15 July 2016

A Layered Approach to Reality. Part I.

This essay will come in several parts. In Part I, I outline an approach to knowledge about the world that combines substance reductionism and structure antireductionism. I try to show how this combination provides for a much richer and realistic discussion about the nature of the world. Importantly, I outline why our descriptions of reality form a series of hierarchical layers. Whether this antireductionism applies only to descriptions of the world (epistemology) or it is how things really are (ontology), is an important question (raised by Nagel 1998). On this question, I have argued for a strong correlation between scientific knowledge and reality in my previous essay, Buddhism and the Limits of Transcendental Idealism (1 Apr 2016). While we cannot know the world directly, comparing notes on experience allows us to reliably infer objective knowledge about the world, i.e the world that exists independently of our senses or knowledge. Of a world beyond comprehension, I believe it is best to remain silent. However, most of what I will say here is about descriptions of the world, and thus mostly applies to epistemology or what we can know.

Having established that this is a valuable approach, in Part II (currently in two instalments) I outline the dynamics of this layered, hierarchical approach to talking about reality. In particular I develop a critique of those who would use the properties of low level descriptions (generally speaking physics) to comment on higher level issues such as freewill or morals. I try to show why mixing up layers leads to incoherence, so that physics cannot inform our understanding of freewill or morality, except through metaphor. The use of physics metaphors at higher levels is counter-indicated by the naive tendency to relentlessly reify all such metaphors.

Finally, as a separate issue, I will tackle how causation fits into this model as an emergent property. Causation is absent from fundamental descriptions of the physical world, which simply describe a world evolving according to certain patterns. David Hume's conclusion that we can observe sequences of events, but not causation as a specific kind of event, still holds true. However, as an emergent property causation is still important, if only because the way we come to understand causation is via acts of will and it therefore informs our definitions of freewill.

The position I'm going to outline in this essay draws very heavily on the book Analysis and the Fullness of Reality by writer, translator, and philosopher, Richard H. Jones (2013). However, I also draw on lectures and books by physicist and science communicator, Sean Carroll (2010a, 2010b, 2012, 2013a, 2013b, 2013c, 2016a, and 2016b). My interest in this subject is lifelong, but a recent turning point was reading a series of blog posts on The Brains Blog by William Jaworski (2016b, 2016c, 2016d, 2016e) which discuss the thesis of his book, Structure and the Metaphysics of Mind (2016a). It was Jaworksi that serendipitously led me to Jones; and Jones that unlocked the issue that I have been thinking about in one way or another for more than forty years now. Some essays on mechanistic models of cognition that appeared on Notes from Two Scientific Psychologists (2016a, 2016b, 2016c, 2016d, 2016e) have given me food for thought while considering the relations between layers.

On the whole I am not concerned here with ancient and traditional theories of the world, but with how we see the world in the 21st Century. However, having defined a kind of philosophical "space", I will mention how traditional Buddhist descriptions of the world fit into this space.

In this essay I take the terms "reality", "world", and "universe" to be synonymous and interchangeable. 


Levels of Description.

The idea that our descriptions of the universe are affected by scale can probably be traced to the inventions of the telescope and microscope in the early 17th Century. These two tools gave us the ability to see the world on different scales for the first time. This ignores myths and other speculations which are not descriptions of the world per se; but what some people thought the world might be like. They were the science fiction of their day. The insights about scale began to be formalised in the 19th Century. In The Philosophical Considerations on the Sciences and the Scientists (1825), August Comte arranged the branches of natural philosophy into a hierarchy based on relative levels of generality and complexity. In modern terms he saw the hierarchy (bottom to top) as physics, chemistry, biology, psychology, and sociology. At the time, this hierarchy was widely considered to reflect reality, in the sense that each science produced accurate knowledge of the world.

In 1843 John Stuart Mill in his System of Logic (see Mill 1868) describes two distinct types of causation: additive causes and combinatory causes. These are my terms for what he called homopathic and heteropathic causes respectively. Additive causes produce effects on the same level if the hierarchy, characterised by aggregation of existing properties and epitomised by the additive quality of forces. By contrast, combinatory causes produce effects (at least) one level up; characterised by novel combinations that are more than the sum of their parts, and epitomised by atoms combining to form molecules with new properties. In 1875 George Lewes referred to the effects of combinatory causes as emergent. This idea of causes having emergent effects is central to modern philosophy of science and yet there is little consensus on what emergent means, nor on the consequences of accepting emergence as a feature of reality. As we will see, some scientists and philosophers still reject the notion of emergence, while for others it is the only way to understand the world. 

European natural philosophers had inherited a simple but rich ontology of four elements: earth, water, fire, and air. Everything in the universe was made of these four elements combining in various ways. They also had a bias towards the view that everything has a cause, sometimes called the Principle of Sufficient Reason (after Leibniz and Spinoza). The principle of sufficient reason survives in a raft of trite aphorisms of the kind, "Everything happens for a reason". The ancients had at various times sought to reduce these four elements to one, seeking a "first cause", but no theory of a single, original substance ever achieved consensus. The failure was inevitable, but instructive for us. It highlights a deep desire for simplicity and unity that continues to guide our search for knowledge. A simple universe is a predictable universe; a predictable universe is a survivable universe. So arguably we evolved to find simple explanations that worked (or rules of thumb). Ideally we would like everything to be reduced to a single cause. One of the enduring appeals of monotheism and a reason that monotheism dominates the world of religion is that it gives us precisely that: a single, first cause and a reason for everything.

Something similar happened in Buddhist India. Early Buddhists, possibly influenced by proto-Nyāya philosophy, adopted a simple but rich ontology with four or six elements, though the elements in this case were qualities or processes rather than substances. They also adopted a model of mental functioning, i.e. pratītya-samutpāda or conditioned co-production, that was then applied to karma and rebirth, and to the physical world. This is not a theory of causation, since causation per se is never discussed, but a theory of when causation occurs, i.e. effects arise only in the presence of the necessary and sufficient conditions. How they arise is unclear, which is a major problem for modern Buddhists trying to defend ancient doctrines. The various Abhidharma projects introduced different roles for conditions in the causation process, though these seem to have been aimed at preserving the doctrine of karma in the light of a conflict between it and dependent arising, i.e. the problem of action at a temporal distance (See for example: Action at a Temporal Distance in the Theravāda. 22 Aug 2014)

Back in Europe, as elemental theory gave way to modern atomic theory, it started to look like we would require a very rich fundamental ontology with dozens of atoms replacing the four elements. In other words the quest for simplicity or unity seemed to be going in the wrong direction. But the atom was not, as the name suggests, indivisible. As natural philosophers, now called "scientists", began to unravel first the atom and then the atomic nucleus, a new sparse ontology beckoned. The discovery that all atoms are made of identical electrons, neutrons, and protons structured in different ways, once again pointed to a sparse ontology, if not a unity. As high-energy physics progressed and other particles began to be discovered, we were once again faced with an expanding ontology.

At around the time same as matter was being dissected, the four fundamental forces were being identified. Later, scientists began to find ways of conceptually unifying the fundamental forces. Then energy and matter were conceptually unified and finally forces understood as an exchange of particles. Again the quest was for simplicity and unity. Efforts towards unity have been disrupted by the discovery that there is more mass in the universe than we can see (dark matter) and that something is causing galaxies to accelerate away from each other (dark energy, though this may be the vacuum energy).

Currently we think of "science" as an ontological monism in which there is one kind of stuff that has a matter/energy duality when seen at certain levels. The most plausible theory is that the world is made up from a relatively large number of quantum fields (one for each type of particle in the standard model) whose vibrations and interactions make up the world. Most physicists would argue that quantum fields are a single class of stuff with different varieties, rather than a raft of different kinds of stuff, so that science counts as a substance monism. The standard models are as yet incomplete at the extreme ends of the scales of mass, energy, and length, though the dynamics of the middle ground of scale, occupied by humans, is mapped out in principle. In terms of substance we are made of atoms which follow patterns constrained by three of the four fundamental forces (gravity, electromagnetic, and weak nuclear). 

Popular histories of science often highlight this move towards the fundamental and the efforts of scientists towards unifying descriptions of the substance of the universe. However, throughout the history of science, including the present, lawful or law-like behaviour has been described at higher levels. In fact these high-level descriptions and methods make up the bulk of what contemporary scientists are concerned with. A few examples are: Boyle's Law relating temperature, pressure and volume of gases; Ohm's law relating voltage, resistance and current;  the laws of fluid mechanics; the periodic table of elements; evolution by natural selection; and the identification and classification of living things (taxonomy). All these examples are attempts to describe high-level properties, without first reducing them to fundamental physics. Most of science happens at these non-fundamental levels. Thus we need to re-evaluate the idea that hardcore reductionism is the acme of all science. It is not.

We can think of a "level" of description as a Lakoffian category. George Lakoff defines a category as based on resemblance to a prototype. With minimal resemblance, membership of a category might be marginal and any given complex item might be a member of more than one category. The categories that seem natural or intuitive to human beings tend to fall in the middle of hierarchies of taxonomy, i.e. they are fairly general, not too specific, but not all inclusive. This seems to be governed by how we perceive and physically interact with the world (Lakoff 1987).

Each of the main branches of science has a typical method or range of methods for interacting with the world. For example, chemistry is a distinct level because of the ways that chemists go about knowledge seeking, i.e. the analysis and synthesis of chemical compounds. Chemists explain things in terms of the interactions of atoms without reference to quarks or quantum fields. Though they work in bulk, their explanations feature idealised situations in which just enough of each kind of atom is present (i.e. abstract chemical equations like O2 + 2H2 → H20). Chemists treat atoms and molecules as autonomous with respect to lower levels, and tend to ignore higher level problems (which are the provinces of biologists, geologists, materials scientists, and engineers). Treating atoms as autonomous works very well in practice. One could try to describe chemistry in terms of quantum physics, but it would be very cumbersome indeed, and it is doubtful whether it could cope with the effects of scaling up the macro scale. Of course physics has made important contributions to our detailed knowledge of how individual atoms react with each other and the properties of molecules, but when the scale is micrograms to kilograms, chemistry is not only accurate and precise, but it is very much simpler than quantum mechanics. The further up the hierarchy we go, the more cumbersome and unwieldy mathematics and physics become as descriptive modes.


Reductionism

The approach of breaking things down and explaining them solely in terms of properties of a lower (and preferably the lowest) level is called reductionism. Reductionism has had its successes in the area of the investigation of what things are made of. And this success has prompted many scientists who sought fundamental laws to assert that everything would be one day reduced to a single theory of everything. They have acknowledge that the universe is complex, but assert that it is an ultimately comprehensible mechanism made from identifiable components, with identifiable properties, taking part in identifiable processes. Where something is not obviously reducible, or even obviously not reducible, some scientists and philosophers claim that it is still reducible in principle. This commitment to reductionism in principle, I refer to as metaphysical reductionism. It is a commitment to reductionism as a metaphysical principle, i.e. a principle which is held to be true, but which is not accessible to empiricism and cannot therefore be tested.

The proponent of metaphysical reductionism is unconcerned by the lack of apparent progress on intractable problems, the absence of tested hypotheses, or the lack of any viable method for achieving reduction in practice. They have faith in reductionism as a metaphysical principle. So even if individual cases (such as the mind) resist all efforts at reduction, there is no reason to doubt that, at some point in the future, the reduction will be achieved. Or else, ignoring all evidence to the contrary, they claim that the reduction has already taken place. If this fails, then the metaphysical reductionist can fall back on the argument that the entity in question doesn't exist (this strategy is known as eliminativism). If the mind, for example, is an illusion, then it does not need to be reduced to a lower level description, because it has been reduced to nothing.

Metaphysical reductionism is similar, in many respects, to a religious commitment. It distorts the field of salience around ideas in much the same way that religious beliefs do: counterfactual information, if it is acknowledged at all, is simply dismissed as not-salient to the issue at hand. Presenting the metaphysical reductionist with contradictory evidence may even reinforce their belief as it does with religieux. The existence of structures with irreducible features, which ought to falsify metaphysical reductionism, is dismissed because the commitment to reduction in principle overrides the salience of any counterfactual information. So metaphysical reductionism is not a belief that one can simply talk a person out of.

One of the problems with metaphysical reductionism is a tacit simplifying assumption. How the universe works, according to Quantum Field Theory, is that the whole universe is in a prior state, all the laws of physics apply, and the universe evolves into a subsequent state according to the pattern outlined by the laws of physics. The laws apply to the whole universe at once with everything interacting with everything else. Reductionists make the simplifying assumption that we can sensibly talk about single particles without reference to any other particles or fields. We can for example solve the wave equation for a single particle, or even for a single hydrogen atom, which tells us what is most likely to happen next for any given state that the particle or atom is in. Although this can allow us to approximate results for a subset of reality, it is not realistic to treat particles in isolation because particles and atoms interact.

To be able to reduce things in principle means that we would have to solve the equations for the whole universe obeying the all the laws of nature (including the laws we don't yet know). The computer powerful enough to do this computation for our universe would look exactly like our universe. For all intents and purposes it would be our universe. Reductionists forget that they have made the simplifying assumption without which their theory would not be practical. They forget that scale matters. Just because it is possible to use approximations like the wave function of a single particle, does not automatically mean that the theory scales up from individual particles to structures. It's not at all clear that QFT does practically scale up to the entire universe, but we know for certain that as currently formulated it does not account for gravity.

In previous essays I've noted that Buddhism, though philosophically pluralistic, tends towards metaphysical reductionism as well: reducing phenomena to dharmas; beings to their skandhas; the world to the four great elements (mahābhūtāḥ); and so on. Early Buddhists explicitly argued, for example, against collocations of skandhas being considered any more than the sum of their parts.  The "being" cannot be found in any skandha individually, nor in the skandhas collectively. Beings are merely aggregates of components with no properties that are not attributable to their parts. This is partly because Buddhists equated existence with permanence. Buddhist "components" are qualities and processes rather than substances, which might offer a slightly more sophisticated view of reality were it not for criterion of permanence and the saturation of Buddhism with mysticism with respect to qualities and processes. Even though the Abhidharma multiplied the number of fundamental dharmas, making the ontology pluralistic, they still saw analysis as the only method for seeing things as they really are. Later, a more holistic approach to observing mind would emerge, variously called mahāmudra, dzogchen, etc, though this is still combined with reductive theories of the mind as having an essence to which it can be reduced via these techniques. The fact that Buddhism tends to metaphysical reductionism is ironic given how hostile some Buddhists are to the reductionism of physicists. This is just one of many unacknowledged antimonies in Buddhism. A further irony is the tendency to reduce all science to "materialism".

Reductionism has been very successful in helping us to understand what the world is made of. However, what things are made of is not the end of ontology, there is also what things are made into. And this leads us to consider the opposite of reductionism.


Antireductionism

John Stuart Mill's prime example of combinatory causes was the the way that atoms combine to create molecules with unique properties, i.e. where the properties of the molecule are not simply the additive properties of the atoms that make them up. In his example, the sodium-chloride (NaCl, i.e. table salt) which forms white crystals is nothing like either of its components: the caustic, yellow-green gas chlorine and the soft, reactive, silvery metal sodium. Sodium-chloride must be studied as sodium-chloride, not as a mixture of chlorine and sodium.* We have to consider that sodium-chloride exists as a compound in its own right, not simply as an aggregate or mixture of chlorine and sodium. Sodium chloride has new properties that are not the sum of the properties of sodium and chlorine atoms. Sodium-chloride acts like sodium-chloride, not like a mixture of sodium and chlorine. Thus, following Jones (2013) and Carroll (2016a) we can say that sodium-chloride is real, it exists and cannot be reduced to its elements. We can now explain these features in terms of the combined wave functions of the elements, but this does not remove sodium-chloride from the picture. An explanatory or descriptive reduction is not the same as a substance reduction. Even explained in terms of QFT, sodium-chloride is still real. 
* Chemistry in 1843 was considerably less sophisticated than it is now. I'm maintaining the simplification because it still illustrates the principle. Dissolved in water sodium-chloride dissociates into sodium (Na+) and chloride (Cl-) ions, but as a substance we still have to think of sodium-chloride as a compound rather than a mixture in order to understand its properties. This basic distinction is still fundamental to chemistry.
Where living things are concerned, an organism can be dissected and analysed, but in order to be understood, it must be studied as a living whole. Organisms, like sodium-chloride, are real and irreducible. This counter to reductionism is sometimes called emergentism, but I will refer to it as antireductionism. Antireductionism is as important in the history of science as reductionism is, but because some prominent scientists have adopted reductionism as a metaphysical position, the importance of antireductionism is overlooked. When it comes down to it, most scientists are actually working in an antireductionist framework.

In his book The Big Picture Sean Carroll observes that:
“It’s not possible to specify the state of a system by listing the state of its subsystems individually. We have to look at the system as a whole, because different parts of the system can be entangled with one another.” (2016: 100. Emphasis added)
It seems that we are forced into antireductionism. Entangle means that systems of particles behave differently than a collection of unentangled particles. Here entanglement is not some new substance, or some new fundamental force, but is a feature of how particles interact and form systems. All entanglement adds to the system is structure. And this feature of systems seems to hold at all levels: parts are capable of interacting in ways that force us to consider systems as a whole rather than simply adding up their parts.

Just to be clear the result of this structure antireduction is not to deny the fundamental reality of the stuff from which the universe is made. The universe is composed of fields. But it is composed into structures whose properties, particularly causal properties, cannot be fully explained in terms of fundamental theories. Ultimately sodium-chloride is fields, but it is also a white crystalline substance. It is the structures that we are saying are real. No new fundamental substance has come into existence. But one cannot season food with sodium metal and chlorine gas. 

If we are to understand reality then we cannot limit our study to what things are made of, but must extend it to what things are made into. And the stuff that matter is made into can be made into other stuff that has still more unique properties. In fact the focus of most of science is at this end of things. This is why our universities have departments of chemistry, geology, geochemistry, biology, biochemistry, genetics, microbiology, and so on. In practice, science does not reduce to physics. And a sizeable majority of scientists have no interest in reducing science to physics, but operate entirely at higher levels. Such scientists certainly use analysis of parts as a tool for understanding a complex whole, but the fact that an object can be analysed as parts, does not mean that it can be reduced to parts. This is particularly true of organisms. Dissecting a frog does give us insights into its physiology, but in order to understand the frog we have to see it alive, going through its life-cycle, performing all its functions. No amount of dissection or physics will give us these insights. But more than this we have to see the frog in its ecological niche, in a network of relationships with all the other species in its environment. Even in principle we will always need to consider some structures, such as organisms, as irreducibly real.

This leads to the important conclusion that science does not reduce to physics, either in practice or in principle. Systems, wholes, and structures are inherent aspects of reality that must be accounted for in any theory of the world or philosophy. Metaphysical reductionism simply cannot explain the universe and it does not.


Conclusion

I've tried to show that metaphysical reductionism fails as a philosophy. Instead we have to take different approaches to substance and structure. Substance does ultimately boil down to fields. Each layer of substance can be understood in terms of lower levels. The world is composed of fields. But this account is incomplete because the substance is also organised into structures that have irreducible properties - properties which are no longer apparent once we start to dissect the structure. The differences that scale make mean that we end up with a reality that has emergent layers.

In terms of the old Buddhist simile, once we take the chariot apart it ceases to be a chariot. But when put together, the chariot performs unique functions that are not an aspect of any of the parts individually, or in the parts in a jumble. Structure makes an irreducible contribution. Assemble a chariot and hitch it to a horse and you have a devastating war machine that allowed Indo-Europeans to conquer huge amounts of territory; or a way for a farmer to move much larger amounts of produce to market. These functions are also part of reality. Similarly, while not finding a soul in a dissected human being, a human being is none-the-less a structure capable of remarkable things. Buddhist thinkers were fatally hampered by the axiom that "real" meant permanent and unchanging. Once we realise that this axiom is not true or accurate, and drop it to allow for temporary or contingent existence, then we can have a more sensible discussion about the role of structure in the universe.

Metaphysical reductionism not only hampers progress in science, it hampers attempts to communicate the results of science. It seems to actively alienate parts of the audience for science (which is everyone). In a previous essay I labelled the failure to effectively communicate evolution to the general public as one of the greatest failures of science to date (The Failure to Communicate Evolution. 18 Sept 2015). Though it was not clear to me at the time I wrote that essay, one of the central causes of this failure has been the adoption of metaphysical reductionism and the reaction to this, at times, aggressive stance. Proponents of metaphysical reductionism are perceived as dogmatic, pompous, and arrogant. And for good reason! A full account of the failures and wrong views of metaphysical reductionism would take me too far from my purpose in writing this. On the other hand those who have reacted to metaphysical reductionism have tended to over-react. As Richard Feynman is supposed to have said:
"Philosophers say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong."
Very often those who reject metaphysical reductionism resort to caricatures of science and scientists, employing strawman arguments to the effect that all scientists are metaphysical reductionists. Ironically, for a reaction against reductionism, the idea that one can treat all scientists as metaphysical reductionists is itself a reductionist strategy! The reactions to the problem are at least as problematic as the problem itself. Neither side has the philosophical or moral high-ground, though both sides act as though they do. And thus they fail to communicate. Science may not reduce to physics, but nor should scientists be reduced to metaphysical reductionists. 

One major problem for philosophy has been the failure to explain the Hard Problem. Unfortunately, clever people tend to think that because they cannot imagine how something might emerge, that nobody can. So a philosopher like David Chalmers concludes from his inability to imagine a solution to the Hard Problem in a framework of substance reductionism, that it cannot be solved and we must turn to substance dualism or worse, panpsychism. The obvious conclusion from an inability to imagine a solution to a problem is "I don't understand", not "This cannot be understood". Certainly, the Hard Problem remains unsolved, but we need to be cautious about defining a problem as insoluble before we fully understand the problem.

Generally speaking, we can best study what the universe is made of using the methods and theories of reductionism. On the other hand, what the stuff is made into requires a different approach that is synthetic rather than analytic; oriented towards wholes rather than parts; and that acknowledges the value of levels of description; i.e. antireductionism. At least some aspects of higher levels seem to be irreducible features of reality and approaching them through metaphysical reductionism is thus counter-productive. Our descriptions of reality are discontinuous across scale. This means that different descriptions, even different kinds of description are required at different scales. Different sciences continue to be viable and productive despite not employing reductive methods or interpretations.

The rest of this essay will be concerned with the relationships between levels of description.

Part II.1 - published 22 July 2016.
Part II.2  - published 29 July 2016.
Part III.  - not yet published

    ~~oOo~~


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    01 July 2016

    The Citta Bottleneck

    This essay critiques one of the central propositions of the Doctrine of Momentariness (kṣaṇavāda), the idea that mental activity occurs in serial, i.e. as a series of moments of mental activity (citta) occurring one at a time.

    As I have previously argued, the Doctrine of Momentariness was a response to the problem of Action at a Temporal Distance. Specifically the principle of dependent-arising specifies that conditions must be present for effects to arise, but karma requires that effects arise a long time after the necessary conditions have ceased. The various Abhidharma projects tried a number of solutions to this problem, but the Doctrine of Momentariness was the most widely adopted. In this doctrine, an action of body, speech or mind, is conditioned by momentary (kṣaṇa) mental activity (citta) with a characteristic intention (cetanā). This citta is the condition for the arising of another identical citta. Each citta arises, persists only long enough to be the condition another identical citta, and then ceases.

    In theory, this creates an unbroken chain of cittas that link the intention behind actions with the eventual manifestation of the results of the action, usually aggregated as rebirth in one or other of the rebirth destinations (gati) or individually as sensations (vedanā). In practice, I have shown that this model only works in the special case that there is only one action and one effect (The Logic of Karma. 16 Jan 2015). No Abhidharma project conceived of the relationship between such cittas as simple. A certain amount of complexity was required to fulfil the requirements of the doctrine of karma. For example, the Sarvāstivāda proposed four types of conditional relation between cittas, while the Theravāda proposed twenty-four types.

    In this essay I will use practical examples to show that a key component of the Doctrine of Momentariness, the axiom that the mind operates one citta at a time, must be false. 


    The Perception of Music.

    Years ago, I attended a concert of the contemporary music ensemble 175 East with a friend. They performed a work by John Cage in which there were long periods of silence. It was remarkable just how long the players could pause between notes and we the audience could still detect the harmonic context of the note that broke the silence. The human brain has this remarkable ability to process notes so that they are not simply perceived as isolated events. Each note we hear becomes part of a context for the other notes so that when we hear them, we construct a musical event rather than simply a noise event. "Music" is what happens in our heads when we hear a bunch of notes and mentally construct relations between them. There is a condition is called amusia, in which this ability is lost through brain damage. People with amusia cannot hear the music in the series of notes arriving at their ears. To them, music is just random sounds. 

    Roughly speaking, the first note in a musical passage establishes a harmonic base (also called the tonic note) and subsequent notes are heard as having a relation to the tonic, as well as to each other. The relations are referred to as harmony. Through choosing the notes that are played together or in a sequence, the composer invokes a particular harmonic "texture", which in turn evokes an emotional response in the listener (and the player). These "textures" can be difficult to articulate directly. Music is often described using visual metaphors like "bright" and "dark". Sometimes we just talk about emotional responses we have and attribute them as intrinsic properties in the music, as in "the music was sad". The range of possible harmonic combinations is very large, so a good deal of subtlety can be conveyed.

    More complex music juxtaposes progressions of chords and melody. Or a passage may have more than one melody running concurrently providing counterpoint, which is a term for complex harmonic textures that result from the interplay of two concurrent harmonic textures interacting. We experience this is a very specific way, but mainly we talk about it in metaphorical terms or in terms of how we feel in response to the music. For some people listening to music conjures up images, though this is not universal.

    Other aspects of music, such as dynamics, tempo, rhythm, and timbre, work together with melody and harmony to produce a potentially infinite range of music experiences. The all important aspect of tension and resolution in music depends on the relation between the note we are hearing now, the first note we heard in any particular passage, the note previous to the present one, and our expectation of what the next note might be. We sense increasing tension when notes follow that would be dissonant when played at the same time. We sense increasing resolution when the notes would be consonant.

    Consonance and dissonance are to some extent objective. The physics of sound and pitch mean that some frequencies blend well together because of reinforcing or cancelling overtones or harmonics. Each note produced by a musical instrument is in fact a complex combination of the main note and combinations of higher pitches from what is called the harmonic series.

    Wikimedia
    The harmonic series was discovered by Pythagoras. It occurs on a guitar string for example when you divide the string length by integers: 2, 3, 4... The main mode of vibration of a string has a maximum amplitude at the centre (1/2) and two mimina at either end (0 and 1). This is called the fundamental mode. The next mode has two maxima at 1/4 and 3/4 of the string length and minima at 0, 1/2, and 1. This first harmonic mode vibrates at twice the frequency, as has a pitch one octave above the fundamental. The next harmonic mode divides the string into three, has a frequency 3x the fundamental and a pitch of one octave plus a fifth. And so on.

    When plucked a guitar string will vibrate in a number of these modes at once, producing a complex waveform. Which modes are prominent depends on the materials of the strings and the guitar body, the space it is being played in, and (at least to some extent) the mind of the person hearing it. The presence of combinations of harmonic modes in a musical instrument produces the distinctive timbre of the instrument. and is also responsible for the objective part of why notes are consonant or dissonant in relation to other notes. In woodwind instruments different timbres are produced by the source of vibrational energy: lips (trumpet and other brass instruments), single reed (saxophone, clarinet) or double reed (oboe, bassoon); and the bore of the chamber, which can be a straight-sided cylinder (clarinet, flute), or conical (cornet, saxophone). Some brass instruments combine a mostly cylindrical bore, with a flaring conical end section.

    The tonic itself and the octave are the most consonant pitches with respect to any tonic: these have the same frequency and double the frequency respectively, and the octave is one of the main overtone pitches in any musical note. The next most consonant is the perfect fifth, with a frequency of 1.5 times the tonic. The third, with a frequency of 1.25 times the tonic, is also consonant. The most dissonant notes are the minor second (one semitone up) and the major seventh (11 semitones up or one semitone down from the octave). 

    The physics of making and combining notes is fascinating. But it does not explain music. Music can be analysed as certain physical events in the world, but cannot be reduced to those events since music is dependent on our minds. When we hear music we are exercising a mental ability to parse the relationship between the notes and linking these emotional responses over time. The amazing thing is that we can comprehend the music in a series of single, spaced-out notes of different pitch, durations etc, just as well as if they had been played all at once. Of course the ability can be honed with practice and learning, but all humans have this innate ability to ability to perceive a series of notes as music.

    Something very similar happens when we process language, i.e. a series of vocal sounds is decoded into words with grammar and syntax. If we did not hold the whole sentence in our minds until the end we would not be able to relate subject to verb to object. While words convey some meaning on their own, the basic unit of communication is the sentence, which exists over a period of time, not in the present moment. If we just "lived in the present moment", we not understand either music or language.


    Cognition and Time

    music requires us to hold recently past sensations in mind, whilst simultan-eously juxtaposing present sensations with those past sensations, and at the same time to form an expectation of what sensations might come next.
    The ability I'm describing is related to a function of the brain known as working memory. The way working memory facilitates our perception of music is quite a complex and I'm going to largely gloss over the details. If you are interested a good place to start is this blog post, Music in working memory. Even without knowing the details, it's clear that in order to experience sounds as music requires us to hold recently past sensations in mind, whilst simultaneously juxtaposing present sensations with those past sensations, and at the same time to form an expectation of what sensations might come next. And to process the emotions evoked by the music as we construct it. Similarly with language. This observation was made by the phenomonologist Edmund Husserl (1859-1938), but I came across the idea by way of an article on Abhidharma theories of mind by Monima Chadha (2015). 

    The element of anticipation is easily overlooked by a recent blog by science writer, Rolf Dengren ( @DengrenRolf) emphasises the role of expectation in perception. Dengren uses this example of degraded images to make the point. Take a look at these images and see if you can tell what they are.


    Most people looking these degraded images for the first time cannot make out what they depict. However, once they are told what the images depict, then they can make them out. A list of what these are images of is included at the bottom of this page. I was astonished at how obvious these images are once I knew what to look for.

    Anticipation plays a big role in music also. The thrill of music often comes when the melody goes off in an unexpected direction, for example by repeating a melody with variations, or by changing key (i.e. changing the actual or implied tonic note) so that the expectation of the listener is confounded. This experience can even be quite thrilling.

    One of the basic ideas of Buddhism is that time can be divided into present, past, and future. In one sense this is our basic intuition about time. It feels like we occupy a present, while memories tell us that time has passed, and imagination predicts future events that have yet to manifest. In fact time is not inherently directional, we experience it as moving in one direction because the early universe was extremely low in entropy and is gradually accumulating entropy. So when we compare our present to our memories, we see events occurring asymmetrically: whole things break all the time, but never spontaneously go from being broken to being whole. This as the so-called arrow of time. And it causes us to form certain expectations of the future. It also means that we can usually tell when a film is being played backwards - the action does not conform to our expectations. So "past" and "future" seem like a natural categories to us. And in fact these are much less problematic than the idea of the "present".

    Trying to define "the present" is clearly very tricky. The definition of the present involves the shortest conceivable time interval, in the Indic terminology, the kṣaṇa. If everything, every phenomenon, is by definition impermanent, then any phenomenon which lasts for more that a single moment threatens to undermine this definition. It almost inevitably leads to the conclusion that the maximum length of time a phenomenon can persist for, is a single moment. And the definition of a single moment must be squeezed down to the smallest conceivable duration. In my essay, Buddhism and Existence (17 Jun 2016), I explained that an arisen phenomenon cannot be described as existing in Buddhist philosophy, because existence always implies permanence. The fact that an arisen phenomenon must cease at some point means that existence can not be applied to it. So for Buddhist doctrine there is an even greater pressure to say that the present cannot extend beyond the smallest conceivable unit of time. The smallest conceivable unit of time these days, the Planck time, is about 10-44s, though practically speaking we can measure time to a precision of about 12 attoseconds (1.2 × 10-17s).

    However, this approach to time is far from useful or coherent. "The present" is a subjective experience which emerges from our interactions with the world over time. The "present", that is the present as it is experienced by a human being, our present, is certainly not a moment in time. It's a subjective experience of time passing constructed in relation to sensate experience, memory and imagination. And in relation to a first person perspective that includes a sense of location in time and space and ownership over experience and actions.

    In a way it is strange that Buddhists should emphasise this particular structure of subjective time, because one of the key meditation experiences is the cessation of perceiving time passing. The fact that time stands still while we meditate, but continues to pass in the world around us, ought to have have been an important datum in the attempt to understand the world. Events continue to flow, even when we do not experience them as doing so. In fact the same happens when we fall asleep - we go to sleep at night, but wake in the morning. Time has passed without our being aware of it. The subjectivity inherent in the experience of time ought to have been obvious to Buddhists. More so when we add that the key Buddhist experience is the reduction or elimination of the first person perspective on experience, which (according to anecdote) removes the sense of being firmly located in time and space, and the sense of ownership of experience. So a Buddhist theory of time in which, in effect, the ego is the point of reference in relation to experience is something of a contradiction.

    On the other hand, at least one sutta (SN 22.62) seems to be saying that talking about past, future, and present is only a linguistic convention (niruttipatha, adhivanacapatha, paññattipatha) in relation to the skandhas. Still, even in this this linguistic interpretation the present is still conceived of as a single moment in time.

    What the perception of music and language shows, is that our awareness includes a present moment, but is not limited to that moment. Awareness is smeared out over time both in the sense of holding past moments in mind and of anticipating the future. If it were not, we couldn't experience music or language. In all likelihood we could not experience change of any sort if our awareness of time were not smeared out.


    Critiquing Momentariness.

    Our ability to process sounds as music or language demonstrates that the axiom that the mind processes one citta at a time is false. In fact we have to hold many things in mind and our perception of time is not limited to a single moment, but relies on extension over time; whilst also anticipating future moments. This is the minimal requirement for a mind which can comprehend music, language, or change. Far from being momentary, the subjective "present moment" is extensive over a period of time. The very concept of a moment in time as described by the Doctrine of Momentariness is doubtful. The "moment" is a rather arbitrary notion with no objective counterpart.

    In my essay The Logic of Karma (16 Jan 2015) I outlined some criticisms of the Doctrine of Momentariness (kṣaṇavāda) with respect to karma. I showed that the doctrine can only work in a mind in which there is only one active karma and no other tributaries to the stream of mental events. Once we try to model two or more karmas or other sensory inputs, the model cannot maintain continuity between condition and effect. All the descriptions of the model I've seen, use the example of a single citta stream. The Doctrine of Momentariness was invented in order to provide continuity between action and consequence under the condition that the absence of the condition requires the absence of the effect. I have shown, the doctrine cannot sustain the required continuity in any real world scenario. It can only work in the special case that there is only one intention giving rise to one outcome (vipāka) - in any given lifetime!

    In the current critique, based on how we perceive music or language, we see that one of the fundamental axioms of the Buddhist model of the mind—i.e. the one citta axiom—is flawed in such a way as to invalidate the model. Cognition simply cannot be confined to the present moment or it would not work the way that it does. The whole idea of the "present moment" is flawed.

    We can now see that in order to solve the continuity problem, not only is our perception of time necessarily extended over many moments, but the mind would have to process many (very many) cittas simultaneously in parallel in order to allow karma to work in the traditional sense. And this still requires the Abhidharma idea of cittas with multiple properties (cetasika) and multiple kinds of conditional relation between cittas. And this is working within a framework in which we stipulate the traditional idea of karma, when in fact there are many challenges to this conception. 


    Conclusion

    I have now shown that the Doctrine of Momentariness is false in two distinct ways. Firstly, in my previous essay, The Logic of Karma, I have shown that the Doctrine of Momentariness cannot provide the continuity required by karma (even though facilitating this continuity is the raison d'être of the doctrine).

    Secondly, observations of mental activity related to music and language show that it cannot operate one citta at a time. It is common enough for meditators to report that in states of deep absorption that thoughts, if they do arise, appear to arise slowly, one at a time. I take this quite seriously, however I dispute the interpretation.

    The problem here is the process of reasoning from an experience in an altered state to an ontology (a universally true statement about what exists or the nature of reality). When we do this, we almost always get it wrong. Buddhists, for example automatically assume that experiences in meditation are more real that ordinary waking experiences. One can see why this might be. We're taught from the beginning that meditation will lead us to experience reality; or indeed the true nature of reality. Meditation experiences, like drug experiences, often seem hyper-real (or more real than waking experience) and thus it seems logical to assume that they are in fact more real; that in having an experience in meditation we have experiencing the true nature of reality. And since absorption involves us being cut off from our normal sensory stimulation, if we are experiencing "reality", then by the logic of Buddhist doctrine we must be experiencing it directly. Also in that state whatever we experience is ipso facto real. Based on the kinds of assumptions that people absorb along with meditation instruction, these conclusions are logical and intuitive. The problem is that the assumptions that underpin this reasoning appear to me to be false. At the very least they are questionable.

    In the clash between traditional Buddhist ideas and modernity, some of us prioritise tradition and some of us prioritise modern knowledge. Part of my project/object is to show that aspects of the tradition, such as the Doctrine of Momentariness, are not coherent even on the tradition's own terms. That is to say, even if we enquire into Buddhist tradition within the worldview of the tradition, ignoring for the moment this clash of cultures, then certain important Buddhist doctrines are incoherent on their own terms.

    However, since we do live under modern conditions, since we do have access to objective knowledge about reality, we really ought to take this into account when trying to explain what Buddhists do when we seek awakening; and what really happens when we experience awakening. Buddhist accounts of reality are anachronistic at best. The value of Buddhism does not lie in its medieval ontology. It lies in methods and approaches to understanding experience. Ultimately, it lies in the value of the radical transformation that is characterised by egolessness. What really interests me as a Buddhist intellectual is how we (re)frame these methods and this radical transformation in a coherent and relevant way; especially how we relate it to the domain of objective knowledge about reality. We need to move Buddhist doctrine along from being a collection a medieval anecdotes and metaphysical speculations.

    ~~oOo~~

    Bibliography.

    Chadha, M. (2015), “Time-Series of Ephemeral Impressions: The Abhidharma-Buddhist View of Conscious Experience,” Phenomenology and Cognitive Sciences: 14 (3), pp. 543–560.


    Update 15 Jul 2016

    Study suggests that preference for consonant over dissonant sounds is culturally defined.
    McDermott, J. H. , Schultz, A. F., Undurraga, E. A. and Godoy, R. A. (2016) Indifference to dissonance in native Amazonians reveals cultural variation in music perception. Nature [Letter published online 13 July 2016].  DOI:10.1038/nature18635
    ~o~

    Degraded images: a) clock, b) plane, c) typewriter, d) bus, e)elephant, f) saw, g) shoe, h) boy with dog, i) old convertible, j) violin.
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