The Lagrangian – possibly the most fundamental mathematical principle in physics

This is something I wrote on Quora, which was ‘upvoted’ by a physics tutor (Mike Milner) and someone with an MSc (Dimitrios Kalemis), which gives it some credence.

I’ve written about all of this before in previous posts, but probably not as succinctly, which hopefully makes it easier to follow.


How does an electron know beforehand that it's a single slit or double slit so it decides whether to create an interference pattern or not?

Obviously it doesn’t. It’s like asking how does a ball thrown in the air know what path to follow? These 2 questions have more in common than you might think.

There is a fundamental principle in physics called the principle of least action, and Richard Feynman used it to describe the trajectory of a ball in a gravitational field and also as the basis for his path integral method of quantum mechanics (QM).

The principle of least action is that the difference between the potential energy and the kinetic energy of a particle will always be a minimum and, mathematically, this is called a Lagrangian. In his book, Six Not-So-Easy Pieces, Feynman demonstrates how this applies to a body in a gravitational field when it follows the path dictated by a geodesic, which, in Einstein’s theory of relativity, is the path of maximum relativistic time. It turns out that this is the shortest path and also the path of least action, as determined by the Lagrangian.

Feynman gives the following analogy. Imagine a lifesaver needing to run along a beach and then swim out to rescue a bather in distress in the surf. The lifesaver could run along the beach (at a diagonal) until he (or she) is perpendicular to the swimmer in the waves and swim out. Or the lifesaver could run straight into the surf and swim diagonally to the swimmer. But the optimum path is something in between these 2 and that’s the path of least action or least time. It’s also the path of light when it refracts through glass or any other medium.

It was Paul Dirac who originally wrote a Lagrangian for QM and Feynman used his result to derive Schrodinger’s equation. Feynman’s approach to the 2 slit problem or any other QM problem was to combine all the possible paths the electron (or a photon) could take. By ‘combine’ this means adding all the phases of the wave function, most of which cancel each other out. Then, using Born’s rule, he derived the probabilities of where the electron would hit the screen on the other side of the slit(s).

In his book, QED, he provides a graphic demonstration using this method to derive the path of a photon hitting a mirror. He says ‘the light goes where the time is least.’

In response to your specific question, the electron’s path is only determined retrospectively after it hits the screen on the other side of the slit(s). Freeman Dyson (who collaborated with Feynman) argues that QM cannot describe the past but only the future. So prior to the electron hitting the screen, QM describes the probabilities of where it will go, which is mathematically dependent on it being able to go everywhere at once. If there are 2 slits then this means it can go through both and if there is only one slit then it can only go through one. So the observation made retrospectively confirms this.

Addendum: Sabine Hossenfelder gives a much more erudite exposition in this video. And I agree with her - it's the closest we have to a 'theory of everything'.

Christianity and Buddhism

Last month’s issue of Philosophy Now (Issue 132, June/July 2019) had as its theme ‘West meets East’, so it was full of articles about Eastern philosophies and comparative philosophy. It led me to revisit this essay I wrote when I was a student some 20 years ago, studying philosophy, and specifically, when I took a unit called Religious Studies.

I should point out that I was brought up Christian, which I rejected in my mid to late teens, and in my 30s I took an interest in Buddhism and neo-Confucianism. So I had some background knowledge before I took the course. One can already see my existentialist leanings. 

Whilst I have previously written a post on Jesus, I haven’t written a post on Siddhārtha Gautama specifically, though I’ve made references to Buddhism in various posts.


‘Most religions envisage the spiritual path as a journey away from the false claims of the illusory self towards an understanding of the Real Self.’ Critically discuss this in relation to at least two of the three traditions studied in this course.

I will address this topic with respect to two of the religious systems under study: Christianity and Buddhism. The terms ‘illusory self’ and ‘Real’ or ‘True Self’ are open to wide interpretation within both systems, but if we perceive life as a journey, then what we are discussing is nothing less than the purpose of that journey as interpreted by both these religions.

This essay is not about the relative merits of Buddhism and Christianity, nevertheless it compares philosophical doctrines and points of view in relation to man’s mortal existence and his destiny. It also compares two views of a metaphysical universe which of course directly impact on how man perceives himself.

Buddhism and Christianity are both religions that evolved from earlier religions: Hinduism and Judaism respectively. Both arise from a distinct personality who remains central to the beliefs of their respective systems. Accordingly, I think there are two parts to these religions, and I intend to discuss both parts. Firstly, there is the part concerned with the personae: their lives as exemplars; and secondly their teachings and the philosophies that evolved therefrom.

Any great man, any personality who had an immense impact on a large body of people, eventually becomes mythologised, and it is the myth that continues and lives in people’s consciousness until it completely displaces the original persona. This is no different with Jesus and Siddhārtha Gautama, but as I will explain later there are more mythic qualities associated with the Christ than with the Buddha.

Historically, myth and religion have been synergistic. A myth, often but not always, includes factual elements, but it is not my intention to distil truth from fiction. For the purpose of this discussion, I’m taking another tact, where the mythic elements are not the focus.

When people refer to ‘The Buddha’, it is generally acknowledged that they are referring to Gautama Buddha or Siddhartha, even though he is not the first or only Buddha. Siddhartha was a prince born of the Ksatriya caste, a warrior and ruling caste, who became an ascetic when he juxtaposed his privileged style of living with the suffering of ordinary people. His impulse was not as simplistic as that however, because he was also aware that sickness, old age and death were burdens on human life that neither privilege nor wealth could avert.

As a result, he spent his entire life searching for the means, psychologically rather than physically, in releasing man’s spirit from this burden. At the age of 35 he achieved a state of enlightenment or awakening: an event which defines Buddhism in its essence. ‘The portrait of the Buddha...  is thus one of a man of both great wisdom and great compassion moved by the spectacle of human suffering and determined to free men from its fetters by a rational system of thought and a way of life.’ (ref. Encyclopaedia Brittanica)

Jesus’ story on the other hand, is told within the context of an enormous history: the history of the Jewish people. But it is more than that because it has mythic consequences relating to Divine judgement and the end of mortal history. But I would prefer, for the purposes of this discussion, to look at Jesus in a human context because I believe that is where his greatest message lies.

Jurgen Moltmann in Man gives a very good account of Jesus that reminds us of Jesus’ basic humanity and how he related to the lowest strata of society rather than those privileged by birth. Jesus provided a role, which to this day, very few people follow. I am not referring to the role of martyr, but to the role of facing the worst in human suffering and human weakness and human oppression, and revealing to such people his common humanity with them. There is a resonance here with Simone Weil’s Essay: On Human Personality; which reminds us that the intelligent person recoils from affliction in the same way ‘flesh recoils from death’.

I believe this is the greatest lesson Christ ever taught: that he was superior to all people, yet he gave his Grace to those least fortunate, regardless of creed, background or social position.

Buddha was not mythologised in the way that Christ was, neither was he a martyr, but in the final analysis these differences are of less significance than the hope they provide to all people through their example, their teachings and their lives. Both Christ and Buddha are not heroes in the traditional sense. They were antiheroes and pacifists, who were both renowned for their incomparable compassion to their fellow man. In this way, by their very lives, they both point to an identity and a destiny that ordinary people can emulate. This of course, is not how either of these religions are defined, but the lives of these men hold as much significance, perhaps even more, than their teachings.

On the other hand, to approach the destiny of the Self from a purely philosophical viewpoint, in either Christianity or Buddhism, one needs to go to the core of their respective beliefs. In Buddhism this is the concept of karma, and in Christianity it is a relationship with God through Christ. This also highlights the fundamental, and some would say irreconcilable differences between their philosophical and religious viewpoints.

Karma is generally understood as a causal connection between man’s actions and his destiny or fate. This causal relationship has metaphysical consequences, because it traverses lives. In other words, action in this life can affect destiny in the next life, which infers that some aspect of the Self is reborn. In Buddhist philosophy this leads to a contradiction because the Buddha explicitly preached a philosophy of no-self: that is no attachment, but also no soul.

Karma is a concept common to Hinduism, and is used as an explanation and rationalisation of the caste system, but Buddha considered the caste tradition inequitable.

More significantly, there is another way of perceiving karma that is best explained by John Hick in Death and Eternal Life, where he discusses the concept of a world karma. Hick explains with this concept that there is no need to consider an individual karma or rebirth, and so overcomes the contradiction. With or without the contradiction, the idea of a universal karma has a certain appeal and finds resonance in other concepts like Jung’s ‘collective unconscious’.

Masao Abe also makes reference to a similar, if not the same concept, when he cites Shin’ichi Hisamatsu’s notion of FAS: “Awakening to the Formless Self”. What Hick and Abe are both inferring is that there is a collective karma of the whole of mankind: past, present and future. What Abe describes as the ‘depth, breadth, and length of human existence’ According to Abe, Hisamatsu identifies this awakening as the same experience as satori (enlightenment in Zen Buddhist terminology).

To many Buddhists, satori, enlightenment or nirvana, is the whole purpose of man’s existence as an individual, and this is what is meant by finding the ‘True Self.’ Personally, I believe there are other perspectives to this question, without denying the significance of satori, and I will return to them later.

But another significant attribute of karma in Buddhist philosophy is that it deals with good and evil in human life without acknowledging a Deity or a Devil. I think this is fundamental in understanding the differences in Buddhist and Christian beliefs and also how they approach the question of the Self and its destiny.

To elaborate we need to examine the other obvious distinction between Christianity and Buddhism, which is that Christianity fundamentally requires a relationship with God. To a large extent, this philosophical nexus also determines the role of Christ.

It is Christ that makes Christianity unique in a way that Buddha doesn’t. As Fritz Buri says: ‘But in distinction to the Buddha, Jesus is not only teacher, but also an actor in the history of existence.’ It is Christ’s resurrection that places him mythically above man, though not immortal. It places him perfectly between God and man. In the Christian perspective, Christ is our connection with God, with Heaven and with a consciousness beyond death. This is the Christian response to both karma and nirvana.

Much of contemporary Christian belief revolves around the idea of being born again; of ‘finding Christ’. Many believers maintain that without this rebirth, which includes the acceptance of Christ as their saviour, there is no possibility of achieving the kingdom of Heaven. Yet according to Matthew this is not enough. In Matthew 7:21, Jesus says it is not enough to use his name: ‘It is not anyone who says to me: “Lord, Lord”, who will enter the Kingdom of heaven, but the person who does the will of my Father in Heaven’.

But in Christian doctrine, it is the metaphorical rebirth that signals a change in spiritual identity. To the orthodox Christian, this is the only path, the only destiny for the Self to consider.

Once again, I believe there are other perspectives to be considered, and it is another passage in Matthew which provides a clue. In Matthew 12:33-37, Jesus maintains that what comes from a man’s mouth (in words) comes from his heart - in this way one can tell evil from good. Specifically: Matthew 12:34; ‘You brood of vipers, how can your speech be good when you are evil? For words flow out of what fills the heart.’

‘What fills the heart’ is perhaps what the True Self is all about, and has resonances with Buddhism as well as other Eastern philosophies, but more importantly, is a key factor in Augustine’s neo-Platonic influenced philosophy: ‘...to reach the good, which is the real, one must “return into” oneself; for it is the spirit at the heart of man’s inmost self that links him to the ultimate reality.’ (ref. Encyclopaedia Brittanica)

In Christianity, the essential element of life’s journey is man’s relationship with God. This relationship is obviously deeply individualistic and despite the rituals and liturgies of the traditional churches, can really only be achieved within an individual’s consciousness. Again, in reference to Augustine: ‘Grace awakens the dormant power of the mind to see God’s image in itself, to see itself, that is, as God’s image.’ In other words, God is found only by looking inside ourselves, not by a leap of imagination into the unknown, conjuring images of a supreme being or a pantheistic spirit. That is not to say that Augustine didn’t recognise God as creator of the Universe, but man’s conscious accessibility to God is an inner journey, not an external relationship.

This, I believe, provides the best insight into the Christian perspective of understanding the Self and its destiny. The state of Grace that the Christian strives for, is to my interpretation, the same state as satori or nirvana, that is the Buddhist’s highest goal.

In Buddhist philosophy, as perceived from a Western perspective, the biggest conceptual hurdle is the belief in karma but not the soul. To overcome this paradox, Buddhist philosophers invoke the concept of no-self, but it tends to create more confusion than resolution.

If one simply dwells on the self or no-self paradox in Buddhism, then I believe one misses the point. The point of the journey of life is to acquire meaning and perhaps also an identity. In Christianity the notion of identity is very clear: it is achieved in a metaphorical rebirth (finding one’s identity in Christ). In Buddhism the purpose of the journey is to achieve satori or nirvana. But if the emphasis is changed from the destination to the journey itself, then it gives a different perspective. It is then concerned with the way we live our lives. It is the notion of karma that gives substance to Buddhist belief, not a concern with self or no-self. Buddha’s teachings on the no-self, I believe, reflect his concern with man’s preoccupation with the self and its unhealthy consequences. Whilst karma can be seen as a stick and carrot approach to religious teaching, this is a misplaced emphasis. If karma is seen instead as man’s connection to the rest of humanity, including past and future humanity, then one begins to grasp the point.

‘Interconnection between the individual and the whole universe is stressed in the Buddhist doctrine of karma.’ (ref. Encylopaedia Brittanica) From this conceptual viewpoint, the notion of individual karma and rebirth can be taken as a secondary consideration, and is neither denied nor affirmed.

But perhaps more relevantly, individual karma and therefore the Self, should not be considered as being independent of our universal or collective karma. That, at least, is my interpretation.

There is still another perspective of the Self, which is man’s purpose given by God. An idea that finds resonance in both Christian and Eastern beliefs. Tu Wei-Ming, a Confucian scholar, expresses it best: ‘...we are guardians of the good earth, the trustees of the mandate of Heaven....embedded in our human nature is the secret code for Heaven’s self-realisation.’

Humankind is above all else, the caretaker of the planet Earth. If one believes in a God, Christian or otherwise, as a creator who explicitly places man in charge of his creation, then the responsibility is huge indeed. Buddhist doctrine, on the other hand, ignores any explicit reference to this responsibility; nevertheless man’s karmic relationship, either individualistic or holistic, points him in the same direction - Earth’s fate has a causal dependency on man’s fate. From this point of view, one cannot ignore that the individual’s journey has a connection to humankind’s collective journey, with or without a heaven, with or without rebirth. From this perspective, the difference between the illusory self and the True Self is perhaps not one of identification but of awareness. An awareness not of Divine inheritance but of responsibility to our inheritance.

In the final analysis, I believe that religion or religious viewpoint is not so much a belief as an attitude. An attitude towards the Universe, towards one’s life and life in general, but above all, an attitude that reflects the Self at its deepest core rather than at a superficial level.

The spiritual journey is a euphemism for the search inside oneself to discover the true nature of the Self so that it may ‘light the world’  (Budda’s last words, purportedly). This is why the artist who has the most impact on us, is the one who digs deepest into his or her psyche. Augustine was right when he said the search for God was an inner journey. It is the inner journey which finds the True Self not the journey in the material world. Both Buddhists and Christians agree that the desire to create a position or an identity for ourselves in the world of business, commerce or social environment is the illusory self. The True Self, through which we engage our relationships to others and to the world at large, is, in the final analysis, the means by which we gain satisfaction from living.





References:

Abe M., Transformation in Buddhism, Buddhist-Christian Studies, Vol.7, 1987, pp.15-20.

Augustine, Encyclopaedia Britannica, Edition 15, 1989, Vol.14, pp.286-390.

Balthasar H.U. von, Engagement with God, trans. J. Halliburton, SPCK, London, 1975, Part 2, ch.4, pp.67-80.

Bultmann R. Existence and Faith, trans. Schubert M. Ogden, Hodder and Stoughton, London, 1961, pp. 248-66.

Buri F., Ingram P. & Streng F. (Eds), Buddhist-Christian Dialogue - Mutual Renewal and Transformation, University of Hawaii Press, Honolulu, 1986.

Burnaby J., ‘Introduction’, in J.Baillie, J.T.McNeill et al. (eds), The Library of Christian Classics, Vol.III, SCM Press, London, 1955, pp.23-31,31-6.

Ching J., Paradigms of the Self in Buddhism and Christianity, Buddhist-Christian Studies, Vol. 4, 1984, pp.31-50.

Cochrane C., Christianity and Classical Culture, Oxford University Press, London, 1944, pp.399-411.

Collins S., Selfless Persons: Imagery and Thought in Therevada Buddhism, Cambridge University Press, 1982, Part IV, pp.218-24.

Coward H., Psychology and Karma, Philosophy East and West, Vol.33, No 1, 1984, pp.54-58.

Fenner P. ‘Cognitive theories of the emotions in Buddhism and Western psychology’, Psychologia, vol.30, 1987, pp.217-27.

Fenner P., The self and its destiny in Buddhism, Religious Systems B,
 Deakin University, Geelong, 1996.

Hick J. Death and Eternal Life, Collins, London, 1976, ch.18, pp.347-60.

Hopkins J. & Rinbochay L., Death, Intermediate State and Rebirth in Tibetan Buddhism, Rider, London, 1979, Introduction, pp.13-21.

Howard W., Christianity according to St. John, Duckworth, London, 1943, ch. IV, pp.81-105.

Lichter D. & Epstein L., ‘Irony in Tibetan notions of the good life’, in C.F. Keyes & E.V. Daniel (eds), Karma. An Anthropological Enquiry, University of California Press, Berkeley, Calif., 1983, Part 2, sn 9, pp.233-38.

McLellan D., Utopian Pessimist: The Life and thought of Simone Weil, 
Poseidon Press,1990.

Moltmann J. Man, SPCK, London, 1974, pp. 16-21, 105-17.

The New Jerusalem Bible - New Testament, Darton, Longman & Todd, Reader’s Edition, 1991.

Newsletter, Religious Systems B, The Self and Its Destiny in Christianity, Hinduism and Buddhism, Deakin University, 1996.

Nordstrom L., Zen and karma, Philosophy East and West, Vol.30, Issue 1, 1980, pp.77-86
.
Paul D. ‘The Structure of consciousness in Paramartha’s purported trilogy’, in Philosophy East and West, Vol.31, No.3, 1981, p.314.

Suzuki D., Zen and Japanese Culture, Bollingen Series LXIV, Princeton University Press, 1959

Tu W., LIFE magazine, Dec. 1988, p.93.

God is not a mathematician; God is in the mathematics

I’ve just read a recently published book, The Universe Speaks in Numbers; How Modern Maths Reveals Nature’s Deepest Secrets by Graham Farmelo. The title says it all really, but the content takes you places you’ve probably never been, intellectually. This book, possibly more than any other book I’ve read, gives you access to the minds of the superstars in theoretical physics, both past and present, but mostly present. It’s like listening to a group of virtuoso musicians and becoming aware of how inadequate you are in the presence of such talent.

It’s written in an historical context, from Newton through Maxwell to Einstein, but rather than lingering in the so-called golden age of physics, it focuses on the last 50 years.

Farmelo covers what he calls ‘the long divorce’, a term coined by Freeman Dyson, covering much of the latter 20th Century, when pure mathematicians and theoretical physicists, not only avoided each other, but were not very accommodating of each other’s contributions.

That all changed very late in the 20th Century, and since then there has been a synergy that has benefited both disciplines. The problem is that theoretical physics has leapfrogged ahead of experimental physics, and, consequently, physicists at the leading edge of high energy physics have become more dependent on mathematical solutions to provide veracity to their ideas. ‘High energy’ means highly confined dimensions, so we are talking about the smallest constituents of matter we currently know or can imagine.

I’ve made the point in previous posts that the ultimate arbiter of truth is evidence, but Farmelo’s book has made me re-evaluate that position. Instead of testing theories with experiments that can’t be performed, theoretical physicists simply adhere to 2 founding principles: quantum mechanics and special relativity. Because those 2 specific theories have been experimentally tested in extremis, they simply ensure that any new theory, no matter at what level, or using whatever mathematical tools they have, must meet both criteria.

The book necessarily covers string theory, from its inception to its current status. But what I found most fascinating was all the discoveries that seemed to have occurred on the side so-to-speak, where mathematics appears to continually underlie the fundamentals of nature in unexpected ways.

I admit to being a sceptic of string theory, due to its 6 additional dimensions that can’t be observed and its plethora of 10⁵⁰⁰ universes. But I must also admit that the people exploring this mathematical world leave me stranded when it comes to intellectual wizardry.

Farmelo repeatedly refers to 2 talks given by Albert Einstein and Paul Dirac, respectively, where they effectively gave a call-to-arms, arguing that mathematics is the key to new theories in physics, with experimental physics providing confirmation rather than having the leading role. Whether by design or accident, this is how physics has evolved in the last 5 decades. As Farmelo expounds, not everyone has been happy with this development, yet there have been successes.

To give one example, mathematical devices called twistors (developed by Roger Penrose in the 1960s) have led to providing accurate predictions in the amplitudes of scattering gluons, which are the mediating particles for quarks in atomic nuclei. This short description belies the convoluted story, involving many theorists in the UK and the US, and the many unexpected discoveries made along the way; including a connection with a mathematical object discovered by Hermann Grassmann in 1844, called eponymously a Grassmannian. It led to another mathematical object called an 'amplituhedron'. One of the co-discoverers, Nima Arkani-Hamed (an American born Iranian, at the Princeton Institute for Advanced Study) said:

This is a concrete example of a way in which the physics we normally associate with space-time and quantum mechanics arises from something more basic.

The ‘something more basic’ is only known mathematically, as opposed to physically. I found this a most compelling tale and a history lesson in how mathematics appears to be intrinsically linked to the minutia of atomic physics.

In the same context, Arkani-Hamed says that ‘the mathematics of whole numbers in scattering-amplitude theory chimes… with the ancient Greeks' dream: to connect all nature with whole numbers.’

There is an assumption by non-physicists that the role of mathematics in understanding nature is a consequence of the fact that we need to measure everything. A common criticism is that people who emphasise the role of mathematics in their theories have ‘mistaken the map for the terrain’.

Einstein was probably the first to use mathematics alone to sculpture a theory independently of observation and experimentation, when he developed his masterpiece, the general theory of relativity. It was his mathematical prediction that gravity would bend light that clinched his theory when few people believed that relativity reflected reality.

In reference to the abovementioned metaphor about the ‘map and terrain’, there is an axiomatic inference that the map is derived from ‘surveying’ the terrain. However, it’s becoming increasingly apparent that the map is discovered before the terrain is even 'explored', which turns the metaphor on its head. It’s not a metaphor I would choose to use, but if you insist, you might have to consider the possibility that the map pre-exists the terrain.

In reference to the title, I’ll retell a joke by mathematical physicist, Robbert Dijkgraaf, from the Princeton Institute for Advanced Study:

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

Sometimes being paranoid is healthy

Not that long ago I wrote a post about how the technology of surveillance and its ever-increasing role in policing was overtaking fiction. As a sometime science fiction writer, it comes with the territory to explore future societies. In my fiction, I really don’t attempt to forecast the future, I simply use a fictional social landscape to explore ideas and, in particular, relationships with advanced technology. There is an element of fantasy in my stories as well.

All governments know the importance of controlling information, called ‘controlling the narrative’, which is why an independent media is essential to a democracy, and it’s also why the most totalitarian governments find ways to imprison journalists who challenge the ‘party narrative’. In the current political climate throughout the Western world, opinions have become polarised on almost every issue, and, as someone recently pointed out, media outlets have become default political mouthpieces. Followers on both sides of politics now want to silence or muzzle media sources that disagree with their particular political point of view.

Very recently, in Australia, following a surprising election win by an incumbent conservative government, media outlets were raided (both public and commercial sources) including an award-winning female journalist’s home. This rang alarm bells from all sides of media. The timing was significant because the 2 different news stories went to air more than a year earlier, yet the raids occurred within a week of winning an election. The Government claims the raids were independent of them; so aren’t they lucky the raids didn’t occur the week before the election instead of the week following.

In the case of the ABC (Australian Broadcasting Corporation), Federal Police officers sat in a room and went through emails and edited them, apparently. Effectively changing records to suit their purpose. If this happens in a democracy, what happens in totalitarian regimes. (Well, journalists are put in jail or assassinated in some cases, like Russia).

Now imagine a future society where everyone is tracked by facial recognition and everyone has a social ‘rating’ which determines what buildings they can enter, what job they can apply for and even what transport they can board, be it a train or a plane. Did I say future? This is already happening in the most populous nation in the world. It’s well known that this same nation controls very exactly what information people can access.

It was less than 20 years ago, when there was a ‘Y2K’ scare, predicting that important utilities and infrastructure would fail when computer clocks ticked over to the year 2000, because their clocks didn’t go beyond that date. As it turned out, the scare was ill-founded, but it highlighted how dependent we are on the internet infrastructure, and how vulnerable it could be in a future transcontinental conflict.

Most people are blissfully unaware of how our computing systems are based on 2 formats that go back decades – Microsoft and Apple – so it would be virtually impossible to introduce a new system from scratch. But what if the internet infrastructure became just as dependent on one system, and as their monopoly grew over the entire world, how hard it would be to ‘disconnect’.

Now, also imagine if the infrastructure that everyone depended on was run by one of the most totalitarian regimes in the world, who had a paranoid obsession with the control of information.

Religion and politics in secular society

This is a letter I wrote to The Weekend Australian, Christmas 2017, so 18 months ago. There was a side-debate at the time, during the same sex marriage debate about ‘religious freedom’. It seemed to me that ‘religious freedom’ was ‘code’ for freedom to discriminate against gays and lesbians, and it’s not over. From what I’ve read and seen, the only arguments against same sex marriage came from conservative religious figures (some being politicians) even if they claimed it was about ‘the sanctity of marriage’.

The letter below alludes to that debate, even though the topic is much broader. It’s really about a perceived conflict between secularism and Christianity in Western societies, including Australia. There is a recurring argument that our Christian heritage provides the moral fabric of our society with the inference that, without it, we’d lose our moral compass. If that was true, and we really followed Christ’s calling, we wouldn’t treat refugees the way we do. In fact, our 2 most conservative Christian leaders, in recent times, have been the most ruthless advocates for persecuting refugees, and of fomenting xenophobic sentiment in the electorate.

The names referenced in the letter below, are journalists or commentators. The Australian is a Murdoch publication, so it has conservative political leanings.



Both Paul Kelly and John Carroll in separate articles (Weekend Australian, Enquirer, 23-24 Dec.2017) seem concerned that the modern secular world that dominates Western societies, and therefore Australia, has forgotten, even ‘turned its back’ on our Christian heritage. I’m officially retiring age, so I grew up in post-war Australia when going to Sunday School and scripture classes (in public schools) was still considered part of a child’s education (neither of my parents were religious; they just thought it was the cultural norm). Strangely, I don’t lament the loss, for want of a better word, the Church’s role in political and secular life, epitomised by the divide between Catholics and Protestants that dominated even the small country town where I grew up.

I found the greater part of Paul Kelly’s lengthy editorial a stimulating read, even when I might proffer alternative views, but his commentary on High Court judge Dyson Heydon’s concerns about the future of Christianity in this country, I found alarmist to say the least:  “The question for the West is how it retains its civilisational heritage if it abandons beliefs in its Christian ethic or, indeed, if its political culture begins to assault that ethic.” Without referencing them specifically, he’s obviously referring to the passing of the recent same-sex-marriage bill in Federal Parliament and the euthanasia bill in the Victorian State Parliament. Both of these have provoked ‘concerns’ from the Catholic church, in particular, who are effectively under siege for the sins they committed in the previous generation.

Personally, I think it’s a landmark moment that gays and lesbians now have the same rights as heterosexual couples. A law that has symbolic and pragmatic importance for the people it affects, and absolutely no effect on the people who oppose it. No one is being forced to have same-sex marriage – it’s a choice. Kelly and his fellow detractors will talk about religious freedom, but it’s only an issue for the people who, for whatever reason, think that homosexuals and lesbians should stay in the closet, or at least, stay out of our churches. If it comes to a choice – and it shouldn’t – between gay and lesbian rights and religious freedom, then it’s a no brainer for most Australians, including the ones like myself, who are heterosexual.

To give credit to The Australian, on the same page as John Carroll’s very lengthy piece on Christmas and the declining relevance of Jesus’ story to most Australians, there is a piece by Helen Dale, who explains, at some length, the pagan roots of Christmas that most Australians are either unaware of or blissfully apathetic about. This created a counter-perspective that was running through my head even while I was reading Carroll’s thesis.

Don Cupitt, a theologian, turned philosopher and author, is a bit of an iconoclast when it comes to religion and Christianity in particular. He’s made the salient point that humanist morality really started with the novel, where moral dilemmas and issues concerning good and evil were resolved without invoking a Deity or scripture. Carroll, to his credit, makes a similar point about the role of literature and popular culture in stimulating our psyche in this regard, without resort to prescriptive Christian ethics. He then goes on to say: “Further, we have now had 150 years of gloomy prediction that the death of God would lead to political anarchy and the moral collapse of the West. That has simply not eventuated.”

For Carroll, the Jesus story is all about imbibing us with meaning, and that is what we are losing. The point is that the Jesus story is mythology and when I was a child, undergoing the religious education I mentioned in my introductory paragraph, I really believed the stories were true, because at that age we believe whatever adults tell us. Like many of my generation, I grew up disillusioned in my mid teens, when I realised the stories were not only mythologised but defied rational analysis. And that is the real reason that Christianity has lost its meaning for most people with a Western education.

In the Review section of the same issue of the Weekend Australian, John Carey reviews a book by Stephen Greenblatt, The Rise and Fall of Adam and Eve, where he charters the literary history of the book of Genesis, from its origins in The Epic of Gilgamesh to Augustine’s seminal re-interpretation as signifying the ‘Fall of Man’. I’m not sure if it’s Carey’s or Greenblatt’s insight, but one of them points out the logical inconsistency in the morality tale: “For if God was all-knowing, why did he forbid Adam and Eve to eat the fruit, knowing they would disobey? Why did he create them at all, since he intended to kill them?”

Both Carroll and Kelly refer to the heritage or legacy that Christian ethics has provided to Western cultures. Well, historically, so-called Christian ethics has created a lot of bigotry, wars, genocide and inquisitional torture. Many contemporary commentators point to the current issues surrounding Islam, claiming that the religion itself is flawed. Well, if Islam is flawed then so is Christianity.

Hugh Mackay, in his book, Right & Wrong; How to Decide for Yourself, warns of the dangers of believing that God is on your side, because then anything can be justified, which is what we’ve witnessed both historically and contemporarily.


Addendum: The same day I posted this, I read an article in the Australian Weekend Magazine (July 20-21, 2019) about Israel Folau and the issue of religious freedom. Folau is a star rugby player with the Australian Rugby Union team and famously posted a piece on Facebook that all homosexuals, adulterers, liars and various other sinners would go to Hell. What created a furor wasn’t so much what he said but that he was sacked from the team (his contract was terminated). I agree with former Australian Human Rights Commissioner, Gillian Triggs, that the Australian Rugby Union went outside their remit.

The incident has brought out the worst on both sides of the debate, and demonstrates what happens when you try to enforce what people are allowed to say in public. Peter Singer is another unexpected supporter of Folau's right to free speech. My attitude is that everyone should be allowed to make complete fools of themselves, whether they be sports stars, TV celebrities, politicians or even the President of the United States.

What does logic reveal about reality?

This is about a loop in our universe (that includes us), and which I’ve long been fascinated by.

To quote from another post I wrote, The introspective cosmos:

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.

This insight is also reflected in Eugene Wigner’s 2 miracles: the miracle that the Universe can be comprehended and the miracle that we have the ability to comprehend it to the degree that we do. Or as Einstein so famously said:

The most incomprehensible thing about the Universe is that it’s comprehensible.

As Wigner explicitly stated and Einstein implicitly believed, the medium for that comprehension is mathematics. This loop, that I alluded to in my opening, is also implicit in Roger Penrose’s 3 worlds.

The question in the title was one I found on Quora. Most of the questions that Quora’s algorithms address to me are either too silly, or too specialist and esoteric for my capabilities to respond.

In this case, after reading the other answers, I thought they had largely missed the mark, and perhaps the point. The authors may draw the same conclusion about my answer.

I found that my answer went in a subtly different direction to what I intended, but resulted in a mini-epiphany. There is a limit to what we can know because there will always be a limit to the mathematics we know, which thus far determines what we know of the cosmos.

My answer to What does logic reveal about reality?


Fundamentally, it reveals that there are limits to what we can know.

Epistemology is the ‘theory of knowledge’ (dictionary definition) - effectively, the study of what we can know. Whereas ontology is defined as ‘the nature of being’, which, in effect, is what we call reality.

Since the Enlightenment, it’s become increasingly apparent that it’s our knowledge of mathematics that determines the limits of what we can know, both at the cosmological and the infinitesimal scale. But mathematics itself has epistemological limits according to Godel’s Incompleteness Theorem.

In effect, Godel proved that, in any axiom based mathematical system, there will be mathematical truths that we can’t prove. In practice, this means that there will always be mathematical truths that lie beyond what we currently know. In this context, ‘what we currently know’ is transient. So even though we may, and will, know more in the future, it will never be complete.

The point is that we use logic to reveal these mathematical truths and so the corollary to Godel’s theorem is that there will always be a limit to what that logic can reveal, no matter how much it has revealed already. Basically, we extend our knowledge by extending our axiomatic system. To give an example: by employing the new axiom, √-1 = i, we uncovered a whole new realm of mathematics.

Some centuries later, we then used that particular mathematics (called complex algebra) to describe a newly discovered phenomena called quantum mechanics (QM). In fact, without that knowledge (revealed by pure logic) quantum mechanics would never have been developed into a consistent and highly successful theory. And arguably, QM is ‘the evanescent substrate on which we all exist’ [or reality] to quote Clifford A Pickover.

And this is the loop: QM is the substrate of the Universe, which created humans which discovered an abstract mathematics, which not only describes, but prescribes the rules for QM.