It all started with Euclid

 I’ve mentioned Euclid before, but this rumination was triggered by a post on Quora that someone wrote about Plato, where they argued, along with another contributor, that Plato is possibly overrated because he got a lot of things wrong, which is true. Nevertheless, as I’ve pointed out in other posts, his Academy was effectively the origin of Western philosophy, science and mathematics. It was actually based on the Pythagorean quadrivium of geometry, arithmetic, astronomy and music.
 
But Plato was also a student and devoted follower of Socrates and the mentor of Aristotle, who in turn mentored Alexander the Great. So Plato was a pivotal historical figure and without his writings, we probably wouldn’t know anything about Socrates. In the same way that, without Paul, we probably wouldn’t know anything about Jesus. (I’m sure a lot of people would find that debatable, but, if so, it’s a debate for another post.)
 
Anyway, I mentioned Euclid in my own comment (on Quora), who was the Librarian at Alexandria around 300BC, and thus a product of Plato’s school of thought. Euclid wrote The Elements, which I contend is arguably the most important book written in the history of humankind – more important than any religious text, including the Bible, Homer’s Iliad and the Mahabharata, which, I admit, is quite a claim. It's generally acknowledged as the most copied text in the secular world. In fact, according to Wikipedia:
 
It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing in 1482.
 
Euclid was revolutionary in one very significant way: he was able to demonstrate what ‘truth’ was, using pure logic, albeit in a very abstract and narrow field of inquiry, which is mathematics.
 
Before then, and in other cultures, truth was transient and subjective and often prescribed by the gods. But Euclid changed all that, and forever. I find it extraordinary that I was examined on Euclid’s theorems in high school in the 20th Century.
 
And this mathematical insight has become, millennia later, a key ingredient (for want of a better term) in the hunt for truths in the physical world. In the 20th Century, in what has become known as the Golden Age of Physics, the marriage between mathematics and scientific inquiry at all scales, from the cosmic to the infinitesimal, has uncovered deeply held secrets of nature that the Pythagoreans, and Euclid for that matter, could never have dreamed of. Look no further than quantum mechanics (QM) and the General Theory of Relativity (GR). Between these 2 iconic developments, they underpin every theory we currently have in physics, and they both rely on mathematics that was pivotal in the development of the theories from the outset. In other words, without the mathematics of complex algebra and Riemann geometry respectively, these theories would have been stillborn.
 
I like to quote Richard Feynman from his book, The Character of Physical Law, in a chapter titled, The Relation of Mathematics to Physics:
 
…what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics... Why? I have not the slightest idea. It is only my purpose to tell you about this fact.
 
The strange thing about physics is that for the fundamental laws we still need mathematics.
 
Physicists cannot make a conversation in any other language. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. She offers her information only in one form.
 
And this has only become more evident since Feynman wrote those words.
 
There was another revolution in the 20th Century, involving Alan Turing, Alonso Church and Kurt Godel; this time involving mathematics itself. Basically, each of these independently demonstrated that some mathematical truths were elusive to proof. Some mathematical conjectures could not be proved within the mathematical system from which they arose. The most famous example would be Riemann’s Hypothesis, involving primes. But the Goldbach conjecture (also involving primes) and the conjecture of twin primes also fit into this category. While most mathematicians believe them to be true, they are yet to be proven. I won’t elaborate on them, as they can easily be looked up.
 
But there is more: according to Gregory Chaitin, there are infinitely more incomputable Real numbers than computable Real numbers, which means that most of mathematics is inaccessible to logic.
 
So, when I say it all started with Euclid, I mean all the technology and infrastructure that we take for granted; and which allows me to write this so that virtually anyone anywhere in the world can read it; only exists because Euclid was able to derive ‘truths’ that stood for centuries and ultimately led to this.

Why you need memory to have free will

 This is so obvious once I explain it to you, you’ll wonder why no one else ever mentions it. I’ve pointed out a number of times before that consciousness exists in a constant present, so the time is always ‘now’ for us. I credit Erwin Schrodinger for providing this insight in his lectures, Mind and Matter, appended to his short tome (an oxymoron), What is Life?
 
A logical consequence is that, without memory, you wouldn’t know you’re conscious. And this has actually happened, where people have been knocked unconscious, then acted as if they were conscious in order to defend themselves, but have no memory of it. It happened to my father in a boxing ring (I didn’t believe him when he first told me) and it happened to a woman security guard (in Sydney) where she shot her assailant after he knocked her out. In both cases, they claimed they had no memory of the incident.
 
And, as I’ve pointed out before, this begs a question: if we can survive an attack without being consciously aware of it, then why did evolution select for consciousness? In other words, we could be automatons. The difference is that we have memory.
 
The brain is effectively a memory storage device, without which we would function quite differently. Perhaps this is the real difference between animals and plants. Perhaps plants are sentient, but without memories they can’t ‘think’. There are different types of memory. There is so-called muscle-memory, whereby when we learn a new skill we don’t have to keep relearning it, and eventually we do it without really thinking about it. Driving a car is an example that most of us are familiar with, but it applies to most sports and the playing of musical instruments. I’ve learned that this applies to cognitive skills as well. For example, I write stories and creating characters is something I do without thinking about it too much.
 
People who suffer from retrograde amnesia (as described by Oliver Sacks in his seminal book, The Man Who Mistook His Wife for a Hat, in the chapter titled, The Lost Mariner) don’t lose their memory of specific skills, or what we call muscle-memory. So you could have muscle-memory and still be an automaton, as I described above.
 
Other types of memory are semantic memory and episodic memory. Semantic memory, which is essential to learning a language, is basically our ability to remember facts, which may or may not require a specific context. Rote learning is just exercising semantic memory, which doesn’t necessarily require a deep understanding of a subject, but that’s another topic.
 
Episodic memory is the one I’m most concerned with here. It’s the ability to recount an event in one’s life – a form of time-travelling we all indulge in from time to time. Unlike a computer memory, it’s not an exact recollection – we reconstruct it – which is why it can change over time and why it doesn’t necessarily agree with someone else’s recollection of the same event. Then there is imagination, which I believe is the key to it all. Apparently, imagination uses the same part of the brain as episodic memory. In effect, we are creating a memory of something that is yet to happen – an attempt to time-travel into the future. And this, I argue, is how free will works.

Philosophers have invented a term called ‘intentionality’, which is not what you might think it is. I’ll give a dictionary definition:
 
The quality of mental states (e.g. thoughts, beliefs, desires, hopes) which consists in their being directed towards some object or state of affairs.
 
Philosophers who write on the topic of consciousness, like Daniel C Dennett and John Searle, like to use the term ‘aboutness’ to describe intentionality, and if you break down the definition I gave above, you might discern what they mean. It’s effectively the ability to direct ‘thoughts… towards some object or state of affairs’. But I see this as either episodic memory or imagination. In other words, the ‘object or state of affairs’ could be historical or yet to happen or pure fantasy. We can imagine events we’ve never experienced, though we may have read or heard about them, and they may not only have happened in another time but also another place – so mental time-travelling.
 
As well as a memory storage device, the brain is also a predictability device – it literally thinks a fraction of a second ahead. I’ve pointed out in another post that the brain creates a model in space and time so we can interact with the real world of space and time, which allows us to survive it. And one of the facets of that model is that it’s actually, minisculy ahead of the real world, otherwise we wouldn’t even be able to catch a ball. In other words, it makes predictions that our life depends on. But I contend that this doesn’t need episodic memory or imagination either, because it happens subconsciously and is part of our automaton brain.
 
My point is that the automaton brain, as I’ve coined it, could have evolved by natural selection, without memory. The major difference memory makes is that we become self-aware, and it gives consciousness a role it would otherwise not possess. And that role is what we call free will. I like a definition that philosopher and neuroscientist, Raymond Tallis, gave:
 
Free agents, then, are free because they select between imagined possibilities, and use actualities to bring about one rather than another.
 
So, as I said earlier, I think imagination is key. Free will requires imagination, which I argue is called ‘aboutness’ or ‘intentionality’ in philosophical jargon (though others may differ). And imagination requires episodic memory or mental time-travelling, without which we would all be automatons; still able to interact with the real world of space and time and to acquire skills necessary for survival.
 
And if one goes back to the very beginning of this essay, it is all premised on the observed and experiential phenomenon that consciousness exists in a constant present. We take this for granted, yet nothing else does. Everything becomes the past as soon as it happens, which I keep repeating, is demonstrated every time someone takes a photo. The only exception I can think of is a photon of light, for which time is zero. Our very thoughts become memory as soon as we think them, otherwise we wouldn’t know we exist, yet we could apparently survive without it.
 
Just today, I read a review in New Scientist (27 April 2024) of a book, The Elephant and the Blind: The experience of pure consciousness – philosophy, science and 500+ experiential reports by Thomas Metzinger. Apparently, Metzinger did an ‘online survey of meditators from 57 countries providing over 500 reports for the book.’ Basically, he argues that one can achieve a state that he calls ‘pure consciousness’ whereby the practitioner loses all sense of self. In effect, he argues (according to the reviewer, Alun Anderson):
 
 That a first-person perspective isn’t necessary for consciousness at all: your sense of self, of a continuous “you”, is part of the content of consciousness, not consciousness itself.
 
A provocative and contentious perspective, yet it reminds me of studies, also reported in New Scientist, many years ago, using brain-scan-imagery, of people experiencing ‘God’ also having a sense of being ‘self-less’, if I can use that term. Personally, I think consciousness is something fundamental with a possible independent existence to anything physical. It has a physical manifestation, if you like, purely because of memory, because our brains are effectively a storage device for consciousness.
 
This is a radical idea, but it is one I woke up with one day as if it was an epiphany, and realised that it was quite a departure from what I normally think. Raymond Tallis, whom I’ve already mentioned, once made the claim that science can only study objects and phenomena that can be measured. I claim that consciousness can’t be measured, but because we can measure brain waves and neuron activity many people argue that we are measuring consciousness.
 
But here’s the thing: if we didn’t experience consciousness, then scientists would tell us it doesn’t exist in the same way they tell us that free will doesn’t exist. I can make this claim because the same scientists argue that eventually AI will exhibit consciousness while simultaneously telling us that we will know this from the way the AI behaves, not because anyone will be measuring anything.

 

Addendum: I came across this related video by self-described philosopher-physicist, Avshalom Elitzur, who takes a subtly different approach to the same issue, giving examples from the animal kingdom. Towards the end, he talks about specific 'isms' (e.g. physicalism and dualism), but he doesn't mention the one I'm an advocate of, which is a 'loop' - that matter interacts with consciousness, via neurons, and then consciousness interacts with matter, which is necessary for free will.

Basically, he argues that consciousness interacting with matter breaks conservation laws (watch the video) but the brain consumes energy whether it's doing a maths calculation, running around an oval or lying asleep. Running around an oval is arguably consciousness interacting with matter - the same for an animal chasing prey - because one assumes they're based on a conscious decision, which is based on an imagined future, as per my thesis above. Also, processing information uses energy, which is why computers get hot, with no consciousness required. I fail to see what the difference is.

Logic rules

I’ve written on this topic before, but a question on Quora made me revisit it.
 
Self-referencing can lead to contradiction or to illumination. It was a recurring theme in Douglas Hofstadter’s Godel Escher Bach, and it’s key to Godel’s famous Incompleteness Theorem, which has far-reaching ramifications for mathematics if not epistemology generally. We can never know everything there is to know, which effectively means there will always be known unknowns and unknown unknowns, with possibly infinitely more of the latter than the former.
 
I recently came across a question on Quora: Will a philosopher typically say that their belief that the phenomenal world "abides by all the laws of logic" is an entailment of those laws being tautologies? Or would they rather consider that belief to be an assumption made outside of logic?

If you’re like me, you might struggle with even understanding this question. But it seems to me to be a question about self-referencing. In other words, my understanding is that it’s postulating, albeit as a question, that a belief in logic requires logic. The alternative being ‘the belief is an assumption made outside of logic’. It’s made more confusing by suggesting that the belief is a tautology because it’s self-referencing.
 
I avoided all that, by claiming that logic is fundamental even to the extent that it transcends the Universe, so not a ‘belief’ as such. And you will say that even making that statement is a belief. My response is that logic exists independently of us or any belief system. Basically, I’m arguing that logic is fundamental in that its rules govern the so-called laws of the Universe, which are independent of our cognisance of them. Therefore, independent of whether we believe in them or not.
 
I’ve said on previous occasions that logic should be a verb, because it’s something we do, and not just humans, but other creatures, and even machines. But that can’t be completely true if it really does transcend the Universe. My main argument is hypothetical in that, if there is a hypothetical God, then said God also has to obey the rules of logic. God can’t tell us the last digit of pi (it doesn’t exist) and he can’t make a prime number non-prime or vice versa, because they are determined by pure logic, not divine fiat.
 
And now, of course, I’ve introduced mathematics into the equation (pun intended) because mathematics and logic are inseparable, as probably best demonstrated by Godel’s famous theorem. It was Euclid (circa 300BC) who introduced the concept of proof into mathematics, and a lynch pin of many mathematical proofs is the fundamental principle of logic that you can’t have a contradiction, including Euclid’s own relatively simple proof that there are an infinity of primes. Back to Godel (or forward 2,300 years, to be more accurate), and he effectively proved that there is a distinction between 'proof' and 'truth' in mathematics, in as much as there will always be mathematical truths that can’t be proven true within a given axiom based, consistent, mathematical system. In practical terms, you need to keep extending the ‘system’ to formulate more truths into proofs.
 
It's not a surprise that the ‘laws of the Universe’ that I alluded to above, seem to obey mathematical ‘rules', and in fact, it’s only because of our prodigious abilities to mine the mathematical landscape that we understand the Universe (at every observable scale) to the extent that we do, including scales that were unimaginable even a century ago.
 
I’ve spoken before about Penrose’s 3 Worlds: Physical, Mental and Platonic; which represent the Universe, consciousness and mathematics respectively. What links them all is logic. The Universe is riddled with paradoxes, yet even paradoxes obey logic, and the deeper we look into the Universe’s secrets the more advanced mathematics we need, just to describe it, let alone understand it. And logic is the means by which humans access mathematics, which closes the loop.
 

 Addendum: I'd forgotten that I wrote a similar post almost 5 years ago, where, unsurprisingly, I came to much the same conclusion. However, there's no reference to God, and I provide a specific example.

Kant’s 300th Birthday (22nd April)

 I wouldn’t have known this if I hadn’t read about it in Philosophy Now. I have to confess I’ve only read the first and most famous of his 3 ‘Critiques’, The Critique of Pure Reason. I have to say that I think Kant was the first philosopher I read where I realised that it’s not about trying to convince everyone you’re right (even though, that’s effectively the methodology) so much as making people think outside their own box.
 
Kant famously attempted to bridge ‘empiricism’ (a la Hume) with ‘reason’ (a la Leibniz), as both necessary in the pursuit of knowledge. In other words, you can’t rely on just one of these fundamental approaches to epistemology. He also famously categorised them as ‘post priori’ and ‘a priori’ respectively, meaning that reason or logic is knowledge gained prior or independently of observation, while empirically derived evidence is derived after an observed event (by necessity). Curiously, he categorised space and time, as a priori, meaning they were mental states. I’ve quoted this often from The Critique of Pure Reason.
 
But this space and this time, and with them all appearances, are not in themselves things; they are nothing but representations and cannot exist outside our minds.
 
I’ve always fundamentally disagreed with this, but the fact that Kant challenges our intuitively held comprehension of space and time, based on our everyday experience, makes one think more deeply about it, if one wants to present a counter-argument.
 
He’s also famous for coining the term, ‘transcendental idealism’, which is like some exotic taxonomy in the library of philosophical ideas. Again, I’ll quote from the source:

All these faculties have a transcendental (as well as an empirical) employment which concerns the form alone, and is possible apriori. 
 
By ‘all these faculties’, he’s talking about our mental faculties to use reason to understand something ‘a priori’. I concluded in an essay I wrote on this very topic, when I studied Kant, that the logical and practical realisation of ‘transcendental idealism’ is mathematics, though I doubt that’s what Kant meant. The fact is that in the intervening 200+ years, epistemology has been dominated by physics, which combines empirical evidence with mathematics in a dialectical relationship, so it’s become impossible to do one without the other. So, in a way, I think Kant foresaw this relationship before it evolved into the profound and materially successful enterprise that we call science.
 
A couple of things I didn’t know. In his early years before he gained tenure, he supplemented his meagre income by private tutoring and hustling at billiards – who would have thought.
 
He also got into trouble with newly elected king, Friedrich Wilhelm II, for his critiques on religion, when he published The General Natural History and Theory of the Heavens in 1755, arguing for a purely physical explanation of the Universe’s origins, a good 200 years before it became acceptable. In effect, he was censored, and he didn’t publish anything else on religion until after Friedrich died, whereupon he immediately made up for lost time.

Sigmund Freud’s and C.S. Lewis’s fictional encounter

Last week I went and saw the movie, Freud’s Last Session, where Anthony Hopkins plays Freud, when he was in London on the very cusp of WW2 and dying of cancer of the mouth, and Mathew Goode plays the Oxford Don, C.S. Lewis. It’s a fictional account, taken from a play I believe, about their meeting at Freud’s home. Its historical veracity is put into question by a disclaimer given after the movie proper finishes, saying that it’s recorded that Freud did, in fact, meet an Oxford Don, but whose identity was never revealed or confirmed.
 
It's the sort of movie that would attract people with a philosophical bent like myself. I thought the cinema better attended than I expected, though it was far from full. Anthony Hopkin’s Freud is playful in the way he challenges Mathew Goode’s Lewis, whilst still being very direct and not pulling any punches. There is an interruption to their conversation by an air-raid siren, and when they go into a bunker, Lewis has a panic-attack, because of his experience in the trenches of WW1. Freud helps him to deal with it in the moment.
 
I’ve read works by both of them, though I’m hardly a scholar. I actually studied Freud in a philosophy class, believe it or not. I’m better read in Jung than Freud. I think Lewis is a good essayist, though I disagree with him philosophically on many counts. Having said that, I expect if I’d met him, I’d have a different opinion of him than just his ideas. I have very good friends who hold almost exactly the same views, so you don’t just judge someone for what they believe, if you get to know them in the flesh.
 
And that’s what came across in this hypothetical exchange – that you have 2 intellectuals who can find mutual respect despite having antithetical views about God and religion and other things, like homosexuality. On that last point, Sigmund’s daughter, Anna, was in a relationship with a woman, which Freud obviously didn’t approve of. In fact, the father-daughter relationship in the movie, was portrayed as very Freudian, where they both seemed to suffer from an unhealthy attachment. Nevertheless, Anna Freud went on to make a name for herself in child psychoanalysis, and there’s a scene where she has to deal with an overbearing and arrogant young man, and her putdown made me want to clap; I just wish I could remember it. Anyway, Anna’s story provides a diversionary, yet not irrelevant, subplot, which makes the movie a bit more than just a two-hander.
 
There are scenes where Mathew Goode’s Lewis has dreams or visions and finds himself in a forest where he comes across a deer and one where he sees a bright overwhelming light. There was a sense in these scenes that he felt he was in the presence of God, and it made me realise that I couldn’t judge him for that. I’ve long argued that God is a personal experience that can’t be shared, but we overlay it with our cultural norms. It was in these scenes that I felt his character was portrayed most authentically.
 

Do you think Hoffman’s theories about reality and perception are true?

I’ve written about this twice before in some detail, but this was a question on Quora, I addressed last year. I include it here because it’s succinct yet provides specific, robust arguments in the negative.
 
There is a temptation to consider Hoffman a charlatan, but I think that’s a bit harsh and probably not true. The point is that he either knows what he’s arguing is virtually indefensible yet perseveres simply out of notoriety, or he really believes what he’s saying. I’m willing to give him the benefit of the doubt. I think he’s gone so far down this rabbit-hole and invested so much of his time and reputation that it would take a severe cognitive dissonance to even consider he could be wrong. And this goes for a lot of us, in many different fields. In a completely different context, just look at those who have been Trump acolytes turned critics.
 
Below is my response to the question:
 
One-word answer, No. From the very first, when I read an academic paper he co-wrote with Chetan Kaprash, titled Objects of Consciousness (Frontiers in Psychology, 17 June 2014), I have found it very difficult to take him seriously. And everything I’ve read and seen since, only makes me more sceptical.

Hoffman’s ideas are consistent with the belief that we live in a computer simulation, though he’s never made that claim. Nevertheless, his go-to analogy for ‘objects’ we consider to be ‘real’ is the desktop icons on your computer. He talks about the ‘spacetime perceptual interface of H. Sapiens’ as a direct reference to a computer desktop, but it only exists in our minds. In fact, what he describes is what one would experience if one were to use a VR headset. But there is another everyday occurrence where we experience this phenomenon and it’s known as dreaming. Dreams are totally solipsistic, and you’ll notice they often defy reality without us giving them a second thought – until we wake up.

So, how do you know you’re not in a dream? Well, for one, we have no common collective memories with anyone we meet. Secondly, interactions and experiences we have in a dream, that would kill us in real life, don’t. Have you ever fallen from a great height in a dream? I have, many times.

And this is the main contention I have with Hoffman: reality can kill you. He readily admitted in a YouTube video that he wouldn’t step in front of a moving train. He tells us to take the train "seriously but not literally", after all it’s only a desktop icon. But, in his own words, if you put a desktop icon in the desktop bin it will have ‘consequences’. So, walking in front of a moving train is akin to putting the desktop icon of yourself in the bin. A good metaphor perhaps, but hardly a scientifically viable explanation of why you would die.

There are so many arguments one can use against Hoffman, that it’s hard to know where to start, or stop. His most outrageous claim is that ‘space and time doesn’t exist unperceived’, which means that all of history, including cosmological history only exists in the mind. Therefore, not only could we have not evolved, but neither could the planets, solar system and galaxies. In fact, the light we see from distant galaxies, not to mention the CMBR (the earliest observable event in the Universe), doesn’t exist unless someone’s looking at it.

Finally, you can set up a camera to take an image of an object (like a wild cat at night) without any conscious object in sight, except maybe the creature it took a photo of. But then, how did the camera only exist when the animal who didn’t see it, created it with its own consciousness?
 

Addendum:

Following my publishing this post, I watched a later, fairly recent video by Hoffman where he gives further reasons for his beliefs. In particular, he states that physics has shown that space and time are no longer fundamental, which is quite a claim. He cites the work of Nima Arkani-Hamed who has used a mathematical object called amplituhedrons to accurately predict the amplitudes of gluons in particle physics. I’ve read about this before in a book by Graham Farmelo (The Universe Speaks in Numbers; How Modern Maths Reveals Nature’s Deepest Secrets). Farmelo tells us that Arkani-Hamed is an American born Iranian, at the Princeton Institute for Advanced Study. To quote Arkani-Hamed directly from Farmelo's book:
 
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.
 
And this appears to be the point that Hoffman has latched onto, which he’s extrapolated to say that space and time are not fundamental. Whereas I drew a slightly different conclusion. In my discussion of Farmelo’s book, I made the following point:


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.
 
I followed this with another reference to Arkani-Hamed.



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.’
 
But, as I pointed out both here and in my last post, mathematical abstractions providing descriptions of natural phenomena are not in themselves physical. I see them as a code that allows us to fathom nature’s deepest secrets, which I believe Arkani-Hamed has contributed to.
 
Hoffman’s most salient point is that we need to go beyond time and space to find something more fundamental. In effect, he’s saying we need to go outside the Universe, and he might even be right, but that does not negate the pertinent, empirically based and widely held belief that space and time are arguably the most fundamental parameters within the Universe. If he’s saying that consciousness possibly exists beyond, therefore outside the Universe, I won’t argue with that, because we don’t know.
 
Hoffman has created mathematical models of consciousness, which I admit I haven’t read or seen, and he argues that those mathematical models lead to the same mathematical objects (abstractions) that Arkani-Hamed and others have used to describe fundamental physics. Therefore, consciousness creates the objects that the mathematics describes. That’s a very long bow to draw, to use a well-worn euphemism.