolved differently as chaos theory tells us, so some other forms of intelligence could have evolved, and possibly have that we are unaware of. The Universe has provided a window for life, consciousness and intelligence to evolve, and we are the evidence. Everything else is speculation.

How chaos drives the evolution of the universe and life

The Cosmic Blueprint is the very first book of Paul Davies I ever read nearly a quarter of a century ago, and I’ve read many others since. I heard him being interviewed about it on a car trip from Melbourne to Mulwala (on the Victorian, New South Wales border) and that was the first time I’d heard of him. The book was published in 1987, so it was probably 1988.

Davies received the Templeton Foundation Prize in 1995, though not the wrath of Dawkins for accepting it. He’s also received the 2002 Michael Faraday Prize from the Royal Society and the 2001 Kelvin Medal and Prize from the UK Institute of Physics. He was resident in Australia for a couple of decades but now resides in the US where he’s an astro-biologist at the University of Arizona.

In America, Davies has been accused of being a ‘creationist in disguise’ by people whose ignorance is only out-weighed by their narrow-mindedness (they think there are atheists and there are creationists with nothing in between). The 2004 edition of this book is published by the Templeton Foundation and the first word in the opening chapter is ‘God’ as part of a quote by Ilya Prigogine, who features prominently in the book. But anyone who thinks this is a thesis for Intelligent Design will be disappointed; it’s anything but. In fact, one of the book’s great virtues is its attempt to explain complexity in the universe and evolution as a natural occurrence and not a Divine one.

I’ve long believed that Davies writes about science and philosophy better than anyone else, not least because he seems to be equally erudite in the disciplines of physics, cosmology, biology and philosophy. He’s not a member of the ‘strong atheist’ brigade, which puts him offside with many philosophers and commentators, but his argument against ID in The Goldilocks Enigma (2006) was so compelling that Stephen Law borrowed it for himself.

I remember The Cosmic Blueprint primarily as introducing me to chaos theory; it was the new kid on the block in popular consciousness with fractals and Mandelbroit’s set just becoming conspicuous in pop culture. Reading it now, I’m surprised at how much better it is than I remember it, but that’s partly due to what I’ve learnt in between. A lot of it would have gone over my head, which is not to say it still doesn’t, but less so than before.

More than any other writer on science, Davies demonstrates how much we don’t know and he doesn’t shy away from awkward questions. In particular, he is critical of reductionism as the only method of explanation, especially when it explains things away rather than explicating them; consciousness and life’s emergence being good examples.

I like Davies because his ideas reflect some of my own ruminations, for example that natural selection and mutations can’t possibly explain the whole story of evolution. We think we are on the edge of knowing everything, yet future generations will look back and marvel at our ignorance just as we do with our forebears.

There is an overriding thesis in The Cosmic Blueprint that is obvious once it’s formulated yet is largely ignored in popular writing. It’s fundamentally that there are two arrows of time: one being the well known 2^nd law of thermodynamics or entropy; and the other being equally obvious but less understood as the increase in complexity at all levels in the universe from the formation of galaxies, stars and planets to the evolution of life on Earth, and possibly elsewhere. Both of which demonstrate irreversibility as a key attribute.  And whilst many see them as contradictory and therefore evidence of Divine intervention, Davies sees them as complementary and part of the universe’s overall evolvement.

Davies explains how complexity and self-organisation can occur when dynamic systems are pushed beyond equilibrium with an open source of energy. Entropy, on the other hand, is a natural consequence of systems in equilibrium.

In the early pages, Davies explains chaotic behaviour with a simple-to-follow example that’s purely mathematical. In particular, he demonstrates how the system is completely deterministic yet totally unpredictable because the initial conditions are mathematically impossible to define. This occurs in nature all the time, like coin tosses, so that the outcome is totally random but only because the initial conditions are impossible to determine, not because the coin follows non-deterministic laws. This is a subtle but significant distinction.

A commonly cited example is cellular automata that can be generated by a computer programme. Stephen Wolfram of the Institute for Advanced Study, Princeton, has done a detailed study of one-dimensional automata that could give an insight into evolution. Davies quotes Wolfram:

“…the cellular automaton evolution concentrates the probabilities for particular configurations, thereby reducing entropy. This phenomenon allows for the possibility of self-organization by enhancing the probabilities of organized configurations and suppressing disorganized configurations.”

Wolfram is cited by Gregory Chaitin, in Thinking about Godel and Turing, as speculating that the universe may be pseudo-random and chaos theory provides an innate mechanism: deterministic laws that can’t be predicted. However, it seems that the universe’s innate chaotic laws provide opportunities for a diverse range of evolutionary possibilities, and the sheer magnitude of the universe in space and time, along with a propensity for self-organisation, in direct opposition to entropy, may be enough to ensure intelligent life as an outcome. The truth is that we don’t know. (Btw, Davies wrote the forward to Chaitin’s book.)

Davies calls this position ‘predestiny’ but he’s quick to qualify it thus: ‘Predestiny is a way of thinking about the world. It is not a scientific theory. It receives support, however, from those experiments that show how complexity and organization arise spontaneously and naturally under a wide range of conditions.’

This view is mirrored in the anthropic principle, which Davies also briefly discusses, but there are two version, as expounded by Frank Tipler and John Barrow in The Anthropic Cosmological Principle: the weak anthropic principle and the strong anthropic principle; and ‘predestiny’ is effectively the strong anthropic principle.

Roughly twenty years later, in The Goldilocks Enigma, Davies elaborates on this philosophical viewpoint when he argues for the ‘self-explaining universe’ amongst a critique of all the current ‘flavours’ of universe explanations: ‘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 is effectively a description of John Wheeler’s speculative cosmic quantum loop explanation of the universe’s existence – it exists because we’re in it. Davies argues that such a universe is ‘self-activating’ to avoid religious connotations: ‘…perhaps existence isn’t something that gets bestowed from outside…’

Teleological is a word that most scientists avoid, but Davies points out that the development of every organism is teleological because it follows a ‘blueprint’ or ‘plan’ entailed in its DNA. How this occurs is not entirely understood, but Davies makes an analogy with software which is apposite, as DNA provides coded instructions that ultimately result in fully developed organisms like us. He explores a concept called ‘downward causation’ whereby information can actually ‘cause’ materialistic events and software in computers provide the best example. In fact, as Davies hypothesises, one could imagine a software programme that makes physical changes to the computer that it’s operating on. Perhaps this is how the ‘mind’ works, which is similar to Douglas Hofstadter’s idea of a ‘strange loop’ that he introduced in Godel Escher Bach (which I reviewed in Feb. 2009) and later explored in another tome called I am a Strange Loop (which I haven’t read).

Davies introduces the concept of ‘downward causation’ in his discussion on quantum mechanics because it’s the measurement or observation that crystallises the quantum phenomenon into the real world. According to Davies, Wheeler speculated that ‘downward causation’ in quantum mechanics is ‘backwards in time’ and suggested a ‘delayed-choice’ thought experiment. To quote Davies: ‘The experiment has recently been conducted, and accords entirely with Wheeler’s expectations. It must be understood, however, that no actual communication with the past is involved.’

It’s impossible to discuss every aspect of this book, covering as it does: chaos theory, fractals, cosmological evolution, biological evolution, quantum mechanics and mind and matter.

Towards the end, Davies reveals some of his own philosophical prejudices, which, unsurprisingly, are mirrored in The Goldilocks Enigma twenty years on.

The very fact that the universe is creative, and that the laws have permitted complex structures to emerge and develop to the point of consciousness – in other words, that the universe has organized its own self-awareness – is for me powerful evidence that there is ‘something going on’ behind it all.

This last phrase elicits the ‘design’ word, many years before Intelligent Design was introduced as a ‘wedge’ tactic for creationists, but Davies has been an outspoken critic of both creationism and ID, as I explained above. Davies strongly believes the universe has a purpose and the evidence supports that point of view. But it’s a philosophical point of view, not a scientific one.

This leads to the logical question: is the universe teleological? I think chaos theory provides an answer. In the same way that chaotic phenomena, which includes all complex dynamics in the universe (like evolution) are deterministic yet unpredictable, the universe could be purposeful yet not teleological. In other words, the purpose is not predetermined but the universe’s dynamics allow purpose to evolve.

The Universe and our place in it

Over the last month I’ve acquired 3 books that are not entirely unrelated. Not surprisingly, they all deal with topics I’ve discussed before.

In order of acquisition they are: Physics and Philosophy by Werner Heisenberg; The Book of Universes by John D. Barrow; and MATHS 1001 by Richard Elwes. Of all these, Heisenberg’s book is probably the least accessible, even though it’s written more for a lay-audience than an academic one.

Elwes’ book is subtitled Absolutely everything you need to know about mathematics in 1001 bite-sized explanations. Under the subtitle is a mini-bite-sized blurb presented as an un-credited quote: ‘More helpful than an encyclopaedia, much easier than a textbook’.

Both of these claims seem unrealistic, yet the blurb is probably closer to the end result than the subtitle. I had this book whilst I spent a recent 4 day sojourn in hospital and it ensured that I never got bored.

But Barrow’s book is the most compelling, not least because he’s not just an observer but a participant in the story. Barrow covers the entire Western history of ‘cosmology’ from Stonehenge to String Theories. This is a book that really does attempt to tell you everything you wanted to know about theories of the universe(s). And Barrow’s book is certainly worth writing a post about, because he revealed things to me that I hadn’t known or considered before.

On the back fly cover, Barrow’s credentials are impressive: ‘Professor of Mathematical Sciences and Director of the Millennium Mathematics Project at Cambridge University, Fellow of Clare Hall, Cambridge, a Fellow of the Royal Society, and current Gresham Professor of Geometry at Gresham College, London.’ As an understatement, the citation continues: ‘His principal area of scientific research is cosmology…’. It’s rare to find someone, so highly respected in an esoteric field, who can write so eloquently and incisively for a lay audience. Paul Davies comes to mind, as does Roger Penrose, both of whom get mentioned in the pages.

Not surprisingly, even though Barrow’s narrative goes from Aristotle to Ptolemy to Copernicus then Galileo, Kepler and Newton, it resides mostly in the 20th Century, specifically post Einstein’s theories of relativity. Einstein’s field equations have really dictated all theoretical explorations into cosmology from their inception to the present day, and Barrow continually reminds us of this, despite all the empirical data that has driven our best understanding of the universe to date, like Hubble’s constant and the microwave background radiation.

One of the revelations I found in this text, is that Alan Guth’s inflationary hypothesis virtually guarantees that there is a multiverse. Inflation is like a bubble and beyond the bubble, which must always lie beyond the horizon of our expanding universe, are all the anomalies and inconsistencies that we expect to find from a Big Bang universe. The hypothesis contains within it the possibility that there are numerous other inflationary bubbles, many of which could have occurred prior to ours. Barrow also points out that, if there are an infinite number of universes, than any event with probability greater than 0 could occur an infinite number of times. Only mathematicians and cosmologists truly understand just how big infinity is and what its consequences are. Elwes’ book (MATHS 1001) also brings this point home, albeit in a different way. Barrow’s point is that if there are an infinite number of universes then there are an infinite number of you(s) doing exactly what you are doing now as well as an infinite number living infinitely different lives. The fact that they will never encounter each other means that they can exist without mutual awareness except as philosophical speculations like I’m doing now.

For most people the thought of an infinite number of themselves living infinitely variable lives is enough to turn them off the infinite multiverse hypothesis. It should also make one reconsider the idea of an infinite afterlife.

The other philosophical concept that Barrow discusses at length is the anthropic principle and how it is virtually unavoidable in the face of our existence. Another of his relevations (to me) was that we don’t live in one of the most ‘probable’ universes. He demonstrates that if we were to produce a bell curve of probable universes that our particular universe exists in the ‘tail’ and not at the peak as one might expect.

As he says: “Universes that don’t produce the possibility of ‘observers’ – and they do not need to be like ourselves – don’t really count when it comes to comparing the theory with the evidence.”

He then goes on to say: “This is most sobering. We are not used to the existence of cosmologists being a significant factor in the evaluation of cosmological theories.”

There is a link between this idea and quantum mechanics, which I’ll return to later. It was explored specifically by John Wheeler and discussed at length by Paul Davies in his book, The Goldilocks Enigma. People are often dismissive about the idea of why there is something rather than nothing. Recently, Stephen Law, in a debate with Peter Atkins, said that this was the wrong question without elaborating on why it was or what the right question might be. The point is that without conscious entities there may as well be nothing, because only conscious entities, like us, give meaning to the universe at all. To dismiss the question is to say that the universe not only has no meaning but should have no meaning. It’s not surprising (to me) that the people who insist our existence has no meaning also insist that we have no free will. I challenge both premises (or conclusions, depending how they’re framed).

Slightly off track, but only slightly; Barrow immediately follows this relevation with another of equal importance. Life in a universe requires both lots of time and lots of space, so we should not be so surprised that we live in such a vast expanse of space bookended by equally vast amounts of time. It is because life requires enormous complexity that it also requires enormous time to create it.

Again, to quote Barrow: “This is why we should not be surprised to find that our universe is so old. It takes lots of time to produce the chemical building blocks needed for any type of complexity. And because the universe is expanding, if it is old, it must be big – billions of light years in extent.”

Stephen Hawking recently created a minor furor when he claimed the entire universe could have arisen from nothing. People who should know better, or should simply read more, were derisive of the statement, believing he was giving fundamentalists ready-made ammunition by kicking an own goal. Back in the 1980s, Paul Davies in his book, God and the New Physics (covers much the same material as Dawkins’ The God Delusion, only in more depth) quotes Alan Guth that “the Universe is the ultimate free lunch”. Barrow also points out that gravity in the way of potential energy (therefore negative energy) can exactly balance all the positive energy of mass and radiation (through E=mc²) so that the energy balance for the entire universe can be zero.

Heisenberg’s uncertainty principle allows that matter (therefore energy) can and is produced all the time (via ‘quantum fluctuations’) albeit for very short periods of time. The shorter the time, the higher the energy, via the relationship of Planck’s constant, h. So a quantum mechanism for producing something from nothing does exist. That it can happen on a cosmological scale is not so improbable if all the principle forces of nature: gravitation, electromagnetic, electroweak and strong nuclear; can all meet as equal magnitude in the crucible we call the Big Bang. In his discussion on ‘grand unification’ Barrow leaves gravity out of it. I’ve glossed over this for the sake of brevity, but Barrow discusses it in detail. He also discusses the asymmetry between matter and anti-matter that allows anything to exist at all. (He wrote another book on 'symmetry-breaking' with Joseph Silk called The Left Hand of Creation.)

Another revelation I found in Barrow’s book was his discussion of string theories, now collectively called M theory, and the significance of Calib-Yau spaces or manifolds, of which there are over 10⁵⁰⁰ possibilities (remember 1 billion is only 10⁹). Significantly, all these predict that gravity can be expressed by Einstein’s field equations. So Einstein still dominates the landscape, though what he would make of this development is anyone’s guess.

This means that our quest for a ‘Theory of Everything’ has led to a multitude of universes of which ours is one in 10⁵⁰⁰. But Barrow goes further when he explains “There are an infinite number of possible universes. The number is too large to be explored systematically by any computer.”

But Barrow’s best revelation is left to the next to last page when he claims that he and Douglas Shaw have recently postulated that the cosmological constant (which ‘adds an additional equation to those first found by Einstein’) is given by the relationship (t_p/t_u)² where t_p is Planck’s fundamental time, 10^-43 sec, and t_u is the current age of the universe, 4.3x10¹⁷ sec. t_p is the smallest quantity of time predicted by quantum mechanics, so is effectively the basic unit of time for the whole universe. By postulating the cosmological constant as a squared ratio dependent on the age of the universe it gives a rational reason, as opposed to a mystical one, why it is the value we observe today of 0.5x10^-121. What’s more, their postulate makes a prediction that the curvature of the universe is -0.0056. Current observations give between -0.0133 and +0.0084, but more accurate maps of the microwave background radiation should ‘be able to confirm or refute this very precise prediction’.

There is an intriguing connection between the anthropic principle and quantum mechanics. The Copenhagen interpretation, led by Bohr and given support by Heisenberg, attempts to bridge the gap between the classical world and the quantum world, by stating that something becomes manifest only after we’ve made a ‘measurement’. I think Bohr took this literally and John Wheeler, who was a loyal disciple of Bohr’s, took it even further when he extrapolated it to the cosmos. Paul Davies explores John Wheeler’s thesis in The Goldilocks Enigma, whereby Wheeler proposes a reverse causal relationship, a cosmological quantum loop in effect, between our observation of the universe and its existence. Most people find this too fantastical to entertain, yet it ties quantum mechanics to the anthropic principle in a fundamental way.

Elwes’ book also discusses quantum mechanics and explicates better than most I’ve read, when he expounds that the wave function (given by Schrodinger’s equation) ‘is no longer a valid description of the state of the particle. It is difficult to avoid the conclusion that whenever someone (or perhaps something) takes a measurement, the quantum system mysteriously jumps from being smoothly spread out, to crystallizing at a specific position.’ (italics in the original)

One can’t help but compare Heisenberg’s book (Physics and Philosophy) with Schrodinger’s (What is Life?), which I reviewed in November 2009. Both men made fundamental contributions to quantum theory, for which they were both awarded Nobel prizes, yet they maintained philosophical differences over its ramifications. Schrodinger’s book is a far better read, not least because it’s more accessible. Both impress upon the reader the significance of mathematics in fathoming the universe’s secrets. Schrodinger appealed to Platonism whereas, to my surprise, Heisenberg appealed to the Pythagoreans, who influenced Plato’s Academy and its curriculum of arithmetic, geometry, astronomy and music – Pythagoras’s quadrivium. In particular, Heisenberg quotes Russell on Pythagoras: “I don’t know of any other man who has been as influential as he was in the sphere of thought.”

Quantum phenomena suggests to me that everything is connected. Why do radioactive half lives follow a totally predictable rule statistically but individually are not predictable at all? It’s like the decay exists at a holistic level rather than a unit level. Planck’s constant gives an epistemological limit to our ability to predict or know. At the other end of the scale, the universe exists for us at a time when we can make sense of it. Barrow, along with Douglas Shaw, entails Planck’s constant as a fundamental unit of time in an equation that suggests we understand it only because we are here at this specific time in its history. There is no other explanation, and maybe there is no other explanation required.


Addendum 1: Scientific American (through Paul J. Steinhardt) have a for-and-against discussion on the merits of Alan Guth's 30 year old inflationary theory, and include a reference to Roger Penrose's ideas that I discussed in a post last January.

Addendum 2: Yes, I've changed the title (Sep 2017).

Science, Philosophy, Religion

In a not-so-recent discussion I had on Stephen Law’s blog, I had trouble convincing some of the participants that, not only is there a difference between science and philosophy, but the distinction is an important one.

In a comment on my last post, Timmo made a reference to Richard Feynman’s book, The Character of Physical Law, which got me re-reading it. You may wonder how these 2 issues are related. Well, in my last post I discussed some of Erwin Schrodinger’s philosophy, and the aforementioned Feynman’s book is probably his most philosophical. Together, they highlight the fact that Feynman’s philosophical musings probably couldn’t be more different than Schrodinger’s, yet I doubt that they would disagree on the science. The same is true of contemporary physicists. For example, Roger Penrose and Stephen Hawking, even though they have collaborated scientifically and even won a joint prize in physics, are philosophically miles apart on the nature of mind. In his book, Shadows of the Mind, Penrose actually invited Hawking to provide a counter-philosophical point of view, which, of course, he did. Likewise, Albert Einstein and Kurt Godel were very good friends, when they were both fellows at the Princeton Institute for Advanced Study, but held philosophically divergent views: Godel was a mathematical Platonist and Einstein was not; yet I’m sure they didn’t disagree on the mathematics of each other’s theories.

As a general rule, philosophy deals with questions, the answers for which are not certain, and in many cases, may never be; whereas science deals with questions, where the answers will decide the ultimate truth, and the limits of truth, for a particular theory. Bertrand Russell made the observation that, in philosophy, there may be no right or wrong answers, but the questions, when addressed in the right spirit, are the bulwark against dogmatism and the conservative resistance we find to genuine questing for knowledge. A corollary to this approach is to beware of those who claim they have answers of certainty to questions of profundity.

You may wonder where religion fits into all this. Well, religion is philosophy taken to the metaphysical extreme, but is often confounded by politics to the extent that some people don’t delineate one from the other. In fact, religion is often confounded with ideology, because, for many people, religion and ideology are unassailable truths. But truth is arguably the most elusive concept in the human world, and in this context is an abuse.

I have 2 ways of defining science. Firstly, a general definition is that science is the study of the natural world in all its manifestations. So this leaves out many aspects of knowledge that are human-based, or what is generically called the humanities: all the arts, and topics like ethics and justice. Arguably, psychology crosses the boundary, and I discussed this briefly in another post, Is psychology a science? (Nov. 08). But the topic of ‘mind’, that was raised by Schrodinger, certainly falls into a category where science, psychology and philosophy all merge, but I don’t want to get too far off the track, so I will return to ‘mind’ later. Interestingly, philosophy is generally considered a humanities subject.

The other definition, which is effectively a working definition, is that science is a dialectic between theory and experimentation or observation. Questions that can’t be answered by experimental analysis generally remain philosophical until they can. An example is AI (artificial intelligence). Will AI ever be sentient? Providing we can agree on a definition of sentience, this question will probably one day be resolved. Until that day, it will remain a philosophical question. But there are other philosophical questions that may never be decided by science. An example is the so-called multiverse (multiple universes) theory. If they exist, we may never find any evidence of them, though one should be careful of never saying never. Metaphysical questions like: does the universe have a purpose? (See my post on this topic, Oct. 07) is an example of a subtly different nature. This is a question that science can’t answer, although almost anyone who gives an answer, one way or the other, uses their scientific knowledge to support it. And this is why the distinction is important. Using science to support a philosophical point of view doesn’t turn philosophy into science, though many people, when lost in their own rhetoric, may infer that it does, whether intentionally or not.

On the subject of the dialectic in science, Feynman, in his book, The Character of Physical Law, gives excellent examples, whilst discussing the evolution of the Universal Theory of Gravitation: specifically, how astronomical observations forced changes to theory and then confirmed theory. In other words, without experimentation and observation, we would have just continued to bark up the wrong tree.

His opening chapter on The Law of Gravitation, an example of Physical Law provides one of the best expositions of this dialectic, including descriptions of the experiments that Galileo performed to show gravity’s universality on Earth. And how Tycho Brahe’s unprecedented accuracy in tracking planetary motion gave Johannes Kepler the key to his 3 laws, which ultimately led Newton to the Universal Theory of Gravity we have today. Yes, it’s been modified by Einstein, as Feynman explains, but Newton was able to marry Kepler’s laws to his calculus that not only clinched the theory but eventually led to predictions of another planet perturbing Neptune’s orbit. The ultimate test of a theory is when it predicts hitherto unobserved events.

String Theory is an example of a theory without the dialectic, so we have innumerable variants of which none can be validated by reality. String Theory is not exactly philosophy either – it’s a mathematical adventure. I would describe it as a mathematical model looking for an experiment to make it a scientifically valid theory. I’m not an expert on the subject, but I provide a review of Peter Woit’s book, Not Even Wrong, in a post I wrote earlier this year (Nature’s Layers of Reality, May 09).

And this leads to the significance of mathematics. No one who discusses physics and philosophy can avoid discussing the role of mathematics, and this includes Feynman. In the edition of Feynman’s book that I have (1992), Paul Davies has written an Introduction. He not only acknowledges Feynman’s influence, unorthodoxy and brilliance as a communicator, but relates a dialogue he once had with him on the philosophy of mathematics.

“…Feynman had an abiding suspicion of philosophers. I once had occasion to tackle him about the nature of mathematics… whether abstract mathematical laws could be considered to enjoy an independent Platonic existence. He gave a spirited and skilful description of why this indeed appears so but soon backed off when I pressed him to take a specific philosophical position. He was similarly wary when I attempted to draw him out on the subject of reductionism.”

Feynman devotes an entire chapter (lecture) to the topic, The Relation of Mathematics to Physics, describing it as a language with reasoning, and sees it as an intellectual construct based on axioms. He doesn’t address Godel’s Incompleteness Theorem, because it’s not strictly relevant to his topic: mathematics in physics. He refers to Newton’s calculus as an ‘invention’, whereas Platonists would call it a ‘discovery’.

But more relevant to this discussion is that he describes 3 different ways of looking at the Universal Theory of Gravity, even though they are all mathematically equivalent. One is ‘action at a distance’ or force mediated by the inverse square law; two is by a ‘potential field’; and three is by the ‘least action’ principle, which is Feynman’s personal favourite, and I discuss it in 2 other post ( Nature’s Layers of Reality, May 09 and The Laws of Nature, Mar.08). The point is that these are philosophical interpretations that would determine how a scientist may investigate a phenomenon further. Feynman prefers the ‘least action’ principle because it applies to the refraction of light as well, and therefore suggests a universal principle.

So there is philosophy within science as well as philosophy outside of science, and, once again, I think the distinction is important. Philosophy within science is more likely to be eventually resolved because it generally leads to new avenues of investigation. Feynman says of this: “…every theoretical physicist who is any good knows six or seven different theoretical representations of exactly the same physics.” By ‘exactly the same physics’ he means the mathematics is equivalent (this will become more evident when I discuss quantum mechanics). In other words, it contributes to the dialectic between theory and empirical evidence. Philosophy outside of science is generally removed from the dialectic, which is why it remains philosophy and not science. Philosophy within science remains philosophy until it can evolve into theory. In quantum mechanics (as I discuss below) theory is effectively deadlocked and has been for many decades. At least, that is the impression I get from what I’ve read on the subject by people who know it.

As an aside, the abovementioned quote was once construed by a philosophical writer (Michael Frayn in The Human Touch) as evidence that theoretical physicists effectively make things up because "nature doesn’t have six or seven different ways to represent itself, or even one." But it’s obvious to me that, even though Feynman referred to theories as ‘guesses’ in his usual cavalier manner, he didn’t doubt the validity of nature’s laws. In the cases he’s referring to, the mathematics is solid, but the philosophical interpretations are not (I elaborate on this below).

Elsewhere in the book, Feynman alludes to a view that we will eventually understand all the laws of physics. This is a philosophical position and one I’ve argued against in the past. My reason is history. We never know what we are going to discover and every resolution of a mystery in science has only revealed more mysteries. I find it hard to imagine that this will ever stop, but I also admit that I don’t want it to stop. Feynman, on the other hand, argues that we will eventually run out of finding new laws: either, because of the limit of our ability to reveal them or the limit of their actual existence. He believes that the 20th Century was a golden age of discovery in physics, and no one can deny that. But each age has uncovered new intellectual territory and nature appears far from revealing all its secrets.

On a related note, I quote Feynman in my post, Nature’s Layers of Reality, (cited by Peter Woit, Not Even Wrong) where he is scathing about String Theory. I’m not in a position to judge String Theory, but I don’t think it’s the scientific Holy Grail as some commentators do, and it does reveal how much we still don’t know. String Theory is an example of where people hope to find a ‘Theory of Everything’. It’s one of the reasons I’m a sceptic, but I could be proven wrong.

In previous posts (specifically Quantum Mechanical Philosophy, Jul.09) I describe how the philosophical implications of quantum mechanics are not resolved, yet as a meta-theory, it is arguably the most empirically successful ever. Paul Davies makes exactly the same point in The Goldilocks Enigma. Quantum mechanics demonstrates, more strikingly than any other endeavour, the fundamental differences that lie between science and philosophy. Philosophically, there is the Copenhagen interpretation (Neils Bohr), the Many Worlds interpretation (Hugh Everitt) and the Hidden Variables interpretation (David Bohm). And there are variations amongst these, which I discuss to some extent in the aforementioned post. These are not just different theories; they all have philosophical implications on how we perceive reality. Epistemologically, it can’t get more serious than that.

The Copenhagen interpretation is generally considered to be the conventional interpretation, but as Feynman says in his book: “…I think I can safely say that nobody understands quantum mechanics”. What he means is that no one can explain quantum phenomena in plain language without creating cognitive or logical contradictions. Schrodinger created a thought experiment, popularly known as Schrodinger’s Cat, that encapsulates this conundrum perfectly, where, theoretically, a cat can be dead and alive at the same time. Ironically, Schrodinger also created (he would say discovered) the mathematical equations that have made quantum mechanics the most successful theory ever.

Mathematically, there are no contradictions or conundrums – Schrodinger’s wave mechanical equations and their derivatives, especially the famous Dirac equation, have not only confirmed existing observed phenomena but predicted new ones. Dirac’s equation not only prescribed quantum electron ‘spin’ as an inherent feature of the equation, but predicted the electron’s anti-particle (the positron) and therefore anti-matter. As Feynman says, the best theories, by far, are those where we get more out than what we've put in. More relevant to this discussion, quantum mechanics demonstrates explicitly that science deals in answers and philosophy deals in questions, and sometimes one is not resolved by the other as we might expect.

And now I must come to ‘mind’ because it’s the one topic that really does cross boundaries (including religion). Feynman doesn’t discuss it, because it’s not relevant to his lectures on physics, but Schrodinger did (see previous post), and so does Penrose, who has written 3 books on the subject that I have read. I haven’t read Daniel Dennett’s Consciousness Explained but I’ve read John Searle’s Mind, and it’s the most accessible I’ve found on the subject thus far. I’ve discussed this in previous posts (Subjectivity: The Mind’s I, June 09) and of course in my last post on Schrodinger. I think Schrodinger makes a couple of salient points, which I’ve alluded to previously. In particular, that there is a subjective aspect to consciousness that makes it ontological as well as epistemological. Searle makes this point as well, in his aforementioned book, as does the Dalai Lama in his book, The Universe in a Single Atom.

Schrodinger, in particular, explains how phenomena like light and sound can be measured and analysed by instruments, and we can even analyse how they are transcribed into nerve impulses in our bodies, but all the instruments and analysis in the world can’t describe or explain the actual experience we have of light and sound. This is a contentious point, but people forget that this is what consciousness is, first and foremost: an experience. And if each and every one of us didn’t have this experience, science would no doubt tell us that it doesn’t exist, in the same way that science tells us that free will doesn’t exist. It is still the greatest enigma in the universe, and is likely to remain that way, possibly for ever.

And this leads to Schrodinger’s second salient point: without ‘mind’ the universe would be meaningless. In an earlier post (The Existential God, Sep.09) I reviewed Don Cupitt’s book, Above Us Only Sky, who goes further and says that without language, there would be no meaning and no ‘truth’. I won’t revisit Cupitt, but one should not confuse meaning with reality, nor ontology with epistemology. To quote Einstein: “The most incomprehensible thing about the universe is that it’s comprehensible.” There are various ways one can interpret that statement but mine is: The greatest mystery of the universe is that it created the ability to understand itself. Paul Davies takes this head-on in The Goldilocks Enigma and elaborates on a philosophical premise proposed by John Wheeler. Wheeler effectively argued that the universe exists as the result of a cosmological-scale quantum loop. Because we observe it, it exists. I’m not going to argue one way or the other with Wheeler, but I agree with Schrodinger that without ‘mind’ there is no point to the universe’s existence, and Davies makes a similar point. At the end of The Goldilocks Enigma he summarises all the philosophical viewpoints that are in currency (including ID, the multiverse and the ‘absurd universe’, probably better known as the accidental universe) ending with Wheeler’s, which he calls The self-explaining universe. To quote: “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.”

In a way I’ve returned to a point I alluded to much earlier: does the universe have a purpose? This is a philosophical question, as I said, but it leads into religion and religious belief. Paul Davies obviously believes it does, and says so, but he’s quick to point out that this does not axiomatically lead to a belief in God. Feynman, whom I’m almost certain was an atheist, makes only one reference to God in his book, when he discusses the hierarchical nature of nature. He explains how the laws of physics can have consequences at a higher level that are unforeseeable yet totally necessary for the universe’s existence as we know it. The example he gives is Hoyle’s and Salpeter’s prediction concerning carbon 12, which arises from the unlikely combination of 3 helium atoms creating a specific new energy level that allows the rest of the elements in the periodic table to exist. Feynman doesn’t make anything metaphysical of this, but he makes the point that nature’s laws at one level have consequences at a higher level of existence that are not readily apparent.

He invokes God (metaphorically, as he’s quick to point out) as either the progenitor of the laws or the ultimate end result; at opposite ends of reality. In an uncharacteristically poetic moment, in another part of the book, he says: “Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry.” He’s indirectly invoking the implication in the title of the Dalai Lama’s book on science and religion The Universe in a Single Atom. The laws of nature are the threads and the tapestry is the universe in all its complexity.

There are no objective religious truths, contrary to what fundamentalists tell us, but there are mathematical truths. And the more we learn about the universe, the more mathematics plays a role. Every book I’ve read on nature’s laws illustrates this fundamental premise. Feynman, Einstein and Hawking would suggest that the mathematics is human reason, but others, like Penrose, Schrodinger and Godel, would argue that mathematics is independent of human thought, albeit we only know it through human thought. Pythagoras and Plato might have argued that God exists in the mathematics and Schrodinger might have argued that God is the ultimate unity of mind (refer my last post). Like Feynman’s metaphorical attribution, they represent opposite ends of reality. At the end of the day, God becomes a metaphor and a projection for what we don’t know, whichever end of reality we posit that projection.

Religion is mind’s quest to find meaning in its own existence. If we were to accept that simple premise without the urge to create an edifice of mythology and political ideology around it, maybe we could all accept each other’s religion.