Showing posts with label Science. Show all posts
Showing posts with label Science. Show all posts

05 October 2018

Quantum Bullshit

I was appalled recently to see that a senior professor of Buddhism Studies—whose work on Chinese Buddhist texts I much admire—had fallen into the trap of trying to compare some concept from Buddhist philosophy to what he calls "quantum mechanics". Unfortunately, as seems almost inevitable in these cases, the account the Professor gives of quantum mechanics is a hippy version of the Copenhagen interpretation proposed by Werner Heisenberg back in the 1920s. In a further irony, this same Professor has been a vocal critic of the secularisation and commercialisation of Buddhist mindfulness practices. The same problems that he identifies in that case would seem to apply to his own misappropriation of quantum mechanics.

As I've said many times, whenever someone connected with Buddhism uses the word "quantum" we can safely substitute the word "bullshit". My use of the term "bullshit" is technical and based on the work of Princeton philosopher Harry Frankfurt (image left). I use "bullshit" to refer to a particular rhetorical phenomenon. Here is the anonymous summary from Wikipedia, which I think sums up Frankfurt's arguments about bullshit precisely and concisely:
“Bullshit is rhetoric without regard for truth. The liar cares about the truth and attempts to hide it; the bullshitter doesn't care if what they say is true or false; only whether or not their listener is persuaded.”
What I am suggesting is that Buddhists who refer to quantum mechanics are not, in fact, concerned with truth, at all. A liar knows the truth and deliberately misleads. The bullshitter may or may not know or tell the truth, but they don't care either way. Their assertions about quantum mechanics may even be true, but this is incidental. The idea is to persuade you of a proposition which may take several forms but roughly speaking it amounts to:
If you sit still and withdraw attention from your sensorium, another more real world is revealed to you.
Certain Buddhists argue that a specific man sitting under a specific tree ca 450 BCE, while ignoring his sensorium, saw such a reality (Though he neglected to mention this). And then this thesis is extended with the proposition:
The reality that one "sees" when one's eyes are closed is very like the descriptions (though not the mathematics) of quantum mechanics.
I imagine that these statements strike most scientists as obviously false. The first hint we had of a quantum world was in 1905 when Einstein formalised the observation that energy associated with atoms comes in discrete packets, which he called "quanta" (from the Latin with the sense "a portion"; though, literally, "how much?"). Even this nanoscale world, which we struggle to imagine, is established by observation, not by non-observation. Equally, there is no sign in early Buddhist texts that the authors had any interest in reality, let alone ultimate reality. They didn't even have a word that corresponds to "reality". They did talk a lot about the psychology of perception and about the cessation of perception in meditation, within the context of a lot of Iron Age mythology. Given that there is no prima facie resemblance between science and Buddhism whatever, we might well ask why the subject keeps coming up.

I think this desire to positively compare Buddhism to quantum mechanics is a form of "virtue signalling". By attempting to align Buddhist with science, the highest form of knowledge in the modern world, we hope to take a ride on the coat-tails of scientists. This is still the Victorian project of presenting the religion of Buddhism as a "rational" alternative to Christianity. Generally speaking, Buddhists are as irrational as any other religieux, it's just that one of the irrational things Buddhists believe is that they are super-rational.

Had it merely been another misguided Buddhism Studies professor, I might have let it go with some pointed comments on social media. Around the same time, I happened to watch a 2016 lecture by Sean Carroll on YouTube called, Extracting the Universe from the Wave Function. Then I watched a more recent version of the same lecture from 2018 delivered at the Ehrenfest Colloquium. The emphasis is different in the two forums and I found that watching both was useful. Both lectures address the philosophy of quantum mechanics, but in a more rigorous way than is popular amongst Buddhists. Sean thinks the Copenhagen interpretation is "terrible" and he convinced me that he is right about this. The value of the lectures is that one can get the outlines of an alternative philosophy of quantum mechanics and with it some decisive critiques of the Copenhagen interpretation. Sean is one of the leading science communicators of our time and does a very good job of explaining this complex subject at the philosophical level.

What is Quantum Mechanics?

It is perhaps easiest to contrast quantum mechanics with classical mechanics. Classical mechanics involves a state in phase space (described by the position and momentum of all the elements) and then some equations of motion, such as Newton's laws, which describe how the system evolves over time (in which the concept of causation plays no part). Phase space has 6n dimensions, where n is the number of elements in the state. Laplace pointed out that given perfect knowledge of such a state at a given time, one could apply the equations of motion to know the state of the system at any time (past or future).

Quantum mechanics also minimally involves two things. A state is described by a Hilbert Space, the set of all possible quantum states, i.e., the set of all wave functions, Ψ(x). It is not yet agreed whether the Hilbert Space for our universe has an infinite or merely a very large number of dimensions.

For the STEM people, there's a useful brief summary of Hilbert spaces here. If you want an image of what a Hilbert Space is like, then it might be compared to the library in the short story The Library of Babel, by Jorge Luis Borges. (Hat-tip to my friend Amṛtasukha for this comparison).

Mathematically, a Hilbert Space is a generalisation of vector spaces which satisfy certain conditions, so that they can be used to describe a geometry (more on this later). One thing to watch out for is that mathematicians describe Hilbert Spaces (plural). Physicists only ever deal with the quantum Hilbert Space of all possible wavefunctions and have slipped into the habit talking about "Hilbert Space" in the singular. Sean Carroll frequently reifies "Hilbert Space" in this way. Once we agree that we are talking about the space defined by all possible wave functions, then it is a useful shorthand. We don't have to consider any other Hilbert Spaces.

The second requirement is an equation that tells us how the wave functions in Hilbert Space evolve over time. And this is Schrödinger's wave equation. There are different ways of writing this equation. Here is one of the common ways:

The equation is a distillation of some much more complex formulas and concepts that take a few years of study to understand. Here, i is the imaginary unit (defined as i2 = -1), ħ is the reduced Planck constant (h/2π). The expression δ/δt represents change over time. Ψ represents the state of the system as a vector in Hilbert Space -- specifying a vector in a space with infinite dimensions presents some interesting problems. Ĥ is the all important Hamiltonian operator which represents the total energy of the system. And note that this is a non-relativistic formulation.

We owe this formalisation of quantum theory to the fact that John von Neumann studied mathematics with David Hilbert in the early 20th Century. Hilbert was, at the time, trying to provide physics with a more rigorous approach to mathematics. In 1915, he invited Einstein to lecture on Relativity at Göttingen University and the two of them, in parallel, recast gravity in terms of field equations (Hilbert credited Einstein so no dispute arose between them). In 1926, Von Neumann showed that the two most promising approaches to quantum mechanics—Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation—could be better understood in relation to a Hilbert Space.

[I'm not sure, but this may the first time a Buddhist has ever given even an overview of the maths in an essay about Buddhism and quantum mechanics.]

By applying the Born Rule (i.e., finding the square of the Wave Function) we can find the probability that any given particle will be found in some location at any given time. A common solution to the wave equation is a map of probabilities. For example, the probability plot for an electron in a resting state hydrogen atom looks like this (where shading represents the range probability and the black in the middle is the nucleus). And btw this is a 2D representation of what in 3D is a hollow sphere.

If we give the electron more energy, the probably map changes in predictable ways. An electron bound to an atom behaves a bit like a harmonic oscillator. A good example of a harmonic oscillator is a guitar string. If you pluck a guitar string you get a complex waveform made from the fundamental mode plus harmonics. The fundamental mode gives a note its perceived pitch, while the particular mixture of harmonics is experienced as the timbre of the note. The fundamental mode has two fixed points at the ends where there is zero vibration, and a maximum in the centre. The next mode, the 2nd harmonic takes more energy to produce and the string vibrates with three minima and two maxima - the pitch is an octave above the fundamental.

Using the fleshy parts of the fingers placed at minima points, it is possible to dampen extraneous vibrations on a guitar string and pick out the harmonics. Such notes have a very different timbre to regular notes. An electron bound to an atom also has "harmonics", though the vibrational modes are three dimensional. One of the striking experimental confirmations of this comes if we split sunlight up into a rainbow, we observe dark patches corresponding to electrons absorbing photons of a precise energy and becoming "excited". One of the first confirmations of quantum mechanics was that Schrödinger was able to accurately predict the absorption lines for a hydrogen atom using it.

And on the other hand, after we excite electrons in, say, a sodium atom, they return to their resting state by emitting photons of a precise frequency (in the yellow part of the visible spectrum) giving sodium lamps their characteristic monochromatic quality. The colour of light absorbed or emitted by atoms allows us to use light to detect them in spectral analysis or spectroscopy. For example, infrared light is good for highlighting molecular bonds; while green-blue visible and ultraviolet light are good for identifying individual elements (and note there are more dark patches towards the blue end of the spectrum).

The wave function applied to the electron in an atom gives us a map of probabilities for finding the electron at some point. We don't know where the electron is at any time unless it undergoes some kind of physical interaction that conveys location information (some interactions won't convey any location information). This is one way of defining the so-called the Measurement Problem.
rugby ball

I have a new analogy for this. Imagine a black rugby ball on a black field, in the dark. You are walking around on the field, and you know where you are from a GPS app on your phone, but you cannot see anything. The only way to find the ball is to run around blindly until you kick it. At the moment you kick the ball the GPS app tells you precisely where the ball was at that moment. But kicking the ball also sends it careering off and you don't know where it ends up.

Now, Buddhists get hung up on the idea that somehow the observer has to be conscious, that somehow consciousness (whatever that word means!) is involved in determining how the world evolves in some real sense. As Sean Carroll, says in his recent book The Big Picture:
“...almost no modern physicists think that 'consciousness' has anything whatsoever to do with quantum mechanics. There are an iconoclastic few who do, but it's a tiny minority, unrepresentative of the mainstream” (p.166).
The likes of Fritjof Capra have misled some into thinking that the very vague notion of consciousness plays a role in the measurement problem. As far as the mainstream of quantum mechanics is concerned, consciousness plays no part whatsoever in quantum mechanics. And even those who think it does have provided no formalism for this. There is no mathematical expression for "consciousness", "observer", or "observation". All of these concepts are completely nebulous and out of place around the wave equation, which predicts the behaviour of electrons at a level of accuracy that exceeds the accuracy of our measurements. In practice, our experiments produce data that matches prediction to 10 decimal places or more. Quantum mechanics is the most accurate and precise theory ever produced. "Consciousness" is the least well-defined concept in the history of concepts. "Observation" is not even defined.

In the image of the black rugby ball on a black field in the dark, we don't know where the ball is until we kick it. However, a ball and a field are classical. In the maths of quantum mechanics, we have no information about the location of the ball until we physically interact with it. Indeed, it appears from the maths that it's not physically in one place until information about location is extracted from the system through a physical interaction. And by this we mean, not a conscious observer, but something like bouncing some radiation off the electron. It's as though every time you take a step there is a possibility of the ball being there and you kicking it, and at some point, it is there and you kick it. But until that moment, the ball is (somehow) smeared across the whole field all at once.

Put another way, every time we take a step there is some probability that the ball is there and we kick it, and there is some probability that the ball is not there and we do not kick it. But as we step around, we don't experience a probability, and we never experience a ball spread out over all locations. Whenever we interact with the system we experience the ball as being at our location or at some specific other location. Accounting for this is at the heart of different interpretations of quantum mechanics.


What every undergraduate physics student learns is the Copenhagen Interpretation of the measurement problem. In this view, the ball is literally (i.e., in reality) everywhere at once and only adopts a location at the time of "measurement" (although measurement is never defined). This is called superposition - literally "one thing on top of another". Superposition is a natural outcome of the Wave Equation; there are huge problems with the Copenhagen interpretation of how mathematical superposition relates to reality.

Firstly, as Schrödinger pointed out with his famous gedanken (thought) experiment involving a cat, this leads to some very counterintuitive conclusions. In my analogy, just before we take a step, the rugby ball is both present and absent. In this view, somehow by stepping into the space, we make the ball "choose" to be present or absent.

Worse, the Copenhagen Interpretation assumes that the observer is somehow outside the system, then interacts with it, extracting information, and then at the end is once again separate from the system. In other words, the observer behaves like a classic object while the system being observed is quantum, then classical, then quantum. Hugh Everett pointed out that this assumption of Copenhagen is simply false.

In fact, when we pick up the cat to put it in the box, we cannot avoid becoming entangled with it. What does this mean? Using the ball analogy if we kick the ball and know its location at one point in time then we become linked to the ball, even though in my analogy we don't know where it is now. If someone else now kicks it, then we instantaneously know where the ball was when it was kicked a second time, wherever we happen to be on the field. It's as though we get a GPS reading from the other person sent directly to our phone. If there are two entangled electrons on either side of the universe and we measure one of them and find that it has spin "up", then we also know with 100% certainty that at that same moment in time, the other electron has spin "down". This effect has been experimentally demonstrated so we are forced to accept it until a better explanation comes along. Thus, in Schrödinger's gedanken experiment, we always know from instant to instant what state the cat is in (this is also counter-intuitive, but strictly in keeping with the metaphor as Schrödinger outlined it).

As you move about the world during your day, you become quantum entangled with every object you physically interact with. Or electrons in atoms that make up your body become entangled with electrons in the objects you see, taste, touch, etc. Although Copenhagen assumes a cut off (sometimes called Heisenberg's cut) between the quantum world and the classical world, Hugh Everett pointed out that this assumption is nonsense. There may well be a scale on which classical descriptions are more efficient ways of describing the world, but if one atom is quantum, and two atoms are, and three, then there is, in fact, no number of atoms that are not quantum, even if their bulk behaviour is different than their individual behaviour. In other words, the emergent behaviour of macro objects notwithstanding, all the individual atoms in our bodies are obeying quantum mechanics at all times. There is no, and can be no, ontological cut off between quantum and classical, even if there is an epistemological cutoff.

In terms of Copenhagen, the argument is that wave function describes a probability of the ball being somewhere on the field and that before it is kicked it is literally everywhere at once. At the time of kicking the ball (i.e., measurement) the wave function "collapses" and the ball manifests at a single definite location and you kick it. But the collapse of the wave function is a mathematical fudge. In fact, it says that before you look at an electron it is quantum, but when you look at it, it becomes classical. Then when you stop looking it becomes quantum again. This is nonsense.

In Schrödinger's cat-in-the-box analogy, as we put the cat in the box, we become entangled with the cat; the cat interacts with the box becoming entangled with it; and so on. How does an observer ever stand outside a system in ignorance and then interact with it to gain knowledge? The answer is that, where quantum mechanics applies, we cannot. The system is cat, box, and observer. There is no such thing as an observer outside the system. But it is even worse because we cannot stop at the observer. The observer interacts with their environment over a period of years before placing the cat in the box. And both cat and box have histories as well. So the system is the cat, the box, the observer, and the entire universe. And there is no way to get outside this system. It's not a matter of whether we (as macro objects) are quantum entangled, but to what degree we are quantum entangled.

This is a non-trivial objection because entanglement is ubiquitous. We can, in theory, speak of a single electron orbiting a single nucleus, but in reality all particles are interacting with all other particles. One can give a good approximation, and some interactions will be very weak and therefore can be neglected for most purposes but, in general, the parts of quantum systems are quantum entangled. Carroll argues that there are no such things as classical objects. There are scale thresholds above which classical descriptions start to be more efficient computationally than quantum descriptions, but the world itself is never classical; it is always quantum. There is no other option. We are made of atoms and atoms are not classical objects.

Carroll and his group have been working on trying to extract spacetime from the wave function. And this is based on an idea related to entanglement. Since 99.99% of spacetime is "empty" they ignore matter and energy for the moment. The apparently empty spacetime is, in fact, just the quantum fields in a resting state. There is never nothing. But let's call it empty spacetime. One can define a region of spacetime in terms of a subset of Hilbert Space. And if you take any region of empty spacetime, then it can be shown to experience some degree of entanglement with all the other regions nearby. In fact, the degree of entanglement is proportional to the distance. What Carroll has suggested is that we turn this on its head and define distance as a function of quantum entanglement between regions of spacetime. Spacetime would then be an emergent property of the wave function. They have not got a mathematical solution to the wave equation which achieves this, but it is an elegant philosophical overview and shows early promise. Indeed, in a much simplified theoretical universe (with its own specific Hilbert Space, but in which Schrödinger's wave equation applies), they managed to show that the degree of entanglement of a region of spacetime determined its geometry in a way that was consistent with general relativity. In other words, if the maths works out they have shown how to extract quantum gravity from just Hilbert Space and the wavefunction.

Other questions arise from this critique of Copenhagen. What is an "event"? What is an "observation"? The problem for Buddhists is that we assume that it has something to do with "consciousness" and that "consciousness" has something to do with Buddhism. The first is certainly not true, while the second is almost certainly not true depending on how we define consciousness. And defining consciousness is something that is even less consensual than interpreting the measurement problem. There are as many definitions as there are philosophers of mind. How can something so ill-defined be central to a science that is all about well-defined concepts?

More on Interpretations

In 2013, some researchers quizzed physicists at a conference about their preferred interpretation of the measurement problem. This gave rise to what Sean Carroll called The Most Embarrassing Graph in Modern Physics:

Sean Carroll comments:
I’ll go out on a limb to suggest that the results of this poll should be very embarrassing to physicists. Not, I hasten to add, because Copenhagen came in first, although that’s also a perspective I might want to defend (I think Copenhagen is completely ill-defined, and shouldn’t be the favorite anything of any thoughtful person). The embarrassing thing is that we don’t have agreement.

Just 42% of those surveyed preferred Copenhagen - the account of quantum mechanics they all learned as undergraduates. Mind you, Carroll's preferred interpretation, Everett, got even less at 18%. However, it may be more embarrassing than it looks, because there are multiple Everettian interpretations. And note that several existing interpretations had no supporters amongst those surveyed (the survey was not representative of the field).

In Carroll's account, Copenhagen has fatal flaws because it makes unsupportable assumptions. So what about the alternatives? I found Carroll's explanation of the Everett interpretation in this lecture quite interesting and compelling. It has the virtue of being parsimonious.

Just like other interpretations, Everett began with Hilbert Space and the Wave Equation. But he stopped there. There are no special rules for observers as classical objects because there are no classical objects (just classical descriptions). In this view, the rugby ball still both exists and does not exist, but instead of the wave function collapsing, the interaction between the ball, the field, the observer, and the world cause "decoherence". If there are two possible outcomes — ball present at this location, ball somewhere else — then both happen, but decoherence means that we only ever see one of them . The other possibility also occurs, but it is as though the world has branched into two worlds: one in which the ball is present and we kick it, and one in which it is somewhere else and we do not kick it. And it turns out that having split in this way there is no way for the two worlds to interact ever again. The two outcomes are orthogonal in Hilbert Space.

While this sounds counterintuitive, Carroll argues that the many worlds are already present in the Hilbert Space and all the other interpretations have to introduce extra rules to make those other worlds disappear. And in the case of Copenhagen, the extra rules are incoherent. Everett sounds plausible enough in itself, but given the number of particles in the universe and how many interactions there are over time, the number of worlds must be vast beyond imagining. And that is deeply counter-intuitive. However, being counter-intuitive is not an argument against a theory of quantum mechanics. Physics at this scale is always going to be counterintuitive because it's not like the world on the scale we can sense. And at this point, it will be useful to review some of the problems associated with differences in scale.

Scale (again)

I've written about scale before. It is such an important idea and so many of our misconceptions about the world at scales beyond those our senses register are because we cannot imagine very small or very large scales.

We understand our world as classical. That's what we evolved for. Modern humans have been around for roughly between 400,000 and 200,000 years. But we discovered that there are scales much smaller than we can experience with our senses only about 400 years ago with the development of the microscope. As our understanding progressed we began to see evidence of the world on smaller and smaller scales. Each time we had to adjust our notions of the universe. At the same time telescopes revealed a very much larger universe than we had ever imagined.

Quantum mechanics developed from Einstein's articles in 1905 and was formalised mathematically in the 1920s. It has never been intuitive and it is so very far from our experience that is unlikely ever to be intuitive.

Humans with good eyesight can see objects at around 0.1 mm or 100 µm. A human hair is about 20-200 µm. A small human cell like a sperm might be 10 µm, and not visible; while a large fat cell might be 100 µm and be visible (just). A water molecule is about 0.0003 µm or 0.3 nanometres (nm = 10-9 m). But at this level, the physical dimensions of an object become problematic because the location in space is governed by quantum mechanics and is a probability. Indeed, the idea of the water molecule as an "object" is problematic. The classical description of the world breaks down at this scale. The average radius of a hydrogen atom at rest is calculated to be about 25 picometres or 25x10-12 m, but we've already seen that the location of the electron circling the hydrogen nucleus is a probability distribution. We define the radius in terms of an arbitrary cut off in probability. The estimated radius of an electron is less than 10−18 m (though estimates vary wildly). And we have to specify a resting state atom, because in a state of excitation the electron probability map is a different shape. It hardly makes sense to think of the electron as having a fixed radius or even as being an object at all. An electron might best be thought of as a perturbation in the electromagnetic field.

The thing is that, as we scale down, we still think of things in terms of classical descriptions and we don't understand when classical stops applying. We cannot help but think in terms of objects, when, in fact, below the micron scale this gradually makes less and less sense. Given that everything we experience is on the macro scale, nothing beyond this scale will ever be intuitive.

As Sean Carroll says, the many worlds are inherent in Hilbert Space. Other theories have to work out how to eliminate all of the others in order to leave the one that we observe. Copenhagen argues for something called "collapse of the wave function". Why would a wave function collapse when you looked at it? Why would looking at something cause it to behave differently? What happened in the universe before there were observers? Everett argued that this is an artefact of thinking of the world in classical terms. He argued that, in effect, there is no classical world, there is only a quantum world. Subatomic particles are just manifestations of Hilbert Space and the Wave Equation. The world might appear to be classical on some scales, but this is just an appearance. The world is fundamentally quantum, all the time, and on all scales.

Thinking in these terms leads to new approaches to old problems. For example, most physicists are convinced that gravity must be quantised like other forces. Traditional approaches have followed the methods of Einstein. Einstein took the Newtonian formulation of physical laws and transformed them into relativity. Many physicists take a classical expression of gravity and attempt to reformulate it in quantum terms - leading to string theory and other problematic approaches. Carroll argues that this is unlikely to work because it is unlikely that nature begins with a classical world and then quantises it. Nature has to be quantum from the outset and thus Everett was on right track. And, if this is true, then the only approach that will succeed in describing quantum gravity will need to start with quantum theory and show how gravity emerges from it. As I say, Carroll and his team have an elegant philosophical framework for this and some promising preliminary results. The mathematics is still difficult, but they don't have the horrendous and possibly insurmountable problems of, say, string theory.

Note: for an interesting visualisation the range of scales, see The Scale of the Universe.


Quantum mechanics is a theory of how subatomic particles behave. It minimally involves a Hilbert Space of all possible wave functions and the Schrödinger wave equation describing how these evolve over time. Buddhism is a complex socio-religious phenomenon in which people behave in a wide variety of ways that have yet to be described with any accuracy. It's possible that there is a Hilbert Space of all possible social functions and an equation which describes how it evolves over time, but we don't have it yet!

Buddhists try to adopt quantum mechanics, or to talk about quantum mechanics, as a form of virtue signalling -- "we really are rational despite appearances", or legitimising. They either claim actual consistency between Buddhism and quantum mechanics; or they claim some kind of metaphorical similarity, usually based on the fallacy that the measurement problem requires a conscious observer. And this is patently false in both cases. It's not even that Buddhists have a superficial grasp of quantum mechanics, but that they have a wrong grasp of it or, in fact, that they have grasped something masquerading as quantum mechanics that is not quantum mechanics. None of the Buddhists I've seen talking or writing about quantum mechanics mention Hilbert Spaces, for example. I'm guessing that none of them could even begin to explain what a vector is let alone a Hilbert Space.

I've yet to see a Buddhist write about anything other than the Copenhagen interpretation. I presume because it is only the Copenhagen interpretation that is capable of being shoehorned into a narrative that suits our rhetorical purposes; I don't see any advantage to Buddhists in the Everett interpretation, for example. Buddhists read — in whacky books for whacky people — that the "observer" must be a conscious mind. Since this suits their rhetorical purposes they do not follow up and thus never discover that the idea is discredited. No one ever stops to wonder what the statement means, because if they did they'd see that it's meaningless.

Thus, Buddhists who use quantum mechanics to make Buddhism look more interesting are not concerned with the truth. They do not read widely on the subject, but simply adopt the minority view that chimes with their preconceptions and use this as a lever. For example, I cannot ever recall such rhetoric ever making clear that the cat-in-the-box thought experiment was proposed by Schrödinger to discredit the Copenhagen interpretation. It is presented as the opposite. Again, there is a lack of regard for the truth. Nor do Buddhists ever present criticisms of the Copenhagen interpretations such as those that emerge from Everett's interpretation. Other criticisms are available.

And this disregard for the truth combined with a concerted attempt to persuade an audience of some arbitrary argument is classic bullshit (as described by Harry Frankfurt). Buddhists who write about quantum mechanics are, on the whole, bullshitters. They are not concerned with the nature of reality, they are concerned with status, especially the kind of status derived from being a keeper of secret knowledge. It's past time to call out the bullshitters. They only hurt Buddhism by continuing to peddle bullshit. The irony is that the truth of Buddhism is far more interesting than the bullshit; it's just much harder to leverage for status or wealth.


Frankfurt, Harry G. On Bullshit. Princeton University Press.

For those concerned about the flood of bullshit there is an online University of Washington course Calling Bullshit.

If you have a urge to learn some real physics (as opposed to the bullshit Buddhist physics) then see Leonard Susskind's lecture series The Theoretical Minimum. This aims to teach you only what you need to know to understand and even do physics (no extraneous mathematics or concepts).

15 April 2016

The Rocky Origins of Life

alkaline hydrothermal vent
In an essay in my series on Vitalism (Crossing the Line Between Death and Life, 30 May 2014), I mentioned the Miller-Urey experiment in 1953 as a breakthrough in the study of abiogenesis - the emergence of living things from non-living matter. It turns out, however, that having produced amino-acids and some other medium-sized organic molecules, nothing much else happens in these "organic soup" style experiments. Getting a soup of organic molecules to do anything interesting has proved an intractable problem and neither electrocution, bombardment with ultraviolet light, nor physical shocks help. New research has shown that Miller's estimates of the early atmosphere of the earth were probably wrong. He assumed the atmosphere of Jupiter would provide a good model for the early atmosphere of the earth: ammonia, methane and hydrogen. However, the heavy asteroid bombardment during the early epoch of the solar system, during which our moon was formed, blasted off the existing atmosphere and it was replaced with an atmosphere of mainly carbon-dioxide and nitrogen, with only traces of methane and other gases. Similar gases make up the modern day atmospheres of both Mars and Venus. Unfortunately, this mix of gases is very much less likely to get even as far as amino-acids in the Miller-Urey set up. So the idea of a naturally occurring organic soup fails on two counts: it probably never existed, and even if it had, nothing interesting happens in sterile soup (more on this below). Some comets and meteorites have a mixture of water and organic compounds similar to those produced by Miller-Urey and thus some of the building blocks of life may have come from space, but this still leaves us with the organic soup problem.

Another hypothesis of how life emerged from non-living matter has recently emerged and been promoted by British scientist, Nick Lane (amongst others), This is described in his book Life Ascending: The Ten Greatest Inventions of Evolution (2009). This hypothesis is known as the Alkaline Hydrothermal Vent Origin of Life. For the full detail of this hypothesis, see Russell et al (2013) and the "further reading". In this essay I will both paraphrase and embellish the version of the theory set out in Lane (2009).

We begin with a caveat. Even if we show that this theory is possible and plausible, it still won't tell us exactly how life began here. That is impossible to know. But if we can show that the chemical reactions that underpin life can be started in similar conditions, then we may be able to better understand life more generally. There will be general rules that govern the emergence of life and we can specify some of those rules. In addition if we can show that life emerging from chemistry is plausible it further undermines any remaining tendency to explain life through forms of Vitalism.

One thing we can already identify is the basic chemistry of life. For example all life on earth involves reducing carbon-dioxide (CO2) to methane (CH4) and water (H2O). Some organisms do this directly, most do it indirectly, but this is what all organisms do at a minimum. And since this doesn't happen spontaneously in an organic soup, we need to specify the kind of conditions in which it will happen.

Signs of Life

via Wikimedia
By 3400 million years ago, the signs of life on earth are unequivocal. The first life seems to have been in the form of bacteria or archaea. Taxonomists now recognise five kingdoms of living things: animal, plant, fungi, bacteria, and archaea. On the surface bacteria and archaea can be indistinguishable, but internally, chemically there are major differences (I'll say more on this later in the essay). Archaea are typically found in niches involving high temperatures, extremes of pH (both acid and alkali) or other factors that would kill most organisms. They are sometimes called extremophiles.

We can see in fossils of this early period, and perhaps earlier, the ratio of carbon isotopes that we expect to see from fossilised living things. This ratio, which sets life apart from non-living chemistry, is the basis of Carbon-14 (14C) dating. We also see fossilised structures of a form of life that we still see in shallow oceans today, i.e. the stromatolite. Archaea and bacteria continued to be the dominant forms of life for 2500 millions years before fossils of complex organisms begin to appear. Arguably they still are the dominant form of life, exploiting a vast range of ecological niches and far outweighing any other form of life in terms of biomass.

Replicators, molecules which copy themselves accurately, seem to be essential to any form of life and thus most existing theories have focussed on how such molecules might have been produced, usually in a soup of organic precursor compounds (like Miller-Urey). However, Lane refers to the various "organic soup" theories as "pernicious" because the idea deflects attention away from the underpinnings of life. As Lane says, if you take a tin of actual (sterilised) soup and leave it for a few million years it does not spawn new life, instead all the complex molecules gradually break down into simpler molecules. In other words following the dictates of thermodynamics the soup goes in the wrong direction. "Zapping" it with electricity or radiation only accelerates the degradation. The laws of thermodynamics means that a soup is far too unlikely a route to life. One can never ignore thermodynamics as they govern everything.

Thermodynamics - The Science of Desire

The physics of matter is a story of attractions and repulsions and thus, according to Lane, "it becomes virtually impossible to write about chemistry without giving in to some sort of randy anthropomorphism." (13-14) I'll do my best. Chemical reactions happen if all the participants want to participate or can be forced to. Molecules "want" to exchange elections or can be induced to overcome their shyness.

The molecules in food want very much to react with oxygen, but don't do so spontaneously, fortunately or we'd all go up in flames! Even reactions that result in a net release of energy often require some "activation energy" to overcome their "shyness" or initial reluctance to react. Another way of looking at the chemistry of life is that it boils down to the juxtaposition of two molecules, hydrogen and oxygen, out of equilibrium. They react with a discharge of energy, leaving warm water. And this is the problem with the organic soup theory - nothing wants to react, so nothing happens. There is no disequilibrium that might drive the necessary reactions. Disequilibrium is a key to life. 

Some origin of life theories focus on RNA, the single-stranded counterpart of DNA, which under certain conditions can self-replicate (normally in a cell RNA replication is dependent on large protein complexes called ribosomes). The idea that a very complex molecule like RNA might have come about without a thermodynamic disequilibrium driving the reactions is not credible. Thus although self-replicating RNA is plausible, there must be more to it. RNA is composed of nucleotides which combine an amino-acid, a sugar (ribose) and a phosphate group. As monomers (ATP), dimers (NADH), and polymers (RNA, DNA), nucleotides play several vital roles in living cells. Although we get amino acids from the Urey-Miller experiment, nucleotides are very much more difficult to make. Nucleotides do not just form spontaneously. One cannot just throw amino acids, ribose, and phosphate into a bucket and expect nucleotides to form. In fact it is worse than this because the conditions required for the synthesis of ribose and amino-acids are very different and they could not happen in the same bucket. They must be synthesised separately and then brought together. But then the reaction will not take place in the presence of water. Nor do nucleotides easily polymerise in the absence of a catalyst to form RNA or DNA. Although aspects of RNA based explanations of the origin of life remain plausible, RNA is certainly not the first step in the direction of life. Many conditions had to exist in order for RNA to be synthesised. If life did not evolve in a chemical soup, where did it come from?

An important clue was the discovery of vents on the sea-floor close to the great ocean ridges where the tectonic plates are forced apart by up-welling magma. These vents, known as "black smokers", spew out hot (300-400°C), acidic water, laden with chemicals, particularly metal and hydrogen sulphides (which account for the dark colour). They support a variety of lifeforms at densities rivalling rain forests. Bacteria use hydrogen sulphide (H2S) to power their metabolism. Effectively they detach the hydrogen from H2S and attach it to carbon dioxide to form organic matter and elemental sulphur (and this is one of the most direct processes for reacting H2 with CO2). This conversion requires energy and it comes from the juxtaposition of two worlds in dynamic disequilibrium, i.e. from cold sea water and the hot vent water. The bacteria that sustain this world live at the margins where the two meet and mix. Then some animals graze on the bacteria and a food chain is established. Or else the bacteria live in symbiotic relationships inside the animals. Tube-worms for example host such bacteria which feed them and because of this do not have a digestive system.

These hot vents became a candidate for the origin of life since the disequilibrium solved the thermodynamic problem. Possible mechanisms for life emerging at these hot vent sites were proposed by German chemist and patent attorney, Günter Wächtershäuser. These involved chemistry taking place on surfaces of iron-pyrites. Unfortunately conditions on the early earth make this route unlikely. Oxygen is still central to the metabolism of the vent archaea and bacteria. They still react hydrogen and oxygen, if only indirectly. There is also the concentration problem, that is, bringing enough of the reactants together in open water to make a self-sustaining reaction. For life to come about organic molecules must dissolve in water and somehow react to form polymers like RNA. But this is extremely unlikely if they are not contained (by a membrane) and concentrated.

Alkaline Vents

Serpentenized olivine
A second kind of hydrothermal vent was predicted Mike Russell, now working at NASA's Jet Propulsion Lab. Russell had conjectured that these other vents would be an even better candidate for the origin of life. Alkaline vents are not volcanic, but rely on the reaction between a type of rock called olivine and sea water. Such rock undergoes a process known as serpentinization after a common form of this rock, serpentine, which is green and thought to resemble the scales of a snake. In serpentinization, water becomes incorporated into the structure of the rock which expands and fractures. The volume of water incorporated in this way is believed to equal the volume of the all the oceans. But the water and rock also chemically react, producing highly (chemically) reduced compounds such as hydrogen, methane and hydrogen sulphide and a high pH value, i.e. the water in serpentinized rock is strongly alkaline. The reaction is also exothermic, i.e. heat producing, and so drives the convection that powers the alkaline vents. The reaction can be represented in simplified form as:

olivine + H2O → serpentinite + H2 + heat


2Fe2+ + 2H2O → 2Fe3+ + 2OH- + H2

Alkaline vent Structure 
Note that hydrogen and methane were key ingredients in the Miller-Urey experiments in the 1950s. Having been first predicted by Russell in the 1980s, living vents were discovered in 2000 during a submarine expedition to the mid-Atlantic. The vents form spectacular coral-like structures (right) that can be 60m in height.

The water coming from these vents is warm (70-80°C), highly alkaline (ph 9-11) and filled with chemicals produced by serpentinization, particularly hydrogen. By contrast, in the early oceans, the water would have been cool, slightly acid (pH ~5.5), and much richer in CO2 and iron than the present day ocean. As the hot, chemical rich water mixes with the cold sea-water some of the chemicals precipitate out to form porous limestone structures, filled with tiny chambers roughly the size of an organic cell. The compartments could provide a natural means of concentrating organic molecules. While modern vents tend to lack iron, the composition of the ocean 4 billion years ago would have meant that the early vents did have iron and other metal compounds (particularly nickel, magnesium, and molybdenum) with catalytic properties embedded in their walls. Mike Russell has argued that the iron/sulphur minerals in these structures resembled enzymes that some modern living cells, especially archaea, use to catalyse chemical reactions. The flow through these early vent structures replenished basic reactants, carried off by-products, and prevented catalyst surfaces from becoming fouled, while also allowing for organic molecules to concentrate. The thin walls of the chambers provided membranes, one of the essential features of living things, with very different conditions of temperature and especially pH on either side, thus creating exactly the kind disequilibrium required to power living things.


The vents provide two kinds of disequilibria that can act as drivers of chemical processes. These are quite technical and I'll try to simplify.
  1. highly reduced electron donors
  2. pH imbalance or proton gradient

Electron Donors

1. Bubbling up from the vent are gases like hydrogen and methane produced by the reaction of water with mantle minerals like olivine. In the presence of iron and molybdenum catalysts in the walls of the vent structures, these come into contact with CO2 and nitrogen oxides dissolved in the water. When hydrogen reacts chemically it readily gives away its single electron to another molecule to create a hydrogen ion or proton. In chemical terms this giving away of an electron is called "reduction". Oxygen is the prototypical acceptor of electrons and thus this side of the reaction is called "oxidation". When iron is oxidised to rust, what is happening is that oxygen in the air is accepting electrons from (i.e. is reduced by) metallic iron (Fe) which is converted into ferrous (Fe2+). Red rust can be further oxidised to black ferric (Fe3+) iron. Atoms will tolerate a net positive or negative charge if they can obtain a more stable arrangement of electrons (this is a consequence of the quantum mechanics of electrons). Serpentinization involves water oxidising ferrous iron in olivine to ferric iron, with water being reduced to hydrogen gas and hydroxide ions.

H2 and CO2 react with a little difficulty. Although the overall reaction is exothermic, meaning that it is thermodynamically favoured, some initial energy is required to get the reaction going and a catalyst to help it along. The catalyst in the archaea that do this reaction directly is a complex of iron, nickel and sulphur atoms, which are very like the kind of minerals deposited at vent sites. "This suggests that the primordial cells simply incorporated a ready-made catalyst" (Lane 28). The activation energy seems to come from the vents themselves, which we can tell from the presence of acetyl thioesters. These molecules are the result of CO2 first reacting with free-radicals of sulphur in the vent water, and these free-radicals provide some of the energy. We will return to this observation below.

The combination results in reactions that produce methanol (CH3OH), methanal (CH2O), and ultimately ethanoic acid (CH3COOH) aka acetic acid). Such molecules can accumulate and concentrate in the cells and this allows for more complex molecules to form and polymerise in tiny versions of the Miller-Urey experimental apparatus. This gives us a more dynamic version of the organic soup. The constant flow of water from the vent solves another problem associated with surface catalysts: fouling. As reactions happen on a surface the products of the reaction build up and prevent new reactants getting to the surface. To have a sustainable reaction at a surface one must combine concentration (enough to bring molecules together) with a flow that carries away products and replenishes reactants. The pores of the vent structures seem to provide for both.

Proton Gradient

2. A feature of all living things is the creation of a proton gradient across a membrane. By this we mean that one side of the membrane has a surplus of protons (in other words an acid pH) and the membrane allows them to diffuse to the other side where there is a deficit (an alkaline pH). Since protons are positively charged this is also amounts to an electrical potential (i.e. a voltage) across the membrane.

In our mitochondria for example, this gradient is achieved by a process called electron chain transport involving four complexes of proteins that pump protons across the membrane to create a pH or proton gradient. These protons then diffuse back into the cell by a process called chemiosmosis, via another protein complex called ATP-Synthase, and in doing so power the creation of adenosine triphosphate 

triphosphate - ribose - amino-acid (adenosine)

At first sight ATP-Synthase appears so miraculous that, like the eye, it is often pointed to as evidence of intelligent design. It is difficult to imagine how something so complex could have evolved from simple steps by chance, though its evolutionary path is in fact known to some extent. ATP synthase is a complex nano-machine. A rotary engine in the cell-membrane is made up of a protein complex (with three subunits) and driven by proton diffusion or chemiosmosis; the engine uses a protein-based crank-shaft to deliver mechanical energy to a separate complex of proteins (with three subunits) inside the cell; the deformation and relaxation of this second complex catalyses the synthesis of ATP from ADP and a phosphate ion. Several good animations are available showing how ATP-Synthase works, for example this YouTube video.

ATP is a universal energy currency in all living cells. It is how energy is stored and moved around the to where it is needed. ATP is a nucleotide, the basic unit, or monomer from which polymers like RNA and DNA are produced. The right-hand group is adenine, an amino-acid, and the middle part is ribose, a saccharide or sugar. And on the left is the phosphate. Compare to the units of DNA or RNA (below):

RNA Nucleotide. Wikimedia

ATP adds two more phosphate groups, the last of which is detachable to make adenosine diphosphate with the release of energy. The reaction that powers life thus looks like this.

ATP ↔ ADP + PO42- + energy

The pH difference between the two bodies of water, kept separate by the membranes of the vent structure creates a voltage across the membrane that can drive a similar kind of reaction, the transformation of orthophosphate into pyrophosphate:

Note how the left-hand side of ATP is very like the pyrophosphate molecule. Russell thinks that pyrophosphate might be the precursor of ATP, that it could do the same job of providing energy to power other reactions, though less efficiently.

Scaling Up.

So in these vents we have the following essential ingredients for chemistry related to life (especially if we consider them as they might have been 4 billion years ago).
  • CO2 and nitrogen-oxides (in seawater) + H2 (in vent water) reacting to form organic molecules
  • Iron-sulphur and other metallic ion complexes that can act as catalysts
  • A mechanism for concentration and replenishment
  • A porous membrane formed from calcium carbonate with distinct environments on either side.
  • A proton gradient
  • Potentially, a pyrophosphate based energy transfer mechanism to provide activation energy for "shy" molecules.
Thus the vents provided natural reactors for sustaining chemical reactions that produce organic molecules in a far more dynamic environment than that envisaged in organic soup theories. They also provide the range of environments necessary to create the conditions for replicators like RNA. However the kind of chemical reactions that might take place in such environments are relatively simple compared with even a bacterial cell, let alone a eukaryote cell. How did we get from there to here? In attempting to answer this question Lane switches from a bottom-up to a top-down perspective.

One of the clues to how life might have proceeded can be found in the common elements of metabolism shared by almost all living cells. By comparing all living things we can reconstruct the common elements shared by all life. In this vein, a paper published in Science on 25 March 2016 (Hutchison et al 2016) has attempted to reduce the genome of a bacteria to just those genes essential for it to live. The resulting partly-synthetic organism has just 473 genes. The function of 149 of them has yet to be determined. Lane discusses the last universal common ancestor of all current forms of life, known by the acronym, LUCA. In order to identify what features LUCA might have possessed scientists compared the two oldest forms of life: archaea and bacteria. Archaea appear very similar to bacteria, but there are important differences in metabolism and biochemistry. Features in which bacteria and archaea differ include,
  • Chemical structure of cell membranes structure
  • Methods of lipid synthesis
  • Methods of glycolysis (conversion of sugars to pyruvate)
  • DNA replication
  • Respiration pathways
Features which bacteria and archaea share include:
  • DNA
  • Ribosome (proteins which transcribe DNA into RNA)
  • RNA to protein translation
  • Krebs cycle
  • ATP synthesis
The features that archaea and bacteria have in common are those likely to have been found in LUCA and those features where they differ were unlikely to be features of LUCA. Note that cell membrane structures are not included in the list of shared features. Archaea and bacteria appear to have separately (and in parallel) evolved lipid-based cell-membranes and methods for synthesising lipids. This is consistent with life having evolved as metabolic pathways in a physical substrate and then later having found ways to create membranes, with bacteria and archaea developing independently. In retrospect, the alkaline vent hypothesis predicts multiple parallel solutions to such problems as cell-membranes and some metabolic pathways.

The Krebs Cycle (aka Citric Acid Cycle) is shared by all forms of life. Lane refers to it as "the metabolic core of the cell". It is central to how we take the complex molecules in food and break them down into hydrogen and carbon-dioxide and in the process produce ATP to power other cell processes.

The cycle can also go backwards. In which case it consumes ATP and produces complex organic molecules, which can be used to build the components of a cell. This backwards Krebs Cycle is not common in life generally, but it is common in the archaea that live in hydrothermal vents. Crucially, given appropriate concentrations of the necessary ingredients including ATP, the chemical reactions of the backwards cycle will happen spontaneously. It is what is sometimes called "bucket chemistry", from the idea that one pours reagents into a bucket and the reactions just happen. And as the products of one step of the process build up in concentration they will automatically start to undergo the next step. No genes are required to mediate this process. It is exactly the kind of reaction that could have got started in the pours of vent structures, perhaps powered initially by pyrophosphate rather than ATP. Once this process got going, side reactions would have been almost inevitable producing amino-acids and nucleotides (the units of the DNA or RNA polymer).

We mentioned acetyl thioesters above. These turn out to be very important, because when they react with CO2 they produce molecules called pyruvates. When our cells take up simple sugars these are broken down by enzymes into pyruvates. These then enter the Krebs Cycle where they are transformed into other molecules to form many building blocks for complex chemistry. So the naturally occurring acetyl thioesters could have produced the pyruvates necessary to set off the backwards Krebs cycle to produce complex organic molecules.
"In other words, a few simple reactions, all thermodynamically favourable, and several catalysed by enzymes with mineral-like clusters at their core... take us straight into the metabolic heart of life, the Krebs cycles, without any more ado." (28)
We now hit the limits of the progress of science. Experiments designed to test how accurate this hypothesis is have been proposed. Lane speculates that peptides and small proteins and RNA are likely products. Some experiments have been performed and generally they seem to throw up problems with the model. So the field is still in the phases of repeatedly testing and redesigning to find the right parameters. However, there is reason to be optimistic that refining the model should produce a self-sustaining series of chemical reactions analogous to the first living systems, and that contain metabolic pathways which hold the key to all life: the proton gradient, a phosphate based energy transfer, and the Krebs cycle. Lane concludes that LUCA, the common ancestor of all life was most likely,
"...not a free-living cell but a rocky labyrinth of mineral cells, lined with catalytic walls composed of iron, sulphur and nickel, and energised by natural proton gradients. The first life was a porous rock..."
The conditions required for all this to happen are unusual, but happen to be exactly the conditions that prevailed on the earth 4 billion years ago. Once the conditions were in place, life was more or less inevitable and probably came about quite quickly.

Of course this story is still quite hypothetical. Some parts of the alkaline vent hypothesis are better attested than others. As far as I can tell the experimental results are still ambiguous, though promising. Other models for origins of life do exist and are being explored. See for example, Keller et. al. (2016), though this group also see a vital role for iron compound catalysis. The more we understand the biochemistry of life, the better we understand what the conditions must have been for the beginning of life. Major advances in understanding that biochemistry are still being made. Elucidating the basic structure of ATP Synthase won Paul Boyer and John E. Walker a Nobel Prize in 1997, less than 20 years ago. This is ongoing work, most of the sources cited in this essay are less than five years old (at the time of writing). 


A sceptical Buddhist reader, if they even got this far, may say, so what? What has any of this got to do with Buddhism? By my own admission, I don't usually countenance the idea that science supports the standard kinds of medieval worldview held by Buddhists. In fact here I am doing the opposite. By showing the plausibility, even the thermodynamic inevitability, of biochemistry emerging from geochemistry, I want to try to eliminate the last vestiges of Vitalism. No supernatural element need be added to the organic soup to make it come alive, merely some form of chemical disequilibrium across a permeable barrier (in our case a proton gradient across porous calcium carbonate). There is no equivalent of the Lord breathing life into Adam or Dr Frankenstein pumping electricity into the monster to shock it into life. Certainly energy must be available, but this is simply energy in the normal sense used by scientists, not some supernatural vital spark. Life proceeding in this manner is no less mysterious, but it is entirely natural. There is no need to introduce any supernatural element. The picture above might not be correct in every detail, but it identifies the basic elements that must be in place for life to be thermodynamically feasible: ie. H2 and CO2 in an environment of disequilibrium separated by a porous membrane, with catalysts present, and a replenishing flow that is balanced out by possibility for concentration of ingredients.

If we accept these ideas, and granted many will not or will find them too speculative, then life requires nothing extra in order to be passed on from one being to another. In the simplest terms, cells divide and the daughter cells go on to become other individuals. What is passed on in modern living cells is a copy of the mother-cell's genes, some of her metabolic equipment, and a section of her enclosing membrane. Nothing supernatural occurs during this process. What occurs is certainly incredibly, almost unimaginably complex and at best incompletely understood. But the broad outlines of it are clear.

I have previously argued that any afterlife is by necessity vitalistic and dualistic. The afterlife exists primarily to fulfil the longing for continued existence and as a mechanism for sustaining the Myth of a Just World. Vitalism and Dualism are the price we pay for fulfilling these longings. If the manner in which we lived is important to an afterlife theory, then that theory demands that information about how lived must survive our physical death in some coherent form. This information is then used to determine our post-mortem fate. Thermodynamics precludes the possibility of this information being preserved because, in our living bodies, the information is encoded in arrangements of atoms. Those atoms become disordered almost as soon as life ends. Nor is there a credible way of transmitting this information from one being to another, even if they were in physical contact. The many Buddhist attempts to explain this information transfer, e.g. a mind-made body (manomaya kāya) or gandharva, do not meet modern standards for theories that make accurate, testable predictions. At best they are myths, at worst they are post hoc rationalisations of something we want to believe despite the evidence.

If we eliminate all forms of Vitalism and Dualism with respect to life, it makes these medieval afterlife views considerably less plausible. If nothing is required to spark matter into life, if there really is no matter/spirit duality, then the idea of something immaterial surviving death is considerably less plausible. Buddhism without the inherent matter/spirit duality, without the supernatural elements changes radically. Karma and rebirth go out the window. The focus becomes how we understand experience and how we can explain the experiences we have during the religious exercises associated with Buddhism.

Because of thermodynamics, religion is basically finished. The death throes are certainly taking a long time, but the world is slowly moving away from seeing life through a religious lens. Buddhism, as a religion in the traditional sense of being concerned with continuity, justice, disembodied spirits, and the afterlife, is finished. We have Hamlet's choice: either embrace the situation and take an active role in shaping the future; or hesitate and allow events to overrun us. But we are not Hamlet, we know how the play ends.



Hutchison, C. A. (2016) Design and synthesis of a minimal bacterial genome. Science, 351 (6280) DOI: 10.1126/science.aad6253

Keller, MA. et al. (2016) Conditional iron and pH-dependent activity of a non-enzymatic glycolysis and pentose phosphate pathway. Science Advances 2(1) DOI: 10.1126/sciadv.1501235

Lane, N. (2009) Life Ascending: The Ten Greatest Inventions of Evolution. W.W. Norton. [While it lasts there is a YouTube video with Nick Lane reading his own chapter on the origin of life accompanied by relevant graphics]

Russell, M. J., Nitschke, W., Branscomb, E. (2013) The inevitable journey to being. Phil Trans Roy Soc Lond B. DOI: 10.1098/rstb.2012.0254

Related reading

Herschy B, et al. (2014) An origin-of-life reactor to simulate alkaline hydrothermal vents. Journal of Molecular Evolution 79: 213-227.

Lane N, and Martin WF. (2012) The origin of membrane bioenergetics. Cell 151: 1406-12.

Lane N, Allen JF, Martin W. (2010) How did LUCA make a living? Chemiosmosis in the origin of life. Bioessays 32: 271-280.

Sousa FL, et al. (2013). Early bioenergetic evolution. Phil Trans Roy Soc Lond B 368: 20130088.

Update 26 Jul 2016
A recent study (by Bill Martin and others) in Nature Microbiology suggests that LUCA was a hydrogen metabolising thermophile. Based on analysis of the common genes in bacteria and archaea it identifies 355 genes as ancestral - i.e. belonging to LUCA.
Weiss, M. C., Sousa, F. L., Mrnjavac, N., Neukirchen, S., Roettger, M., Nelson-Sathi, S. & Martin, W. F. (2016). The physiology and habitat of the last universal common ancestor. Nature Microbiology 1, Article number: 16116. doi:10.1038/nmicrobiol.2016.116.
For a discussion of the article see
Errington, Jeff. (2016). Study tracing ancestor microorganisms suggests life started in a hydrothermal environment. PhysOrg. 26 July 2016.

18 Feb 2017
In Daniel C. Dennett's new book From Bacteria to Bach and Back he references a paper which shows how ribo-nucleotides can be synthesised bypassing the phase of having ribose and an amino acid, which in some cases are very difficult to stick together.
Szostak, J.W. (2009) Origins of life: Systems chemistry on early Earth. Nature. 2009 May. Available from the authors website.

01 April 2016

Buddhism & The Limits of Transcendental Idealism

Arthur Schopenhauer
In one chapter of his book on the philosophy of Schopenhauer, Bryan Magee mounts a vigorous defence of Transcendental Idealism. In doing so he seems to me to sum up a good deal of what is wrong with philosophy both in terms of starting assumptions and in terms of method. Schopenhauer, and in particular Magee's account of Schopenhauer, has been very influential on some of my colleagues in the Triratna Buddhist Order, so in this essay I'll highlight some of the problems with Magee's approach to reality.

Magee's first task is to clearly distinguish Transcendental Idealism from Idealism more generally. Idealism is a form of substance monism, a kind of polar opposite of Materialism. Both views are arguments about what is real, which is to say they are ontologies. Idealists argue that everything is just the mind, that nothing exists outside the mind. Clearly this entails a particular view of the mind that is very different from how a materialist sees it and makes it hard to explain other minds. It's a view that appeals to some Buddhists who are influenced by Yogācāra or Advaita Vedanta. But Magee is quick to point out that his is not what Kant had in mind when he coined the term Transcendental Idealism. In trying to bridge the gap between Hume, who argued that we can know nothing, and Newton, who demonstrated that we can know a great deal, Kant reasoned that in understanding sense impressions we superimpose structure onto experience in the form of what he called "a priori judgements". These include our concepts of space, time, and causation. These concepts are metaphysical. In this way Kant was able to embrace the knowledge derived from empirical methods, while accommodating Hume's critique of knowledge. Because a priori judgements enable us to make sense of experience, we cannot have experiences without them, but they come from our side, not from the world. At the same time Kant was able to embrace Newtons' practically derived knowledge. It is not that reality itself is created by our minds (Mono-substance Idealism), but that the world that we discern is a creation of the mind (hence "Idealism"), while reality itself remains beyond what we can discern (hence "Transcendental").

It was partly learning about this Kantian distinction between the world as we experience it (phenomena) and the world as it really is (noumena), that helped to clarify my own views about the Buddha's focus on experience. The early Buddhists use of language suggests that they were concerned only with the world of experience, the world that arises from the conditions of sense object, sense faculty and sense cognition. They were not concerned with reality. The early Buddhists seem to have understood that this world of experience (ayaṃ loko) was not "the world" (idaṃ sarvaṃ) as perceived by some of their contemporaries, but that it only emerged where our sense faculties were impinged on by the world. They did not explicitly place reality beyond our knowledge, but they had nothing to say about that reality, so we don't know what, if anything, they thought about it. A variety of inferences might be drawn from this silence, the most neutral is that they were disinterested in the question. This silence however is very significant in light of later Buddhist claims to understand reality through introspection.

Magee goes further however and argues that because the world of our experience is a creation of our mind, based on sense experience overlaid with a priori judgements, that reality must be utterly different from what we experience.
"... while it is possible for us to perceive or experience or think or envisage only in categories... determined by our own apparatus, whatever exists cannot in itself exist in terms of those categories, because existence as such cannot be in categories at all. This must mean that in an unfathomably un-understandable way whatever exists independently of experience must in and throughout its whole nature different from the world of our representations." (73) 
Now as I understand Kant, he was saying that reality is beyond knowing; whereas as Magee is saying that it is beyond comprehension, i.e. not simply that we can never know anything about a mind-independent reality, but that we lack the capacity to begin to understand it. I will offer two responses to this metaphysical speculation: what I call the "navigation argument" (which is a variety of the argument Johnson made against Berkeley), and the "other minds argument".

The Navigation Argument

Magee argues that both Kant and Schopenhauer differentiate themselves from either Realism or Idealism. In Magee's words:
"... [Kant and Schopenhauer] say, our perceptions and conceptions cannot be all there is, but cannot be 'like' what exists in addition to them, so what else there is cannot consist of an independently existing world which corresponds to them; however, since they constitute the limits of what we can envisage, we cannot form any notion of what there is besides." (74)
In the first place we can undermine Magee's assertion by pointing out that we navigate the world pretty well. If reality were utterly different from how we experience it, then we would certainly fall over, bang into things, and get lost a lot more often than we do. Effectively if the world were utterly different from how we experience it, we would not be able to navigate it. Experience would inevitably lead us into gross errors as though we were acting at random. But this is not what happens. So the world that exists independently of our minds must at the very least, on the human scale, be somewhat like the way we perceive it. Or more accurately the mental model we make of the world must be not unlike the world. As Justin Barrett observes:
"Nonreflective beliefs often correspond nicely to reality. This reliability comes from the observations that the mental tools responsible for these beliefs exist in large part because of their contribution to human survival throughout time." (2004: 9)
All too often we find the philosopher isolated from this kind of practical observation. Magee argues from an abstract perspective and does not take the time to check whether his conjecture is consistent with what we observe in practice. And in this case he seems to be wrong. But it emerges that Magee believes himself to be arguing with other philosophers, not with scientists.

Magee mentions "empiricist philosophers" several times (e.g. 73-74) and sets about refuting their views on this subject:
"After two hundred years, empiricist philosophers still usually give the impression of proceeding on the assumption that, by and large, reality must roughly correspond to our conception of it." (74)
This seems to be typical of Magee. He seems not to have gotten over his bad experiences of philosophers at Oxford University in the 1950s and is always arguing against them. In this case he may well be accurately portraying the attitude of empiricist philosophers, I wouldn't know. But he seems to have overlooked the attitude of scientists who are, generally speaking, not philosophers. Most scientists in the last century or so have been aware that scientific knowledge have undermined the idea that reality corresponds to experience. Einstein showed in 1915, for example that time is not absolute, but dependent on the frame of reference. Most scientists take the world described by quantum mechanics to be more fundamental than the physics of scales of mass, energy and length relevant to human experience, and thus more real. Most people in the know seem to hold the view that the quantum world is not only counter-intuitive but incomprehensible. So in fact the average scientist is probably more sympathetic to Magee's view than Magee is to that of empirical philosophers. Whether the quantum scale world is more real is moot and I'll come back to this point.

Some people may be wondering what a real philosopher of science sounds like. What kinds of problems are they interested in and what kinds of approaches do they take. Serendipitously I found a relevant, short (21:21) YouTube video recently. In this video, Eleanor Knox gives an overview of the field of philosophy of science with respect to theories of quantum gravity in her talk The Curious Case of the Vanishing Spacetime. She provides a brief definition of the philosophy of physics. Knox is particularly interested in theories of quantum gravity in which spacetime is not fundamental, i.e. where spacetime is not one of the starting assumptions of the theory, but may emerge as a  special property under certain conditions. If the criteria for reality is that a quality is fundamental rather than emergent, then such theories seem to say that spacetime is not real. What I'm getting at here is that Magee's characterisation of empirical philosophy seems completely divorced from the actual practice of Empiricism by scientists and from modern philosophy of science. I'm pretty sure that my colleagues who cite Schopenhauer don't realise this. It's not simply because the book is now 20 years old. A good deal of the theory that requires us to reconsider our notions of reality were in place long before he started writing. Magee is not even arguing with the most up-to-date notions of his own time, let alone our time. It seems that he still imagines himself to be in a combative relationship with his former (now long dead) professors.

The most serious problem with Magee's speculations about reality is that if there were a world that existed independently and was utterly unlike the experiences we have, it is questionable whether we could have experiences. If reality is utterly unlike experience, then surely it would produce experiences that are utterly incomprehensible. And by this I do not mean the kinds of experience usually associated with the supernatural, since we find these difficult to explain, but they are inevitably like something we know. An experience of something utterly incomprehensible would literally defy comprehension. We would not be able to parse the experience as an experience. Indeed one might argue that such experiences could be happening all the time and that we are unable to comprehend them so we don't comprehend them, at all. Such a reality would not impinge on our phenomenal world at all. Magee would then be forced to bifurcate reality into that part of reality which does correspond to experience (at least to some extent) and that part which was utterly unlike experience. However, any claim to knowledge based on something unknowable is ipso facto a false claim, since claims to knowledge must rest on something knowable. Magee has gone beyond the limits of valid epistemology. There's simply no way for him to know anything at all about the reality he posits. To say that it is incomprehensible is still a definite statement, a claim to knowledge where by his own definition no knowledge can be obtained. There is literally nothing that could be said about a reality that is completely unlike experience. The concept is nonsensical at it's root.

The other side to this is our old friend "comparing notes". I previously wrote about this in 2014, inspired by Physicist Sean Carroll's quip - "If the blind dudes just talked to each other, they would figure out it was an elephant before too long." (Is Experience Really Ineffable?, 4 Jul 2014; Carroll has since changed his Twitter bio). Magee's philosophy tacitly dismisses the possibility of comparing notes. I'm not sure why philosophers think like this, but Buddhist philosophers do it too. It's like the whole system of thinking about the world has to work without anyone ever having a discussion about what they are experiencing. As if every philosopher is too caught up in their own mind to acknowledge that they are not alone. But other minds are vitally important to how we think about the world, which brings us to my other argument.

Other Minds

If we eliminate Idealism, as we must, then we are forced to accept that there are other minds that also experience the world and with whom we can compare notes. To illustrate the relevance of this, we can use the example of a tennis game. It is one thing if I am alone at Wimbledon watching Novak Djokovic play Roger Federer. My head turns this way and that watching the ball. We cannot really generalise from this observation - I might be fantasising or hallucinating. I might observe accurately, but still come to false conclusions about the situation. It is something else again if a second person joins me and they move their head and eyes in the same way that I move mine. Our observations must be coordinated by something. And because it effects both of us at once, cannot be dependent on either of our individual minds. In other words the simplest case of comparing notes establishes objects that are external to our minds. If that coordinating factor is not reality itself, then we have to go in for some convoluted arguments to explain this coordination. Like epicycles to explain the motion of the planets in an earth centred model of the solar-system. If, as Magee argues, reality were utterly different from experience, one would have to add a coordinating factor separate from reality by being comprehensible to account for the fact that two of us appear to be tracking the same object at the same time. Again we get back to the two tier reality and we add the problem of the relation between reality and the post-hoc coordinating factor that we have invented.

Now fill the Wimbledon stadium with thousands of people, all of whom follow the ball back and forth simultaneously in a coordinated way, while looking at it from a range of angles. And add the millions who watch the TV coverage. This coordination is incredibly difficult to explain if reality is completely different from experience. By comparing notes on experience we can make inferences about what reality is like, at least on any scale that we can observe it at (there may be scales at which we cannot observe reality). And such observations are the business of the physical sciences. To be sure this is not the same as direct knowledge of reality; the knowledge is only inferred. But with care we can construct theories which reliably, accurately, and precisely predict how reality behaves within the margin of error inherent in all observations. The recent detection of the Higgs Boson and gravity waves are astounding examples of such predictions. Reality is still transcendental, it is still beyond our individual ken; but it is empirically real in the sense that through comparing notes and repetition we can infer what it is like.

In these kinds of arguments philosophers seem to be looking to make a true/false or real/unreal distinction. The scientist on the other hand wants to know whether the theory about reality makes accurate and precise predictions. Newton's theory of gravity is strictly speaking false, so a philosopher might say that it is uninteresting. But it does make accurate and precise predictions for all of our earth bound activities, and even for sending a spaceship to the moon. The first inaccurate prediction of Newton's theory was the precession of the orbit of Mercury which is affected by conditions not accounted for by Newton. This failure refutes Newton's theory in a relativistic frame and this lead to rethinking how we conceptualise gravity away from forces of attraction between masses towards a theory in which mass bends spacetime and bent spacetime constrains how masses move. We are not attached to the earth by an attractive force, but instead follow curved paths through bent spacetime whenever we try to escape the earth. However, the scientist doesn't see this as the end of the story, they see Newton's theory as a partial expression of a more accurate theory, which is accurate when certain conditions apply. When we look at the world in a non-relativistic frame, it behaves as though masses exert an attractive force on each other and Newton's gravity equation accurately and precisely describes how masses behave within the margins of error that we can measure them. The true/false dichotomy puts unhelpful limits on how we can proceed to better know our world and discourages inquiry.

The scientific method of knowledge seeking has revealed more and more about the universe we live in at different scales. We have learned that some of those scales are difficult, if not impossible, to imagine. The human mind struggles at both the largest scales and the smallest. At the largest scale for example we have the universe beginning with a big bang that no one yet understands and a universe filled with mass we cannot see and governed by a force which is accelerating the expansion of the universe that we cannot measure directly (aka dark matter and dark energy). The mainstream theories as they stand are incomplete, even though they are still accurate and precise at other scales - the solar system for example. The Big Bang involves infinities - an infinitely small universe with infinite energy density. One of the basic rules of thumb in physics that I learned in high-school is that if you do a sum and the answer is infinity, then you've made a mistake. Something like a big bang must have happened, but it cannot be exactly as current theories describe it, because of the infinities. The theory is incomplete and with any luck it will turn out to be like Newton, a description of a special case that is encompassed by a more general theory. At the other end of the scale, the nano-scale and beyond, some of us are capable of understanding the maths developed to describe the behaviour of matter/energy, but the underlying reality is impossible to understand. So in this sense Magee is correct. But scale is hugely important in these discussions.

If we look at atoms we do not see the dark energy that is accelerating galaxies away from each other. If we look at quarks we do not see the way that electrons around atoms make them hang together and form compounds. If we look at galaxies we do not see quantum behaviour. If we simply look at the world with our human senses we see the world on a particular scale. How and where we look at the universe has a huge impact on what kind of universe we see. This is important for Buddhists to remember as well. The Buddha was only commenting on the universe as it can be observed with the naked senses, i.e. on the world of experience. Buddhist doctrine has nothing to say about the universe on the cosmic, the micro- or nano- scales. It has nothing to say about the Big Bang, galaxies, microbes, atoms, quarks or fields. All these are beyond the scope of ancient Buddhism. These are important limits that Buddhists need to acknowledge. One cannot understand reality on different scales through introspection! There are no insights into Relativity or quantum mechanics to be had in meditation. It is past time that we stopped fooling ourselves on this score.

This brings us back to the question of the relationship between the scales. Is one scale more real than another? Is either the cosmic- or the nano-scale more real than the world we observe with our senses? Many scientists would argue that quantum mechanics is a more accurate description of reality. This is a problem of reductive explanations. If something can be explained in terms of other simpler things (all of chemistry in terms of 96 elements, electrons, and the electro-magnetic force) then the assumption is that the simpler thing is not just more fundamental (hence "fundamental particles"), but somehow more real. Is it accurate? The acme of a reductive approach is to find the most basic entities and forces with which one can describe reality. But this does not take into account either the effects of scale or the effects of complexity. Consider for example that it is not possible to predict the weather any more accurately based on quantum mechanics or relativity, than it is using classical mechanics. Despite having near perfect knowledge of the molecules of the atmosphere and the energy in the system, our understanding falls short. Therefore a reductive knowledge of chemistry and physics does not constitute knowledge of reality where weather is concerned. Nor for any other complex system with emergent properties (like a living being).

Chemists can be deceived by the simple systems we set up in the lab. If you fill a balloon with hydrogen gas and oxygen gas and apply a flame to get a big bang, a fireball, and some water (I've done this many times). This is accurate as far as it goes. As is the equation 2H2 + O2 → H20. But only as far as it goes. A simple system like this is a very narrow window into reality. For a start a gram of hydrogen gas contains about 60,221,412,900,000,000,000,000 molecules of hydrogen! This number, the Avogadro Constant, is unimaginably large. In order to understand the processes that are involved and formulate general laws, we have to do many experiments like this, burning many different fuels with oxygen, using many different oxidisers with hydrogen, many different combinations, under many different conditions of temperature and pressure. And even then, pure hydrogen and pure oxygen never exist in nature, so even if we know how these two elements react, we have to take into account the constant presence of other molecules and how they react. For example it turns out that in the balloon experiment the visible fireball is caused by carbon atoms in the rubber of the balloon. Hydrogen itself burns with a colourless flame (or more accurately emits light that is not visible to the human eye when it oxidises).

Nor does quantum mechanics give us a better understanding of celestial mechanics, because on the cosmic scale the individual effects of so many quanta interacting are lost in the smearing of probabilities. A one gram object, say a very pure diamond made only of sextillions of carbon atoms, does not behave in the same way as a single carbon atom, or a single election, or a quark, or a perturbation in the quantum fields. Behaviour and properties are scale dependent. Under these constraints what does "real" even mean?

To understand what reality is like, reductive explanations have to work alongside holistic explanations, each element must be seen in context. And in a sense this is why philosophy can be so frustrating - it sometimes seems as though humans, and in particular, the human mind, is seen by philosophers as operating in isolation. And yet humans are social. Taking one human in isolation may tell us something about humans, but blinds us to the nature of humans, because we are adapted to living in large groups with layers of intimacy (the Dunbar numbers: 15, 50, 150, 500, 1500, 5000 ...). Our nature really only becomes apparent in interactions at these different scales: in relationships of varying intimacy. A quirk of history has made us fascinated by individual psychology, when in fact we ought to pay a great deal more attention to social psychology. The intellectual shape of Imperialist Europe has emphasised individualism, selfishness, competition, and ruthlessness, because these qualities are what justify Imperialism and Mercantilism. This often blinds us to the importance of collectives, empathy, cooperation and altruism. Nothing about nature, for example, suggests that the former are more important than the latter. Indeed it seems that we see cooperation and symbiosis at all levels of life. The "selfish gene" is Neoliberalism applied to biology. We could describe life in terms of "altruistic molecules" such as ATP which exists to facilitate other life sustaining reactions. The metaphor is no less accurate and perhaps more apt.

Our lives are all about shared experiences. Which is why people like me write essays like this! It's not so much a matter of if we compare notes, but that we are constantly communicating about our experience and our disposition towards it and processing what other people are telling us about theirs. Just as pure hydrogen is never found in nature, an individual human is only a theoretical construct. We are all social, all of the time. Even misanthropes and hermits must be understood in relation to social norms. The contents of our minds are constantly influenced by our environment, both in the sense of the social situation (long term and present) and by non-human external influences.

Psychology and philosophy wrongly prioritise the individual and their point of view. Philosophers like Magee try to argue what reality is like based on the individual's point of view, when they ought to be thinking in terms of how collectives of humans work together to understand their experiences. Shared experiences define us and our world. And they allow us insights into what the world is really like beyond the way that we discern it through our sensory faculties.


I understand Kant's Transcendental Idealism to be a truism, for individuals. It is unavoidable that we, as individuals, are virtually always describing our experience, rather than the world itself. The limitation may not apply to someone capable of close and repeated examination of experience. Newton plainly made some enormous strides in understanding reality through his observations of light for example. And we think also of Galileo with his telescope; Hook with his microscope; and so on. But even then, if others had not succeeded in making the same observations at some point, we might not remember these names. We don't usually notice this distinction between experience and the world, largely because our models of the world are so very successful at allowing us to navigate the world. However the world is, it cannot be so different from how we experience it, or this would not be so. Samuel Johnson's dismissal of Berkeley's Idealism is actually quite powerful.
"After we came out of the church, we stood talking for some time together of Bishop Berkeley's ingenious sophistry to prove the nonexistence of matter, and that every thing in the universe is merely ideal. I observed, that though we are satisfied his doctrine is not true, it is impossible to refute it. I never shall forget the alacrity with which Johnson answered, striking his foot with mighty force against a large stone, till he rebounded from it -- 'I refute it thus.'" Boswell: The Life of Samuel Johnson, LL.D. (1791) 
Philosophers dismiss this (Magee explicitly dismisses it) as though Boswell did not see Johnson kick that stone and the two of them had not shared an understanding of what happened when he did. As though a third party would not have seen something too. As though thousands of people watching a tennis ball flying back and forward between two players were not seeing the same ball. In denying that this is happening, they also fail to propose any other mechanism for coordinating experience which would be required if it were not reality that was doing it. Why anyone find this kind of philosophy interesting is a mystery to me.

The fact is that we are not alone. We can combine our observations to make inferences about the world that are accurate, i.e. that lead to beliefs that yield expected results when one acts upon them. We do this all the time. So a form of collective and/or inferential Realism also seems to me to be useful. Mercier and Sperber have tried to show that reason itself is a collective activity. Collectively we overcome the limits of the individual mind, we can accurately infer knowledge beyond the barrier of experience and can understand how things really are, though how things are depends to some extent on what scale we are looking at. The kind of universe we see depends on scale at which we examine it.

The other point to make about this way of looking at reality, is that it demystifies and disenchants the notion of the noumenal. Yes, to some extent it is true that there is a noumenal world which underlies the world of phenomena, the world as we experience it. But it is far less mysterious than some would like us to believe. The counter-intuitive aspects of quantum mechanics aside, the world at the scale we experience it is quite comprehensible as the very accurate and precise laws of classical physics and chemistry show (c.f. Sean Carroll's blog The World of Everyday Experience, in One Equation and related essays). It's not that the noumenal world is some kind of "higher" reality that gives the phenomenal world meaning or explains God or anything of that nature. The noumenal world is simply the mundane facts of how our universe operates: it boils down to the way that fields interact and couple to produce matter and energy as we experience them. There's no succour in the noumenal for the longings of the religious and/or Romantics for a higher purpose for human life. God is not in the gaps.

If we Buddhists accept this definition, and accept that introspection does not lead to insight into reality, it leaves the field clear for the physical sciences to describe reality and leave us to continue to work with the domain of experience. And thus allows for a great deal of compatibility between Buddhism and Science. And this is not a compatibility that rests on bogus claims of similarity between ancient and modern knowledge. It's a compatibility based on clearly demarcating who has expertise where. What might be unnerving for Buddhists is that our expertise on experience is now under a strong challenge from scientists who've begun to take an interest in experience itself. They are beginning to describe phenomena like our sense of self in the kind of detail with could only dream of. Many Buddhists (traditional and modern) are too weighed down by intellectual baggage to ever break free. Buddhism is due a radical intellectual make-over. But we have core competencies that will continue to be relevant for the foreseeable future. We just have to get over ourselves and get on with doing what we do best.



Barrett, Justin L. (2004) Why Would Anyone Believe in God? Altamira Press.

Magee, Bryan. (1997) The Philosophy of Schopenhauer. 2nd Ed. Clarendon Press.