The Mirror Paradox

The mirror paradox is best stated as a question: why is a mirror image seen as left to right reversed but not top to bottom? I’m not sure why this is always seen as a philosophical conundrum, when it involves science, and, to a lesser extent, psychology. Having said that, I’ve rarely seen it explained correctly, so maybe it is a philosophical conundrum after all. Certainly, Stephen Law, in his excellent book, Philosophy, believes it’s ‘a puzzle science cannot solve’. But I beg to differ: it’s a real optical phenomenon entailed by the 3 dimensional spatial world in which we live.

In the Oxford Companion to the Mind (1987), Richard L. Gregory (Professor of Neuropsychology at University of Bristol, UK) in my view, talked all around the solution, without actually delivering it. He certainly understood that there is no rotation in the mirror (see below). However, he seemed to think (like Stephen Law and Umberto Eco) that there is no reversal at all, though he once obliquely referred to an 'inversion', so maybe he knew without knowing that he knew.

In 2002, whilst working in America, I read Umberto Eco’s Kant and the Platypus, which was as stimulating a book as I’ve ever read on epistemology, though I think it would be a difficult read for anyone who wasn’t familiar with Kant, at least at a rudimentary level. When I had completed it, I wrote a long letter to Umberto, who acknowledged receipt of my letter but never followed up with a response. I learned later that he had a fight with throat cancer, so I take it as no slight that he didn’t respond further.

In one of his chapters, he gives a lengthy discourse on the mirror paradox, and that was one of my points of contention. He argued that a mirror ‘reverses nothing’, but a second reflection did reverse left to right, which restores the image to what we normally see. I pointed out to him that this was illogical, nevertheless there is a specific case where he is correct. I will return to this specific example at the end of my discourse. I need to say that I have great respect for both Stephen Law and Umberto Eco, as both of these men are far more knowledgeable than me in their respective fields.

Most people explain the mirror reflection in terms of rotation, as it appears that the mirror rotates the image around, and this is particularly compelling for mirror-reflected writing, as I explicate below. But this merely raises another question, effectively transcribing the paradox, not solving it. Why does it rotate the image about the vertical axis, not the horizontal axis? Stephen Law gives an analogy: if you walk through a door that opens on the right side, why does it open on the left side when you come back the other way? The answer is because you turn yourself around. Law argues that if we lived in zero gravity, whereby you could turn yourself upside down to open the door, it would still open the same way, so the implication is that it’s gravity that creates the emphasis on the vertical axis. In fact, Stephen Law speculates that if we lived in a weightless environment then perhaps the ‘mirror puzzle would not even be a puzzle’. But I believe he'd be wrong: it's the left-right symmetry of the human body that creates the emphasis on horizontal over vertical reflection.

All these explanations and descriptions seem to overlook the fact that there is no rotation in the mirror at all – in fact, it’s the lack of rotation that gives us mirror reflection. I believe that most of these explanations actually appreciate this fact; they just fail to explain it. But I have been keeping you in suspense – the answer to this puzzle is deceptively simple: the mirror doesn’t reverse left to right, or top to bottom, it reverses back to front. We live in 3 dimensions, not 2, and a mirror reverses everything in the dimension perpendicular to its plane. So the rotation is a genuine illusion (it doesn’t happen), but the reversal is a true optical phenomenon.

Below is an edited version of my exposition that I sent to Umberto Eco.

Normally, if we want to see something back to front we have to turn it around. Generally we do this by turning the object through its vertical axis but we can also turn it through its horizontal axis. If we turn it through its vertical axis, as happens when someone turns to face us, their left side appears on our right and their right side appears on our left. This is unavoidable. But they could also turn to face us by standing on their hands, in which case they would appear upside down but their left side would still be on our left and their right side on our right. Then if they stood by doing a half cart wheel they would resume their normal stance but left to right would be reversed. The mirror quite literally reverses the image back to front without rotating it through any axis at all. So we don’t see the image upside down but likewise we don’t see the left side on the right or the right side on the left. This is the illusion pure and simple. The illusion, when we face a mirror, is that it appears to rotate us around a vertical axis, when in fact it doesn’t, it turns us back to front. If we look at something between us and the mirror, we see the front of it facing us, and the back of it facing us in the mirror. This is the key to the illusion. When we look at ourselves in a mirror we expect to see ourselves as others see us, but we can only do this when we have 2 mirrors, which appears to really rotate everything about the vertical axis (as Eco contended), but, in actuality, restores front to back to front again. But I’m fast-forwarding - I will elaborate on double reflections later.

In other respects we are not fooled by the mirror’s conservation of left and right. If we see in the mirror someone standing behind us and to our left, we automatically look over our left shoulder, not our right. Where we are fooled is when we reach for something on a table between us and a mirror, as in the case of an object on a dressing table or a bathroom bench top, while watching the object in the mirror. If we reach for an object at the back of the table, we appear in the mirror to be reaching forward towards us, rather than away. Likewise, if we drag an object on the table towards us, we appear in the mirror to be pushing it backwards not forwards. If you doubt this, try shaving or combing your hair with your left hand instead of your right (or your right hand if you're left-handed). We’ve trained our preferred hand through years of practice.

When we look in the rear view mirror at a car parked behind us while standing at a traffic light, we see that the driver is sitting on the same side of the car as we are and we are not confused. Because we know the car is behind us, the same as in the previous example, when we knew that the person standing behind us in the mirror was on our left or right side just as the mirror dictated. If the car was traveling towards us, we would expect to see the driver on the opposite side to us because the car has been turned around it’s vertical axis. If we turned around to look at the driver behind us at the traffic light, we would still see that he or she is on the same side of the car as we are, because both cars are facing the same direction, even though we have turned around to look backwards. Therefore, when we look at the driver in the rear view mirror we can see that left and right have been conserved. So why is it that when we look at the number plate we have to read it backwards, as if it's been rotated?

Writing not only provides the best illustration of the illusion, it also provides the best means to understand it. If you hold up a page of a book with writing on both sides while facing a mirror, the side facing you is readable, but the side facing the mirror is mirror-reversed. However, if the page was transparent, then the writing on the other side would also appear mirror reversed exactly as it does in the mirror. Take a sheet of plastic or cellophane, or anything clear that can be written on. If you hold up this transparent sheet so that the writing is mirror-reversed to you then it will also appear mirror-reversed in the mirror. Likewise if you hold it up so that the writing is readable to you then it will appear readable in the mirror. So where did the illusion of rotation go?

The illusion has gone but the reversal hasn't. Because when you hold up the sheet so you can read it, you are looking at the front of the sheet whereas the image you see in the mirror is the back of the sheet. Left to right is not reversed but front to back is. The front you see in the mirror is actually the back to you. If you were to place yourself between the sheet and the mirror, without changing its orientation, you would see the writing mirror-reversed. The mirror mirror-reverses the back of the sheet. And, of course, you would have to turn yourself around to read it, which only emphasises the illusion that the mirror rotates the image, but actually it doesn’t. The reason writing always appears reversed left to right, is because we always turn it left to right to face the mirror. We do the rotation, not the mirror.

This brings me to the third image created by a second mirror. If you set a book upright on a dressing table (or a table with a mirror behind it) with the front cover facing you, then the back cover will be mirror-reversed in the mirror. If you then took a small mirror (say a shaving mirror) and place it between yourself and the book, but facing back into the main mirror (or background mirror) you can create a third image of the cover in the main mirror. This is very easy to do by small adjustment of the angle of the foreground mirror. Naturally enough (but only because we know in advance) we can read the front cover in the third image exactly as it appears to us on the table. If we didn’t already know this, I believe it would be a complete surprise. The important point is that the image is not rotated at all, it is simply reversed back to front twice, using an intermediary mirror that is facing away from us.

In fact the foreground mirror behaves in exactly the same way as the transparent sheet I referred to in the previous example. If you could see through the foreground mirror so it’s image could be read from the back (in other words if it was a transparent screen with the book cover projected onto it) we would be able to read it exactly as we can in its reflection in the background mirror. The point is though, that the foreground mirror reverses the image, not from left to right but back to front. The foreground mirror only has the writing in the right order because it is facing away from us. If you were to place yourself between it and the background mirror (and turn yourself around) you would see the writing is mirror-reversed as you would with the transparent sheet. So the background mirror mirror-reverses the foreground mirror.

But, as I alluded to earlier, there is a specific situation, and a common one, where a second mirror does translate the image directly from left to right, which upholds the illusion of rotation. We often find ourselves in a bar, or a bathroom, with 2 vertical mirrors joined at right angles like 2 walled mirrors. In this case the image you would see is a double reflection no matter which mirror you looked in. In fact, if there were 2 extended wall mirrors, then there would be 4 images of you, including the prime image. If you were to press your finger into the corner, you would see 4 symmetrical images of it, one of which would be you. Another unique feature of this third image is that it would always remain in the corner of the room as you moved about, whereas the other 2 images would follow you around. This also means, of course, that everyone in the room would see themselves in the corner (assuming they had a clear line of sight).

The (apparent) non-reversed image results from a secondary reflection coming off a primary reflection that you cannot see, because the two reflections simultaneously 'swap' over on the adjacent mirrors. This, in fact, does resemble a rotation about the vertical axis, simply because the mirrors are joined on a vertical axis. And this is what led Umberto Eco to argue that the first mirror image is not reversed left to right but the second image is. He is correct, in this specific case, but only because we create a virtual vertical axis of rotation by the very careful alignment of the 2 mirrors.

So now I have turned a simple answer into more than 2,000 words, and either have confused you completely or explained a common phenomenon thoroughly. I hope the latter.

Footnote: I had a brief discussion with Stephen Law on this topic. We agree to disagree over my belief that science does solve this puzzle. You can visit his post on this subject (and our dialogue) at the following: http://stephenlaw.blogspot.com/2007/04/mirror-puzzle-solution.html And explore the rest of his excellent site.

Addendum 1: If you think this exhausts the subject of mirrors, you should read Richard Feynman's quantum mechanical explanation of reflection in his truly fantastical book, QED, The Strange Theory of Light and Matter.

Addendum 2: There is something I need to tidy up. There is one situation where a mirror does reverse an image left to right, and it’s literally the exception that proves the rule, because it doesn’t reflect the image back to itself.

If you set up a mirror at 45 degrees along its vertical axis, it allows you to see around corners and there are lots of examples in car parks and other places. Note that you can’t see what’s behind you as you would normally expect from a mirror. Most of these (seen in real life) are convex so that you can see more using a smaller mirror.

The best way to demonstrate this is with a graphic that shows how the light rays reflected at 45 degrees axiomatically reverse their relative orientation from left to right. Note that if you were to tilt a mirror at 45 degrees along the horizontal axis, it would turn an image on the ground (facing you) upside down.

The Problem with Democracy

Anyone who has read my posts on Trust (Apr.08) and Human Nature (Nov.07) will know that I already extol the merits of democracy. In fact, I think it is the best form of governance yet devised by humankind, but, then, I’m one of the few lucky ones who really does reap the benefits from this political system. I live in a country where changes of government and leadership occur without violence, bloodshed or even the need for large exchanges of money. Yes, deals are done, but, as proven by our most recent election, it is the populace who makes the final decision, and in an emphatic manner. To quote Confucius, ‘to rule truly means to serve’, and, in a genuine democracy, if the government doesn’t serve its people then it gets sacked. And, paradoxically, that is part of the problem that I allude to in the title of this post.

Many commentators lament the fact, especially in the current age of climate change, oil shock and looming famine, that, because of our election processes, governments are ham-strung when it comes to implementing long term agendas. But I believe this problem can be analysed in a more precise fashion. Let’s start with oil. I can remember reading in a small unobtrusive column in Scientific American in the late 1990s, of a highly respected expert in oil exploration (no, I don’t remember his name, only that his credentials were solid and his message was dire) forewarning that oil production would become a serious issue before 2010. So we’ve had ample time to pursue other sources of energy as well as more efficient means to use and distribute what we had.

Ironically, when I was working in Houston on an oil-related project in 2001, I read in USA Today that petrol consumption, per capita in the US, was the same as it was 25 years earlier. I can remember driving the US highways and seeing huge pickup trucks with semi-trailer size turntables towing ‘trailers’ (caravans for the rest of us English speaking nations) or motor homes towing a ‘compact’ or even a small jeep behind them. While I was there, registrations in trucks overtook registrations in cars for the first time (trucks include pickups and SUVs in the US). This, I learned later, was the direct result of political intervention because America had lost the car market to the Japanese, and the American motor industry was now dependent on ‘trucks’ for their livelihood.

An English TV car show, Top Gear, a couple of years ago, revealed that the biggest selling car in the entire world was in fact a Ford pickup truck. The show’s host, Jeremy Clarkson, pointed out that there were more examples of this specific vehicle on the road than people living in Australia. We live in a consumer society: consumption literally drives the economy; and that is why this situation not only exists, but is encouraged.

Also, while I was in Houston, someone lent me a book about the moon written by a professor of cosmology (sorry, I’ve forgotten his name). One of the chapters dealt with a subject that bears no relation to the moon whatsoever: the ozone hole over Antarctica. The author told the whole story of how a scientist predicted in the early 1970s that CFCs could affect the ozone layer. Even when his prediction came true his prognosis was ignored, debated and generally discounted. It took more than a decade to overcome the political inertia and misinformation fed by corporate interests before anything was finally done. Exactly the same scenario now applies to climate change. I read an article by a motoring journalist, earlier this decade, citing the ozone hole as an example of ‘crying wolf’ because the predicted catastrophe never happened. The journalist seemed unaware that it was averted only because of global political intervention in response to scientific advice.

As I related in a previous post, Living in the 21^st Century (Sep. 07), I was one of a rare few who heard the scientific adviser to the English government (again, I don’t remember his name) give a lecture, at Oxford University in 2000, on the coming ‘pinch’ we will all experience in food, water, and energy as the result of global population pressure. I still wonder today, as I did then, why he was delivering this message to a small audience of academics rather than the politicians who apparently appointed him. The obvious, and cynical, answer is that the message was the wrong one because it would not win votes or elections.

Earlier this week I saw an interview with David Attenborough by Andrew Denton (on Australian ABC TV) whom Denton introduced as ‘the most traveled person on the planet’. When asked if he was an ‘optimist’ or a ‘pessimist’, Attenborough responded negatively. He lamented the effects of population growth on both the human and animal world and could see no easy resolution; an issue I’ve already commented on in the abovementioned post.

What have all these issues got in common? They all involve scientists advising governments, and the population in general, well in advance, that action needs to be taken on a global scale or we will all suffer economically, environmentally and health-wise. So why are they ignored? They are ignored at the time of their revelation because, they are not only future forecasts, and therefore debatable, but they require action and commitment on a large scale, and, more significantly, they won’t be supported by the very people who elect governments into power. And this leads to the problem with democracy: action is only taken when the people who elect governments are directly affected by the consequences of global issues. All scientific advisers will tell you, that, by the time that happens, it is simply too late.

In last week’s New Scientist (14 June 2008) there is a well-researched and well-articulated article written by Debora Mackenzie, entitled What Price More Food? She gives it the sub-heading: ‘It’s the crisis the world should have seen coming’; just like oil production shortages; just like climate change; and just like water crises, both future and present.

Economic growth is the universal paradigm that all governments and politicians swear by. It is the only criterion by which to judge the ‘health’ of a nation. Unfortunately, as I pointed out in Living in the 21^st Century, it is currently linked to population growth. Tell any economic rationalist that zero population growth should be the goal and they will have a seizure. I’m merely stating the obvious, but the obvious is easy to ignore when its consequences, and therefore its resolution, can be postponed.

None of this is helped when we have a global religious institution determined to maintain its anachronistic standards on issues like birth control and contraception. Recently the Vatican attempted to portray itself as a 21^st Century institution by announcing some new ‘mortal sins’ that include possible research into gene therapy – in other words, the demonisation of science. Personally, I find the Vatican’s stance on birth control and the use of condoms, in particular, morally irresponsible at best, and reprehensible at worst. As I’ve said elsewhere, ignorance is the greatest enemy facing the 21^st Century, and unfortunately the Vatican is clearly part of the problem when it could be part of the solution.

Am I a pessimist or an optimist? Well, I’m a pessimist if we maintain the status quo, but I’m an optimist if we adopt a more politically amenable approach to science. We have both the intellectual ability and the technological resources to change a great deal. Global communication is a key instrument, I believe, in educating people at grass roots level and engaging in public debate, as I’m attempting to do now.

Politicians on the ‘right’ see science as subordinate to economic imperatives. There is still a strong belief that ‘market forces’ will overcome all our global ills, including climate change, food shortages and everything else. They may even be right, but it’s an imbalanced approach when it’s obvious that the global-majority-poor suffer the brunt of these ‘forces’ and the global-minority-wealthy remain the least affected. The wealthy are obviously in the best position to effect the greatest change, but they will only act when their ‘constituents’ are directly affected, hence the problem explicit in the title of this essay.

Politicians on the ‘left’, on the other hand, are more ready to demonise science; they see it as part of the problem rather than part of the solution. Genetic engineering is a case in point, where they ignore the fact that all of the food we consume today is the result of genetic manipulation by humans over centuries (yes, even before Darwin); so it’s all ‘unnatural’, strictly speaking. The aforementioned article in New Scientist makes it clear that market forces and corporate interests have not delivered the result that the world obviously needs, but, equally, the author points out that genetic manipulation, either by breeding or specific gene splicing, is the only means we have to resolve this situation, and, more significantly, the technology exists today.

My point, I guess, is that science can deliver solutions and problems, depending on how it is employed. But we are in a period of unprededented growth (the world population has doubled in my lifetime) being driven by an almost religious dedication to an economic paradigm that is a significant contributor to the problem. There needs to be a balance introduced into the equation that not only allows for zero population growth but actively encourages it. Female emancipation and education is part of the solution, as many people, including Attenborough, acknowledge. But there also needs to be a recognition that scientists are the harbingers of future problems, and we ignore them at the cost to the quality-of-life for future generations. The 21^st Century will be remembered, either as the century we turned things around or the century where we lost the best part of what we have gained. I truly, sincerely hope that my pessimism (and David Attenborough’s) is ill-founded.

Is there a God?

This was the 'Question of the Month' posed in Philosophy Now, Issue 65 (January/February 2008).

To be put into perspective, this post should be read with one of my earlier posts, God, theism, atheism (Aug.07), and possibly also Does the Universe have a Purpose? (Oct.07) I need to add the significant caveat that I don’t expect others to believe what I believe. Religion is a very personal, even intimate, experience. As I said in that earlier posting, I believe atheism is a perfectly valid and honest point of view. I only have a problem with atheists when they insist they are axiomatically intellectually superior to theists, in the same way that some theists believe they are axiomatically morally superior to atheists. Both points of view are equally fallacious to me.

I’ve made the point previously that there is only one objective and honest religious truth: we don’t know. The corollary to this is that religion is an experience that is as subjective as consciousness itself.

Below is my submission to Philosophy Now.

To answer this question one must ask another: what is God? Even if the answer to the original question is in the negative then one must explain God away as a cultural artefact or a myth or a psychological phenomenon. I believe a good starting point is 19^th century philosopher Ludwig Feuerbach’s statement: ‘God is the outward projection of man’s inner nature’. Yet it’s more complex than that, as it always manifests itself as an interaction. Firstly, I believe that God is an experience, and I readily concede that if a person has had no experience, that they would call God, then they would logically be atheists. I make this assertion from the simple pragmatic fact that the only experience we have of God is in our minds, not out there. Some people have this experience and some don’t. Those who don’t tend to think that those who do are either irrational or delusional. Those who do tend to rationalise their experience within a cultural context. So the answer to this question is very personal and very subjective. Whilst one can rationalise a ‘creator’ God based on the freakish laws of nature that culminated in our conscious existence, the experience of God is independent of any such rationalisation. 

For me, God is a response to introspection at the deepest level, that comes from one's sense of connection to humanity and even to other living things – in other words, to nature. If one considers that we live on a grain of sand on a beach amongst a shoreline of beaches separated by oceans from other shorelines of beaches, one gets the sense of our truly inconsequential existence, yet it also produces a great humility. It is a sense of a greater purpose that leads one to consider God, either as an entity, or a source, or perhaps a destination. It is only because we have the mind to stretch beyond our mortal existence, in this way, that we believe in its possibility. This perception of something far greater, beyond us, can create supreme humility or supreme egotism – it depends on the beholder.

Footnote: The best book I've read on this subject is Karen Armstrong's The History of God. As I mention in response to a comment below, The Unconscious God by Viktor Frankl gives another perspective again.

I also point out in my response to the same comment that I appreciate that different people have different ideas of what or who God is. I think that is an important, and often overlooked, point.

Addendum: I came across this quote in the I Ching, which seems appropriate.

"There, in the depths of the soul, one sees the Divine, the One... To know this One means to know oneself in relation to the cosmic forces. For this One is the ascending force of life in nature and man."

Aristotle, Confucius, Ethics and Happiness

This is an essay I wrote whilst a student after I read Aristotle’s Ethics, one of the true classics. Anyone can buy it, even in paperback – it’s still in print, thanks to Penguin. It’s quite incredible that the ruminations of thinkers from 500 to 300BC are still relevant today, yet despite the façade that we present, is humanity any more civilized today than it was then? I think, that as long as hypocrisy dominates integrity in politics, civilization will struggle to achieve its unstated goal.

Even slavery still exists, though in a more insidious form. At least, back in Aristotle’s time, a slave was called a slave, whereas today they are called ‘illegals’ or ‘indentured’ in cases where it has been legalised. For the sake of clarity, I call slavery the practice of ‘bonding’ an ‘employee’ with a debt they can’t pay off, so they effectively work for nothing. It’s much more common than people realise, and it’s not just prostitutes or the underworld who are involved. I’m slightly off track, but it’s a detour that makes relevant my belief that, though history makes us more aware, it takes an unclouded eye to see the truth up close.

The essay originally had the title: What is the connection between happiness and moral behaviour? Those who have read my post on Human Nature will recognise that I’ve lifted the reference to Plato’s dialogue on the ‘just and unjust man’ straight from this essay.

This is not a comparison, by the way, between Aristotle and Confucius, which I understand has been done by others, though I don’t know who those others are. Nevertheless, both men saw themselves as teachers and both had an influence that spans well over 2,000 years. Leaving aside the world's three most famous mystics: Buddha, Jesus and Mohammed; arguably, only Pythagoras’s legacy has had a greater influence on the global cultural evolution of the past 2,500 years (read Kitty Ferguson’s The Music of Pythagoras). Below is the original essay (I've removed all the references, but most of the quotes are either from the Penguin edition of Ethics or, for Confucius, from Encyclopaedia Britannica).

Whilst no one would consider happiness and morality as mutually exclusive, there has been a tendency, both from our Christian traditions and Freud’s pleasure principle, to consider them as a necessary compromise. However as early as the 4th Century BC, both Aristotle, and to some extent Plato before him, challenged this most pervasive view of humanity. Leaving Plato’s arguments aside for the time being, Aristotle’s treatment in his Nicomachean Ethics is by far the most comprehensive and leads the way in developing a philosophical nexus for happiness and moral behaviour.

It is a central theme of Aristotle’s Ethics that happiness is the greatest ‘good’, and while this is discussed specifically in Chapter vii, Book I, it reoccurs in his discussions on Virtue, Friendship and Contemplation. Like most seminal works of the intellect, Aristotle’s Ethics is significant not only for what it contains, but for what one believes is missing. It is in filling in the gaps that one grasps the greatest insights and inspiration from his work. I will attempt to elucidate on what I perceive are the strengths of Aristotle’s arguments, as well as discuss the Ethics’ shortcomings in light of what others have contributed to the subject.

Firstly the word happiness is less than ideal as a translation for 'eudaimonia' as many point out, including Jonathan Barnes in his introduction to the Penguin edition. In fact many use the term: ‘the good life’, but it too is less than ideal. To quote Barnes: ‘... the eudaimon is the man who makes a success of his life and actions, who realises his aims and ambitions as a man, who fulfils himself.’ But later in the same passage he confuses us by saying: ‘It will not, of course, do to replace “happiness” by “success” or “fulfilment” as a translation of eudaimonia...’

But leaving Barnes comments aside, in the aforementioned Book I it is obvious when Aristotle is talking about happiness, he is talking about a lifelong event: it is in effect the sum of a person’s life. ‘One swallow does not make a summer... Similarly neither can one day, or a brief space of time, make a man blessed and happy.’ He makes it clear he is not talking about fleeting moments of pleasure that we all experience; he is talking about achieving our highest potential as human beings. ‘..happiness demands not only complete goodness but a complete life.’ In his concluding Book X, he goes further and gives this attribute an almost religious significance.

It seems to me that there are two aspects of Aristotle’s happiness or eudaimonia, and they are intrinsically related. One is to do with our day to day conduct and the pursuit of personal goals, and the other is to do with our interaction with others. It is obvious that these two facets of living cannot be separated, yet Aristotle fails to make this connection explicit.

The central tenet of Aristotle’s treatise on virtue is the much discussed ‘golden mean’. He gives examples, from how to manage money to bravery. A man too deficient in courage behaves cowardly, but the man too confident in his own abilities is foolhardy. I found Aristotle’s elaboration and exposition on ‘the golden mean’ longwinded to the point of being tiresome, but there is one brief passage which everyone can relate to, and which encapsulates the concept of eudaimonia as it arises in our everyday lives.

‘By virtue I mean moral virtue since it is this that is concerned with feelings and actions.... But to have these feelings at the right times on the right grounds towards the right people for the right motive and in the right way is to feel them to an intermediate, that is to the best, degree; and this is the mark of virtue.’

Aristotle considered this passage so important that he virtually repeats it in his summing up of Book II. The point about this passage, and its reiteration, is that it brings together both aspects of eudaimonia that I alluded to above: as a means of living one’s life and relating to others. Aristotle makes the additional point that this constitutes a moral virtue, but that is better understood when one reviews his thesis on friendship. It is in regard to friendship that I find the two aspects of eudaimonia most closely aligned.

The thrust of Aristotle’s discussion is that true friendship, as opposed to utilitarian friendship, is in itself a moral virtue, and that a friendship of this quality is dependent upon an individual’s moral character. Aristotle was aware that one cannot obtain a good friendship unless one is oneself a good person. In some respects, Aristotle used his particular concept of friendship as a measure of a person’s goodness or moral character. I believe this is the key to Aristotle’s philosophy, because living requires by necessity an interaction with others and the quality of that interaction by and large determines the quality of our lives. Whilst this is as much psychology as philosophy, it is the essence of both living a ‘good life’ and of being a ‘good person’.

If Aristotle’s discussion on friendship is his most accessible and most readily appreciated, his discussion on contemplation is probably the most vague and the most open to diverse interpretations. He concludes the Ethics with a discussion on contemplation, raising it as the highest goal for philosophy and life in general. In this regard it takes on religious significance. Barnes criticises Aristotle’s thesis because Aristotle argues that it is only acquired knowledge that is worth contemplating not research, but I think this misses the point completely. There are two other philosophers who can throw light on this subject: one who influenced Aristotle and one who did not.

Appendix A by Hugh Tredennick of the Penguin edition provides a synopsis of Pythagoras’s philosophy and influence with particular reference to his religious views. Pythagoras is best remembered as a mathematician who first perceived and quantified the relationship between mathematics and musical tones. But Tredennick points out that he was first a religious teacher, who believed in the transmigration of the soul ‘...his view of philosophy as a way of life, a contemplative activity for the emancipation of the soul’; shows the influence Pythagoras apparently obtained from his travels in the East (according to Encyclopaedia Britannica, 1989, but Ferguson, 2008, says that this belief came from Orphism, not Eastern influences as many believe). Tredennick also makes the point that this view no doubt influenced Plato and Aristotle. Here we have the idea of contemplation as a means of not only achieving virtue but of achieving immortality in a religious sense. But it is another philosopher who lived in Pythagoras’s time, whom I believe, provided a better exposition of contemplation as a form of self-realisation.

One cannot help but perceive similarities between Aristotle’s Ethics and the teachings of Confucius who lived approximately 2 centuries earlier, as both were concerned with the moral character of individuals and the application of ethics in political life. But Confucius’s ideas on contemplation are closer to contemporary ideas in psychology than Aristotle’s and therefore are more accessible. His view of contemplation is looking inward at the deepest inner self. Confucius (in Chinese, K’ung-fu-tzu) was a strong believer in self-knowledge and self-examination as a path to moral rectitude.

This view is probably best expressed in the modern idiom as soul-searching, whereby one attempts a higher degree of self-honesty, which is not only echoed in modern psychotherapy, but also in Sartre’s idea of ‘authenticity’. Confucius also understood the significance of our relationship with others in achieving enlightenment of the soul or self. From the annalects: ‘A man of humanity, wishing to establish himself, also establishes others, and wishing to enlarge himself also enlarges others. The ability to take as analogy of what is near at hand can be called the method of humanity.’(6:30)

But unlike Aristotle, Confucius would have argued that eudaimonia in the form of success and fulfilment is possible even when a man faces adversity and misfortune. Confucius knew this from personal experience. (He spent 12 years in self-imposed exile, and was unemployed and homeless, but during this period his circle of students increased and his reputation flourished.) It is also the theme of innumerable narratives, some fiction and some not, that continue to inspire us. But if we take either the Pythagorean or the Confucian view of contemplation, then Aristotle’s argument for making contemplation the best means for an individual to achieve the highest ‘good’ starts to acquire validity. It could be argued of course that Aristotle’s conclusion fails to make this clear, but I at least can see a valid argument even if I have to construct that argument myself.

As I intimated in my introduction, it is what I believe Aristotle left out of his Ethics that contributes most to a nexus of happiness and morality. This is best understood I believe by contemplating Plato’s dialogues on the ‘just’ and ‘unjust’ man. The basic argument is that the unjust man can get away with whatever he wants if he’s in a position of power or persuasion, and being unjust has no negative consequences for him, only for others. On the other hand, under these circumstances a just person can never be happy because he can simply never win and therefore will always be the unfortunate one. Plato’s argument is that the just man is temperate and can curb his appetites and desires with his rational abilities. There is a great deal that can be contended with this point of view, and it doesn’t address the issue of happiness and morality as being concordant, but to focus on this aspect of Plato’s dialogues would be a digression. The essential element missing from Plato’s argument, and unrevealed in Aristotle’s thesis, is the social consequence of being just or unjust.

To put the argument another way, one should consider rewards as a criteria for happiness or beneficence. What are the rewards for being just compared to the rewards for being unjust? Simply put, the rewards for being unjust are material rewards assuming one can get away with it. The rewards for being just are less tangible but they are related to the notion of a social contract. Not the social contract of the 19th Century but the more intimate social contract inherent in Aristotle’s friendship. The rewards for being just are friendship, loyalty and trust. It can be argued that these rewards also exist for the unjust man but they are contingent on his material possessions, wealth and power - in other words they are utilitarian. For the just man these rewards extend beyond immediate close associates and they are based on the man’s character, nothing else.

There is another negative effect resulting from being unjust which is more subtle. The unjust person must necessarily create a distorted perception of his or her world. The unjust man or woman suffers from a dishonesty to the self not unlike Sartre’s notion of mauvaise foi. The unjust person believes that his or her rewards are justifiably earned and the fate of those less fortunate are self-inflicted. Even Hitler believed that what he was doing was for the betterment of our world. The unjust person often believes, contrary to the perceptions of others, that his or her view of the world is completely just. This psychological component of the just and unjust person is not considered by Plato, or Aristotle for that matter, possibly because of the distorted perceptions that existed within their own society. After all, no one at that time, no matter how enlightened, would have taken into consideration the plight of slaves in a discussion of what was just and unjust, or of what constituted a ‘good person’.