How can I know when I am wrong?

 Simple answer: I can’t. But this goes to the heart of a dilemma that seems to plague the modern world. It’s even been given a name: the post-truth world.  

I’ve just read a book, The Psychology of Stupidity; explained by some of the world’s smartest people, which is a collection of essays by philosophers, psychologists and writers, edited by Jean-Francois Marmion. It was originally French, so translated into English; therefore, most of the contributors are French, but some are American. 

 

I grew up constantly being reminded of how stupid I was, so, logically, I withdrew into an inner world, often fuelled by comic-book fiction. I also took refuge in books, which turned me into a know-it-all; a habit I’ve continued to this day.

 

Philosophy is supposed to be about critical thinking, and I’ve argued elsewhere that critical analysis is what separates philosophy from dogma, but accusing people of not thinking critically does not make them wiser. You can’t convince someone that you’re right and they’re wrong: the very best you can do is make them think outside their own box. And, be aware, that that’s exactly what they’re simultaneously trying to do to you.

 

Where to start? I’m going to start with personal experience – specifically, preparing arguments (called evidence) for lawyers in contractual engineering disputes, in which I’ve had more than a little experience. Basically, I’ve either prepared a claim or defended a claim by analysing data in the form of records – diaries, minutes, photographs – and reached a conclusion that had a trail of logic and evidence to substantiate it. But here’s the thing: I always took the attitude that I’d come up with the same conclusion no matter which side I was on.

 

You’re not supposed to do that, but it has advantages. The client, whom I’m representing, knows I won’t bullshit them and I won’t prepare a case that I know is flawed. And, in some cases, I’ve even won the respect of the opposing side. But you probably won’t be surprised to learn how much pressure you can be put under to present a case based on falsehoods. In the end, it will bite you.

 

The other aspect to all this is that people can get very emotional, and when they get emotional they get irrational. Writing is an art I do well, and when it comes to preparing evidence, my prose is very dispassionate, laying out an argument based on dated documents; better still, if the documents belong to the opposition.

 

But this is doing analysis on mutually recognised data, even if different sides come to different conclusions. And in a legal hearing or mediation, it’s the documentation that wins the argument, not emotive rhetoric. Most debates these days take place on social media platforms where people on opposing sides have their own sources and their own facts and we both accuse each other of being brainwashed. 

 

And this leads me to the first lesson I’ve learned about the post-truth world. In an ingroup-outgroup environment – like politics – even the most intelligent people can become highly irrational. We see everyone on one side as being righteous and worthy of respect, while everyone on the other side is untrustworthy and deceitful. Many people know about the infamous Robbers Cave experiment in 1954, where 2 groups of teenage boys were manipulated into an ingroup-outgroup situation where tensions quickly escalated, though not violently. I’ve observed this in contractual situations many times over.

 

One of my own personal philosophical principles is that beliefs should be dependent on what you know and not the other way round. It seems to me that we do the opposite: we form a belief and then actively look for evidence that turns that belief into knowledge. And, in the current internet age, it’s possible to find evidence for any belief at all, like the Earth being flat.

 

And this has led to a world of alternate universes, where the exact opposite histories are being played out. The best known example is climate change, but there are others. Most recently, we’ve had a disputed presidential election in the USA and the efficaciousness of vaccines in combatting the coronavirus (SARS-Cov-2 or COVD-19). What all these have in common is that each side believes the other side has been duped.

 

You might think that something else these 3 specific examples have in common is left-wing, right-wing politics. But I’ve learned that’s not always the case. One thing I do believe they have in common is open disagreement between purported experts in combination with alleged conspiracy theories. It so happens that I’ve worked with technical experts for most of my working life, plus I read a lot of books and articles by people in scientific disciplines. 

 

I’m well aware that there are a number of people who have expertise that I don’t have and I admit to getting more than a little annoyed with politicians who criticise or dismiss people who obviously have much more expertise than they have in specific fields, like climatology or epidemiology. One only has to look to the US, where the previous POTUS, Donald Trump, was at the centre of all of these issues, where everything he disagreed with was called a ‘hoax’, and who was a serial promoter of conspiracy theories, including election fraud. Trump is responsible for one of those alternative universes where President Elect, Joe Biden, stole the election from him, even though there is ample testimony that Trump tried to steal the election from Biden.

 

So, in the end, it comes down to who do you trust. And you probably trust someone who aligns with your ideological position or who reinforces your beliefs. Of course, I also have political views and my own array of beliefs. So how do I navigate my way?

 

Firstly, I have a healthy scepticism about conspiracy theories, because they require a level of global collaboration that’s hard to maintain in the manner they are reported. They often read or sound like movie scripts, with politicians being blackmailed or having their lives threatened and health professionals involved in a global conspiracy to help an already highly successful leader in the corporate world take control of all of our lives. This came from a so-called ‘whistleblower’, previously associated with WHO.

 

The more emotive and sensationalist a point of view, the more traction it has. Media outlets have always known this, and now it’s exploited on social media, where rules about accountability and credibility are a lot less rigorous.

 

Secondly, there are certain trigger words that warn me that someone is talking bullshit. Like calling vaccines a ‘bio-weapon’ or that it’s the ‘death-jab’ (from different sources). However, I trust people who have a long history of credibility in their field; who have made it their life’s work, in fact. But we live in a world where they can be ridiculed by politicians, whom we are supposed to respect and follow.

 

At the end of the day, I go back to the same criteria I used in preparing arguments involved in contractual disputes, which is evidence. We’ve been living with COVID for 2 years now and it is easy to find statistical data tracking the disease in a variety of countries and the effect the vaccines have had. Of course, the conspiracy theorists will tell you that the data is fabricated. The same goes for evidence involving climate change. There was a famous encounter between physicist and television presenter, Brian Cox, and a little known Australian politician who claimed that the graphs Cox presented, produced by NASA, had been corrupted.

 

But, in both of these cases, the proof is in the eating of the pudding. I live in a country where we followed the medical advice, underwent lockdowns and got vaccinated, and we’re now effectively living with the virus. When I look overseas, at countries like America, it was a disaster overseen by an incompetent President, who advocated all sorts of ‘crank cures’, the most notorious being bleach, not to mention UV light. At one point, the US accounted for more than 20% of the world’s recorded deaths.

 

And it’s the same with climate change where, again, the country I live in faced record fires in 2019/20 and now floods, though this is happening all over the globe. The evidence is in our face, but people are still in denial. It takes a lot of cognitive dissonance to admit when we’re wrong, and that’s part of the problem.

 

Philosophy teaches you that you can have a range of views on a specific topic, and as I keep saying: only future generations know how ignorant the current generation is. That includes me, of course. I write a blog, which hopefully outlives me and one day people should be able to tell where I was wrong. I’m quite happy for that, because that’s how knowledge grows and progresses.

Beliefs, prejudices and theories; where is truth?

 During COVID, New Scientist started doing a lot of online events, including courses and ‘talks’ by experts in various fields. I watched one of these talks last week by Claudia De Rahm titled What We Don’t Know About Gravity, which I thought was very good. It was informative and thought-provoking and therefore deserves special mention. Claudia is a young woman, Professor of Physics at Imperial College London, with a distinct Italian accent. She gestures a lot while she’s talking and exudes passion. Sometimes her face appeared childlike, especially at the end when she conveyed her appreciation to the presenter, Martin Davies. She’s won a number of awards and she’s done research in particle physics, gravity and cosmology.

 

One of the first things she told us is that Einstein’s GR (general theory of relativity) comes with its own ‘proof’ of its limitations. She didn’t use the word proof, but she demonstrated what she meant. If one tries to apply QM to Einstein’s mathematical theory you get probabilities of over 100%. I never knew this, but I found it a remarkable revelation. From what I could gather, it happens near the Planck scale where the curvature of spacetime becomes so large the physics breaks down. She pointed out that this doesn’t occur near the event horizon of a black hole, so for everything we can observe, GR is perfectly valid. But I was astounded to learn that GR predicts its own failure at certain scales of the Universe.

 

She also questioned whether GR breaks down at the other extreme of scale, given that there is disagreement on how fast the Universe is expanding to a significant degree (in her own words, ‘the chance of it being a fluke is 1 part in 14,000’). Of course, she also explained how 95% of the Universe is ‘missing’, meaning it can’t be accounted for. Personally, I think we’re ripe for another scientific revolution comparable to the one that occurred 100 years ago, which in turn was comparable to the one created by Copernicus, Galileo, Kepler and Newton.

 

This highlights a point I’ve raised before: the significance of scale in determining which ‘natural laws’ dominate, though they all seem to obey a Lagrangian (based on my limited knowledge of physics). Roger Penrose argues that scale is dependent on mass. If the Universe was all radiation then scale becomes irrelevant. This is essential for his CCC (Conformal Cyclic Cosmology) model of the Universe to work. Penrose also argues that there is no time without mass, because time is always zero for a photon. This creates a paradox, because the photon has an energy dependent on its frequency, which has no meaning without time. I’ve no doubt Penrose can resolve that, but I don’t know how. Perhaps gravity resolves that conundrum. But, as the Universe exists in its current epoch within our range of observations, scale plays a significant, even critical role in determining which mathematical formulations we use to model it.

 

Claudia tip-toed around the argument about whether gravity is a force or not, but gave me the impression she believes it isn’t. She did point out that a gravitational wave effectively creates a force and there are tidal forces, but this is not what people mean when they argue that there is a ‘force of gravity’ in the Newtonian sense. In answer to a question at the end, she pointed out that “gravity is related to the very structure of spacetime; you can never switch it off”.

 

On the subject of GR’s inherent limitations around a singularity inside a black hole, she seemed optimistic that new physics would overcome this eventually. Along with the questions around dark energy and dark matter, that comprise 70% and 25% of the Universe respectively, I think that only a revolution in physics and cosmology will rescue it. Towards the end of the talk, she put up a slide showing all the current theories in the running, without discussing any of them or mentioning any personal favourites she might have. She literally covered the screen with balloons of speculative ideas, demonstrating the burgeoning interest in this field.

 

And this segues into something else she said in answer to a question, where someone asked if all the current theories should be ‘thrown in the rubbish bin’ and replaced with something completely different. She pointed out that the current theories work extremely well, and whatever you replace them with has to, at the very least, account for what we already ‘know’, and you can’t just ‘throw them in the rubbish bin’. This touches on the subject of my last post where people sometimes argue that we really don’t ‘know’ anything and we only have 'beliefs'. In science, all theories have limitations. Truth is cumulative in science; just because we don’t know everything, it doesn’t mean that what we do know is wrong and should be thrown out. Personally, I don’t think there will ever be a TOE (theory of everything) simply because there’s never been one in the past, and people have always ‘believed’ that we know almost everything, which history has proved, repeatedly, is untrue.

 

And this brings me to the subject of pet theories or pet prejudices. If Claudia has her own pet theories she didn’t elaborate, yet I’m sure she has. People much smarter than me have their pet prejudices, some of which differ dramatically, so they can’t all be right, and that also applies to me. But, having said that, I like to think my prejudices are well informed and I acknowledge those who share them, and sometimes those who don’t.

 

I will quickly talk about one that is relevant and that is time. I contend that consciousness exists in a constant present, while everything we observe has already happened, which is why we ‘feel’ like we’re travelling through time. According to relativity theory, we are travelling through time just by standing still. But when we move, we start travelling through space and, as a consequence, we travel through time more slowly – that is, time slows down. In fact, if we could travel through space at the speed of light, we would stop travelling through time altogether. But here’s the thing: that’s only true in our specific frame of reference. There could be another frame of reference, like the horizon of the observable universe where space itself travels at the speed of light. I discussed this in another post.

 

This infers that everything travels through time and not just consciousness. However, while our consciousness remains in a constant present, our thoughts don’t. Our thoughts become memories as soon as we think them, otherwise we wouldn’t even know we think. Consciousness exists on the edge of time and so does the universe itself. I’ve no reason to believe that the edge of time we all experience isn’t concordant with the edge of time for the whole Cosmos. This is considered naive thinking, but it’s one of my pet prejudices.

Symptoms of living in a post-truth world

 I recently had 2 arguments with different people, who took extreme positions on what we mean by truth. One argued that there is no difference between mathematical truths and truths in fiction – in fact, he described mathematics, that is not being ‘applied’, as ‘mathematical fiction’. The other argued that there is no objective truth and everything we claim to know are only ‘beliefs’, including mathematics. When I told her that I know there will always be mathematics that remain unknown, she responded that I ‘believe I know’. I thought that was an oxymoron, but I let it go. The trivial example, that there are an infinite number of primes or an infinite number of digits in pi, should put that to rest, or so one would think. 

Norman Wildberger, whom I’ve cited before, says that he doesn’t ‘believe’ in Real numbers, and neither does he believe in infinity, and he provides compelling arguments. But I feel that he’s redefining what we mean by mathematics, because his sole criterion is that it can be computed. Meanwhile, we have a theorem by Gregory Chaitin who contends that there are infinitely more incomputable Real numbers than computable Real numbers. People will say that mathematics is an abstract product of the mind, so who cares. But, as Paul Davies says, ‘mathematics works’, and it works so well that we can comprehend the Universe from the cosmic scale to the infinitesimal. 

 

Both of my interlocutors, I should point out, were highly intelligent, well-educated and very articulate, and I believe that they really believed in what they were saying. But, if there is no objective truth, then there are no 'true or false' questions that can be answered. To take the example I’ve already mentioned, it’s either true or false that we can’t know everything in mathematics. And if it’s false, then we must know everything. But my interlocutor would say that I claimed we’d never know and I can’t say I know that for sure. 

 

Well, putting aside the trivial example of infinity, there are proofs based on logic that says it’s true and that’s good enough for me. She claimed that logic can be wrong if the inputs are wrong, which is correct. In mathematics, this is dependent on axioms, and mathematics like all other sciences never stands still, so we keep getting new axioms. But it’s the nature of science that it builds on what went before, and, if it’s all ‘belief’, then it’s a house built on sand. And if it's a house built on sand, then all the electronic gadgets we use and the satellite systems we depend on could all crash without warning, but no one really believes that.

 

So that’s one side of the debate and the other side is that truths in art have the same status as truths in science. There are a couple of arguments one can use to counter this, the most obvious being that a work of art, like Beethoven’s 5^th, is unique – no one else created that. But Pythagoras’s theorem could have been discovered by anyone, and in fact, it was discovered by the Chinese some 500 years before Pythagoras. I write fiction, and while I borrow tropes and themes and even plot devices from others, I contend that my stories are unique and so are the characters I create. In fact, my stories are so unique, that they don’t even resemble each other, as at least one reader has told me.

 

But there is another argument and that involves memes, which are cultural ideas, for want of a better definition, that persist and propagate. Now, some argue that virtually everything is a meme, including scientific theories and mathematical theorems. But there is a difference. Cultural memes are successful because they outlive their counterparts, but scientific theories and mathematical theorems outlive their counterparts because they are successful. And that’s a fundamental distinction between truth in mathematics and science, and truth in art.

Addendum: I just came across this video (only posted yesterday) and it’s very apposite to this post. It’s about something called Zero Knowledge Proof, and it effectively proves if someone is lying or not. It’s relevance to my essay is that it applies to true or false questions. You can tell if someone is telling the truth without actually knowing what that truth is. Apparently, it’s used algorithmically as part of blockchain for bitcoin transactions.

 

To give the example that Jade provides in her video, if someone claims that they have a proof of Riemann’s hypothesis, you can tell if they’re lying or not without them having to reveal the actual proof. That’s a very powerful tool, and, as a consequence, it virtually guarantees that a mathematical truth exists for a true or false proposition; in this hypothetical case, Riemann’s hypothesis, because it’s either true or false by definition.

Our eternal fascination with Light and Dark

 Someone on FaceBook posted one of those inane questions: If you could delete one thing in the world what would it be? Obvious answers included war, hate, evil, and the like; so negative emotive states and consequences. My answer was, ‘Be careful what you wish for’.

What I find interesting about this whole issue is the vicarious relationship we have with the ‘dark side’ through the lens of fiction. If one thinks about it, it starts early with fairy tales and Bible stories. Nightmares are common in our childhood where one wakes up and is too scared to go back to sleep. Fear is an emotion we become familiar with early in our lives; I doubt that I was an exception, but it seems to me that everyone tries to keep children innocent these days. I don’t have children, so I might have it wrong.

 

Light and dark exists in the real world, but we try to keep it to the world of fiction – it’s a universal theme found in operas, mythologies and TV serials. I write fiction and I’m no exception. If there was no dark in my stories, they’d have no appeal. You have to have nemeses, figures of various shades of grey to juxtapose the figures of light, even if the light shines through flawed, imperfect glass.

 

In life we are tested, and we judge ourselves accordingly. Sometimes we pass and sometimes we fail. The same thing happens with characters in fiction. When we read a story we become actors, which makes us wonder how we’d behave in the same situation. I contend that the same thing happens in dreams. As an adult, I’ve always seen dreams as what-if scenarios and it’s the same with stories. I’ve long argued that the language of stories is the language of dreams and I think the connection is even stronger than that. I’m not surprised that storytellers will tell you that they dream a lot.

 

In the Judaeo-Christian religion I grew up with, good and evil were stark contrasts, like black and white. You have God, Christ and Satan. When I got older, I thought it a bit perverse that one feared God as much as Satan, which led me to the conclusion that they weren’t really that different. It’s Christ who is the good guy, willing to forgive the people who hate him and want him dead. I’m talking about them as fictional characters, not real people. I’m sure Jesus was a real person but we only have the myth by which to judge him.

 

The only reason I bring all this up, is because they were the template we were given. But fearing someone you are meant to love leads to neurosis, as I learned the hard way. A lot of people of my generation brought up the next generation as atheists, which is not surprising. The idea of a judgemental, schizophrenic father was past its use-by-date.

 

There is currently a conflict in Ukraine, which has grabbed the world’s attention in a way that other wars have not. It’s partly because of our Euro-centric perspective, and the fact that the 2 biggest and world-changing conflicts of the 20^th Century both started in Europe. And the second one, in particular, has similarities, given it started with a dictator invading a neighbour, when he thought the world would look the other way.

 

There is a fundamental flaw in the human psyche that we’ve seen repeated throughout history. We have a tendency to follow charismatic narcissistic leaders, when you think we should know better. They create an army (not necessarily military) of supporters, but for whom they have utter contempt. This was true of Hitler, but also true of Trump and Putin.

 

Ukraine’s leader, Volodymyr Zelenskyy, like Trump, became a TV celebrity, but in a different vein. He was a satirical comedian who sent up the country’s leader, who was a Russian stooge, and then ran for office where he won by 70%. I believe this is the real reason that Putin wants to bring him down. If he’d done the same thing in Russia, he would have been assassinated while still a TV personality. It’s well known that Putin has attempted to assassinate him at least twice since the invasion, but assassinating opponents in a foreign country is a Putin specialty.

 

Zelenskyy and Putin represent, in many Western people’s minds, a modern day parable of good and evil. And, to me, the difference is stark. Putin, like all narcissists, only cares about himself, not the generals that have died in his war, not the barely out of school conscripts he’s sent into battle and certainly not the Russian people who will suffer enormous deprivations if this continues for any length of time. On the other hand, Zelenskyy doesn’t care about his self-preservation, because he would rather die for a principle than live the rest of his life in shame for deserting his country when it needed him most. Zelenskyy is like the fictional hero we believe in but know we couldn’t emulate.

 

It's when we read or watch fiction that the difference between right and wrong seems obvious. We often find ourselves telling a character, ‘don’t do that, don’t make that decision’, because we can see the consequences, but, in real life, we often seem to lose that compass.

 

My father was in a war and I know from what he told me that he didn’t lose that particular compass, but I also know that he once threatened to kill someone who was stealing from the wounded he was caring for. And I’ve no doubt he would have acted on it. So his compass got a bit bent, because he’d already seen enough killing to last several lifetimes.

 

I’ve noticed a theme in my own writing, which is subconscious, not intentional, and that is my protagonists invariably have their loyalty tested and it ends up defining them. My villains are mostly self-serving autocrats who have a hierarchical view of humanity where they logically belong at the top.

 

This is a meandering post, with no conclusion. We each of us have ambitions and desires and flaws. Few of us are ever really tested, so we make assumptions based on what we like to believe. I like something that Socrates said, who’d also been in battle.

 

To live with honour in this world, actually be what you try to appear to be.

What is existentialism?

 A few years back, I wrote a ‘vanity piece’, My philosophy in 24 dot points, which I admit is a touch pretentious. But I’ve been prompted to write something more substantive, in a similar vein, whilst reading Gary Cox’s How to Be an Existentialist; or How to Get Real, Get a Grip and Stop Making Excuses. I bought this tome (the 10^thAnniversary Edition) after reading an article by him on ‘Happiness’ in Philosophy Now (Issue 147, Dec 2021/Jan 2022). Cox is an Honorary Research Fellow at the University of Birmingham, UK. He’s written other books, but this one is written specifically for a general audience, not an academic one. This is revealed in some of the language he uses, like ‘being up shit creek’.

 

I didn’t really learn anything about existentialism until I studied Sartre in an off-campus university course, in my late 40s. I realised that, to all intents and purposes, I was an existentialist, without ever knowing what one was. I did write about existentialism very early in the life of this blog, in the context of my own background. The thing is that one’s philosophical worldview is a product of one’s milieu, upbringing and education, not to mention the age in which one lives. I grew up in a Western culture, post WW2, and I think that made me ripe for existentialist influences without being conscious of it. I lived in the 60s when there was a worldwide zeitgeist of questioning social mores against a background of a religious divide, the Vietnam war and the rise of feminism. 

 

If there is a key word or mantra in existentialism, it’s ‘authenticity’. It’s the key element in my 3 Rules for Humans post, and it’s also the penultimate chapter in Cox’s aforementioned book. The last chapter is on counselling and is like a bookend.

 

As Cox himself points out, existentialism is not a ‘school’ of philosophy in the way ‘analytical philosophy’ or ‘logical positivism’ are. There’s not really a set of rules – it’s more about an attitude and how to live a life without losing your soul or self-respect. It’s not an epistemology, nor an ideology, even though it’s probably associated with a liberal outlook, as I hope will become clear.

 

Many commentators associate existentialism with atheism, the absurd and nihilism. I agree with Cox that it’s actually the opposite of nihilism; if anything, it’s about finding purpose. As I wrote in a post last year:

 

If the Universe has any meaning at all, it’s because it created sentient beings who find meaning against the odds that science tells us are astronomical, both literally and figuratively. Existentialism is about finding purpose in an absurd universe, which is the opposite of nihilism.

 

And that’s the most important lesson of existentialism: if you are to find a purpose, only you can do that; it’s not dependent on anyone else, be they family, a spouse, an employer or a mentor. And logically, one could add, it’s not dependent on God either.

 

Cox doesn’t talk about God at all, but he does talk quite a lot about consciousness and about it being ‘nothing’ (materialistically). He very fleetingly gives mathematics as an example of something else that’s not ‘corporeal’, specifically numbers. Very curious, as I think that both mathematics and consciousness are ‘special’ in that they are distinct, yet intimately connected to the physical world, but that’s another topic.

 

He also talks about consciousness having a special relationship with time. I’ve said that consciousness is the only thing that exists in a constant present, whereas Cox says the opposite, but I believe we mean the same thing. He says consciousness is forever travelling from the past to the future, whereas I say that the future is forever becoming the past while only consciousness exists in the present – the experiential outcome is the same.

 

So how does God enter the picture? God only exists in someone’s consciousness – it’s part of one’s internal state. So, you can be ‘authentic’ and believe in God, but it’s totally an individualistic experience – it can’t be shared. That’s my interpretation, not anyone else’s, I should emphasise.

 

An important, even essential, aspect of all this is a belief in free will. You can’t take control of your life if you don’t have a belief in free will, and I would argue that you can’t be authentic either. And, logically, this has influenced my prejudices in physics and cosmology. To be consistent, I can’t believe we live in a deterministic universe, and have argued strongly on that point, opposing better minds than mine.

 

Existentialism has some things in common with Buddhism, which might explain why Eastern philosophy seemed to have an influence on the 60s zeitgeist. Having said that, I think the commonality is about treating life as a journey that’s transient. Accepting the impermanence and transience of life, I believe, is part of living authentically.

 

And what do I mean by ‘authentic’ in this context? Possibly, I never really appreciated this until I started writing fiction. I think anyone who creates art strives to be authentic, which means leaving your ego out of your work. I try to take the attitude that it’s my characters’ story, not mine. That’s very difficult to explain to anyone who hasn’t experienced it, but I know that actors often say something similar.

 

In my professional life, my integrity was everything to me. I often worked in disputatious environments and it was important to me that people could trust my word and my work. Cox talks about how existentialism intrinsically incorporates our interactions with others. 

 

Freedom is a much-abused, misappropriated term, but in existentialism it has a specific meaning and an interdependent relationship with responsibility – you can’t divorce one from the other. Freedom, in existentialism, means ‘free to choose’, hence the emphasis on free will. It also means, if you invoke the term, that the freedom of others is just as important as your own.

 

One can’t talk about authenticity without talking about its opposite, ‘bad faith’ (mauvaise foi), a term coined by Sartre. Bad faith is something that most of us have experienced, be it working in a job we hate, staying in a destructive relationship or not pursuing a desired goal in lieu of staying in our comfort zone.

 

Of course, sometimes we are in a situation outside our control, so what do we do? Speaking from personal experience, I think one needs to take ownership of one’s response to it; one needs to accept that only YOU can do something about it and not someone else. I’ve never been a prisoner-of-war, but my father was, and he made 3 attempts to escape, because, as he told the Commandant, ‘It’s my job’.

 

I’ve actually explored this in my own fiction. In my last story, two of my characters (independently) find themselves in circumstances of ‘bad faith’. I only analyse this in hindsight – don’t analyse what you write while you’re writing. In fact, one of those characters is attracted to another character who lives authentically, though neither of them ‘think’ in those terms.

Addendum: Someone asked me to come up with a single sentence to describe this. After sleeping on it, I came up with this:

Be responsible for what you are and who you become. That includes being responsible for your failures. (2 sentences)

We are not just numbers, but neither is the Universe

 A few years back I caught up with someone I went to school with, whom I hadn’t seen in decades, and, as it happened, had studied civil engineering like me. I told him I had a philosophy blog where I wrote about science and mathematics, among other things. He made the observation that mathematics and philosophy surely couldn’t be further apart. I pointed out that in Western culture they had a common origin, despite a detour into Islam, where mathematics gained a healthy and pivotal influence from India. 

I was reminded of this brief exchange when I watched this Numberphile video on the subject of numbers, where Prof Edward Frankel (UC Berkeley) briefly mentions the role of free will in our interaction with mathematics.

 

But the main contention of the video is that numbers do not necessarily have the status that we give them in considering reality. In fact, this is probably the most philosophical video I’ve seen on mathematics, even though Frankel is not specifically discussing the philosophy of mathematics.

 

He starts off by addressing the question whether our brain processes are all zeros and ones like a computer, and obviously thinks not. He continues that in another video, which I might return to later. The crux of this video is an in-depth demonstration of how a vector can be represented by a pair of numbers. He points out that the numbers are dependent on the co-ordinate system one uses, which is where ‘free will’ enters the discussion, because someone ‘chooses’ the co-ordinate system. He treats the vector as if it’s an entity unto itself, which he says ‘doesn’t care what co-ordinates you choose’. Brady, who is recording the video, takes him up on this point: that he’s effectively personifying the vector. Frankel acknowledges this, saying that it’s an ‘abstraction within an abstraction.’

 

Now, Einstein used vectors in his general theory of relativity, and one of the most important points was that the vectors are independent of the co-ordinate system. So we have this relationship between a mathematical abstraction and physical reality. People often talk about mistaking the ‘map for the terrain’ and Frankel uses a different metaphor where he says, ‘don’t confuse the menu for the meal’. I agree with all this to a point.

 

My own view is that there are 2 aspects of mathematics that are conflated. There is the language of mathematics, which includes the numbers and the operations we use, and which are ‘invented’ by humans. Then there are the relationships, which this language describes, but which are not prescribed by us. There is a sense that mathematics takes on a life of its own, which is why Frankel can talk about a vector as if it has an independent existence to him. Then there is Einstein who incorporated vectors into his mathematical formulation to describe how gravity is related to spacetime. 

 

Now here’s the thing: the relationship between gravity and spacetime still exists without humans to discover it or describe it. Spacetime is the 3 dimensions of space and 1 of time that, along with gravity, allows planets to maintain orbits over millions of years. But here’s the other thing: without mathematics, we would never know that or be able to describe it. It’s why some claim that mathematics is the language of nature. Whether Frankel agrees or not, I don’t know.

 

In the second video, Brady asks Frankel if he thinks he’s above mathematics, which makes him laugh. What Frankel argues is that there are inner emotional states, like ‘falling in love’, which can’t be described by mathematics. I know that some people would argue that falling in love is a result of biochemical algorithms, nevertheless I agree with Frankel. You can construct a computer model of a hurricane but it doesn’t mean that it becomes one. And it’s the same with the brain. You might, as someone aspired to do, create a computer model of a human brain, but that doesn’t mean it would think like one.

 

This all brings me back to Penrose’s 3 worlds philosophy of the mathematical, the mental and the physical and their intrinsic relationships. In a very real way, numbers allow us to comprehend the physical world, but it is not made of numbers as such. Numbers are the basis of the language we use to access mathematics, because I believe that’s what we do. I’ve pointed out before, that equations that describe the physical world (like Einstein’s) have no meaning outside the Universe, because they talk about physical entities like space and time and energy – things we can measure, in effect.

 

On the other hand, there are mathematical relationships, like Riemann’s hypothesis, for example, that deals with an infinity of primes, which literally can’t be contained by the Universe, by definition. At the end of the 2^ndvideo, Frankel quickly mentions Godel’s Incompleteness Theorem, which he describes in a nutshell by saying that there are truths in mathematics that can’t be formally proven. So there is a limit on what the human mind can know, given a finite universe, yet the human mind is 'not a mathematical machine’, as he so strongly argues.

 

He discusses more than I’ve covered, like his contention that our fixation with the rational is ‘irrational’, and there is no proof for the existence or non-existence of God. So, truly philosophical.