The Library of Babel

 You may have heard of this mythic place. There was an article in the same Philosophy Now magazine I referenced in my last post, titled World Wide Web or Library of Babel? By Marco Nuzzaco. Apparently, Jorge Luis Borges (1899-1986) wrote a short story, The Library of Babel in 1941. A little bit of research reveals there are layers of abstraction in this imaginary place, extrapolated upon by another book, The Unimaginable Mathematics of Borges’ Library of Babel, by Mathematical Professor, William Goldbloom Bloch, published in 2008 by Oxford University Press and receiving an ‘honourable mention’ in the 2009 PROSE Awards. I should point out that I haven’t read either of them, but the concept fascinates me, as I expound upon below.
 
The Philosophy Now article compares it with the Internet (as per the title), because the Internet is quickly becoming the most extensive collection of knowledge in the history of humanity. To quote the author, Nuzzarco:
 
The amount of information produced on the Internet in the span of 10 years from 2010 to 2020 is exponentially and incommensurably larger than all the information produced by humanity in the course of its previous history.
 
And yes, the irony is not lost on me that this blog is responsible for its own infinitesimal contribution. But another quote from the same article provides the context that I wish to explore.
 
The Library of Babel contains all the knowledge of the universe that we can possibly gain. It has always been there, and it always will be. In this sense, the knowledge of the library reflects the universe from a God’s eye perspective and the librarians’ relentless research is to decipher its secrets and its mysterious order and purpose – or maybe, as Borges wonders, the ultimate lack of any of these.
 
One can’t read this without contemplating the history of philosophy and science (at least, in the Western tradition) that has attempted to do exactly that. In fact, the whole enterprise has a distinctive Platonic flavour to it, because there is one sense in which the fictional Library of Babel is ‘real’, and it links back to my last post.
 
I haven’t read Borges’ or Bloch’s books, so I’m simply referring to the concept alluded to in that brief quote, that there is an abstract landscape or territory that humans have the unique capacity to explore. And anyone who has considered the philosophy of mathematics knows that it fulfills that criterion.
 
Mathematics has unlocked more secrets about the Universe than any other endeavour. There is a similarity here to Paul Davies’ metaphor of a ‘warehouse’ (which he expounds upon in this video) but I think a Library is an even more apposite allusion. We are like ‘librarians’ trying to decipher God’s view of the Universe that we inhabit, and to extend the metaphor, God left behind a code that only we can decipher (as far as we know) and that code is mathematics.
 
To quote Feynman (The Character of Physical Law, specifically in a chapter titled The Relation of Mathematics to Physics):
 
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 if we have the knowledge of Gods then we also have the power of Gods, and that is what we’re witnessing, right now, in our current age. We have the power to destroy the world on which we live, either in a nuclear conflagration or runaway climate change (we are literally changing the weather). But we can also use the same knowledge to make the world a more inhabitable place, but to do that we need to be less human-centric.
 
If there is a God, then (he/she) has left us in charge. I think I’ve written about that before. So yes, we are the ‘Librarians’ who have access to extraordinary knowledge and with that knowledge comes extraordinary responsibilities.

 

In the beginning there was logic

 I recently read an article in Philosophy Now (Issue 154, Feb/Mar 2023), jointly written by Owen Griffith and A.C. Paseau, titled One Logic, Or Many? Apparently, they’ve written a book on this topic (One True Logic, Oxford University Press, May 2022).
 
One of the things that struck me was that they differentiate between logic and reason, because ‘reason is something we do’. This is interesting because I’ve argued previously that logic should be a verb, but I concede they have a point. In the past I saw logic as something that’s performed, by animals and machines as well as humans. And one of the reasons I took this approach was to distinguish logic from mathematics. I contend that we use logic to access mathematics via proofs, which we then call theorems. But here’s the thing: Kurt Godel proved, in effect, that there will always be mathematical ‘truths’ that we can’t prove within any formal system of mathematics that is consistent. The word ‘consistent’ is important (as someone once pointed out to me) because, if it’s inconsistent, then all bets are off.
 
What this means is that there is potentially mathematics that can’t be accessed by logic, and that’s what we’ve found, in practice, as well as in principle. Matt Parker provides a very good overview in this YouTube video on what numbers we know and what we don’t know. And what we don’t know is infinitely greater than what we do know. Gregory Chaitin has managed to prove that there are infinitely greater incomputable numbers than computable numbers, arguing that Godel’s Incompleteness Theorem goes to the very foundation of mathematics.
 
This detour is slightly off-topic, but very relevant. There was a time when people believed that mathematics was just logic, because that’s how we learned it, and certainly there is a strong relationship. Without our prodigious powers of logic, mathematics would be an unexplored territory to us, and remain forever unknown. There are even scholars today who argue that mathematics that can’t be computed is not mathematics, which rules out infinity. That’s another discussion which I won’t get into, except to say that infinity is unavoidable in mathematics. Euclid (~300 BC) proved (using very simple logic) that you can have an infinite number of primes, and primes are the atoms of arithmetic, because all other numbers can be derived therefrom.
 
The authors pose the question in their title: is there a pluralism of logic? And compare a logic relativism with moral relativism, arguing that they both require an absolutism, because moral relativism is a form of morality and logic relativism is a form of logic, neither of which are relative in themselves. In other words, they always apply by self-definition, so contradict the principle that they endorse – they are outside any set of rules of morality or logic, respectively.
 
That’s their argument. My argument is that there are tenets that always apply, like you can’t have a contradiction. They make this point themselves, but one only has to look at mathematics again. If you could allow contradictions, an extraordinary number of accepted proofs in mathematics would no longer apply, including Euclid’s proof that there are an infinity of primes. The proof starts with the premise that you have the largest prime number and then proves that it isn’t.
 
I agree with their point that reason and logic are not synonymous, because we can use reason that’s not logical. We make assumptions that can’t be confirmed and draw conclusions that rely on heuristics or past experiences, out of necessity and expediency. I wrote another post that compared analytical thinking with intuition and I don’t want to repeat myself, but all of us take mental shortcuts based on experience, and we wouldn’t function efficiently if we didn’t.
 
One of the things that the authors don’t discuss (maybe they do in their book) is that the Universe obeys rules of logic. In fact, the more we learn about the machinations of the Universe, on all scales, the more we realise that its laws are fundamentally mathematical. Galileo expressed this succinctly in the 17th Century, and Richard Feynman reiterated the exact same sentiment in the last century.
 
Cliffard A Pickover wrote an excellent book, The Paradox of God And the Science of Omniscience, where he points out that even God’s omniscience has limits. To give a very trivial example, even God doesn’t know the last digit of pi, because it doesn’t exist. What this tells me is that even God has to obey the rules of logic. Now, I’ve come across someone (Sye Ten Bruggencate) who argued that the existence of logic proves the existence of God, but I think he has it back-to-front (if God can’t breach the rules of logic). In other words, if God invented logic, ‘He’ had no choice. And God can’t make a prime number nonprime or vice versa. There are things an omnipotent God can’t do and there are things an omniscient God can’t know. So, basically, even if there is a God, logic came first, hence the title of this essay.

Why do we read?

This is the almost-same title of a book I bought recently (Why We Read), containing 70 short essays on the subject, featuring scholars of all stripes: historians, philosophers, and of course, authors. It even includes scientists: Paul Davies, Richard Dawkins and Carlo Rovelli, being 3 I’m familiar with.
 
One really can’t overstate the importance of the written word, because, oral histories aside, it allows us to extend memories across generations and accumulate knowledge over centuries that has led to civilisations and technologies that we all take for granted. By ‘we’, I mean anyone reading this post.
 
Many of the essayists write from their personal experiences and I’ll do the same. The book, edited by Josephine Greywoode and published by Penguin, specifically says on the cover in small print: 70 Writers on Non-Fiction; yet many couldn’t help but discuss fiction as well.
 
And books are generally divided between fiction and non-fiction, and I believe we read them for different reasons, and I wouldn’t necessarily consider one less important than the other. I also write fiction and non-fiction, so I have a particular view on this. Basically, I read non-fiction in order to learn and I read fiction for escapism. Both started early for me and I believe the motivation hasn’t changed.
 
I started reading extra-curricular books from about the age of 7 or 8, involving creatures mostly, and I even asked for an encyclopaedia for Christmas at around that time, which I read enthusiastically. I devoured non-fiction books, especially if they dealt with the natural world. But at the same time, I read comics, remembering that we didn’t have TV at that time, which was only just beginning to emerge.
 
I think one of the reasons that boys read less fiction than girls these days is because comics have effectively disappeared, being replaced by video games. And the modern comics that I have seen don’t even contain a complete narrative. Nevertheless, there are graphic novels that I consider brilliant. Neil Gaiman’s Sandman series and Hayao Miyazake’s Nausicaa of the Valley of the Wind, being standouts. Watchmen by Alan Moore also deserves a mention.
 
So the escapism also started early for me, in the world of superhero comics, and I started writing my own scripts and drawing my own characters pre-high school.
 
One of the essayists in the collection, Niall Ferguson (author of Doom) starts off by challenging a modern paradigm (or is it a meme?) that we live in a ‘simulation’, citing Oxford philosopher, Nick Bostrom, writing in the Philosophical Quarterly in 2003. Ferguson makes the point that reading fiction is akin to immersing the mind in a simulation (my phrasing, not his).
 
In fact, a dream is very much like a simulation, and, as I’ve often said, the language of stories is the language of dreams. But here’s the thing; the motivation for writing fiction, for me, is the same as the motivation for reading it: escapism. Whether reading or writing, you enter a world that only exists inside your head. The ultimate solipsism.

And this surely is a miracle of written language: that we can conjure a world with characters who feel real and elicit emotional responses, while we follow their exploits, failures, love life and dilemmas. It takes empathy to read a novel, and tests have shown that people’s empathy increases after they read fiction. You engage with the character and put yourself in their shoes. It’s one of the reasons we read.
 
 
Addendum: I would recommend the book, by the way, which contains better essays than mine, all with disparate, insightful perspectives.
 

The apparent dichotomous relationship between consciousness and determinism

 Someone (Graham C Lindsay) asked me a question on Quora:

Is it true that every event, without exception, is fully caused by its antecedent conditions?

 Graham Lindsay is Scottish, a musician (50 years a keyboard player) and by his own admission, has a lot of letters after his name. I should point out that I have none. The Quora algorithm gave me the impression that he asked me specifically, but maybe he didn't. As I say at the outset, David Cook gives a more erudite answer than me. It so happens, I've had correspondence with David Cook (he contacted me) and he sent me a copy of his book of poetry. He's a retired psychiatrist and lecturer.

In fact, I recommend that you read his answer in conjunction with mine - we take subtley different approaches without diverging too far apart.

I concede that there's not a lot that's new in this post, but I've found that rearranging pre-existing ideas can throw up new insights and thought-provocations.

Thanks for asking me, I feel flattered. To be honest, I think David Cook gives a better and more erudite answer than I can. I’d also recommend you ask Mark John Fernee (physicist with University of Queensland) who has some ideas on this subject.

I’ll start with Fernee, because he argues for determinism without arguing for superdeterminism, as Sabine Hossenfelder does. To answer the question directly, it appears to be true to the best of our knowledge. What do I mean by that? Everything in the Universe that has happened to date seems to have a cause, and it would appear that there is a causal chain going all the way back to the Big Bang. The future, however, is another matter. In the future we have multiple paths that are expressed in QM as probabilities. In fact, Freeman Dyson argued that QM can only describe the future and not the past. As another Quora contributor (David Moore) pointed out, you can only have a probability less than one for an event in the future. If it’s in the past, it has a probability of One.

In the Universe, chaos rules at virtually every level. A lot of people are unaware that even the orbits of the planets are chaotic, so they are only predictable within a range of hundreds of millions of years. Hossenfelder (whom I cited earlier) has a YouTube video where she demonstrates how a chaotic phenomenon always has a limited horizon of predictability (for want of a better phrase). With the weather it’s about 10 days. This doesn’t stop the Universe being deterministic up to the present, while being unpredictable in the future. The thing about chaotic phenomena is that if you rerun them you’d get a different outcome. This applies to the Universe itself. The best known example is the tossing of a coin, which is a chaotic event. It’s fundamental to probability theory that every coin toss is independent of previous tosses.

Regarding QM, we all know that Schrodinger’s equation is deterministic and time-reversible. However, as Fernee points out, the act of ‘measurement’ creates an irreversible event. To quote Paul Davies:

The very act of measurement breaks the time symmetry of quantum mechanics in a process sometimes described as the collapse of the wave function... the rewind button is destroyed as soon as that measurement is made.

David Cook, in his answer, mentions the role of imagination in his closing paragraph and I don’t think that can be overstated. To quote another philosopher, Raymond Tallis:

Free agents, then, are free because they select between imagined possibilities, and use actualities to bring about one rather than another.

I feel this is as good a description of free will as you can get. And like David, I think imagination is key here. And this raises the issue of consciousness, because I’m unsure how it fits into the scheme of things. As Schrodinger pointed out, consciousness exists in a constant present, which means that without memory you wouldn’t know you are conscious. And this has actually happened, where people have behaved consciously without being aware of it. It happened to my father when he was knocked unconscious in a boxing ring, and I know of other incidents. In my father’s case, he got back on his feet and knocked out his opponent – when he came to, he was standing over his opponent with no memory of what happened.

I tell this anecdote, because it begs a question. If we can respond to events that are harmful or life-threatening without conscious awareness, then why do we need consciousness?

All evidence of consciousness points to a neural substrate dependency. We don’t find consciousness in machines despite predictions that we eventually will. But it seems to me that consciousness acts outside the causal chain of the Universe. We have the ability, as do other sentient creatures, to perform actions on our physical environment that are purely determined by imagination, therefore thought. And we can even use thought to change the neural pathways in our brains, like a feedback loop, or as Douglas Hofstadter coined it, a ‘strange loop’.

 

Addendum: For my own benefit, I've coined the terms, 'weak determinism' and 'strong determinism', to differentiate between deterministic causality and superdeterminism respectively. I know there's a term called 'compatible determinism', from Hume, which, according to other sources, is the same as weak determinism, as I expound on below.

The point is that weak determinism (causality) is compatible with free will, which is what Hume argued, according to the Stanford Encyclopedia reference (linked above). However, Hume famously challenged the very idea of causality, whereas I'd argue that 'weak determinism' is completely dependent on causality being true and a universal principle. On the other hand, 'strong determinism' or superdeterminism (as advocated by Sabine Hossenfelder) axiomatically rules out free will, so there is a fundamental difference.

For the sake of clarity, the determinism I refer to in my essay (and its title) is weak determinism.

What grounds morality?

 In the most recent issue of Philosophy Now (No 153, Dec 2022/Jan 2023), they’ve published the answers to the last Question of the Month: What Grounds or Justifies Morality? I submitted an answer that wasn’t included, and having read the 10 selected, I believe I could have done better. In my answer, I said, ‘courage’, based on the fact that it takes courage for someone to take a stand against the tide of demonisation of the ‘other’, which we witness so often in history and even contemporary society.
 
However, that is too specific and doesn’t really answer the question, which arguably is seeking a principle, like the ‘Golden Rule’ or the Utilitarian principle of ‘the greatest happiness to the greatest number’. Many answers cited Kant’s appeal to ‘reason’, and some cited religion and others, some form of relativism. All in all, I thought they were good answers without singling any one out.
 
So what did I come up with? Well, partly based on observations of my own fiction and my own life, I decided that morality needed to be grounded in trust. I’ve written about trust at least twice before, and I think it’s so fundamental, because, both one-on-one relationships (of all types) and society as a whole, can’t function properly without it. If you think about it, how well you trust someone is a good measure of your assessment of their moral character. But it functions at all levels of society. Imagine living in a society where you can’t say what you think, where you have to obey strict rules of secrecy and deception or you will be punished. Such societies exist.
 
I’ve noticed a recurring motif in my stories (not deliberate) of loyalties being tested and of moral dilemmas. Both in my private life and professional life, I think trust is paramount. It’s my currency. I realised a long time ago that if people don’t trust me, I have no worth.

Kant and modern physics

 I wrote a post on Kant back in February 2020, but it was actually an essay I wrote more than 20 years earlier, when I was a student of philosophy. I would not be able to improve on that essay, and I’m not about to try now. In that essay, I argue that Kant’s great contribution to philosophy, and epistemology in particular, was his idea of the ‘thing-in-itself’, which may remain forever unknowable, as we only have our perceptions of ‘things’.
 
In other posts, I have sometimes argued that the ‘thing-in-itself’ is dependent on the scale that we can observe it, but there is something deeper that I think only became apparent in the so-called golden age of physics in the 20th Century. In a more recent post, I pointed out that both relativity theory and quantum mechanics (the 2 pillars of modern physics) are both observer dependent. I argue that there could be an objective ontology that they can’t describe. I think this is more obvious in the case of special relativity, where different observers literally measure different durations of both space and time, but I’m getting ahead of myself.
 
On Quora, there are 4 physicists whom I ‘follow’ and read regularly. They are Viktor T Toth, Richard Muller, Mark John Fernee and Ian Miller. Out of these, Miller is possibly the most contentious as he argues against non-locality in QM (quantum mechanics), which I’m not aware of any other physicist concurring with. Of course, it’s Bell’s Inequality that provides the definitive answer to this, of which Miller has this to say:
 
If you say it must because of violations of Bell’s Inequality, first note that the inequality is a mathematical relationship that contains only numbers; no physical concept is included.
 
But the ‘numbers’ compare classical statistical outcomes with Born statistical outcomes and experiments verify Born’s results, so I disagree. Having said that, Miller makes pertinent points that I find insightful and, like all those mentioned, he knows a lot more about this topic than me.
 
For example, concerning relativity, he argues that it’s the ruler that changes dimension and not the space being measured. He also points out, regarding the twin paradox, that only one twin gains energy, which is the one whose clock slows down. Note that clocks are also a form of ‘ruler’, but they measure time instead of space. So you can have 2 observers who ‘measure’ different durations of space and time, but agree on ‘now’, when they reunite, as is the case with the twin paradox thought experiment.
 
This point is slightly off-track, but not irrelevant to the main focus of this post. The main focus is an academic paper jointly written by Shaun Maguire and Richard Muller, titled Now, and the Flow of Time. This paper is arguably as contentious as Miller’s take on non-locality and Bell, because Muller and Maguire argue that ‘space’ can be created.
 
Now, Viktor T Toth is quite adamant that space is not created because space is not an entity, but a ‘measurement’ between entities called ‘objects’. Now, it has to be said, that Muller has stated publicly on Quora that he has utmost respect for Toth and neither of them have called each other out over this issue.
 
Toth argues that people confound the mathematical metric with ‘space’ or ‘spacetime’, but I’d argue that this mathematical metric has physical consequences. In another post, I reference another paper, recommended to me by Mark John Fernee (authored by Tamara M. Davis and Charles H. Lineweaver at the University of New South Wales) which describes how a GR Doppler shift intrinsically measures the expansion of space.
 
The general relativistic interpretation of the expansion interprets cosmological redshifts as an indication of velocity since the proper distance between comoving objects increases. However, the velocity is due to the rate of expansion of space, not movement through space, and therefore cannot be calculated with the special relativistic Doppler shift formula. (My emphasis)
 
As I explain in that post: ‘What they are effectively saying is that there is a distinction between the movement of objects in space and the movement of space itself.’
 
The spacetime metric that Toth refers to provides a reference frame for c, the speed of light. So, whilst a spacetime metric (‘space’ by another name) can travel faster than light with respect to us (so over the horizon of the observable universe), an observer situated in that metric would still measure light as c relative to them.
 
Muller’s and Maguire’s paper goes even further, saying that space is created along with time, and they believe this can be measured as ‘a predicted lag in the emergence of gravitational radiation when two black holes merge.’ I won’t go into the details; you would need to read the paper.
 
A conclusion implicit in their theory is that there could be a universal now.
 
A natural question arises: why are the new nows created at the end of time, rather than uniformly throughout time, in the same way that new space is uniformly created throughout the universe.
 
The authors then provide alternative arguments, which I won’t go into, but they do ponder the fundamental difference between space and time, where one is uni-directional and the other is not. As far as we know, there is no ‘edge’ in space but there is in time. Muller and Maguire do wonder if space is ‘created’ throughout the Universe (as quoted above) or at an ‘edge’.
 
You may wonder how does Kant fit into all this? It’s because all these discussions are dependent on what we observe and what we theorise, both of which are perceptions. And, in physics, theorising involves mathematics. I’ve argued that mathematics can be seen as another medium determining perceptions, along with all the instruments we’ve built that now include the LHC and the Hubble and Webb telescopes.
 
Sabine Hossenfelder, whom I often reference on this blog these days, wrote a book, called Lost in Math, where she interviews some of the brightest minds in physics and challenges the pervading paradigm that mathematics can provide answers to questions that experimentation can’t – string theory being the most obvious.

Before the revolution in cosmology, created by Copernicus and built on by Galileo, Kepler and Newton, people believed that the Sun went round the Earth and that some objects in the night sky would occasionally backtrack in their orbits, which was explained by epicycles. That was overturned, and now it seems obvious that, in fact, the Earth rotates on its axis and orbits the sun along with all the other planets, which explains our ‘perception’ that sometimes the planets go ‘backwards.’
 
I wonder if the next revolution in science and cosmology may also provide a ‘simpler’ picture, where there is a ‘universal now’ that explains the age of the Universe, the edge of time that we all experience and non-locality in QM.
 
Of course, I’m probably wrong.

Addendum: This is Richard Muller talking about time on Quora.