The Singularity Prophecy

This is not a singularity you find in black holes or at the origin of the universe – this is a metaphorical singularity entailing the breakthrough of artificial intelligence (AI) to transcend humanity. And prophecy is an apt term, because there are people who believe in this with near-religious conviction. As Wilson da Silva says, in reference to its most ambitious interpretation as a complete subjugation of humanity by machine, ‘It’s been called the “geek rapture”’.

Wilson da Silva is the editor of COSMOS, an excellent Australian science magazine I’ve subscribed to since its inception. The current April/May 2009 edition has essay length contributions on this topic from robotics expert, Rodney Brooks, economist, Robin Hanson, and science journalist, John Horgan, along with sound bites from people like Douglas Hofstadter and Steven Pinker (amongst others).

Where to start? I’d like to start with Rodney Brooks, an ex-pat Aussie, who is now Professor of Robotics at Massachusetts Institute of Technology. He’s also been Director of the same institute’s Computer Science and Artificial Intelligence Lab, and founder of Heartland Robotics Inc. and co-founder of iRobot Corp. Brooks brings a healthy tone of reality to this discussion after da Silva’s deliberately provocative introduction of the ‘Singularity’ as ‘Rapture’. (In a footnote, da Silva reassures us that he ‘does not expect to still be around to upload his consciousness to a computer.’)

So maybe I’ll backtrack slightly, and mention Raymond Kurzweil (also the referenced starting point for Brooks) who does want to upload (or download?) his consciousness into a computer before he dies, apparently (refer Addendum 2 below). It reminds me of a television discussion I saw in the 60s or 70s (in the days of black & white TV) of someone seriously considering cryogenically freezing their brain for future resurrection, when technology would catch up with their ambition for immortality. And let’s be honest: that’s what this is all about, at least as far as Kurzweil and his fellow proponents are concerned.

Steven Pinker makes the point that many of the science fiction fantasies of his childhood, like ‘jet-pack commuting’ or ‘underwater cities’, never came to fruition, and he would put this in the same bag. To quote: ‘Sheer processing power is not a pixie dust that magically solves all your problems.’

Back to Rodney Brooks, who is one of the best qualified to comment on this, and provides a healthy dose of scepticism, as well as perspective. For a start, Brooks points out how robotics hasn’t delivered on its early promises, including his own ambitions. Brooks expounds that current computer technology still can’t deliver the following childlike abilities: ‘object recognition of a 2 year-old; language capabilities of a 4 year-old; manual dexterity of a 6 year-old; and the social understanding of an 8 year-old.’ To quote: ‘[basic machine capability] may take 10 years or it may take 100. I really don’t know.’

Brooks states at the outset that he sees biological organisms, and therefore the brain, as a ‘machine’. But the analogy for interpretation has changed over time, depending on the technology of the age. During the 17^th Century (Descartes’ time), the model was hydrodynamics, and in the 20^th century it has gone from a telephone exchange, to a logic circuit, to a digital computer to even the world wide web (Brooks’ exposition in brief).

Brooks believes the singularity will be an evolutionary process, not a ‘big bang’ event. He sees the singularity as the gradual evolvement of machine intelligence till it becomes virtually identical to our own, including consciousness. Hofstadter expresses a similar belief, but he ‘…doubt[s] it will happen in the next couple of centuries.’ I have to admit that this is where I differ, as I don’t see machine intelligence becoming sentient, even though my view is in the minority. I provide an argument in an earlier post (The Ghost in the Machine, April 08) where I discuss Henry Markram’s ‘Blue Brain’ project, with a truckload dose of scepticism.

Robin Hanson is author of The Economics of the Singularity, and is Associate Professor of Economics at George Mason University in Virginia. He presents a graph of economic growth via ‘Average world GDP per capita’ on a logarithmic scale from 10,000BC to the last 4 weeks. Hanson explains how the world economy has made quantum leaps at historical points: specifically, the agricultural revolution, the industrial revolution and the most recently realised technological revolution. The ‘Singularity’ will be the next revolution, and it will dwarf all the economical advances made to date. I know I won’t do justice to Hanson’s thesis, but, to be honest, I don’t want to spend a lot of space on it.

For a start, all these disciples of the extreme version of the Singularity seem to forget how the other half live, or, more significantly, simply ignore the fact that the majority of the world’s population doesn’t live in a Western society. In fact, for the entire world to enjoy ‘Our’ standard of living would require 4 planet earths (ref: E.O. Wilson, amongst others). But I won’t go there, not on this post. Except to point out that many of the world’s people struggle to get a healthy water supply, and that is going to get worse before it gets better; just to provide a modicum of perspective for all the ‘rapture geeks’.

I’ve left John Horgan’s contribution to last, just as COSMOS does, because he provides the best realism check you could ask for. I’ve read all of Horgan’s books, but The End of Science is his best read, even though, once again, I disagree with his overall thesis. It’s a treasure because he interviews some of the best minds of the latter 20^th Century, some of whom are no longer with us.

I was surprised and impressed by the depth of knowledge Horgan reveals on this subject. In particular, the limitations of our understanding of neurobiology and the inherent problems in creating direct neuron-machine interfaces. One of the most pertinent aspects, he discusses, is the sheer plasticity of the brain in its functionality. Just to give you a snippet: ‘…synaptic connections constantly form, strengthen, weaken and dissolve. Old neurons die and – evidence is overturning decades of dogma – new ones are born.’

There is a sense that the brain makes up neural codes as it goes along - my interpretation, not Horgan's - but he cites Steven Rose, neurobiologist at Britain's Open University, based in Milton Keyes: 'To interpret the neural activity corresponding to any moment ...scientists would need "access to [someone's] entire neural and hormonal life history" as well as to all [their] corresponding experiences.'

It’s really worth reading Horgan’s entire essay – I can’t do it justice in this space – he covers the whole subject and puts it into a perspective the ‘rapture geeks’ have yet to realise.

I happened to be re-reading John Searle’s Mind when I received this magazine, and I have to say that Searle’s book is still the best I’ve read on this subject. He calls it ‘an introduction’, even on the cover, and reiterates that point more than once during his detailed exposition. In effect, he’s trying to tell us how much we still don’t know.

I haven’t read Dennett’s Consciousness Explained, but I probably should. In the same issue of COSMOS, Paul Davies references Dennett’s book, along with Hofstadter’s Godel, Escher, Bach, as 2 of the 4 most influential books he’s read, and that’s high praise indeed. Davies says that while Dennett’s book ‘may not live up to its claim… it definitely set the agenda for how we should think about thinking.’ But he also adds, in parenthesis, that ‘some people say Dennett explained consciousness away’. I think Searle would agree.

Dennett is a formidable philosopher by anyone’s standards, and I’m certainly not qualified, academically or otherwise, to challenge him, but I obviously have a different philosophical perspective on consciousness to him. In a very insightful interview over 2 issues of Philosophy Now, Dennett elaborated on his influences, as well as his ideas. He made the statement that ‘a thermostat thinks’, which is a well known conjecture originally attributed to David Chalmers (according to Searle): it thinks it’s too hot, or it thinks it’s too cold, or it thinks the temperature is just right.

Searle attacks this proposition thus: ‘Consciousness is not spread out like jam on a piece of bread… If the thermostat is conscious, how about parts of the thermostat? Is there a separate consciousness to each screw? Each molecule? If so, how does their consciousness relate to the consciousness of the whole thermostat?’

The corollary to this interpretation and Dennett’s, is that consciousness is just a concept with no connection to anything real. If consciousness is an emergent property, an idea that Searle seems to avoid, then it may well be ‘spread out like jam on a piece of bread’.

To be fair to Searle (I don't want to misrepresent him when I know he'll never read this) he does see consciousness being on a different level to neuron activity (like Hofstadter) and he acknowledges that this is one of the factors that makes consciousness so misunderstood by both philosophers and others.

But I’m getting off the track. The most important contribution Searle makes, that is relevant to this whole discussion, is that consciousness has a ‘first person ontology’ yet we attempt to understand it solely as a ‘third person ontology’. Even the Dalai Lama makes this point, albeit in more prosaic language, in his book on science and religion, The Universe in a Single Atom. Personally, I find it hard to imagine that AI will ever make the transition from third person to first person ontology. But I may be wrong. To quote my own favourite saying: 'Only future generations can tell us how ignorant the current generation is'.

There are 2 aspects to the Singularity prophecy: we will become more like machines, and they will become more like us. This is something I’ve explored in my own fiction, and I will probably continue to do so in the future. But I think that machine intelligence will complement human intelligence rather than replace it. As we are already witnessing, computers are brilliant at the things we do badly and vice versa. I do see a convergence, but I also see no reason why the complementary nature of machine intelligence will not only continue, but actually improve. AI will get better at what it does best, and we will do the same. There is no reason, based on developments to date, to assume that we will become indistinguishable, Turing tests notwithstanding. In other words, I think there will always remain attributes uniquely human, as AI continues to dazzle us with abilities that are already beyond us.

P.S. I review Douglas Hofstadter's brilliant book, Godel, Escher, Bach: an Internal Golden Braid in a post I published in Feb.09: Artificial Intelligence & Consciousness.

Addendum: I'm led to believe that at least 2 of the essays cited above were originally published in IEEE Spectrum Magazine prior to COSMOS (ref: the authors themselves). Addendum 2: I watched the VBS.TV Video on Raymond Kurzweil, provided by a contributor below (Rory), and it seems his quest for longevity is via 'nanobots' rather than by 'computer-downloading his mind' as I implied above.

Tampa revisited

I never intended this to be a political blog, but the front page of this morning’s Age (Melbourne daily) reignited a righteous anger I first expressed in writing in 2001 (before 9/11). The article tells of how 2 Asylum seekers from Afghanistan, Tour Gul and Mohammed Hussain have been confirmed killed by the Taliban, after their application for asylum was rejected by the Australian government and they were deported (in 2002). I’m not an expert on international law, but I suspect Australia has breached UN Human Rights obligations in this regard. The gory details are that Tour Gul was shot through the head, and Mohammed Hussain was thrown down a well in front of members of his own family along with a grenade (according to The Age).

The Age had previously reported that 11 asylum seekers on Nauru (part of the Australian government’s notorious ‘Pacific solution’, following the Tampa incident) had been killed by the Taliban following their deportation. According to Phil Glendenning, director of social justice agency, The Edmund Rice Centre, ‘who spent six years traveling the world to investigate the fate of rejected asylum seekers… 11 deaths was a conservative figure.’

The Tampa incident involved a Norwegian container ship, captained by Arne Rinnan, who picked up refugees from a sinking ‘people smuggler’ vessel, after being notified of their plight by the RAAF, if I have the story right (a proper account can be found here). Then after he picked them up he was instructed to take them to Indonesia, not to Australia. That's right: after Australian authorities requested for someone to pick them up, the 'good Samaritan' was then told to take them away from Australian territorial waters, and thanks for your help.

This provided a grandstanding opportunity for Australian Prime Minister, John Howard, on the eve of an election to show how tough he was with refugees and win the xenophobic vote for Australia, after they had been primed by Pauline Hanson. The gutless opposition, knowing which way the votes were running, became the non-opposition and sealed their fate. Arne Rinnan was awarded a medal, by the way, in his own country. I thought he was the one decent and courageous soul to emerge out of the whole affair (after all he stood up to the Australian Government, even when bullied by our military). I was in America at the time of the election, and consequently wrote a letter to the re-elected Prime Minister expressing my personal disgust – something I had never done previously. (For you American readers, John Howard was later tagged 'the man of steel' by George W.)

I alluded very vaguely to this incident, or the social dynamics that surround it, in my closing arguments on an early post, Evil (Oct.07). What galls me is that we live such a privileged life yet we feel so threatened by these people who are literally in desperate straits. It makes me ashamed to be Australian, but it doesn’t surprise me. The Attorney General of the time, Philip Ruddock, seemed to take all these cases personally, and was determined to make any refugee’s life even worse than it already was. It was his unstated goal to make their life an absolute misery – I referred to him as the Australian Minister for Misery – and he did an exemplary job. The mental health damage he did to innumerable vulnerable people, including children, cannot be overestimated. Of course, these people have no vote, and no one to stand up for them, with a few outstanding exceptions, so the Government knew they could treat them like chaff.

Ex Prime Minister, Malcolm Fraser (same political party as Howard), was one of the few to speak out, and made the point in an early interview, well before Tampa, when Pauline Hanson first rose to prominence: ‘Evil always arises when we blame all of a society’s ills on one group of people.’

The irony is that we now have troops in Afghanistan fighting the Taliban, whereas in 2002 it was considered a ‘safe’ country for these political asylum seekers, fleeing the enemy we are now mortally engaged with.

Addendum: it would be remiss of me not to mention some of the advocates as well as Malcolm Fraser; in particular, Julian Burnside QC. In 2005, some Liberal party backbenchers (same party as Howard) including Petro Georgiou and Judi Moylan (whom I corresponded with) put a bill through parliament that stopped children being kept in mandatory detention (as refugees). John Howard liked to tout the virtues of his Christianity and Christian values. It should be obvious from other posts on this blog, that I'm definitely not a Christian, but Howard's policy towards refugees was the antithesis of the Jesus character depicted in biblical stories, whether he be fictional or real.

The problems with fundamentalism

It’s a sad indictment that I should feel it necessary to write this post, but the blogosphere, at least considerable sections of it, are full of it. Notice the use of the plural, though there is one specific problem that compounds all the others – it’s called intolerance. Not that long ago, in the land I inhabit, we had our own brush with intolerance that had ramifications right across the nation and across the political spectrum – she was called Pauline Hanson.

I’ve always had a tendency to analyse, even when the issues are emotive and personal. What I found interesting about the Pauline Hanson phenomenon is that she created intolerance in people like myself who are normally tolerant. Pauline Hanson taught me that I’m intolerant of intolerance. Pauline, a fish and chip shop proprietor, who became a parliamentarian, created a political storm that pretty well divided a country and even divided families. The link with fundamentalism is that fundamentalists, like Pauline Hanson, create intolerance on both sides.

This is why someone like Richard Dawkins, with whom I share many of his arguments, not only shows contempt for anyone with religious beliefs but contempt for anyone who is tolerant of people with religious beliefs (just read his introduction to the paperback edition of The God Delusion). So, whilst I support Dawkins in his fight against religious fundamentalism completely, I don’t support his fight against religion per se at all. I don’t agree with a black and white view of the world, that he tends to portray, which is divided between atheists and religious fundamentalists, and therefore one must take one side or the other. I wish to lay out my slate that there is a world that can include atheists and religious believers. My role models for this perspective are Karen Armstrong and the Dalai Lama.

I write a lot about science and mathematics on this blog, but almost every essay includes an aside to explain why the mysteries of the universe cannot be resolved by the invocation of God. It seems to me that many people don’t appreciate that a philosophical argument that uses science to support it, doesn’t necessarily turn it into a scientific argument. I believe that even Dawkins makes this error when he introduces the anthropic principle, in concert with the concept of the multiverse, as if it’s a scientific argument rather than a philosophical argument supported by both known and speculative science (The God Delusion). There is nothing wrong with Dawkins’ argument – it’s philosophical in the same way that Paul Davies produces an alternative philosophical argument in The Goldilocks Enigma, only, with Davies, one is more aware that it is philosophical. I make this distinction because many fundamentalists don’t seem to appreciate that a philosophical argument that includes scientific evidence or a mathematical proof is not of itself a scientific or mathematical proof. There are no philosophical proofs in my view (refer my Mar.08 post: What is philosophy?).

But I’m getting off the track before I’ve even started. If one reads a lot of science, like I do, then one sees a history of investigation at many levels where the solution of one mystery reveals other mysteries that we didn’t even know existed. I contend therefore, that it’s quite possible, even reasonable to assume, that we will never know all the mysteries of the natural universe, let alone resolve them. It is for this reason that any sceptic of science, which includes all religious fundamentalists that I’ve read or heard or argued with, can find a hole in any area of science, which they believe they can exploit.

It follows, according to their logic, that the answer to any mystery, still unresolved by science, can therefore be found in the Bible, as if the Bible has provided all the information we currently have on the natural world. Therefore the Genesis explanation, of man being made from dirt and woman from a man’s rib, overturns all the scientific evidence of biological evolution discovered in the last 2 centuries. ID and creationism are not about studying science, despite the camouflage rhetoric to the contrary, they are about proving that the Bible is true. For Christian fundamentalists, the Bible is the only source of truth in the earthly world. Despite all the discoveries of science, especially in the last 500 years, any conflict with biblical scripture, whether apparent or real, rules science invalid. It is on this battle-line that I firmly side with Dawkins.

Mathematics and physics are my private passion, and I’m currently reading about Paul Dirac’s discovery of an equation that didn’t just predict anti-matter but insisted upon its existence. In 1928, Dirac took the recently formed Schrodinger equations of quantum mechanics and Einstein’s equations of special relativity, and in resolving their apparent dichotomy, not only justified evidence already known yet unexplained (the magnetic moment of electrons), but predicted the electron’s anti-particle, the positron. This is an intellectual achievement that is monumental in its consequences, comparable to Einstein’s equation: E= mc². There is nothing in the Bible to compare with this. Imagine if the Bible told us that God created anti-matter alongside matter. On the contrary, the Bible tells us about a global flood that is physically impossible, a woman turned into salt, a child born from a woman who never had sexual intercourse, and I think the sun stops at some point, which was a particular point of contention that the Catholic Church had with Galileo in 1633 (ref: Livio, see previous post).

So while Christian fundamentalists want equal time to teach ID or creationism, or whatever they want to call it, in a science class alongside evolution, someone should point out to them the discrepancies between biblical myths and scientific theories, as well as the criteria involved (refer my Nov.07 post, Is evolution fact? Is creationism myth?).

My point is that yes, there are lots of questions still unsolved in science, including questions inherent in evolutionary theory, but the successes of science far outweigh any explanation of the natural world found in any religious text, so there is no logic, and absolutely no justification, in replacing science with a biblical account in any area of the sciences at all.

I contend that there are questions science can’t answer. Philosophical questions on why humans look for meaning in their lives or the resolution of moral dilemmas. This latter issue leads to the argument, that I’ve heard from a number of religious fundamentalists, that without a belief in God one is a moral relativist. I find this a truly bizarre conclusion and it’s always presented as if it’s self-evident – there can be no alternative. You either believe in God and have morals or you don’t believe in God and you’re amoral. They should read Hugh Mackay’s book, Right & Wrong; how to decide for yourself, which is the best book on the subject I’ve read.

There are a number of ways of looking at morality. For a start, you can read a book that prescribes everything you do, from how to treat slaves to whether you should eat pork, and what you can do on what days of the week, and also throws in 10 solid statements, or rules, on how to get along with your fellow man. But there are other approaches, like a meta-philosophical approach, attempted by people like John Stuart Mill, and before him, some ancients like Plato and Aristotle, and even a Chinese bloke called Confucius. Then there’s Hugh Mackay’s approach where you look at every situation on its merits and decide for yourself. No, that’s not moral relativism. Moral relativism is where you accept whatever any culture decides for itself, which may include cultural practices like the mutilation of girls’ genitalia at puberty, or the public beating of someone for selling meat on the wrong day of the week, or a woman having to be sacrificed at her husband’s funeral. That’s moral relativism; atheism is rarely a factor at all.

Then there is your conscience: one of the most misunderstood but most manipulated characteristics of human nature. Religious fundamentalists may tell you, or imply, that your conscience is God whispering in your ear, but in reality, your conscience is conditioned by your culture and your upbringing. Freud called it the super-ego. Your conscience is what made you feel guilty about masturbating when you were an adolescent – not God whispering in your ear at all, though it can be made to feel that way.

Hugh Mackay explains the dangers of taking your morals from God, because once you believe that, you can justify any action, like flying a fully loaded aeroplane into an occupied building. That is not an isolated example – just look at the Crusades, the Inquisition, and any number of atrocities justified in the name of God. Mackay is not anti-religion by any means, and explains that religion is more about finding meaning in your life.

Dawkins, if I read him correctly, is contemptuous of people finding meaning through religion. But according to Dawkins, we are just ‘gene-replicating organisms’, therefore any intellectual ruminations concerning our raison d’etre must be a waste of time. No, he’s never said that, but it’s the only logical conclusion: we live for our genes; they don’t exist for our benefit. So, I do see a role for religion, which makes me a bit of a weirdo. But at least I can acknowledge that my religion is nothing special compared to anyone else’s. You see, I grew up in a culture where religion was considered something very personal, like your most intimate thoughts, so you never discussed it unless you were invited to. I also realised that if everyone followed that precept then people with different religious views could get along just fine. In fact, I contend that everyone’s religious point of view is unique to them, so why should I intrude or insist that mine is better?

But this in itself begs another question: why do I argue with fundamentalists? Because fundamentalists believe the exact opposite to this: that everyone should believe the same thing, which is exactly what they believe, and, what’s more, they have the text to prove it. But this text, when taken literally, conflicts with current scientific thinking, so now we have scientists in opposition to all religious belief. As I said or alluded to at the beginning: intolerance breeds intolerance to itself.

Is God a mathematician?

There is a quote from Physics Nobel Laureate, Eugene Wigner, that appears in the first sentence on the front fly leaf cover of Mario Livio’s book, Is God a Mathematician? Actually, it's the title of Wigner's famous essay: The remarkable effectiveness of Mathematics in the Natural Sciences. On the back fly leaf cover we learn that ‘Mario Livio is a senior astrophysicist and head of the Office of Public Outreach at the Hubble Space Telescope Science Institute in Baltimore, Maryland.’ He’s also written a few other books on mathematics, including The Golden Ratio and The Equation That Couldn’t be Solved (neither of which I’ve read).

Wigner’s quote is the one that Livio keeps returning to and attempting to address, rather than any real attempt to address the question on the cover of his book. So I will do the same.

It’s a very good read: erudite, thought-provoking and as balanced as one could expect from someone who has their own philosophical standpoint. I’ve addressed this issue on 2 previous posts: Is mathematics evidence of a transcendental realm? (Jan.08) and Where does mathematics come from? (Sep.07). The Jan.08 post is effectively a review of Gregory Chaitin’s book, Thinking about Godel and Turing, and the Sep.07 post is more of a critique, than a review, of George Lakoff’s and Rafael Nunez’s book, Where Mathematics Comes From. Livio gives a good account of Lakoff’s and Nunez’s views, but he doesn’t mention Chaitin (even in the bibliography).

I don’t wish to reiterate ideas I’ve already explored in those posts, but I do wish to say that Livio demonstrates why scholars like him publish books, and amateurs like me only publish on a blog.

Livio’s book covers topics as varied as statistics and probability theory, Euclidean and non-Euclidian geometry, and logic - all in revelatory detail, yet easy to read. The most interesting topic as far as I was concerned was on knots, and their application to biology and the most recent theoretical investigations in cosmology (string theory).

He also gives brief biographies on, what he considered to be, the giants in mathematics: Archimedes, Galileo, Descartes and Newton.

But it is an extended quote from Wigner that establishes the tone, if not the intent, of Livio’s treatise:

‘The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.’

Livio effectively encapsulates his position when he states that there are 2 aspects of mathematics which he calls: ‘active’ and ‘passive’. By ‘active’ he means the deliberate use of mathematics as a tool to investigate and understand natural phenomena. This aspect supports the view that mathematics is ‘invented’ rather than ‘discovered’. We humans, with our preternatural intellectual abilities, create mathematical models that provide accurate facsimiles of nature’s laws, and can even formulate predictions and forecasts by employing the ‘scientific method’.

To appreciate what Livio means by ‘passive’ it is best to quote his own words:

‘But there is a “passive” side to the mysterious effectiveness of mathematics, and it is so surprising that the “active” aspect pales by comparison. Concepts and relations explored by mathematicians only for pure reasons – with absolutely no application in mind – turn out decades (or sometimes centuries) later to be the unexpected solutions to problems grounded in physical reality!’

(I make a similar point, though not as eloquently, in my Mar.08 post, The Laws of Nature.)

Livio gives a number of examples of this ‘passive’ aspect of mathematics, but amongst the most commonly known are: Maxwell’s equations predicting electromagnetic waves traveling at the speed of light (an example of a pure mathematical construction predicting a yet-to-be discovered physical phenomenon); and Einstein using Riemann’s geometry to postulate his General Theory of Relativity (an example of pure mathematics employed for a completely unexpected natural phenomenon). One must remember that, no one, during Riemann’s time, thought the universe was other than Euclidean, which meant Riemann’s geometry was considered to be purely intellectual play with no possible application in reality.

This leads to a view held by Roger Penrose, which is expounded upon in a couple of his books, The Emperor’s New Mind and Shadows of the Mind, and is also referenced by Livio. Penrose makes the observation that there are 3 aspects of the world of mathematics, and they all interrelate. He refers to them as the ‘Platonic world’, the ‘Mental world’ and the ‘Physical world’. He depicts their interrelationship pictorially, a bit like the rock, paper, scissors game. I will try and explain.

Human thought can grasp some of the Platonic world, but not all of it, which we apply to the Physical world, even though some of it seems beyond our abilities of comprehension. Likewise the Physical world seems to incorporate some of the Platonic world but not all of it. So far so consistent. The enigma is turned into the rock, scissor, paper analogy when one realises that the human mind is a product of the physical world, which can then comprehend the Platonic world, of which the Physical world is a ‘shadow’. This is effectively the way Livio explains it as well, but without the analogy.

This leads me to what I consider to be the greatest mystery of the Universe: that it created the means to comprehend itself. As Einstein famously said: ‘The most incomprehensible thing about the universe is that it is comprehensible.’ Now I don’t know if Einstein was making a metaphysical statement, as he certainly wasn’t a Platonist like Penrose or his good friend and Princeton colleague, Kurt Godel. But without mathematics, it is clear that our comprehension of the universe would be severely limited indeed, and whether Einstein was referring specifically to that or not, I would suggest that his statement only makes sense in that context.

This leads to another point that Livio makes, almost in passing, but I consider to be highly relevant and it is to do with the most abused of concepts: ‘truth’.

I recently had an argument with a blogger (Armageddon Thru To You), who referred to

‘absolutes of truth’ which override all so-called scientific truths. I contended that the only truths I can be sure of are mathematical truths, and he responded: ‘There are absolutes of truth that humanists cannot understand because they don't acknowledge the existence of a perfect being (God)’.

This is relevant to Livio’s book, because he spends 6 pages on the subject of Galileo’s famous confrontation with the Catholic Church in 1633. He ends this section with the following commentary:

‘Still, at a time when there are attempts to introduce biblical creationism as an alternative “scientific” theory (under the thinly veiled title of “intelligent design”), it is good to remember that Galileo already fought this battle almost four hundred years ago – and won!’

 I make a similar reference to Galileo and compare it to the current ID/Creationism debate in my Nov.07 post, Is evolution fact? Is creationism myth?

These days, no one wants to get into an argument about whether the earth goes round the sun or not, so they think it’s irrelevant, but, as Livio points out, in 1600, the Catholic Church saw it as a direct intervention on its intellectual turf. It contradicted the Bible, and as far as they were concerned, the Bible was sacrosanct: the Word of God or ‘absolute truth’, to quote my aforementioned interlocutor. I’ve no doubt that there will come a day when evidence of evolution will be so monumental that only the most die-hard fundamentalists will question it – in other words, it will be no more contentious than Galileo’s position is today.

My point being that one can’t read a text like Livio’s and not be struck by how much we have learnt from the study of science, none of which appears in the Bible or any other religious text. An appeal to ‘absolute truth’ not only rings hollow in the face of thousands of years of accumulated knowledge, it beggars credulity. Mathematics has provided us with more truths, both in abstraction and in physical reality, than any other endeavour. To attempt to trump it with ‘absolute truth’ is to make a mockery of the human intellect.

And this brings me, to what I consider, to be the most revelatory portion of Livio’s book. The relevance of the study of knots to our understanding of DNA. Livio explains how a mathematical ‘discovery’ by John Horton Conway in the 1960s also describes the way enzymes ‘unknot’ DNA to allow for ‘replication or transcription’ (Livio’s description).

DNA is one of the greatest mysteries of the universe – a code for life itself. It raises the metaphysical question of why does the universe exist? Most scientists and philosophers would say it is an accident. Paul Davies attempts to address the question in his book, The Goldilocks Enigma, by expanding on an original idea proffered by his mentor, John Wheeler, that there is a causal loop between conscious intelligence and the universe itself. In a way, it attempts to address the mystery I alluded to in Einstein’s famous quote: that the universe created the means to comprehend itself.

The answers to this question are neither biblical nor scientific – they are philosophical. And perhaps it’s best to quote Bertrand Russell from The Problems of Philosophy, as Livio does in his closing paragraph of his book:

‘Thus, to sum up our discussion of the value of philosophy; Philosophy is to be studied, not for the sake of any definite answers to its question, since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all because, through the greatness of the universe, which philosophy contemplates, the mind is also rendered great, and becomes capable of that union with the universe which constitutes its highest good.’ (Emphasis is mine)

P.S. I sent this post as a link to Mario Livio, and I've posted his response in a comment below.

Addendum 1: I came across this very relevant quote in It Must be Beautiful; Great Equations of Modern Science, edited by Graham Farmelo (Granta books, 2002).

'One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.' (Heinrich Hertz, on Maxwell's equations of electromagnetism.)

Addendum 2:  I've written specifically about Eugene Wigner's famous essay in a later post.

Addendum 3: I've changed the title of the post to reflect the title of Livio's book.

Godel, Escher, Bach - Douglas Hofstadter's seminal tome

The original title of this post was Artificial Intelligence and Consciousness.

This is perhaps the hardest of subjects to tackle. I’ve just finished reading Douglas R. Hofstadter’s book, Godel, Escher, Bach: an Eternal Golden Braid, which attempts to address this very issue, even if in a rather unusual way.

Earlier in the same year (last year) I read Roger Penrose’s book, Shadows of the Mind, which addresses exactly the same issue. What is interesting is that, in both cases, the authors use Godel’s Incompleteness Theorem to support completely different, one could say, opposing, philosophical viewpoints. Both Penrose and Hofstadter are intellectual giants compared to me, but what I find interesting is that both apparently start with their philosophical viewpoints and then find arguments to support them, rather than the other way round. Hofstadter quotes, more than once, the Oxford philosopher, J.R. Lucas, whom he obviously respects, but philosophically disagrees with. Likewise, I found myself often in agreement with Hofstadter on many of his finer points, but still in disagreement with his overall thesis. I think it’s obvious from other posts on this blog, that I am much closer to Penrose’s philosophy in many respects, not just on AI.

Having said all that, this is a very complex and difficult subject, and I’m not at all sure I can do it justice. What goes hand in hand with the subject of AI, and Hofstadter doesn’t shy away from this, is the notion of consciousness. Can AI ever be conscious in the way we are? Hofstadter says yes, and Penrose, I believe, would say no. (Penrose effectively argues that algorithm-using machines – computers - will never think like humans.) Another person who has much to say on this subject is John Searle, and he would almost certainly say no, based on his famous ‘Chinese Room’ thought experiment. (I expound on this in my Apr.08 post: The Ghost in the Machine).

Larry Niven in one of his comments on his own blog, in response to one of my comments, made the observation that science hasn’t resolved the brain/mind conundrum, and gave it as an example of ‘…the impotence of scientific evidence to affect philosophical debates…’ (I’m sure if I’ve misinterpreted him, or quoted him out of context, he’ll let me know.)

To throw a googly into the mix, since Hofstadter first published the book 30 years ago, a lot of work has been done in this area, and one of the truly interesting ideas is the Bayesian model of the brain based on Bayesian probability, proposed by Karl Friston (New Scientist 31 May 08). In a nutshell, Friston proposes that the brain functions on the same principle at all levels, which is to make an initial assessment then modify it based on additional information. He claims this works even at the neuron level, as well as the cognitive level. (I report on this in my July 08 post titled, Epistemology; a discussion.) I even extrapolate this up the cognitive tree to include the scientific method, whereby we hypothesise, follow up with experimentation or observation, then modify the hypothesis accordingly.

Hofstadter makes a similar point about ‘default options’ that we use in everyday observations, like the way we use stereotypes. It’s only by evaluating a specific case in more detail that we can break away from a stereotypic interpretation of an event. This is also an employment of the Bayesian principle, but Hofstadter doesn’t say this because it hadn’t been proposed at the time he wrote it.

What Searle points out in his excellent book, Mind, is that consciousness is an experience, which is so subjective that we really don’t know if anyone else experiences it the way we do – we only assume they do. Stephen Law writes about this in his book, The Philosophy Gym, and I challenged him (by snail mail at the time) that this was a conceit on his part, because he obviously expected that people who read his book, could think like him, which means they must be conscious. It was a good natured jibe, even though I’m not sure he saw it that way at the time, but he was generous in his reply.

Descartes famous statement, ‘I think therefore I am’, has been pilloried over the centuries since he wrote it, but I would contend that ‘I think’ is a tautology, because ‘I’ is your thoughts and nothing else. This gets to the heart of Hofstadter’s thesis, that we, individually, are all ‘strange loops’. Hofstadter employs Godel’s Theorem in an unusual, analogous way to make this contention: we are ‘strange loops’. By strange loop, Hofstadter means that we can effectively look at all the levels of our thinking except the ground level, which is our neurons. In between we have symbols, which is language, which we can discuss and analyse in a dispassionate way, just like I’m doing now. I can talk about my own thoughts and ideas as if they weren’t mine at all. Consciousness, in Hofstadter’s model (for want of a better word) is the top level, and neurons are the hardware level. In between we have the software (symbols) which is effectively language.

I think language as software is a good metaphor but not necessarily a literal interpretation. Software means algorithms, which are effectively instructions. Whilst language obviously contains rules, I don’t see it as particularly algorithmic, though others, including Hofstadter, may disagree. On the other hand, I do see DNA as algorithmic in the way it creates organisms, and Hofstadter makes the same leap of interpretation.

The analogy with Godel’s Theorem is that, in any formal mathematical system, there will always exist a mathematical statement that expresses something about the system but can’t be found in the system, if I’ve got it right. In other words, there will always exist the possibility of a ‘correct’ mathematical statement that is not part of the original formal system, which is why it is called the Incompleteness Theorem – no mathematical formal system can ever be complete in that it will include all mathematical statements. In this analogy, the self or ‘I’ is like a Godelian entity that is a product of the system but not contained in it. Again, my interpretation may not be what Hofstadter intended, but it’s the best I can make of it. It exists at another level, I think is what Hofstadter would say.

In another part of the book, Hofstadter makes a direct ‘mapping’ which he calls a ‘dogmap’ (play on words for dogma) where he compares DOGMA I ‘Molecular Biology’ with DOGMA II ‘Mathematical Logic’, using Godel’s Theorem ‘self-referencing’ as directly comparable to DNA/RNA’s ‘self reproduction’. He admits this is an analogy but later acknowledges that the same mapping may be possible from Godel's Theorem to consciousness.

Even without this allusion by Hofstadter, and no Godelian analogy required, I see a direct comparison between the way DNA/RNA creates complex organisms and the way neurons create thoughts. In both cases there is a gulf of layers in between that makes one wonder how they could have evolved. Of course, this is grist for ID advocates and I’ve even come across a blogger (Sophie) who quotes Hofstadter to make this very point.

In one of my earliest posts on this blog (The Universe’s Interpreters, Sep. 07) I make the point that the universe consists of worlds within worlds, and the reason we can comprehend it to the extent that we do, is because we can conjure concepts within concepts ad infinitum. Hofstadter makes a similar point, though not in the same words, but at least 2 decades before I thought of it.

DNA/RNA exists at a level far removed from the end result, which is a living complex organism, yet there is a direct causal relationship. Neurons are cells that exist at a level far removed from the end result, which is consciousness, yet there is a direct causal relationship.

These 2 cases, DNA to complex organisms and neurons to consciousness, I think remain the 2 greatest mysteries of the natural world. To say that they can only be explained by invoking a ‘Designer’ (God) is to say we’ve uncovered everything we know about the universe at all of its levels of complexity and only God can explain everything else. I would call this the defeatist position if it was to be taken seriously. But, in effect, the ID advocates are saying that whilst any mysteries remain in our comprehension of the universe, there will always be a role for God. Once we find an explanation for these mysteries, there will be other mysteries, perhaps at other levels, that we can still employ God to explain. So the argument will never stop. Before Newton it was the orbits of the planets, and before Mendel it was the passing down of genetic traits. Now it is the origin of DNA. The mysteries may get deeper but past experience says that we will find an answer and the answer won’t be God (see my Dec .08 post: The God hypothesis; not).

As a caveat to the above argument, I've said elsewhere (Emergent phenomena, Oct. 08) that we may never understand consciousness as a direct mathematical relationship to neuron activity (although Penrose pins his hopes on quantum phenomena). And I'm unsure that we will ever be able to explain how it becomes an experience, and that's one of the reasons I'm sceptical that AI will ever have that experience. But this lack of understanding is not evidence of God; it's just evidence of our lack of understanding.

To quote Confucius: 'To realise that you know something when you do, and to realise that you do not know when you do not, this is knowing.' Or to quote his near contemporary, Socrates, who put it more succinctly: 'The height of wisdom is to know how thoroughly ignorant we are.'

My personal hypothesis, completely speculative with no scientific evidence at all, is that maybe there is a feedback mechanism that goes from the top level to the bottom level that we’ve yet to discover. They are both mysteries that most people don’t contemplate and it took Hofstadter’s book, written over 3 decades ago, to bring them fully home to me, and to appreciate how analogous they are: base level causally affects top level, yet complexity of one level seems independent to complexity of the other - there is no obvious 1 to 1 correlation. (Examples: it can take a combination of genes to express a single trait; there is not a specific 'home' in the brain for specific memories.)

I guess it’s this specific revelation that I personally take from Hofstadter’s book, but I really can’t do it justice. It is one of the best books I’ve read, even though I don’t agree with his overall thesis: machines will eventually think like humans, therefore they will have consciousness.

In my one and only published novel, ELVENE, there is an AI entity, Alfa, who plays an important role in the story. I was very careful in my construction of Alfa to demonstrate that he didn’t think like humans (yes, I gave him a gender and that’s explained) but that he was nevertheless extremely intelligent and able to converse with humans with cognitive ease. But I don’t believe Alfa was conscious albeit he may have given that impression (this is fiction, remember). I agree with Searle, in that simulated intelligence at a very high level will be achievable, but it will remain a simulation. AI uses algorithms and brains don’t – on this, I agree with Penrose. On the other hand, Hofstadter argues that we use rule-based software in the form of ‘symbols’, which we call language. I’m sure whoever reads this will have their own opinions.

Addendum 1: I've just read (today, 21 Feb.09) an article in Scientific American (January 2009) that tackles the subject: From Atoms to Traits. It points out that there is good correlation between genes and traits, and expounds on the latest knowledge in this area. In particular, it gives a good account (by examples) of how random changes 'feed' the natural selection 'engine' of evolution. I admit that there is still much to be learned, but, if you follow this topic at all, you will know that discoveries and insights are being made all the time. The mystery of how genes evolved, as opposed to the organisms that they create, is still unsolved in my view. Martin A. Nowak, a Harvard University mathematician and biologist, profiled in Scientific American (October 2008) believes the answer may lie in mathematics: Can mathematics solve the origin of life? An idea hypothesised by Gregory J. Chaitin in his book, Thinking about Godel and Turing, which I review in my Jan.08 post: Is mathematics evidence of a transcendental realm?

Addendum 2: I changed the title to more accurately reflect the content of the post.

Zen; an interpretation

I recently bought a copy of Godel, Escher, Bach: an Eternal Golden Braid, the Pulitzer Prize winning book by Douglas R.Hofstadter. In fact, I bought the 20th anniversary edition, which includes an overview that effectively explains in synopsis each chapter of the book. The author did this, apparently, because he felt that so many people misinterpreted his intentions. The book is not about Zen at all, as he states himself, yet it’s his simplistic and dismissive representation of Zen that has prompted me to write this post (not quite true - see below).

Naturally, I had heard of the book and its companion, I am a Strange Loop, which I understand expands on some aspects of this one. I have acquired a copy of that as well, though I’m yet to read it. I think I’ve come across this book at just the right time for me. If I had read it 20 years ago (actually, originally published 30 years ago), I would have struggled with it. But, as it is, I think I’m reading it at just the right time of my philosophical development, especially in regard to mathematical philosophy. The book, which is quite lengthy and comprehensive, explores the very areas of philosophy that I’m interested in.

But whilst everything he says about logic is both enlightening and refreshing, as well as scholarly, I disagree with his interpretation of Zen, which he seems to portray as the antithesis of logic. It’s like he uses Zen as a reference for a perspective of non-logic, so his interpretation is that Zen is a 'non-state' (he elaborates on this later in the book). But I don't think Zen is about logic at all - in fact, it's a state of mind. My own interpretation is that Zen represents a particular state of mind when one is intensely involved in some activity. Now the activity could be physical, like tennis or playing cricket, or driving a car; or it could be mental like writing a story or painting a portrait, or playing a musical instrument.

What they all have in common is that it is a mental state where one feels removed, like one is totally involved yet one is ‘not there’, as virtuoso violinist and amateur surfer, Richard Tognetti, once said (no, he's not a Zen Buddhist to my knowledge). So it is a contradictory sense, or, at the very least, paradoxical. My own take on this is that one’s ego is not involved yet one feels totally engaged. It requires one to be completely in the moment, and what I’ve found in this situation is that time disappears. Sportsmen call it being ‘in the zone’ and it’s something that most of us have experienced at some time or another (Refer Addendum 3 below).

So I can understand why Hofstadter may interpret Zen as the representation of ‘contradiction’; even though it implies he’s never experienced a Zen state, or, if he has, he calls it something else. It is contradictory in explanation but not in experience. (To be fair, as I got further into the book, Hofstadter reveals that he knows a lot more about Zen than I first thought.)

Godel, Escher, Bach is an extraordinary and brilliant book, and I don’t wish to take anything away from Hofstadter’s achievement. He’s in another league to me altogether (after all, he has a PhD in solid state physics). For a start, he gives the best exposition of Godel's Incompleteness Theorem I've read, using a number of metaphors and allegorical dialogues, including one with Zen koans.

On the subject of Zen, I’m not a good practitioner, but I don’t try to be. From what I’ve read on Zen, it ideally requires ‘unattachment’, which also includes unattachment to goals and dreams. But without goals and dreams, what do people live for? So it seems contradictory to life, if one takes it literally. But, as a state of mind for when one is involved in an intense, challenging yet rewarding activity, it makes perfect sense. By the way, one only experiences a reward in this sense, when one is challenged. That’s why the most frustrating things in life are also the most rewarding. When one realises that, then one can achieve a sense of perspective as well as purpose. (I make a similar point in one of my earliest posts, The Meaning of Life, Aug.07.)

P.S. For all you pedants, 'unattachment' is not a 'proper' word (should be detachment) but in this context, detachment gives the wrong connotation. Unattachment means exactly that.

Addendum 1: I would challenge anyone to read Hofstadter's book without being forced to view things differently that they previously took for granted. I'm currently about one third through the book, and I am sure I will write another post on it when I'm finished.

Addendum 2: Daisetz Suzuki is the best writer on Zen I've read (in English). In particular, Zen and Japanese Culture (originally published 1959; my copy, 1973).

Addendum 3: I know, I keep adding to this when I should write another post, but my blog is not so much a journal as a collection of essays. On page 387 (Penguin 20th Anniversary Edition) Hofstadter quotes Escher: "While drawing I sometimes feel as if I were a spiritualist medium, controlled by the creatures I am conjuring up." I suspect many artists have felt this way, including myself when writing, and this is what I mean when I say the ego is not engaged. In fact, I have used this exact same description of my own writing on occasion. Australian actress, Kerry Armstrong, once made the point that acting doesn't involve the ego at all, quite the contrary, and I would make the same point about creating characters in fiction. So Hofstadter has described what I consider to be a Zen state of mind, by quoting Escher, but with no reference to Zen at all.

For a more edifying discussion of Hofstadter's book, see the next post: Artificial Intelligence & Consciousness.