Understanding Einstein’s special theory of relativity

In imagining a Sci-Fi scenario, I found a simple way of describing, if not explaining, Einstein’s special theory of relativity.

Imagine if a flight to the moon was no different to flying half way round the world in a contemporary airliner. In my scenario, the ‘shuttle’ would use an anti-gravity drive that allows high accelerations without killing its occupants with inertial forces. In other words, it would accelerate at hyper-speeds without anyone feeling it. I even imagined this when I was in high school, believe it or not.

The craft would still not be able to break the speed of light but it would travel fast enough that relativistic effects would be observable, both by the occupants and anyone remaining on the Earth or at its destination, the Moon.

So what are those relativistic effects? There is a very simple equation for velocity, and this is the only equation I will use to supplement my description.

v = s/t

Where v is the velocity, s is the distance travelled and t is the time or duration it takes. You can’t get much simpler than that. Note that s and t have an inverse relationship: if s gets larger, v increases, but if t gets larger, v decreases.

But it also means that for v to remain constant, if s gets smaller then so must t.

For the occupants of the shuttle, getting to the moon in such a short time means that, for them, the distance has shrunk. It normally takes about 3 days to get to the Moon (using current technology), so let’s say we manage it in 10 hrs instead. I haven’t done the calculations, because it depends on what speeds are attained and I’m trying to provide a qualitative, even intuitive, explanation rather than a technical one. The point is that if the occupants measured the distance using some sort of range finder, they’d find it was measurably less than if they did it using a range finder on Earth or on the Moon. It also means that whatever clocks they were carrying (including their own heartbeats) they would show that the duration was less, completely consistent with the equation above.

For the people on the Moon awaiting their arrival, or those on Earth left behind, the duration would be consistent with the distance they would measure independently of the craft, which means the distance would be whatever it was all of the time (allowing for small variances created by any elliptic eccentricity in its orbit). That means they would expect the occupants’ clocks to be the same as theirs. So when they see the discrepancy in the clocks it can only mean that time elapsed slower for the shuttle occupants compared to the moon’s inhabitants.

Now, many of you reading this will see a conundrum if not a flaw in my description. Einstein’s special theory of relativity infers that for the occupants of the shuttle, the clocks of the Moon and Earth occupants should also have slowed down, but when they disembark, they notice that they haven’t. That’s because there is an asymmetry inherent in this scenario. The shuttle occupants had to accelerate and decelerate to make the journey, whereas the so-called stationary observers didn’t. This is the same for the famous twin paradox.

Note that from the shuttle occupants’ perspective, the distance is shorter than the moon and Earth inhabitants’ measurements; therefore so is the time. But from the perspective of the moon and Earth inhabitants, the distance is unchanged but the time duration has shortened for the shuttle occupants compared to their own timekeeping. And that is special relativity theory in a nutshell.


Footnote: If you watch videos explaining the twin paradox, they emphasise that it’s not the acceleration that makes the difference (because it’s not part of the Lorentz transformation). But the acceleration and deceleration is what creates the asymmetry that one ‘moved’ respect to another that was ‘stationary’. In the scenario above, the entire solar system doesn’t accelerate and decelerate with respect to the shuttle, which would be absurd. This is my exposition on the twin paradox.

Addendum 1: Here is an attempted explanation of Einstein’s general theory of relativity, which is slightly more esoteric.

Addendum 2: I’ve done a rough calculation and the differences would be negligible, but if I changed the destination to Mars, the difference in distances would be in the order of 70,000 kilometres, but the time difference would be only in the order of 10 seconds. You could, of course, make the journey closer to lightspeed so the effects are more obvious.

Addendum 3: I’ve read the chapter on the twin paradox in Jim Al-Khalili’s book, Paradox: The Nine Greatest Enigmas in Physics. He points out that during the Apollo missions to the moon, the astronauts actually aged more (by nanoseconds) because the time increase by leaving Earth’s gravity was greater than any special relativistic effects experienced over the week-long return trip. Al-Khalili also explains that the twin who makes the journey, endures less time because the distance is shorter for them (as I expounded above). But, contrary to the YouTube lectures (that I viewed) he claims that it’s the acceleration and deceleration creating general relativistic effects that creates the asymmetry.

Are natural laws reality?

In a not-so-recent post, I mentioned a letter I wrote to Philosophy Now challenging a throwaway remark by Raymond Tallis in his regular column called Tallis in Wonderland. As I said in that post, I have a lot of respect for Tallis but we disagree on what physics means. Like a lot of 20th Century philosophers, he challenges the very idea of mathematically determined natural laws. George Lakoff (a linguist) is another who comes to mind, though I’m reluctant to put Tallis and Lakoff in the same philosophical box. I expect Tallis has more respect for science and philosophy in general, than Lakoff has. But both of them, I believe, would see our ‘discovery’ of natural laws as ‘projections’ and their mathematical representation as metaphorical.

There is an aspect of this that would seem to support their point of view, and that’s the fact that our discoveries are never complete. We can always find circumstances where the laws don’t apply or new laws are required. The most obvious examples are Einstein’s general theory of relativity replacing Newton’s universal theory of gravity, and quantum mechanics replacing Newtonian mechanics.

I’ve discussed these before, but I’ll repeat myself because it’s important to understand why and how these differences arise. One of the conditions that Einstein set himself when he created his new theory of gravity was that it reduced to Newton’s theory when relativistic effects were negligible. This feat is quite astounding when one considers that the mathematics, involved in both theories, appear, on the surface, to have little in common.

In respect to quantum mechanics, I contend that it is distinct from classical physics and the mathematics reflects that. I should point out that no one else agrees with this view (to my knowledge) except Freeman Dyson.

Newtonian mechanics has other limitations as well. In regard to predicting the orbits of the planets, it quickly becomes apparent that as one increases the number of bodies the predictions become more impossible over longer periods of time, and this has nothing to do with relativity. As Jeremy Lent pointed out in The Patterning Instinct, Newtonian classical physics doesn’t really work for the real world, long term, and has been largely replaced by chaos theory. Both classical and quantum physics are largely ‘linear’, whereas nature appears to be persistently non-linear. This means that the Universe is unpredictable and I’ve discussed this in some detail elsewhere.

Nature obeys different rules at different levels. The curious thing is that we always believe that we’ve just about discovered everything there is to know, then we discover a whole new layer of reality. The Universe is worlds within worlds. Our comprehension of those worlds is largely dependent on our knowledge of mathematics.

Some people (like Gregory Chaitin and Stephen Wolfram) even think that there is something akin to computer code underpinning the entire Universe, but I don’t. Computers can’t deal with chaotic non-linear phenomena because one needs to calculate to infinity to get the initial conditions that determine the phenomenon’s ultimate fate. That’s why even the location of the solar system’s planets are not mathematically guaranteed.

Below is a draft of the letter I wrote to Philosophy Now in response to Raymond Tallis’s scepticism about natural laws. It’s not the one I sent.


Quantities actually exist in the real world, in nature, and they come in specific ratios and relationships to each other; hence the 'natural laws'. They are not fictions, we did not make them up, they are not products of our imaginations.

Having said that, the wave function in quantum mechanics is a product of Schrodinger's imagination, and some people argue that it is a fiction. Nevertheless, it forms the basis of QED (quantum electrodynamics) which is the most successful empirically verified scientific theory to date, so they may actually be real; it's debatable. Einstein's field equations, based on tensors, are also arguably a product of his imagination, but, according to Einstein's own admission, the mathematics determined his conclusion that space-time is curved, not the other way around. Also his famous equation, E= mc², is mathematically derived from his special theory of relativity and was later confirmed by experimental evidence. So sometimes, in physics, the map is discovered before the terrain.

The last line is a direct reference to Tallis’s own throwaway line that mathematical physicists tend to ‘confuse the map for the terrain’.

What makes humans unique

Now everyone pretty well agrees that there is not one single thing that makes humans unique in the animal kingdom, but most people would agree that our cognitive abilities leave the most intelligent and social of species in our wake. I say ‘most’ because there are some, possibly many, who argue that humans are not as special as we like to think and there is really nothing we can do that other species can’t do. They would point out that other species, if not all advanced species, have language, and many produce art to attract a mate and build structures (like ants and beavers) and some even use tools (like apes and crows).

However, I find it hard to imagine that other species can think and conceptualise in a language the way we do or even communicate complex thoughts and intentions using oral utterances alone. To give other examples, I know of no other species that tells stories, keeps track of days by inventing a calendar based on heavenly constellations (like the Mayans) or even thinks about thinking. And as far as I know, we are the only species who literally invents a complex language that we teach our children (it’s not inherited) so that we can extend memories across generations. Even cultures without written scripts can do this using songs and dances and art. As someone said (John Hands in Cosmo Sapiens) we are the only species ‘who know that we know’. Or, as I said above, we are the only species that ‘thinks about thinking’.

Someone once pointed out to me that the only thing that separates us from all other species is the accumulation of knowledge, resulting in what we call civilization. He contended that over hundreds, even thousands of years, this had resulted in a huge gap between us and every other sentient creature on the planet. I pointed out to him that this only happened because we had invented the written word, based on languages, that allowed us to transfer memories across generations. Other species can teach their young certain skills, that may not be genetically inherited, but none can accumulate knowledge over hundreds of generations like we can. His very point demonstrated the difference he was trying to deny.

In a not-so-recent post, I delineated my philosophical ruminations into 23 succinct paragraphs, covering everything from science and mathematics to language, morality and religion.  My 16th point said:



Humans have the unique ability to nest concepts within concepts ad-infinitum, which mirror the physical world.

In another post from 2012, in answer to a Question of the Month in Philosophy  Now: How does language work?; I made the same point. (This is the only submission to Philosophy Now, out of 8 thus far, that didn’t get published.)

I attributed the above ‘philosophical point’ to Douglas Hofstadter, because he says something similar in his Pulitzer Prize winning book, Godel Escher Bach, but in reality, I had reached this conclusion before reading it.

It’s my contention that it is this ability that separates us from other species and that has allowed all the intellectual endeavours we associate with humanity, including stories, music, art, architecture, mathematics, science and engineering.

I will illustrate with an example that we are all familiar with, yet many of us struggle to pursue at an advanced level. I’m talking about mathematics, and I choose it because I believe it also explains why many of us fail to achieve the degree of proficiency we might prefer.

With mathematics we learn modules which we then use as a subroutine in a larger calculation. To give a very esoteric example, Einstein’s general theory of relativity requires at least 4 modules: calculus, vectors, matrices and the Lorentz transformation. These all combine in a metric tensor that becomes the basis of his field equations. The thing is, if you don’t know how to deal with any one of these, you obviously can’t derive his field equations. But the point is that the human brain can turn all these ‘modules’ into black boxes and then the black boxes can be manipulated at another level.

It’s not hard to see that we do this with everything, including writing an essay like I’m doing now. I raise a number of ideas and then try to combine them into a coherent thesis. The ‘atoms’ are individual words but no one tries to comprehend it at that level. Instead they think in terms of the ideas that I’ve expressed in words.

We do the same with a story, which becomes like a surrogate life for the time that we are under its spell. I’ve pointed out in other posts that we only learn something new when we integrate it into what we already know. And, with a story, we are continually integrating new information into existing information. Without this unique cognitive skill, stories wouldn’t work.

But more relevant to the current topic, the medium for a story is not words but the reader’s imagination. In a movie, we short-circuit the process, which is why they are so popular.

Because a story works at the level of imagination, it’s like a dream in that it evokes images and emotions that can feel real. One could imagine that a dog or a cat could experience emotions if we gave them a virtual reality experience, but a human story has the same level of complexity that we find in everyday life and which we express in a language. The simple fact that we can use language alone to conjure up a world with characters, along with a plot that can be followed, gives some indication of how powerful language is for the human species.

In a post I wrote on storytelling back in 2012, I referenced a book by Kiwi academic, Brian Boyd, who points out that pretend play, which we all do as children (though I suspect it’s now more likely done using a videogame console) gives us cognitive skills and is the precursor to both telling and experiencing stories. The success of streaming services indicates how stories are an essential part of the human experience.

While it’s self-evident that both mathematics and storytelling are two human endeavours that no other species can do (even at a rudimentary level) it’s hard to see how they are related.

People who are involved in computer programming or writing code, are aware of the value, even necessity, of subroutines. Our own brain does this when we learn to do something without having to think about it, like walking. But we can do the same thing with more complex tasks like driving a car or playing a musical instrument. The key point here is that they are all ‘motor tasks’, and we call the result ‘muscle memory’, as distinct from cognitive tasks. However, I expect it relates to cognitive tasks as well. For example, every time you say something it’s like the sentence has been pre-formed in your brain. We use particular phrases, all the time, which are analogous to ‘subroutines.’

I should point out that this doesn’t mean that computers ‘think’, which is a whole other topic. I’m just relating how the brain delegates tasks so it can ‘think’ about more important things. If we had to concentrate every time we took a step, we would lose the train of thought of whatever it was we were engaged in at the time; a conversation being the most obvious example.

The mathematics example I gave is not dissimilar to the idea of a ‘subroutine’. In fact, one can employ mathematical ‘modules’ into software, so it’s more than an analogy. So with mathematics we’ve effectively achieved cognitively what the brain achieves with motor skills at the subconscious level. And look where it has got us: Einstein’s general theory of relativity, which is the basis of all current theories of the Universe.

We can also think of a story in terms of modules. They are the individual scenes, which join together to form an episode, which form together to create an overarching narrative that we can follow even when it’s interrupted.

What mathematics and storytelling have in common is that they are both examples where the whole appears to be greater than the sum of its parts. Yet we know that in both cases, the whole is made up of the parts, because we ‘process’ the parts to get the whole. My point is that only humans are capable of this.

In both cases, we mentally build a structure that seems to have no limits. The same cognitive skill that allows us to follow a story in serial form also allows us to develop scientific theories. The brain breaks things down into components and then joins them back together to form a complex cognitive structure. Of course, we do this with physical objects as well, like when we manufacture a car or construct a building, or even a spacecraft. It’s called engineering.

When real life overtakes fiction

I occasionally write science fiction; a genre I chose out of fundamental laziness. I knew I could write in that medium without having to do any research to speak of. I liked the idea of creating the entire edifice - world, story and characters - from my imagination with no constraints except the bounds of logic.

There are many subgenres of sci-fi: extraterrestrial exploration, alien encounters, time travel, robots & cyborgs, inter-galactic warfare, genetically engineered life-forms; but most SF stories, including mine, are a combination of some of these. Most sci-fi can be divided into 2 broad categories – space opera and speculative fiction, sometimes called hardcore SF. Space operas, exemplified by the Star Wars franchise, Star Trek and Dr Who, generally take more liberties with the science part of science fiction.

I would call my own fictional adventures science-fantasy, in the mould of Frank Herbert’s Dune series or Ursula K Le Guin’s fiction; though it has to be said, I don’t compete with them on any level.

I make no attempt to predict the future, even though the medium seems to demand it. Science fiction is a landscape that I use to explore ideas in the guise of a character-oriented story. I discovered, truly by accident, that I write stories about relationships. Not just relationships between lovers, but between mother and daughter, daughter and father(s), protagonist and nemesis, protagonist and machine.

One of the problems with writing science fiction is that the technology available today seems to overtake what one imagines. In my fiction no one uses a mobile phone. I can see a future where people can just talk to someone in the ether, because they can connect in their home or in their car, without a device per se. People can connect via a holographic form of Skype, which means they can have a meeting with someone in another location. We are already doing this, of course, and variations on this theme have been used in Star Wars and other space operas. But most of the interactions I describe are very old fashioned face-to-face, because that's still the best way to tell a story.

If you watch (or read) crime fiction you’ll generally find it’s very suspenseful with violence not too far away. But if you analyze it, you’ll find it’s a long series of conversations, with occasional action and most of the violence occurring off-screen (or off-the-page). In other words, it’s more about personal interactions than you realise, and that’s what generally attracts you, probably without you even knowing it.

This is a longwinded introduction to explain why I am really no better qualified to predict future societies than anyone else. I subscribe to New Scientist and The New Yorker, both of which give insights into the future by examining the present. In particular, I recently read an article in The New Yorker (Dec, 17, 2018) by David Owen about facial-recognition, called Here’s Looking At You, that is already being used by police forces in America to target arrests without any transparency. Mozilla (in a podcast last year) described how a man had been misidentified twice, was arrested and subsequently lost his job and his career. I also read in last week’s New Scientist (15 Dec. 2018) how databases are being developed to know everything about a person, even what TV shows they watch and their internet use. It’s well known that in China there is a credit-point system that determines what buildings you can access and what jobs you can apply for. China has the most surveillance cameras anywhere in the world, and they intend to combine them with the latest facial recognition software.

Yuval Harari, in Homo Deus, talks about how algorithms are going to take over our lives, but I think he missed the mark. We are slowly becoming more Orwellian with social media already determining election results. In the same issue of New Scientist, journalist, Chelsea Whyte, asks: Is it time to unfriend the social network? with specific reference to Facebook’s recently exposed track-record. According to her: “Facebook’s motto was once ‘move fast and break things.’ Now everything is broken.” Quoting from the same article:

Now, the UK parliament has published internal Facebook emails that expose the mindset inside the company. They reveal discussions among staff over whether to collect users’ phone call logs and SMS texts through its Android app. “This is a pretty high-risk thing to do from a PR perspective but it appears that the growth team will charge ahead and do it.” (So said Product Manager Michael LeBeau in an email from 2015)

Even without Edward Snowden’s whistle-blowing expose, we know that governments the world over are collecting our data because the technological ability to do that is now available. We are approaching a period in our so-called civilised development where we all have an on-line life (if you are reading this) and it can be accessed by governments and corporations alike. I’ve long known that anyone can learn everything they need to know about me from my computer, and increasingly they don’t even need the computer.

In one of my fictional stories, I created a dystopian world where everyone had a ‘chip’ that allowed all conversations to be recorded so there was literally no privacy. We are fast approaching that scenario in some totalitarian societies. In Communist China under Mao, and Communist Soviet Union under Stalin, people found the circle of people they could trust got smaller and smaller. Now with AI capabilities and internet-wide databases, privacy is becoming illusory. With constant surveillance, all subversion can be tracked and subsequently prosecuted. Someone once said that only societies that are open to new ideas progress. If you live in a society where new ideas are censored then you will get stagnation.

In my latest fiction I’ve created another autocratic world, where everyone is tracked because everywhere they go they interact with very realistic androids who act as servants, butlers and concierges, but, in reality, keep track of what everyone’s doing. The only ‘futuristic’ aspect of this are the androids and the fact that I’ve set it on some alien world. (My worlds aren’t terra-formed; people live in bubbles that create a human-friendly environment.)

After reading these very recent articles in New Scientist and TNY, I’ve concluded that our world is closer to the one I’ve created in my imagination than I thought.


Addendum 1: This is a podcast about so-called Surveillance Capitalism, from Mozilla. Obviously, I use Google and I'm also on FaceBook, but I don't use Twitter. Am I part of the problem or part of the solution? The truth is I don't know. I try to make people think and share ideas. I have political leanings, obviously, but they're transparent. Foremost, I believe, that if you can't put your name to something you shouldn't post it.

The search for ultimate truth is unattainable

Someone lent me a really good philosophy book called Ultimate Questions by Bryan Magee.  To quote directly from the back fly leaf cover: “Bryan Magee has had an unusually multifaceted career as a professor of philosophy, music and theatre critic, BBC broadcaster and member of [British] Parliament.” It so happens I have another of his books, The Story of Philosophy, which is really a series of interviews with philosophers about philosophers, and I expect it’s a transcription of radio podcasts. Magee was over 80 when he wrote Ultimate Questions, which must be prior to 2016 when the book was published.

This is a very thought-provoking book, which is what you'd expect from a philosopher. To a large extent, and to my surprise, Magee and I have come to similar positions on fundamental epistemological and ontological issues, albeit by different paths. However, there is also a difference, possibly a divide, which I’ll come to later.

Where to start? I’ll start at the end because it coincides with my beginning. It’s not a lengthy tome (120+ pages) and it’s comprised of 7 chapters or topics, which are really discussions. In the last chapter, Our Predicament Summarized, he emphasises his view of an inner and outer world, both of which elude full comprehension, that he’s spent the best part of the book elaborating on.

As I’ve discussed previously, the inner and outer world is effectively the starting point for my own world view. The major difference between Magee and myself are the paths we’ve taken. My path has been a scientific one, in particular the science of physics, encapsulating as it does, the extremes of the physical universe, from the cosmos to the infinitesimal.

Magee’s path has been the empirical philosophers from Locke to Hume to Kant to Schopenhauer and eventually arriving at Wittgenstein. His most salient and persistent point is that our belief that we can comprehend everything there is to comprehend about the ‘world’ is a delusion. He tells an anecdotal story of when he was a student of philosophy and he was told that the word ‘World’ comprised not only what we know but everything we can know. He makes the point, that many people fail to grasp, that there could be concepts that are beyond our grasp in the same way that there are concepts we do understand but are nevertheless beyond the comprehension of the most intelligent of chimpanzees or dolphins or any creature other than human. None of these creatures can appreciate the extent of the heavens the way we can or even the way our ancient forebears could. Astronomy has a long history. Even indigenous cultures, without the benefit of script, have learned to navigate long distances with the aid of the stars. We have a comprehension of the world that no other creature has (on this planet) so it’s quite reasonable to assume that there are aspects of our world that we can’t imagine either.

Because my path to philosophy has been through science, I have a subtly different appreciation of this very salient point. I wrote a post based on Noson Yanofsky’s The Outer Limits of Reason, which addresses this very issue: there are limits in logic, mathematics and science, and there always will be. But I’m under the impression that Magee takes this point further. He expounds, better than anyone else I’ve read, that there are actual limits to what our brains can, not only perceive, but conceptualise, which leads to the possibility, most of us ignore, that there are things beyond our kin completely and always.

As Magee himself states, this opens the door to religion, which he discusses at length, yet he gives this warning: “Anyone who sets off in honest and serious pursuit of truth needs to know that in doing that he is leaving religion behind.” It’s a bit unfair to provide this quote out of context, as it comes at the end of a lengthy discussion, nevertheless, it’s the word ‘truth’ that gives his statement cogency. My own view is that religion is not an epistemology, it’s an experience. What’s more it’s an experience (including the experience of God) that is unique to the person who has it and can’t be shared with anyone else. This puts individual religious experience at odds with institutionalised religions, and as someone pointed out (Yuval Harari, from memory) this means that the people who have religious experiences are all iconoclasts.

I’m getting off the point, but it’s relevant in as much that arguments involving science and religion have no common ground. I find them ridiculous because they usually involve pitting an ancient text (of so-called prophecy) against modern scientific knowledge and all the technology it has propagated, which we all rely upon for our day-to-day existence. If religion ever had an epistemological role it has long been usurped.

On the other hand, if religion is an experience, it is part of the unfathomable which lies outside our rational senses, and is not captured by words. Magee contends that the best one can say about an afterlife or the existence of a God, is that ‘we don’t know’. He calls himself an agnostic but not just in the narrow sense relating to a Deity, but in the much broader sense of acknowledging our ignorance. He discusses these issues in much more depth than my succinct paraphrasing implies. He gives the example of music as something we experience that can’t be expressed in words. Many people have used music as an analogy for religious experience, but, as Magee points out, music has a material basis in instruments and a score and sound waves, whereas religion does not.

Coincidentally, someone today showed me a text on Socrates, from a much larger volume on classical Greece. Socrates famously proclaimed his ignorance as the foundation of his wisdom. In regard to science, he said: “Each mystery, when solved, reveals a deeper mystery.” This statement is so prophetic; it captures the essence of science as we know it today, some 2500 years after Socrates. It’s also the reason I agree with Magee.

John Wheeler conceived a metaphor, that I envisaged independently of him. (Further evidence that I’ve never had an original idea.)

We live on an island of knowledge surrounded by a sea of ignorance.
As our island of knowledge grows, so does the shore of our ignorance.

I contend that the island is science and the shoreline is philosophy, which implies that philosophy feeds science, but also that they are inseparable. By philosophy, in this context, I mean epistemology.

To give an example that confirms both Socrates and Wheeler, the discovery and extensive research into DNA provides both evidence and a mechanism for biological evolution from the earliest life forms to the most complex; yet the emergence of DNA as providing ‘instructions’ for the teleological development of an organism is no less a mystery looking for a solution than evolution itself.

The salient point of Wheeler's metaphor is that the sea of ignorance is infinite and so the island grows but is never complete. In his last chapter, Magee makes the point that truth (even in science) is something we progress towards without attaining. “So rationality requires us to renounce the pursuit of proof in favour of the pursuit of progress.” (My emphasis.) However, 'the pursuit of proof’ is something we’ve done successfully in mathematics ever since Euclid. It is on this point that I feel Magee and I part company.

Like many philosophers, when discussing epistemology, Magee hardly mentions mathematics. Only once, as far as I can tell, towards the very end (in the context of the quote I referenced above about ‘proof’) he includes it in the same sentence as science, logic and philosophy as inherited from Descartes, where he has this to say: “It is extraordinary to get people, including oneself, to give up this long-established pursuit of the unattainable.” He is right in as much as there will always be truths, including mathematical truths, that we can never know (refer my recent post on Godel, Turing and Chaitin). But there are also innumerable (mathematical) truths that we have discovered and will continue to discover into the future (part of the island of knowledge). As Freeman Dyson points out, 'Mathematics is forever', whilst discussing the legacy of Srinivasa Ramanujan's genius. In other words, mathematical truths don't become obsolete in the same way that science does.

I don’t know what Magee’s philosophical stance is on mathematics, but not giving it any special consideration tells me something already. I imagine, from his perspective, it serves no special epistemological role, except to give quantitative evidence for the validity of competing scientific theories.

In one of his earlier chapters, Magee talks about the ‘apparatus’ we have in the form of our senses and our brain that provide a limited means to perceive our external world. We have developed technological means to augment our senses; microscopes and telescopes being the most obvious. But we now have particle accelerators and radio telescopes that explore worlds we didn’t even know existed less than a century ago.

Mathematics, I would contend, is part of that extended apparatus. Riemann’s geometry allowed Einstein to perceive a universe that was ‘curved’ and Euler’s equation allowed Schrodinger to conceive a wave function. Both of these mathematically enhanced ‘discoveries’ revolutionised science at opposite ends of the epistemological spectrum: the cosmological and the subatomic.

Magee rightly points out our almost insignificance in both space and time as far as the Universe is concerned. We are figuratively like the blink of an eye on a grain of sand, yet reality has no meaning without our participation. In reference to the internal and external worlds that formulate this reality, Magee has this to say: “But then the most extraordinary thing is that the world of interaction between these two unintelligibles is rationally intelligible.” Einstein famously made a similar point: "The most incomprehensible thing about the Universe is that it’s comprehensible.”

One can’t contemplate that statement, especially in the context of Einstein’s iconic achievements, without considering the specific and necessary role of mathematics. Raymond Tallis, who writes a regular column in Philosophy Now, and for whom I have great respect, nevertheless downplays the role of mathematics. He once made the comment that mathematical Platonists (like me) 'make the error of confusing the map for the terrain.’ I wrote a response, saying: ‘the use of that metaphor infers the map is human-made, but what if the map preceded the terrain.’ (The response wasn’t published.) The Universe obeys laws that are mathematically in situ, as first intimated by Galileo, given credence by Kepler, Newton, Maxwell; then Einstein, Schrodinger, Heisenberg and Bohr.

I’d like to finish by quoting Paul Davies:

We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.

This, of course, is another way of formulating Roger Penrose’s 3 Worlds, and it’s the mathematical world that is, for me, the missing piece in Magee’s otherwise thought-provoking discourse.


Last word: I’ve long argued that mathematics determines the limits of our knowledge of the physical world. Science to date has demonstrated that Socrates was right: the resolution of one mystery invariably leads to another. And I agree with Magee that consciousness is a phenomenon that may elude us forever.

Addendum: I came across this discussion between Magee and Harvard philosopher, Hilary Putnam, from 1977 (so over 40 years ago), where Magee exhibits a more nuanced view on the philosophy of science and mathematics (the subject of their discussion) than I gave him credit for in my post. Both of these men take their philosophy of science from philosophers, like Kant, Descartes and Hume, whereas I take my philosophy of science from scientists: principally, Paul Davies, Roger Penrose and Richard Feynman, and to a lesser extent, John Wheeler and Freeman Dyson; I believe this is the main distinction between their views and mine. They even discuss this 'distinction' at one point, with the conclusion that scientists, and particularly physicists, are stuck in the past - they haven't caught up (my terminology, not theirs). They even talk about the scientific method as if it's obsolete or anachronistic, though again, they don't use those specific terms. But I'd point to the LHC (built decades after this discussion) as evidence that the scientific method is alive and well, and it works. (I intend to make this a subject of a separate post.)

Can AI be self-aware?

I recently got involved in a discussion on Facebook with a science fiction group on the subject of artificial intelligence. Basically, it started with a video claiming that a robot had discovered self-awareness, which is purportedly an early criterion for consciousness. But if you analyse what they actually achieved: it’s clever sleight-of-hand at best and pseudo self-awareness at worst. The sleight-of-hand is to turn fairly basic machine logic into an emotive gesture to fool humans (like you and me) into thinking it looks and acts like a human, which I’ll describe in detail below.

And it’s pseudo self-awareness in that it’s make-believe, in the same way that pseudo science is make-believe science, meaning pretend science, like creationism. We have a toy that we pretend exhibits self-awareness. So it is we who do the make-believe and pretending, not the toy.

If you watch the video you’ll see that they have 3 robots and they give them a ‘dumbing pill’ (meaning a switch was pressed) so they can’t talk. But one of them is not dumb and they are asked: “Which pill did you receive?” One of them dramatically stands up and says: “I don’t know”. But then waves its arm and says, “I’m sorry, I know now. I was able to prove I was not given the dumbing pill.”

Obviously, the entire routine could have been programmed, but let’s assume it’s not. It’s a simple TRUE/FALSE logic test. The so-called self-awareness is a consequence of the T/F test being self-referential – whether it can talk or not. It verifies that it’s False because it hears its own voice. Notice the human-laden words like ‘hears’ and ‘voice’ (my anthropomorphic phrasing). Basically, it has a sensor to detect sound that it makes itself, which logically determines whether the statement, it’s ‘dumb’, is true or false. It says, ‘I was not given a dumbing pill’, which means its sound was not switched off. Very simple logic.

I found an on-line article by Steven Schkolne (PhD in Computer Science at Caltech), so someone with far more expertise in this area than me, yet I found his arguments for so-called computer self-awareness a bit misleading, to say the least. He talks about 2 different types of self-awareness (specifically for computers) – external and internal. An example of external self-awareness is an iphone knowing where it is, thanks to GPS. An example of internal self-awareness is a computer responding to someone touching the keyboard. He argues that “machines, unlike humans, have a complete and total self-awareness of their internal state”. For example, a computer can find every file on its hard drive and even tell you its date of origin, which is something no human can do.

From my perspective, this is a bit like the argument that a thermostat can ‘think’. ‘It thinks it’s too hot or it thinks it’s too cold, or it thinks the temperature is just right.’ I don’t know who originally said that, but I’ve seen it quoted by Daniel Dennett, and I’m still not sure if he was joking or serious.

Computers use data in a way that humans can’t and never will, which is why their memory recall is superhuman compared to ours. Anyone who can even remotely recall data like a computer is called a savant, like the famous ‘Rain Man’. The point is that machines don’t ‘think’ like humans at all. I’ll elaborate on this point later. Schkolne’s description of self-awareness for a machine has no cognitive relationship to our experience of self-awareness. As Schkone says himself: “It is a mistake if, in looking for machine self-awareness, we look for direct analogues to human experience.” Which leads me to argue that what he calls self-awareness in a machine is not self-awareness at all.

A machine accesses data, like GPS data, which it can turn into a graphic of a map or just numbers representing co-ordinates. Does the machine actually ‘know’ where it is? You can ask Siri (as Schkolne suggests) and she will tell you, but he acknowledges that it’s not Siri’s technology of voice recognition and voice replication that makes your iphone self-aware. No, the machine creates a map, so you know where ‘You’ are. Logically, a machine, like an aeroplane or a ship, could navigate over large distances with GPS with no humans aboard, like drones do. That doesn’t make them self-aware; it makes their logic self-referential, like the toy robot in my introductory example. So what Schkolne calls self-awareness, I call self-referential machine logic. Self-awareness in humans is dependent on consciousness: something we experience, not something we deduce.

And this is the nub of the argument. The argument goes that if self-awareness amongst humans and other species is a consequence of consciousness, then machines exhibiting self-awareness must be the first sign of consciousness in machines. However, self-referential logic, coded into software doesn’t require consciousness, it just requires machine logic suitably programmed. I’m saying that the argument is back-to-front. Consciousness can definitely imbue self-awareness, but a self-referential logic coded machine does not reverse the process and imbue consciousness.

I can extend this argument more generally to contend that computers will never be conscious for as long as they are based on logic. What I’d call problem-solving logic came late, evolutionarily, in the animal kingdom. Animals are largely driven by emotions and feelings, which I argue came first in evolutionary terms. But as intelligence increased so did social skills, planning and co-operation.

Now, insect colonies seem to put the lie to this. They are arguably closer to how computers work, based on algorithms that are possibly chemically driven (I actually don’t know). The point is that we don’t think of ants and bees as having human-like intelligence. A termite nest is an organic marvel, yet we don’t think the termites actually plan its construction the way a group of humans would. In fact, some would probably argue that insects don’t even have consciousness. Actually, I think they do. But to give another well-known example, I think the dance that bees do is ‘programmed’ into their DNA, whereas humans would have to ‘learn’ it from their predecessors.

There is a way in which humans are like computers, which I think muddies the waters, and leads people into believing that the way we think and the way machines ‘think’ is similar if not synonymous.

Humans are unique within the animal kingdom in that we use language like software; we effectively ‘download’ it from generation to generation and it limits what we can conceive and think about, as Wittgenstein pointed out. In fact, without this facility, culture and civilization would not have evolved. We are the only species (that we are aware of) that develops concepts and then manipulates them mentally because we learn a symbol-based language that gives us that unique facility. But we invented this with our brains; just as we invent symbols for mathematics and symbols for computer software. Computer software is, in effect, a language and it’s more than an analogy.

We may be the only species that uses symbolic language, but so do computers. Note that computers are like us in this respect, rather than us being like computers. With us, consciousness is required first, whereas with AI, people seem to think the process can be reversed: if you create a machine logic language with enough intelligence, then you will achieve consciousness. It’s back-to-front, just as self-referential logic creating self-aware consciousness is back-to-front.

I don't think AI will ever be conscious or sentient. There seems to be an assumption that if you make a computer more intelligent it will eventually become sentient. But I contend that consciousness is not an attribute of intelligence. I don't believe that more intelligent species are more conscious or more sentient. In other words, I don't think the two attributes are concordant, even though there is an obvious dependency between consciousness and intelligence in animals. But it’s a one way dependency; if consciousness was dependent on intelligence then computers would already be conscious.


Addendum: The so-called Turing test is really a test for humans, not robots, as this 'interview' with 'Sophia' illustrates.