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.
Friday, 2 August 2019
Wednesday, 24 July 2019
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.
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.
Sunday, 21 July 2019
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.
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.
Sunday, 30 June 2019
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.
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.
Sunday, 26 May 2019
Evolution of culture; a uniquely human adaption
I finally got around to reading Sapiens; A Brief History of Humankind by Yuval Noah Harari, after someone lent me a copy. I’d already read and reviewed his follow-up book, Homo Deus, so I’m reading them in the reverse order. I have to say he makes bleak reading, yet you feel there’s a lot of truth in his words. Having said that, I still feel I can challenge him on some issues to provide a more optimistic outlook. He is both provocative and thought-provoking, which are not necessarily one and the same thing.
He makes the point, which I’ve long known, that what separates us from all other species is that we have undertaken a cultural evolution that has long overtaken our biological evolution. This was accelerated by the invention of script, which allowed memories to be recorded and maintained over generations, some of which have lasted millennia. Of course, we already had this advantage even before we invented script, but script allowed an accumulation of knowledge that eventually led to the scientific revolution, which we’ve all benefited from since the enlightenment and has accelerated in the last 2 centuries particularly.
One of Harari’s recurring themes is that much of our lives are dependent on fictions and myths, and these have changed as part of our cultural evolution in a way that we don’t appreciate. Jeremy Lent makes similar observations in his excellent book, The Patterning Instinct, though he has a subtly different emphasis to Harari. Harari gives the impression that we are trapped in our social norms and gives examples to make his case. He points out that past societies were very hierarchical and everyone literally knew their place and lived within that paradigm. In fact, the consequences of trying to live outside one’s social constraints could be dire, even fatal. The current paradigm, at least in Western societies, is one of ‘individualism’, which he also explored in his follow-up book, with the warning that it could be eroded, if not eliminated, by the rise of AI, but I won’t discuss that here.
He effectively argues that these ‘fictions’, that we live by, rule out the commonly held belief that we can change our circumstances or that there is an objective morality that we can live by. In other words, he claims our lives are ruled by myths that we accept without question, and the only thing that changes are the myths themselves.
I take his point, but throughout history - at least from around 500BC - there have been iconoclasts who have challenged the reigning paradigm of their time. I will mention four: Socrates, Jesus, Buddha and Confucius. The curious point is that none of these wrote anything down (we only have their ‘sayings’) yet they are still iconic figures more than 2,000 years after their time. What they have in common is that they all challenged the prevailing ‘myth’ (to use Harari’s term) that there was a ‘natural order’ whereby those who ruled were ordained by gods, compared to those who served.
They all suffered for their subversions: Jesus and Socrates were executed, Confucius was exiled into poverty and the Buddha was threatened but not killed. Jesus challenged the church of his day, and that was the logical cause of his execution, not the blasphemy that he claimed to be ‘the son of god’. A lot of words were put in Jesus’ mouth, especially in the Bible. Jesus stood up for the disenfranchised and was critical of the church and the way it exploited the poor. He wouldn’t have been the only rabble-rouser of his time in Roman occupied Palestine but he was one of the most charismatic.
Buddha challenged the caste system in India as unjust, which made him logically critical of the religious-based norms of his time. He challenged the ‘myth’ that Harari claims everyone would have accepted without question.
Confucius was critical of appointments based on birth rather than merit and argued that good rulers truly served their people, rather than the other way round. Not surprisingly, his views didn’t go down very well with the autocracy of his time. He allegedly proposed the dictum of reciprocity: ‘Don’t do to others what you wouldn’t want done to yourself’. An aphorism also attributed to Jesus, which has more pertinence if one considers that it crosses class boundaries.
As for Socrates, I think he was the original existentialist in that he made a special plea to authenticity: ‘To live with honour in this world, actually be what you try to appear to be.’ Socrates got into trouble for supposedly poisoning the minds of the young, but what he really did was to make people challenge the pervading paradigm of his time, including the dominion of gods. He challenged people to think for themselves through argument, which is the essence of philosophy to this day.
To be fair to Harari, he gives specific attention to the feminist paradigm (my term, not his, as I don’t see it as a fiction or a myth). But I do agree that money, which determines so much in our societies, is based on a very convenient fiction and a great deal of trust. Actually, some level of trust is fundamental to a functioning society. In fact, I’ve argued elsewhere that, without trust: truth, justice and freedom all become forfeit.
The feminist paradigm is very recent, yet essential to our future. I recently saw an interview with Melinda Gates (currently in Australia) who made the salient point that it’s contraception that allows women to follow a destiny independent of men. Not surprisingly, it’s the ‘independent of men’ bit that has created, and continues to create, the greatest obstacle to their emancipation.
One of the more interesting discussions, I found, was Harari’s argument that political ideologies are really religions. I guess it depends on how you define religion. This is how Harari defines it, simultaneously giving a rationale to his thesis:
If religion is a system of human norms and values that is founded on belief in a superhuman order, then Soviet Communism was no less a religion than Islam.
I’m not convinced that political ideologies are dependent on a belief in a ‘superhuman order’, but they are premised on abstract ideas of uncontested ‘truth’, and, in that sense, they are like religions.
Contrary to what many people think, political thinking of ‘right’ and ‘left’ are largely determined by one’s genes, although environment also plays a role. Basically, personality traits like conscientiousness and goal-oriented leadership over people-based leadership are what are considered right-leaning traits; and agreeableness and openness (to new ideas) are considered left-leaning traits. Neuroticism would probably also be considered a left-leaning trait. Notice that all the left-leaning traits are predominant in artistic or creative people and this is generally reflected in their politics.
Curiously, twin studies have shown that a belief in God is also, at least partly, a genetically inherited trait. But I don’t believe there is any correlation between these two belief systems: God and politics. I know of people on the political right who are atheists and I know people on the political left who are theists.
I know that in America there seems to be a correlation between the political right and Christian fundamentalism, but I think that’s an Americanism. In Australia, it has little impact. We’ve very recently elected a Pentecostal as PM (Prime Minister) but I don’t believe that had any bearing on his election. We’ve had two atheist PMs in my lifetime (one of whom was very popular indeed), which would be unthinkable in America. The truth is that in some cultures religion is bound irretrievably with politics, and it can be hard for anyone who’s lived their entire lives in that culture to imagine there are political regimes where religion is a non-issue.
And this brings me to Harari’s next contentious point:
Even though liberal humanism sanctifies humans, it does not deny the existence of God, and is, in fact, founded on monotheistic beliefs.
Again, I think this is a particular American perspective. I would argue that liberal humanism has arisen from an existentialist philosophy, even though most people, who advocate and follow it, have probably never studied existential philosophy. There was a cultural revolution in Western societies in the generation following World War 2, and I was a part of it. Basically, we rejected the Christian institutions we were raised in, and embraced the existentialist paradigm that the individual was responsible for their own morality and their own destiny. No where was this more evident than in the rise of feminism, aided ineluctably by on-demand contraception.
So contrary to Harari’s argument, I think the humanist individualism that defines our age (in the West) was inextricably linked to the rejection of the Church. None of us knew what existentialism was, but, when I encountered it academically later in life, I recognised it as the symptomatic paradigm of my generation. We had become existentialists without being ideologically indoctrinated.
I feel Harari is on firmer ground when he discusses the relationship between the scientific revolution and European colonial expansion. I’ve argued previously, when discussing Jeremy Lent’s The Patterning Instinct, that Western European philosophy begat the scientific revolution because, under Galileo, Kepler and Newton, they discovered the relationship between mathematics and the movements of stellar objects – the music of the spheres, to paraphrase the ancient Greeks. The Platonic world of mathematics held the key to understanding the heavens. Subsequent centuries progressed this mathematical paradigm even further with the discovery of electromagnetic waves, then quantum mechanics and general relativity, leading to current theories of elementary nuclear particles and QED (quantum electrodynamics).
But Harari makes the case that exploration of foreign lands and peoples went hand-in-hand with scientific exploration of flora, fauna and archaeological digs. He argues that only Europeans acknowledged that we were ignorant of the wider world, which led to a desire for knowledge, rather than an acceptance that what our myths didn’t tell us was not worth knowing or exploring. Science had the same philosophy: that our ignorance would lead us to always search for new theories and new explanations, rather than accept the religious dogma that knowledge outside the Bible was not worthy of consideration.
So I would agree there was a synergy here, that was both destructive and empowering, depending on whether you were the European conqueror or the people being subjugated and ruthlessly exploited for the expansion of empire.
Probably the best part of the book is Harari’s description of capitalism and how it has shaped history in the last 400 years. He explains how and why it works, and why it’s been so successful. He also points out its flaws and its dark side. The book is worth reading for this section alone. He also explains how the free market, if left to its own devices, would lead to slavery. Instead, we have the exploitation of labour in third world countries, which is the next best thing, or the next worse thing, depending on your point of view.
This logically leads to a discussion on the consumerism paradigm that drives almost everything we do in modern society. Economic growth is totally dependent on it, but, ecologically, it’s a catastrophe in progress.
One of his more thought-provoking insights is in regard to how communal care-taking in law enforcement, health, education, even family dynamics, has been taken over by state bureaucracies. If one reads the neo-Confucian text, the I Ching, one finds constant analogies between family relationships and relationships in the Court (which means government officialdom). It should be pointed out that the I Ching predates Confucius, but contemporary texts (Richard Willem’s translation) have a strong Confucian flavour.
I can’t help but wonder if this facilitated China’s adoption of Communism almost as a state religion. Family relationships and loyalties still hold considerable sway in Asian politics and businesses. Nepotism is much more prevalent in Asian countries than in the West, I would suggest.
One of my bones of contention with Harari in Homo Deus was his ideas on happiness and how it’s basically a consequence of biochemistry. As someone who has lived for more than half a century in the modern post-war world, I feel I’m in a position to challenge his simplistic view that people’s ‘happiness setting’ doesn’t change as a consequence of external factors. To quote from Sapiens:
Buying cars and writing novels do not change our biochemistry. They can change it for a fleeting moment, but it is soon back to its set point.
Well, it works for me. Nothing has given me greater long term happiness than writing a novel and getting it into the public arena – the fact that it’s been a total financial failure is, quite frankly, irrelevant. I really can’t explain that, but it’s probably been the single most important, self-satisfying event of my life. I can die happy. Also I enjoy driving possibly more than any other activity, so owning a car means more to me than just having personal transport. I used to ride motorcycles, so maybe that explains it.
I grew up in a volatile household, which I’ve delineated elsewhere, and when I left home, the first 6 years were very depressing indeed. Over decades I turned all that around, so I think Harari’s ‘happiness setting’ is total bullshit.
But my biggest disagreement with Harari, which I alluded to before, is my advocacy for existentialist philosophy which he replaces with ‘the religion of liberal individualism’. Even though I can see similarities with Buddhism, I wouldn’t call existentialism a religion. Harari pre-empts this objection by claiming all ideologies, be they political or cultural, are no different to any religion. However, I have another objection of my own, which is that when Harari talks about religion, he is really talking about dogma.
In an issue of Philosophy Now (Issue 127, Aug/Sep 2018), Sandy Grant, who is a philosopher at University of Cambridge, defines dogma as an ‘appeal to authority without critical thinking’. I’ve previously defined philosophy as ‘argument augmented by analysis’, which is the antithesis of dogma. In fact, I would go so far as to say that philosophy has been historically an antidote to religion, going all the way back to Socrates.
Existentialism is a humanist philosophy (paraphrasing Sartre) but it requires self-examination and a fundamental honesty to oneself, which is the opposite of the narcissism implied in Harari’s religion of self-obsession, which he euphemistically calls ‘liberal individualism’.
Harari is cynical, if not dismissive, about the need for purpose in life, yet I would argue that it’s fundamental. I would recommend Viktor Frankl’s Man’s Search for Meaning. Frankl was a holocaust survivor and psychologist, who argued that we find meaning in relationships, projects and adversity. In fact, I would contend that the whole meaning of life is about dealing with adversity, which is why it is the theme of every work of fiction ever recorded.
If I go back to the title of this post, which I think is what Harari’s book is all about, there is a hierarchy of ‘needs’ (not Maslow’s) that a society must provide to ensure what Harari calls ‘happiness’, which is not so much economical as psychological. Back in July 2015, I wrote one of my 400 word mini-essays in response to a Question of the Month in Philosophy Now. The only relevant part is my conclusion, which effectively says that a functioning society is based on trust.
You can’t have truth without trust; you can’t have justice without truth; you can’t have freedom without justice; and you can’t have happiness without freedom.
I think that succinctly answers Harari’s thesis on happiness. Biochemistry may play a role, but people won’t find happiness if all those prerequisites aren’t met, unless, of course, said people are part of a dictatorship’s oligarchy.
A utopian society would allow everyone to achieve their potential – that’s the ideal. The most important consequence of an existentialist approach is that you don’t forfeit your aspirations for the sake of family or nation or church or some other abstract ideal that Harari calls religion.
While on this subject, I will quote from another contributor to Philosophy Now (Issue 110, Oct/Nov 2015), Simon Clarke, who is talking about John Stuart Mill, but who expresses my point of view better than I can.
An objectively good life, on Mill’s (Aristotelian) view, is one where a person has reached her potential, realizing the powers and abilities she possesses. According to Mill, the chief essential requirement for personal well-being is the development of individuality. By this he meant the development of a person’s unique powers, abilities, and talents, to their fullest potential.
He makes the point, which I’ve long known, that what separates us from all other species is that we have undertaken a cultural evolution that has long overtaken our biological evolution. This was accelerated by the invention of script, which allowed memories to be recorded and maintained over generations, some of which have lasted millennia. Of course, we already had this advantage even before we invented script, but script allowed an accumulation of knowledge that eventually led to the scientific revolution, which we’ve all benefited from since the enlightenment and has accelerated in the last 2 centuries particularly.
One of Harari’s recurring themes is that much of our lives are dependent on fictions and myths, and these have changed as part of our cultural evolution in a way that we don’t appreciate. Jeremy Lent makes similar observations in his excellent book, The Patterning Instinct, though he has a subtly different emphasis to Harari. Harari gives the impression that we are trapped in our social norms and gives examples to make his case. He points out that past societies were very hierarchical and everyone literally knew their place and lived within that paradigm. In fact, the consequences of trying to live outside one’s social constraints could be dire, even fatal. The current paradigm, at least in Western societies, is one of ‘individualism’, which he also explored in his follow-up book, with the warning that it could be eroded, if not eliminated, by the rise of AI, but I won’t discuss that here.
He effectively argues that these ‘fictions’, that we live by, rule out the commonly held belief that we can change our circumstances or that there is an objective morality that we can live by. In other words, he claims our lives are ruled by myths that we accept without question, and the only thing that changes are the myths themselves.
I take his point, but throughout history - at least from around 500BC - there have been iconoclasts who have challenged the reigning paradigm of their time. I will mention four: Socrates, Jesus, Buddha and Confucius. The curious point is that none of these wrote anything down (we only have their ‘sayings’) yet they are still iconic figures more than 2,000 years after their time. What they have in common is that they all challenged the prevailing ‘myth’ (to use Harari’s term) that there was a ‘natural order’ whereby those who ruled were ordained by gods, compared to those who served.
They all suffered for their subversions: Jesus and Socrates were executed, Confucius was exiled into poverty and the Buddha was threatened but not killed. Jesus challenged the church of his day, and that was the logical cause of his execution, not the blasphemy that he claimed to be ‘the son of god’. A lot of words were put in Jesus’ mouth, especially in the Bible. Jesus stood up for the disenfranchised and was critical of the church and the way it exploited the poor. He wouldn’t have been the only rabble-rouser of his time in Roman occupied Palestine but he was one of the most charismatic.
Buddha challenged the caste system in India as unjust, which made him logically critical of the religious-based norms of his time. He challenged the ‘myth’ that Harari claims everyone would have accepted without question.
Confucius was critical of appointments based on birth rather than merit and argued that good rulers truly served their people, rather than the other way round. Not surprisingly, his views didn’t go down very well with the autocracy of his time. He allegedly proposed the dictum of reciprocity: ‘Don’t do to others what you wouldn’t want done to yourself’. An aphorism also attributed to Jesus, which has more pertinence if one considers that it crosses class boundaries.
As for Socrates, I think he was the original existentialist in that he made a special plea to authenticity: ‘To live with honour in this world, actually be what you try to appear to be.’ Socrates got into trouble for supposedly poisoning the minds of the young, but what he really did was to make people challenge the pervading paradigm of his time, including the dominion of gods. He challenged people to think for themselves through argument, which is the essence of philosophy to this day.
To be fair to Harari, he gives specific attention to the feminist paradigm (my term, not his, as I don’t see it as a fiction or a myth). But I do agree that money, which determines so much in our societies, is based on a very convenient fiction and a great deal of trust. Actually, some level of trust is fundamental to a functioning society. In fact, I’ve argued elsewhere that, without trust: truth, justice and freedom all become forfeit.
The feminist paradigm is very recent, yet essential to our future. I recently saw an interview with Melinda Gates (currently in Australia) who made the salient point that it’s contraception that allows women to follow a destiny independent of men. Not surprisingly, it’s the ‘independent of men’ bit that has created, and continues to create, the greatest obstacle to their emancipation.
One of the more interesting discussions, I found, was Harari’s argument that political ideologies are really religions. I guess it depends on how you define religion. This is how Harari defines it, simultaneously giving a rationale to his thesis:
If religion is a system of human norms and values that is founded on belief in a superhuman order, then Soviet Communism was no less a religion than Islam.
I’m not convinced that political ideologies are dependent on a belief in a ‘superhuman order’, but they are premised on abstract ideas of uncontested ‘truth’, and, in that sense, they are like religions.
Contrary to what many people think, political thinking of ‘right’ and ‘left’ are largely determined by one’s genes, although environment also plays a role. Basically, personality traits like conscientiousness and goal-oriented leadership over people-based leadership are what are considered right-leaning traits; and agreeableness and openness (to new ideas) are considered left-leaning traits. Neuroticism would probably also be considered a left-leaning trait. Notice that all the left-leaning traits are predominant in artistic or creative people and this is generally reflected in their politics.
Curiously, twin studies have shown that a belief in God is also, at least partly, a genetically inherited trait. But I don’t believe there is any correlation between these two belief systems: God and politics. I know of people on the political right who are atheists and I know people on the political left who are theists.
I know that in America there seems to be a correlation between the political right and Christian fundamentalism, but I think that’s an Americanism. In Australia, it has little impact. We’ve very recently elected a Pentecostal as PM (Prime Minister) but I don’t believe that had any bearing on his election. We’ve had two atheist PMs in my lifetime (one of whom was very popular indeed), which would be unthinkable in America. The truth is that in some cultures religion is bound irretrievably with politics, and it can be hard for anyone who’s lived their entire lives in that culture to imagine there are political regimes where religion is a non-issue.
And this brings me to Harari’s next contentious point:
Even though liberal humanism sanctifies humans, it does not deny the existence of God, and is, in fact, founded on monotheistic beliefs.
Again, I think this is a particular American perspective. I would argue that liberal humanism has arisen from an existentialist philosophy, even though most people, who advocate and follow it, have probably never studied existential philosophy. There was a cultural revolution in Western societies in the generation following World War 2, and I was a part of it. Basically, we rejected the Christian institutions we were raised in, and embraced the existentialist paradigm that the individual was responsible for their own morality and their own destiny. No where was this more evident than in the rise of feminism, aided ineluctably by on-demand contraception.
So contrary to Harari’s argument, I think the humanist individualism that defines our age (in the West) was inextricably linked to the rejection of the Church. None of us knew what existentialism was, but, when I encountered it academically later in life, I recognised it as the symptomatic paradigm of my generation. We had become existentialists without being ideologically indoctrinated.
I feel Harari is on firmer ground when he discusses the relationship between the scientific revolution and European colonial expansion. I’ve argued previously, when discussing Jeremy Lent’s The Patterning Instinct, that Western European philosophy begat the scientific revolution because, under Galileo, Kepler and Newton, they discovered the relationship between mathematics and the movements of stellar objects – the music of the spheres, to paraphrase the ancient Greeks. The Platonic world of mathematics held the key to understanding the heavens. Subsequent centuries progressed this mathematical paradigm even further with the discovery of electromagnetic waves, then quantum mechanics and general relativity, leading to current theories of elementary nuclear particles and QED (quantum electrodynamics).
But Harari makes the case that exploration of foreign lands and peoples went hand-in-hand with scientific exploration of flora, fauna and archaeological digs. He argues that only Europeans acknowledged that we were ignorant of the wider world, which led to a desire for knowledge, rather than an acceptance that what our myths didn’t tell us was not worth knowing or exploring. Science had the same philosophy: that our ignorance would lead us to always search for new theories and new explanations, rather than accept the religious dogma that knowledge outside the Bible was not worthy of consideration.
So I would agree there was a synergy here, that was both destructive and empowering, depending on whether you were the European conqueror or the people being subjugated and ruthlessly exploited for the expansion of empire.
Probably the best part of the book is Harari’s description of capitalism and how it has shaped history in the last 400 years. He explains how and why it works, and why it’s been so successful. He also points out its flaws and its dark side. The book is worth reading for this section alone. He also explains how the free market, if left to its own devices, would lead to slavery. Instead, we have the exploitation of labour in third world countries, which is the next best thing, or the next worse thing, depending on your point of view.
This logically leads to a discussion on the consumerism paradigm that drives almost everything we do in modern society. Economic growth is totally dependent on it, but, ecologically, it’s a catastrophe in progress.
One of his more thought-provoking insights is in regard to how communal care-taking in law enforcement, health, education, even family dynamics, has been taken over by state bureaucracies. If one reads the neo-Confucian text, the I Ching, one finds constant analogies between family relationships and relationships in the Court (which means government officialdom). It should be pointed out that the I Ching predates Confucius, but contemporary texts (Richard Willem’s translation) have a strong Confucian flavour.
I can’t help but wonder if this facilitated China’s adoption of Communism almost as a state religion. Family relationships and loyalties still hold considerable sway in Asian politics and businesses. Nepotism is much more prevalent in Asian countries than in the West, I would suggest.
One of my bones of contention with Harari in Homo Deus was his ideas on happiness and how it’s basically a consequence of biochemistry. As someone who has lived for more than half a century in the modern post-war world, I feel I’m in a position to challenge his simplistic view that people’s ‘happiness setting’ doesn’t change as a consequence of external factors. To quote from Sapiens:
Buying cars and writing novels do not change our biochemistry. They can change it for a fleeting moment, but it is soon back to its set point.
Well, it works for me. Nothing has given me greater long term happiness than writing a novel and getting it into the public arena – the fact that it’s been a total financial failure is, quite frankly, irrelevant. I really can’t explain that, but it’s probably been the single most important, self-satisfying event of my life. I can die happy. Also I enjoy driving possibly more than any other activity, so owning a car means more to me than just having personal transport. I used to ride motorcycles, so maybe that explains it.
I grew up in a volatile household, which I’ve delineated elsewhere, and when I left home, the first 6 years were very depressing indeed. Over decades I turned all that around, so I think Harari’s ‘happiness setting’ is total bullshit.
But my biggest disagreement with Harari, which I alluded to before, is my advocacy for existentialist philosophy which he replaces with ‘the religion of liberal individualism’. Even though I can see similarities with Buddhism, I wouldn’t call existentialism a religion. Harari pre-empts this objection by claiming all ideologies, be they political or cultural, are no different to any religion. However, I have another objection of my own, which is that when Harari talks about religion, he is really talking about dogma.
In an issue of Philosophy Now (Issue 127, Aug/Sep 2018), Sandy Grant, who is a philosopher at University of Cambridge, defines dogma as an ‘appeal to authority without critical thinking’. I’ve previously defined philosophy as ‘argument augmented by analysis’, which is the antithesis of dogma. In fact, I would go so far as to say that philosophy has been historically an antidote to religion, going all the way back to Socrates.
Existentialism is a humanist philosophy (paraphrasing Sartre) but it requires self-examination and a fundamental honesty to oneself, which is the opposite of the narcissism implied in Harari’s religion of self-obsession, which he euphemistically calls ‘liberal individualism’.
Harari is cynical, if not dismissive, about the need for purpose in life, yet I would argue that it’s fundamental. I would recommend Viktor Frankl’s Man’s Search for Meaning. Frankl was a holocaust survivor and psychologist, who argued that we find meaning in relationships, projects and adversity. In fact, I would contend that the whole meaning of life is about dealing with adversity, which is why it is the theme of every work of fiction ever recorded.
If I go back to the title of this post, which I think is what Harari’s book is all about, there is a hierarchy of ‘needs’ (not Maslow’s) that a society must provide to ensure what Harari calls ‘happiness’, which is not so much economical as psychological. Back in July 2015, I wrote one of my 400 word mini-essays in response to a Question of the Month in Philosophy Now. The only relevant part is my conclusion, which effectively says that a functioning society is based on trust.
You can’t have truth without trust; you can’t have justice without truth; you can’t have freedom without justice; and you can’t have happiness without freedom.
I think that succinctly answers Harari’s thesis on happiness. Biochemistry may play a role, but people won’t find happiness if all those prerequisites aren’t met, unless, of course, said people are part of a dictatorship’s oligarchy.
A utopian society would allow everyone to achieve their potential – that’s the ideal. The most important consequence of an existentialist approach is that you don’t forfeit your aspirations for the sake of family or nation or church or some other abstract ideal that Harari calls religion.
While on this subject, I will quote from another contributor to Philosophy Now (Issue 110, Oct/Nov 2015), Simon Clarke, who is talking about John Stuart Mill, but who expresses my point of view better than I can.
An objectively good life, on Mill’s (Aristotelian) view, is one where a person has reached her potential, realizing the powers and abilities she possesses. According to Mill, the chief essential requirement for personal well-being is the development of individuality. By this he meant the development of a person’s unique powers, abilities, and talents, to their fullest potential.
Thursday, 9 May 2019
The Universe's natural units
It’s well known that Einstein’s general theory of relativity and quantum mechanics (QM) are incompatible. Actually, Viktor T. Toth (IT pro and part-time physicist) claims ‘incompatible’ is a misnomer, in as much as:
We can do quantum field theory just fine on the curved spacetime background of general relativity.
Then he adds this caveat:
What we have so far been unable to do in a convincing manner is turn gravity itself into a quantum field theory.
These carefully selected quotes are from a recent post by Toth on Quora where he is a regular contributor. His area of expertise is in cosmology, including the study of black holes. On another post he explains how the 2 theories are mathematically ‘incompatible’ (my term, not his):
The equation is Einstein’s field equation for gravitation, the equation that is, in many ways, the embodiment of general relativity:
Rμν−12Rgμν=8Ï€GTμν.
The left-hand side of this equation represents a quantity formed from the spacetime metric, which determines the “deformation of spacetime”. The right-hand side of this equation is a quantity that is formed from the energy, momentum, angular momentum and internal stresses and pressure of matter.
He then goes on to explain that, while the RHS of the equation can be reformulated in QM nomenclature, the LHS can’t. There is a way out of this, which is to ‘average’ the QM side of the equation to get it into units compatible with the classical side, and this is called ‘semi-classical gravity’. But, again, in his own words:
…it is hideously inelegant, essentially an ad-hoc averaging of the equation that is really, really ugly and is not derived from any basic principle that we know.
Anyway, the point of this mini-exposition is that there is a mathematical conflict, if not an incompatibility, inherent in Einstein’s equation itself. One side of the equation can be expressed quantum mechanically and the other side can’t. What’s more, the resolution is to ‘bastardise’ the QM side to make it compatible with the classical side.
You may be wondering what all this has to do with the title of this post. The fundamental constant at the heart of general relativity is, of course, G, the same constant that Newton used in his famous formula:
On the other hand, the fundamental constant used in QM is Planck’s constant, h, most famously used by Einstein to explain the photo-electric effect. It was this paper (not his paper on relativity) that garnered Einstein his Nobel prize. It’s best known by Planck’s equation:
E = hf
Where E is energy and f is the frequency of the photon. You may or may not know that Planck determined h empirically by studying hot body radiation, where he used it to resolve a particularly difficult thermodynamics problem. From Planck’s perspective, h was a mathematical invention and had no bearing on reality.
G was also determined empirically, by Cavendish in 1798 (well after Newton) and, of course, is used to mathematically track the course of the planets and the stars. There is no obvious or logical connection between these 2 constants based on their empirical origins.
There is a third constant I will bring into this discussion, which is c, the constant speed of light, which also involves Einstein, via his famous equation:
E = mc2
Now, having set the stage, I will invoke the subject of this post. If one uses Planck units, also known as ‘natural units’, one can see how these 3 constants are interrelated.
I will introduce another Quora contributor, Jeremiah Johnson (a self-described ‘physics theorist’) to explain:
The way we can arrive at these units of Planck Length and Planck Time is through the mathematical application of non-dimensionalization. What this does is take known constants and find what value each fundamental unit should be set to so they all equal one. (See below.)
Toth (whom I referenced earlier) makes the salient point that many people believe that the Planck units represent the physical smallest component of spacetime, and are therefore evidence, if not proof, that the Universe is inherently granular. But, as Toth points out, spacetime could still be continuous (or non-discrete) and the Planck units represent the limits of what we can know rather than the limits of what exists. I’ve written about the issue of ‘discreteness’ of the Universe before and concluded that it’s not (which, of course, doesn’t mean I’m right).
Planck units in ‘free space’ are the Universe’s ‘natural units’. They are literally the smallest units we can theoretically measure, therefore lending themselves to being the metrics of the Universe.
The Planck length is
1â„“P=1.61622837∗10−35m
And Planck time is
1tP=5.3911613∗10−44s
If you divide one by the other you get:
1â„“P/1tP=299,792,458m/s
Which of course, is the speed of light. As Johnson quips: “Isn’t that cool?”
Now, Max Planck derived these ‘natural units’ himself by looking at 5 equations and adjusting the scale of the units so as they would not only be consistent across the equations, but would non-dimensionalise the constants so they all equal 1 (as Johnson described above).
In fact, the definition of the Plank units (except charge) includes both G andh (which is h/2Ï€). I checked the relationship between h and G, by calculating G from h, knowing the Planck units for length and time. In effect, I reverse-engineered the calculation, having to find the Planck mass from h then putting it into the formula for G.
The point is that I was able to derive G from h using Planck units. The Universe lends itself to portraying a consistency across metrics and natural phenomena based on units derived from constants that represent the extremes of scale, h and G. The constant, c, is also part of the derivation, and is essential to the dimension of time. It’s not such a mystery when one realises that the ‘units’ are derived from empirically determined constants
We can do quantum field theory just fine on the curved spacetime background of general relativity.
Then he adds this caveat:
What we have so far been unable to do in a convincing manner is turn gravity itself into a quantum field theory.
These carefully selected quotes are from a recent post by Toth on Quora where he is a regular contributor. His area of expertise is in cosmology, including the study of black holes. On another post he explains how the 2 theories are mathematically ‘incompatible’ (my term, not his):
The equation is Einstein’s field equation for gravitation, the equation that is, in many ways, the embodiment of general relativity:
Rμν−12Rgμν=8Ï€GTμν.
The left-hand side of this equation represents a quantity formed from the spacetime metric, which determines the “deformation of spacetime”. The right-hand side of this equation is a quantity that is formed from the energy, momentum, angular momentum and internal stresses and pressure of matter.
He then goes on to explain that, while the RHS of the equation can be reformulated in QM nomenclature, the LHS can’t. There is a way out of this, which is to ‘average’ the QM side of the equation to get it into units compatible with the classical side, and this is called ‘semi-classical gravity’. But, again, in his own words:
…it is hideously inelegant, essentially an ad-hoc averaging of the equation that is really, really ugly and is not derived from any basic principle that we know.
Anyway, the point of this mini-exposition is that there is a mathematical conflict, if not an incompatibility, inherent in Einstein’s equation itself. One side of the equation can be expressed quantum mechanically and the other side can’t. What’s more, the resolution is to ‘bastardise’ the QM side to make it compatible with the classical side.
You may be wondering what all this has to do with the title of this post. The fundamental constant at the heart of general relativity is, of course, G, the same constant that Newton used in his famous formula:
On the other hand, the fundamental constant used in QM is Planck’s constant, h, most famously used by Einstein to explain the photo-electric effect. It was this paper (not his paper on relativity) that garnered Einstein his Nobel prize. It’s best known by Planck’s equation:
E = hf
Where E is energy and f is the frequency of the photon. You may or may not know that Planck determined h empirically by studying hot body radiation, where he used it to resolve a particularly difficult thermodynamics problem. From Planck’s perspective, h was a mathematical invention and had no bearing on reality.
G was also determined empirically, by Cavendish in 1798 (well after Newton) and, of course, is used to mathematically track the course of the planets and the stars. There is no obvious or logical connection between these 2 constants based on their empirical origins.
There is a third constant I will bring into this discussion, which is c, the constant speed of light, which also involves Einstein, via his famous equation:
E = mc2
Now, having set the stage, I will invoke the subject of this post. If one uses Planck units, also known as ‘natural units’, one can see how these 3 constants are interrelated.
I will introduce another Quora contributor, Jeremiah Johnson (a self-described ‘physics theorist’) to explain:
The way we can arrive at these units of Planck Length and Planck Time is through the mathematical application of non-dimensionalization. What this does is take known constants and find what value each fundamental unit should be set to so they all equal one. (See below.)
Toth (whom I referenced earlier) makes the salient point that many people believe that the Planck units represent the physical smallest component of spacetime, and are therefore evidence, if not proof, that the Universe is inherently granular. But, as Toth points out, spacetime could still be continuous (or non-discrete) and the Planck units represent the limits of what we can know rather than the limits of what exists. I’ve written about the issue of ‘discreteness’ of the Universe before and concluded that it’s not (which, of course, doesn’t mean I’m right).
Planck units in ‘free space’ are the Universe’s ‘natural units’. They are literally the smallest units we can theoretically measure, therefore lending themselves to being the metrics of the Universe.
The Planck length is
1â„“P=1.61622837∗10−35m
And Planck time is
1tP=5.3911613∗10−44s
If you divide one by the other you get:
1â„“P/1tP=299,792,458m/s
Which of course, is the speed of light. As Johnson quips: “Isn’t that cool?”
Now, Max Planck derived these ‘natural units’ himself by looking at 5 equations and adjusting the scale of the units so as they would not only be consistent across the equations, but would non-dimensionalise the constants so they all equal 1 (as Johnson described above).
In fact, the definition of the Plank units (except charge) includes both G and
The point is that I was able to derive G from h using Planck units. The Universe lends itself to portraying a consistency across metrics and natural phenomena based on units derived from constants that represent the extremes of scale, h and G. The constant, c, is also part of the derivation, and is essential to the dimension of time. It’s not such a mystery when one realises that the ‘units’ are derived from empirically determined constants
Addendum: For a comprehensive, yet easy-to-read, historical account, I’d recommend John D. Barrow’s book, The Constants of Nature; From Alpha to Omega.
Addendum (13 April 2023): According to Toth, the Planck units don't provide a limit on anything:
...the Planck scale is not an inherent limit of anything. It is simply the set of “natural” units that characterize Nature.
So the Planck scale is not a physical limit or a limit on what can be observed; rather, it’s a limitation of the theory that we use to describe the quantum world.
Read his erudite exposition on the subject here:
https://www.quora.com/Why-is-the-Planck-length-the-smallest-measurable-length-Why-cant-it-be-smaller/answer/Viktor-T-Toth-1
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