Ursula Le Guin's acceptance speech at the American Book Awards 2014

An acerbic commentary on the publishing industry from someone who's been in it for a long, long time; very successfully, I might add.

I've added Neil Gaiman's intro because it says so much about both of them.

I came across this by accident; posted as recently as November last year.

I'm a huge fan: Left Hand of Darkness, The Dispossessed and the Earthsea Quartet, which I re-read not that long ago. She's one of the greats: up there with Isaac Asimov, Robert Heinlein, Frank Herbert and Arthur C Clarke.

In memory of Joe Cocker: 1944 - 2014

With a Little Help from my Friends (Cologne Concert)

The Letter (Cologne)

Just a small tribute to someone who gave us something special. An inspiration and a legend.
'With a Little Help From my Friends' never fails to give me goose bumps, but on this occasion both these songs make me teary-eyed in their final moments.

Theory, knowledge and truth

Bear with me while I give a little backstory. Julia Zemiro, the effervescent host of RocKwiz (a brilliant show for those who are missing out) has made a TV series called ‘Home Delivery’ where she takes a celebrity (all comedians, either UK or Oz) back to their home town. In a recent episode she took Ruth Jones, an award-winning UK comedienne back to her home town in Wales. As part of the tour, she visited her church where a number of events in her life took place, apparently.

Given the context, Julia asked her if she was a ‘believer’. I thought Jones’ answer so candid and honest, it’s worth repeating. She said she believes there is something ‘greater than us’ but we really ‘have no idea’. Maybe not her exact words but certainly her sentiment. It was the admission of ignorance and humility that struck me – so different to any theological statement one cares to hear. And I realised, by the sheer contrast implicit in her statement, why I have such an issue with the Church; well, any church, basically. Because they all claim to know what they can’t possibly know and preach it with the absolute certainty that dogma requires.

And despite what they all claim, there is no text anywhere in the world that can tell us what, if any, greater purpose there is. Now, I’m not opposed to the idea that there could be a greater purpose and I have no problem with people believing that (like Ruth Jones). I only have a problem when they claim to know what that purpose is and what one must do (in this life) to achieve it.

When I was a philosophy student, a lecturer made the salient point that there are things one believes and things one knows and it’s important to keep in mind that what one believes should be contingent upon what one knows and not the converse. This is perfectly logical, even common sense, yet it’s extraordinary the mental gymnastics some people will perform to maintain a contrary position. To give an example, I read an account where William Lane Craig, in a conversation with the author of a Christian text, defended his belief that Mary conceived Jesus without having sex.

And this brings me to the fundamental epistemological divide that exists between science and religion, as we see it discussed and abused in the so-called Western world. Because science is essentially about knowledge, about what we know as opposed to what we might speculate and philosophise about, even though the boundaries sometimes get a bit blurred.

The success of science, over a period of 2500 years, if one wants to go back to Thales and Pythagoras, has arisen from a combination of theory, mathematics and empirical evidence. Now, whilst there is not a lot of mathematics in the biological sciences, it’s the discovery of DNA, with its inherent ‘software-like’ code that underpins all of biology and evolutionary theory in particular. And like the other disciplines of science, mathematics (in the form of knot theory) is informing us as to how DNA actually manages to function.

But out of that triumvirate, it is empirical evidence that ultimately holds sway. We can find truth in mathematics independently of any physical parameters, but when we apply our mathematics to physical theories, only physical evidence tells us if the theory is true. An example is string theory, which is a mathematical model of the universe predicting up to 11 dimensions, yet, whilst no evidence can be found to confirm it, it really does remain just a theory. Whereas Einstein’s theories of relativity (the special and general theory) are proven facts, as is quantum mechanics. Evolution, I would argue, is also a fact, simply because the evidence that proves it’s true could just as readily prove it’s wrong (the evidence is not neutral). So theories can be facts and not ‘just a theory’.

But all scientific knowledge is contingent on future knowledge which is how it has evolved. For example, Newton’s theories were overtaken by Einstein’s theories, yet the equations governing relativity theory reduce to Newton’s equations when relativistic effects are negligible. As someone once pointed out (John Worrall, London School of Economics, 1989) it’s the mathematics that survives from one physical theory to the next that informs us what aspect of the original theory was true. Again, referring to Newton and Einstein, gravity obeys an inverse square law in both their theories.

As I’ve described on another post when I reviewed Noson S. Yanofsky’s excellent book, The Outer Limits of Reason, there are limits to knowledge at all levels. So science acknowledges that it’s impossible to know everything, yet there is every reason to believe that our knowledge will increase for as long as humanity can survive. At the end of my last post, I pointed out that an implication of Godel’s Incompleteness Theorem is that mathematics is infinite, which means that there is no end to what we can discover.

So where does philosophy sit and where does religion sit amongst all this scientific knowledge? Well, I would suggest that there is an interface between science and philosophy that will always exist because philosophy quests for answers that are currently beyond our reach, some of which, like multiverses and Artificial Intelligence, may be resolved or may not.

A few years back, I said that religion is the mind’s quest to find meaning for its own existence, and I think that this is a perfectly logical and healthy thing for a mind to do. But religion, as it has evolved culturally, is full of mythology dressed up as truth. That is not to say that the figures who feature prominently in these religions are necessarily fictional, but the stories that have arisen in their wake are mythological in content. People like Jesus, Mohammed, Buddha, even Confucius, never wrote anything down so we are left with their ‘sayings’ (Mohammed was illiterate, which is why the Quran is probably in verse). But myth is very hard to shake once it takes hold in the collective consciousness of a population, and once it becomes ‘religion’ it becomes heretical to even question it.

Unfortunately, much of the debate between science and religion stems from what people think constitutes truth. Truth can exist in fiction, but in the form of life-lessons rather than narrative facts. When people believe that a narrative containing mythical elements is true, they will often argue that the mythical elements really happened by giving them supernatural attributes (like the example provided by Craig above). This is anathema to a scientifically trained mind and as far from any truth they would care to entertain.

So when people use the Bible as a criterion for scientific truth, it is certain to create conflict. Four hundred years ago, Galileo was threatened with torture by the Vatican for proposing that the Earth went round the Sun instead of the converse, as was then believed. The Vatican’s contention was that this contradicted a passage in the Bible that claims that God stopped the Sun moving in the sky. Now, we all know (thanks to pure science) that God could not have stopped the sun moving in the sky because the sun doesn’t move at all relative to the Earth’s orbit.

Yet still, in the 21st Century, we have people (like Ken Ham) claiming that the book of Genesis, which is full of mythological events like a snake that talks and a woman made from a man’s rib and a man made from dirt and a piece of fruit that turns people evil, nevertheless overrules all of modern science. I apologise on behalf of all Australia for unleashing Ken Ham onto the modern world, where he clearly doesn’t belong.

I once posted a question on his website asking for the nomination of one scientific discovery in the past 2500 years that has been made from studying the Scriptures. Not surprisingly, I never received a reply.

A few hundred years before Christ was born, Euclid, who was Librarian at the famous Library of Alexandria, wrote his seminal text, The Elements. This is arguably one of the most important texts ever written, certainly more important than any religious text as it contains real transcendental truths in the form of mathematical proofs. Mathematics is the only knowledge we have that transcends the Universe. As John Barrow quipped in one of his many books (citing Dave Rusin): Mathematics is the only part of science you could continue to do if the Universe ceased to exist.

It is hard to go past mathematics if you want truths, especially truths that are independent of humanity and the Universe itself. Of course, not everyone agrees with this Platonic sentiment, but it’s hard to avoid when one considers that there are an infinite number of primes that we can’t possibly know or an infinite string of digits in pi that we know must exist yet can’t possibly cognise. Mathematics is transcendent simply because it embraces infinity on so many levels.

To quote Barrow again, in a slightly more serious tone:

Mathematics is part of the world, and yet transcends it. It must exist before and after the Universe. Most scientists and mathematicians… work as though there were an unknown realm of truth to be discovered.

A book for geeks

Matt Parker is a mathematical entertainer, as oxymoronic as that sounds, because apparently, in the UK, he does stand-up comedic mathematics and mathematical-based magic tricks with cards. Originally a school teacher from Oz, he has the official title of Public Engagement in Mathematics Fellow at Queen Mary University of London.

He’s written a very accessible book called Things to Make and Do in the Fourth Dimension, where he attempts to introduce the reader to more obscure areas of mathematics by wooing them with games and little-known intriguing mathematical facts.

For example: if you square any prime number greater than 3 and take off 1 you’ll find it’s divisible by 24.  As he says: ‘That sentence can freak out even the most balanced mathematician.’ In a section at the back, called The Answers in the Back of the Book, he provides an easy-to-follow proof that shows this applies to any number that is not factored by 2 or 3 – so not just prime numbers. Obviously, any prime number above 2 or 3 fits that category as well. So the converse is not true: a number divisible by 24 plus 1 is not necessarily a squared prime. Otherwise, as Parker points out, we would have a very easy ready-made method of finding all primes, which we haven’t.

Basically, he is a mathematical enthusiast and he wants to share his enthusiasm. As anyone who reads my blog would know, I’m familiar with a fair sample of mathematical concepts and esoterica, so I don’t believe I’m the audience that Parker is seeking. Having said that, he managed to augment my knowledge considerably, like in the previous paragraph. Another example is his description of how to make binary computer logic gates by just using dominoes that actually can perform a calculation. In fact, he and a team of mathematicians spent 6  hours setting up a 10,000 domino ‘computer’ that took 48 seconds to compute 6 + 4 = 10, performed at the Manchester Science Festival in October 2012.

The title of this post is apt: geeks would love this book; yet Parker’s objective, one feels, is to make mathematics attractive to a wider audience. In particular, those who were turned off maths in their high school years, if not before. One of the virtues I found in this book is his selective use of visual representation, even of the simplest kind. I’m not just talking about graphs of exotic equations like Zeta functions and perspective drawings of Platonic solids or even 2D renderings of tesseracts (4D cubes), but rough hand-drawn sketches and sometimes just a list of numbers to demonstrate a series or sequence. I found these most helpful in understanding a tricky concept.

We are visual creatures because sight is our prime medium for comprehending the world. It should be no surprise that visualising an abstract concept, mathematical or otherwise, is the shortest way to understanding it. I work a lot with engineers and when they want to explain something they invariably draw a picture.

The problem with maths in education is that it’s a cumulative subject. More esoteric topics are dependent on lesser ones. If a student falls behind, the gap between what they’re expected to know and what they can actually achieve grows over the years of schooling.

Books like Parker’s attempt to short-circuit this process. He tries to introduce the reader to the more ‘sexy’ aspects of mathematics without grinding them into the ground with mind-bending exercises. His Answers in the Back of the Book allows the more adventurous and less intimidated reader to understand a topic more fully, whilst not burdening a less experienced reader with mind-expanding exercises. It is possible to read this book and come away with both a sense of awe at its magisterial wonder and an appreciation of how maths literally drives our digital world without having to do a lot of mental gymnastics. On the other hand, Parker is letting you into some of the secrets of the priesthood without feeling like you’ve done a PhD.

Although it is divided chapter by chapter into separate topics, this is a book that should be read in the order it is presented. Parker often references material already covered, partly to demonstrate how the mathematical world is so interconnected. To give an example, he sneaks up on the famous Zeta function in a way that makes it appear less intimidating then it really is, yet still manages to explain its relationship to Riemann’s famous hypothesis and the distribution of primes. I was disappointed that he didn’t explain that the non-trivial zeros, which are both the core mystery and ultimate unsolved puzzle, are in fact complex numbers involving the imaginary axis. However, he explains this in a later chapter when he introduces the reader to imaginary numbers and the ‘complex plane’.

Pythagoras famously said (or so we are led to believe, as he never wrote anything down) that everything is numbers. In the digital world this is literally true, and one of Parker’s most illuminating chapters explains how everything you do on your smart-phone from pictures to texting to music are all rendered by 0s and 1s.

Parker is very clever in that he discusses highly esoteric mathematical topics like the Zeta function (already mentioned), quarternions (imaginary numbers in 4D),  the so-called Monster or Friendly Giant in 196,833 dimensions, computer-generated self-correcting algorithms using binary arithmetic, multiple infinities, knot theory’s relevance to DNA not getting tangled and Klein bottles (4D bottles in 3D); without discussing more fundamental topics like logarithms, trigonometry or calculus. He doesn’t even explain the fundamental relationship between polar co-ordinates and Cartesian co-ordinates that makes imaginary numbers such a widely used tool.

He doesn’t get philosophical until the very end of the book, when he discusses the relevance of Godel’s Incompleteness Theorem to the study of mathematics for ever (quite literally). As I’m sure I’ve mentioned in previous posts, implicit in Godel’s Theorem is the fact that mathematics is never-ending, therefore it’s a human activity that will never stop. Also Parker points out that there could be other universes with other dimensions to ours, but any hypothetical residents (he calls them ‘hypertheticals’) would still discover the same mathematics as us, assuming they have the intellect to do so.

The 2 faces of IS: avenger of Muslims and genocidal ideologues

I apologise in advance to overseas readers (outside Australia) who can’t view this, but this interview on ABC’s Lateline current affairs programme on Thursday (8 Oct) was a standout. Emma Alberici, a well respected television journalist and previous foreign correspondent with ABC’s European bureau, interviews, or attempts to interview, Wassim Doureihi, member of Hizb ut-Tahir; an organisation which has been banned in many countries, but not Australia or the UK. This link gives a good summary of that interview, but it’s also ABC, so maybe unavailable outside Oz.

A lecture was held by the group’s Arabic spokesperson, Ismail Al-Wahwah, at Lakemba, Sydney last night, which, according to the SMH and Guardian (links), was not much different in rhetoric to Doureihi’s diatribe a few days earlier. Basically, they claim the current situation in Iraq is a direct consequence of America’s, and its allies’, involvement in that conflict, as well as earlier conflicts involving Muslims. And that, apparently, justifies everything that IS does. Though Doureihi never actually condones IS, he went to extraordinary lengths to avoid discussing their actions and/or strategy when talking to Alberici, which frustrated her enormously.

There are a couple of issues I wish to address: firstly, the sheer distortion in Dourheihi’s argument that doesn’t match the evidence; and secondly, the possible motivation behind people’s desire to join this ‘fight’ and how they manage to justify its atrocities.

Doureihi repeatedly asserted that the current conflict in Iraq is all about foreign occupation. But there is no foreign occupation in Iraq at present – the current Western forces have been invited by the Iraqi democratically elected government (as Alberici pointed out) – and IS arose in Syria, where there is no Western intervention at all, and moved into Iraq before the West got involved. Besides, IS are not attacking a foreign occupation in Iraq (the Westerners they behead are not military personnel); they are attacking people who have lived there for generations, mainly Kurds and Yazidi. In fact, they are committing genocide against these people, which has nothing to do with any foreign occupation.

One can argue about the wisdom of the West’s intervention in Iraq under Bush, especially considering the legerdemain of the so-called WMDs (Weapons of Mass Destruction) that never existed, and its woefully poor execution under Cheney and Rumsfeld. But you have to draw a very long bow to argue that IS have entered Iraq to right the wrongs of that misadventure, when they kill all males who won’t convert to Islam and sell all their women into slavery.

A few years back, I read The Islamist by Ed Hussain, who was radicalised in Great Britain, as a student, before becoming disillusioned and returning to a more moderate position on Islam. It’s an insightful book in that it distinguishes between the religion of Islam as practiced by many Muslims living in secular societies and the political ideology of extremists who want to reshape the world into a totalitarian Islamic state. Hussain believed, at the time, the entire world would inevitably become a ‘Caliphate’, not least because it was ‘God’s Will’. What turned Hussain around was when a student was stabbed to death by a member of his own group. Hussain suddenly realised he wanted no part of an organisation that saw killing non-adherents as part of its creed.

When IS first declared itself a caliphate, an Australian academic (I can’t recall his name or his department) made the observation, in regard to Muslims in Indonesia, that just the idea of a caliphate would have enormous appeal that many would find hard to resist. In other words, many see this as some sort of Islamic nirvana, a new ‘world order’, where all wrongs will be made right and all peoples will be made to see and understand God’s wisdom and be guided by it through Sharia law. Naturally, this is anathema to anyone living in a Western democratic secular society, and is seen as turning back the clock centuries, before the Enlightenment and before the European renaissance and before modern scientific relevations, not to mention undoing generations of women’s independence of men, whether sexually, financially or educationally.

And this is the nexus of this conflict: it’s a collision of ideas and ideals that has no compromise. IS and its ilk, the Taliban in Afghanistan and Boko Haram in Africa, are fighting against the 21st Century. They know as well as we do, that there is no place for them, politically, in the world’s global future, and they can only rail against this by killing anyone who does not agree with their vision, and committing all women to marital slavery.

Finally, there is a comment by an Australian Islamist fighting in Syria, who believes that IS’s tactics of beheading journalists and aid workers is justified because their deaths are insignificant compared to the hundreds of innocent people (including children) killed by Western sponsored air raids. If these deaths can ‘blackmail’ America and its allies into not killing innocents then it is worth it, according to him.

David Kilcullen, an Australian expert on Afghanistan and a former adviser to Condoleezza Rice during the Bush administration, is one of the few who argued against drone strikes in Pakistan because they would ‘recruit’ jihadists. The abovementioned apologist for IS would suggest that such a belief was justified.

However, IS don’t just behead Westerners; it’s one of their psychological tactics against anyone who doesn’t convert to their specific brand of Islam. It’s meant to horrify and terrorise all their enemies, whoever they might be, and it succeeds.

Contrary to popular belief and popular crime thrillers, most people who perform evil acts, as perceived by most societies, don’t believe that what they are doing is evil and can always find a way to justify it. No where is this more acute than when the perpetrators believe that they have ‘God on their side’.

Mathematics as religion

I’ve just read John D. Barrow’s Pi in the Sky, published in 1992, and hard to get, as it turns out. I got a copy through Amazon UK, who had one in stock, and it’s old and battered but completely intact and legible, which is the main thing.

Those of you who regularly read my blog (not many of you, I suspect) will know that I’ve read lots of Barrow’s books, possibly The Book of Universes is the best, which I reviewed in May 2011.

Pi in the Sky is a very good title because it alludes to the Platonist philosophy of mathematics that seems to dominate both mathematics and physics as it’s practiced, in contrast to how many of its practitioners would present it. Barrow points out, both in his introduction and his concluding remarks (after 250+ pages), that Platonism has religious and mystical connotations that are completely at odds with both mathematics and science as disciplines.

He points out that there is a divide between mathematicians and physicists and economists and sociologists in the way they approach and view mathematics. For the economist and sociologist, mathematics is a tool that humans invented and developed, which can be applied to a range of practical applications like weather forecasting, economic modelling and analysis of human behaviours.

On the other hand, pure mathematicians and physicists see an ever-increasing complex landscape that has not only taken on an existence of its own but is becoming the only means available to understanding the most secret and fundamental features of the universe, especially at the extremities of its scale and birth.

This is an ambitious book, with barely an equation in sight, yet it covers the entire history of mathematics from how various cultures have represented counting (both in the present and the ancient past) to esoteric discussions on Godel’s theorem, Cantor’s transfinite sets and philosophical schools on ‘Formalism’, ‘Constructivism’, ‘Intuitionism’ and ‘Inventism’. Naturally, it covers the entire history of Platonism from Pythagoras to Roger Penrose. It’s impossible for me to go into any detail on any of these facets, but it needs to be pointed out that Barrow discusses all these issues in uncompromising detail and seems to pursue all philosophical rabbits down their various warrens until he’s exhausted them.

He makes a number of interesting points, but for the sake of brevity I will highlight only a couple of them that I found compelling:

‘Once an abstract notion of number is present in the mind, and the essence of mathematics is seen to be not the numbers themselves but the collection of relationships that exists between them, then one has entered a new world.’

This is a point I’ve made myself, though I have to say that Barrow has a grasp of this subject that leaves me well behind in his wake, so I’m not claiming any superior, or even comparable, knowledge to him. It’s the relationships between numbers that allows algebra to flourish and open up doors we would never have otherwise discovered. It is the interplay between ingenious human invention and the discovery of these relationships that creates the eternal philosophical debate (since Plato and Aristotle, according to Barrow): is mathematics invented or discovered?

One cannot discuss this aspect of mathematics without looking at the role it has played in our comprehension of the natural world: a subject we call physics. Nature’s laws seem to obey mathematical rules, and many would argue that this is simply because we need to quantify nature in order to study it, and once we quantify something mathematics is automatically applied. This quantification includes, not just matter, but less obvious quantifiable entities, like heat, gravity, electromagnetism and entropy. However, as Barrow points out, the deeper we look at nature the more dependent we become on mathematics to comprehend it, to the point that there is no other means at our disposal. Mathematics lies at the heart of our most important physical theories, especially the ones that defy our common sense view of the world, like quantum mechanics and relativity theory.

The point is that these so-called ‘laws’ are all about ‘relationships’ between physical entities that find analogous mathematical ‘relationships’ that have been discovered ‘abstractly’, independently of the physics. There may not be a Platonic realm with mathematical objects like triangles and the like but the very peculiar relationships which constitute the art we call mathematics have sometimes found concordant relationships in what we call the ‘laws of nature’. It is hard for the physicist not to believe that these ‘mathematical’ relationships exist independently of our minds and possibly the universe itself, especially since this mathematical ‘Platonic’ universe seems to contain relationships that our universe (the one we inhabit) does not.

In 2010, or thereabouts, I read Marcus du Sautoy’s excellent book, Finding Moonshine, which is really all about dimensions. The most fantastical part of this book was the so-called ‘Atlas’, which was a project largely run by John Conway with a great deal of help from others (in the 1970s), which compiled all 26 ‘sporadic groups’ that I won’t attempt to explain or define. Part of the compilation included a mathematical object called the ‘Monster’ which existed in 196,883 dimensions. Then a friend and colleague of Conway’s, John Mackay, discovered a most unusual and intriguing connection between ‘The Monster’ and another mathematical entity called a ‘modular function’ in number theory, even though it first appeared as an apparent ‘coincidence’ - as no reason could be conceived - but a sequence in the modular function could be matched to the sequence of ‘dimensions’ in which the Monster could exist.

I’m only telling snippets of this story – read du Sautoy’s book for the full account – but it exemplifies how completely unforeseen and unlikely connections can be found in disparate fields of mathematics. The more we explore the world of mathematics, the more it surprises us with relationships we didn’t foresee; it’s hard to ignore the likelihood that these relationships exist independently of our discovering them.

Because the only mathematics we know is a product of the human mind, it can be, and often is, argued that without human intelligence it wouldn’t exist. But no one presents that argument concerning other areas of human knowledge like the laws of physics, where experimentation can validate or refute them. However, no one denies that mathematics contains ‘truths’ that are even more unassailable than the physics we observe. And herein lies the rub: these ‘truths’ would still be true even without our knowledge of them.

This brings me to the second insight Barrow made that caught my attention:

He points out that our mathematical theories describing the first three minutes of the Universe predict specific ratios of the earliest ‘heavier’ elements: deuterium, 2 isotopes of helium and lithium, which are 1/1000, 1/1000, 22 and 1/100,000,000 respectively; with the remaining (roughly 78% ) being hydrogen. And this has been confirmed by astronomical observations. He then makes the following salient point:

‘It confirms that the mathematical notions that we employ here and now apply to the state of the Universe during the first three minutes of its expansion history at which time there existed no mathematicians… This offers strong support for the belief that the mathematical properties that are necessary to arrive at a detailed understanding of events during those first few minutes of the early Universe exist independently of the presence of minds to appreciate them.’

As Barrow points out more than once, not all conscious entities have a knowledge of mathematics – in fact, it’s a specialist esoteric discipline that only the most highly developed societies can develop, let alone disseminate. Nevertheless, mathematics has provided a connection between the human mind and the machinations of the Universe that even the Pythagoreans could not have envisaged. I’ve said this before and Marcus du Sautoy has said something similar: it’s like a code that only a suitably developed intelligent species can decipher; a code that hides the secret to the Universe’s origins and its evolvement. No religion I know of can make a similar claim.