Towards a Science of Events : Introduction
June 28th, 2010 at 4:58 pm (Mathematics, Philosophical Issues, Science)
“One never steps twice into the same river” (Heraclitus).
A Reasonable Assumption
It would seem that there is something. I do not myself see how the previous statement can possibly be untrue: it is perhaps an example of that rare bird, a necessarily true statement that is not just an empty definition. Amongst philosophers, to my knowledge, only the Greek Sophist, Gorgias, is on record as having maintained that there was strictly nothing at all (1) : certainly no variety of oriental mysticism goes anything like so far.
So, in what does this ’something’ consist? The school of thought that we may trace back to Democritus (most of whose works have been lost), argues that the really fundamental entities must be a good deal smaller, and in consequence more numerous, than those we are more familiar with. Parmenides, on the other hand, took exactly the opposite view : that there is only one ‘thing’. Most human beings, according to Parmenides’ school of thought, are afflicted with a persistent error of judgment which makes them split up into pieces what is in reality completely unified. We have, then, on the one hand pluralism and on the other, monism, the Many and the One.
Empiricists consider that the world we know through our sense (or at least think we know) is the proper place to start and end our investigations. As against this, we might suppose that the world we see and hear is entirely dependent on abstract principles not directly accessible to the senses: this is the transcendentalist point of view. How then are we to get to know these hidden principles? By logical and rational argument, by mystic intuition, by cosmic memory — such are a few of the very many answers given to this question. For the Pythagoreans these hidden principles were mathematical in nature, by which we should understand ‘numerical’; for Plato and his followers all items in the phenomenal world were copies of eternal Forms or Ideas existing in the Beyond.
Western Science
The world-view of Western science (originally known as ‘Natural Philosophy’), the most successful belief system in history, has been consistently pluralist and those sympathetic to Parmenides’ unified vision of reality have tended to be poets and mystics. “Nothing exists except atoms and void” was Democritus’ succinct answer to enquiries about the nature of ultimate reality. If we understand by ‘void’ something not entirely negative but a sort of stage or receptacle for the moving atoms, a precursor of Einstein’s Space/Time, Democritus’s vision is with us still.
To these two major players, Newton added a third: Force. From the beginning this entity was regarded with some suspicion by continental scientists since it seemed the very sort of metaphysical entity that they wanted to relegate to the rubbish dump (2). Nevertheless, it proved to be essential. We have, then, the world-view of triumphant Mechanism : minute, indestructible, resistant bodies knocking against each other with mathematically predictable consequences, and, when distant, held together by an all-pervading Force of Universal Attraction.
In the nineteenth century, new entities were added, notably the electro-magnetic field. Twentieth century discoveries showed that Democritus’ atoms could be decomposed into elementary particles which were scarcely ‘things’ in the normal sense at all : the viewpoint of Classical Physics turned out to be a sort of ladder which, once one has climbed up it, one kicks disdainfully away (as a French physicist friend of mine once put it).
The world-view of Western science has never been completely empiricist since it contains a strong element of ‘Idealism’ which goes back to Pythagoras via Plato. The emphasis on experiment and observation is empiricist but the crucial role of mathematics and the firm belief in ‘physical law’ is transcendentalist. To see this, one has only to compare the world-view of modern scientists with that of the ancient Greeks or that of the Chinese. For the ancient Greeks, the Platonists at any rate, the behaviour of celestial bodies was regular and predictable, the behaviour of most terrestrial bodies, and in particular human beings, was erratic and unpredictable since it was subject to ‘Fortune’. And, according to Needham, the absence of a belief in ‘natural law’ was the main reason why the Chinese, at one time centuries ahead of the West technologically, failed to give birth to modern science as we understand it. “If any law were involved [in the operations of the cosmos]… such a law would have to be expressed in a language indecipherable to man and not a law established by a creator conceived in our image” (quoted Prigogine, Order Out of Chaos p. 48).
For Newton and Leibnitz, however, the mathematical principles which presided over the functioning of the universe were ideas in the mind of the Divine Architect, and, moreover, these laws could actually be known and stated. This belief in unalterable law has, somewhat surprisingly, survived the demise of a Creator God and the havoc caused by quantum indeterminacy, chaos theory and so forth. It is only very recently, and with evident reluctance, that physicists have admitted that the value of certain constants (such as g) may have changed ‘over time’, while the idea that ‘the laws of physics’ could have evolved, somewhat in the way in which the constitution and behaviour of living things has evolved, remains a serious heresy. The very attempt to find a ‘Grand Unified Theory’ is based on the conviction that there exist certain principles which are true ‘in all places and for all time’ and which are somehow independent of the universe in which they are exemplified. But, as writers like Nietzsche, William James and more recently Dr. Sheldrake have pointed out, the cast-iron belief in ‘natural law’ is disguised transcendentalism, is Platonism stripped of its geometric trappings.
A materialistic World-View
Western culture is ‘thing-orientated’, has been consistently materialist from the days of its inception in Athens and Alexandria. The concept of the ’soul’ as something different from, and antagonistic to, the body is a Middle Eastern (Persian) rather than a European notion. Christian doctrine affirmed, and still affirms, the ‘resurrection of the body‘ (Apostles’ Creed) and medieval theologians seem to have considered that even supernatural beings had some spatial extension, hence the debates about how many angels could stand on the head of a pin. Ideas of solidity, continuity, indestructibility, dominate : no major religious, philosophic or even artistic movement in the West has started with the premise that everything is evanescent. The contrast with the East could not be more complete (3).
Linguistic theorists such as Whorf have pointed to the ‘object orientation’ inherent in the grammatical structure of Indo-European languages, subject, cupola, predicate. Something is presented to our attention and then properties are attributed to it : in effect nothing ‘happens’. “The SAE (Standard Average European) microcosm has analyzed reality largely in terms of what it calls ‘things’, bodies and quasibodies, plus modes of extensional but formless existence that it calls ’substances’ or ‘matter’” (Whorf, Language, Thought and Reality p. 147). Whorf contrasts this with the ‘action orientated’ languages of certain Amerindian societies such as Hopi and Shawnee.
For Buddhism — Hinayana at any rate — the ultimate constituents of reality are not cells or atoms but dharma, point-instants unextended in space and instantaneous : they appear from nowhere and disintegrate into nothingness all the time. These ‘elements’ (literal translation of dharma) do not, however, arise at random but are subject to what the Buddhist logicians (Kamalasila, Vasubandhu) call ‘Dependent Origination’, a ‘force’ which in the moral context manifests itself as karma.
Events not Things
It has long occurred to me that it should be possible to describe material reality, and possibly ‘immaterial reality’ as well, not in terms of ‘objects’ and ‘forces’ but strictly in terms of events in Space/Time which are subject to certain causal principles. In what follows events and not things will be taken as the ‘irreducibles’ of physical reality : objects will be defined as (almost) identically repeating event-clusters, as groups of events which possess ‘persistence’ .
What, then, are ‘events’? Being basic there is nothing more fundamental in terms of which they can be described : the best one can do is to see what it is we have in mind when we use the word (4).
The first thing to note about an ‘event’ is that it is entire, all of a piece. It makes no sense to speak of ‘half an event’. When there is change or progression, we speak of process, of a ’sequence’ of events, not a single happening.
Secondly, an event is conceived as having entirely negligible extent spatially and temporally : an event is punctual. On a physics Space/Time graph an event is marked as a point.
Thirdly an event is perfectly definite: it either occurs or does not occur and there is in general immediate agreement amongst observers as to whether an event has taken place or not (provided it is a macroscopic, easily noticed event). An event is, in this respect, very different from a feeling, a wish, an assumption or an idea. (It should be noted that dream occurrences certainly appear to be definite — exactly what makes us feel that they are in some sense ‘real’.)
Fourthly, an event usually gives rise to other events, hardly ever seems to stand alone without predecessors or successors : an event has effects, consequences, i.e. is efficacious.
These four properties are, I believe, the main ones we intuitively associate with an ‘event’, judging by the way we use the term.
Of course, whether or not we class something as an event depends on the scale. A battle, classed as an event in history books, can be decomposed into a specific number of cavalry charges and rounds of ammunition fired, an evening ‘dance’ can be split up into a specific number of separate dances. So these ‘events’ are not, in point of fact, entire and they are extended spatially and temporally. Even a blow with an axe can be split up into a sequence of energetic movements. However, when we refer to these things as ‘events’ we do conceive them as being ‘all of a piece’, as unextended spatially and temporally : it is only when we shift our perspective that we break them down into a stream or conglomeration of smaller events. It is as if we had at the back of our minds a clear notion of what constitutes an ‘event’.
Can this process of decomposing ‘events’ be continued indefinitely? This I personally find very difficult to comprehend, and thus to accept : there must seemingly be a limit when we arrive at events which cannot be split up any farther.
Thus the first Principle of Eventrics, that there exist events which cannot be further decomposed and which will be called ultimate events. All those properties that we attribute to ordinary events and which turn out to be only approximately true for them, are strictly true for ultimate events.
Ultimate Event Principle
All phenomena are made up of a specific number of ultimate events; ultimate events are themselves indivisible and are not reducible to anything else.
The Locality
If ultimate events are to have occurrence, there must seemingly be a place where they can and do occur. The only other possibility is to view them as ‘making their own place’ as and when necessary, which at least assumes there is nothing ‘in the way’ to prevent occurrence. Once again, I believe it more reasonable to assume the place of occurrence as pre-existing. The totality of places where events may have occurrence will be termed The Locality. It will be attributed the bare minimum of features at this point and the reader is asked to keep out of the way, as far as this is possible, any notions he or she may have about ‘Space/Time’ gleaned from physics textbooks, or, for that matter, science fiction. All we require of the Locality is that :
1. it allows ultimate events to have occurrence; and
2. it obliges ultimate events to be distinct one from another.
(2.) is required because we do not want ultimate events to merge with pre-existing ones, for this would result in us having no perception of them as distinct events — and it is one of the fundamental properties of ultimate events that they are self-contained and unique. Essentially, we want the Locality to consist of a limitless (or at least very extensive) collection of ’spots’, each of which may receive one and only one event. If we do this, an ultimate event will be absolutely and precisely localized, not just approximately localized as most real-life events are.
This gives the Localization Principle
Every ultimate event has occurrence at a particular spot on the Locality, and no two ultimate events can have occurrence at the same spot.
Note that this relation between (ultimate) events and spots is not necessarily one-one : it is not stipulated that all spots on the Locality must be filled.
The Localization Principle does not in itself endow the Locality with any ‘geometrical properties’ but it does endow it with extent. Whether this ‘extent’ is limitless or not, we do not at the moment need to assume : the issue is somewhat analogous to the current issue of whether the ‘universe’ (not a term of Eventrics) will expand for ever, or will contract back into the nothingness from which it came. If the Locality is indeed limited in extent, then at some stage ‘everything would come to an end’ not because of any explosion or other calamity but simply because there will be no places where ultimate events can have occurrence (unless there is a built-in facility which enables occupied spots to be ‘emptied’ of their contents). We assume for the moment at least that the Locality is not full and that there are plenty of available spots.
Occurrence
An event either comes about or it does not, there is no halfway-house. It is true that very occasionally we do speak of the ‘partial occurrence’ of an event such as an eclipse of the moon but this is to contrast a perfectly distinct event, the ‘partial’ eclipse, from another which we are familiar with (a total eclipse). When dealing with entities that cannot be divided, it makes little sense to speak in this way : an ultimate event cannot be partially anything at all, it either is or it is not.
It remains to ensure that an ultimate event either occurs or does not occur and not both at one and the same ‘time’. This is the Principle of Exclusion which is needed to make sure that the world of events is coherent .
A spot on the Locality is either occupied by an ultimate event or it is empty, but not both at once.
The Exclusion Principle plays the same role in Eventrics as the Principle of Non-Contradiction plays in (classical) logic. In theory, any absurd and impossible eventuality in Eventrics ought to be traceable back to a violation of the Exclusion Principle in much the same way as a false argument in mathematics can (in principle) be traced back to a ‘contradiction’, i.e. an assertion in conflict with the basic axioms of the logical or mathematical system.
Classical physics assumes the Exclusion Principle : indeed without it observational and experimental science would be a waste of effort. There would, for example, be no point in predicting that a total eclipse of the sun would take place at a particular place and time, if it were also possible for it not to take place there. Quantum Mechanics, in the orthodox ‘Copenhagen’ interpretation at any rate, does not seemingly verify the Principle of Exclusion but this is precisely what makes it so worrisome despite its phenomenal success (5).
It should be noted that the Exclusion Principle, as formulated, is observer-independent , i.e. is true for any possible observer though not, of course, necessarily in the same manner or ‘at the same time’ for each one of them. I say this because of eventual problems with respect to Relativity. If I witness the explosion of a supernova, this event undoubtedly ‘has occurrence’ on the Locality irrespective of my state of motion and location. And if it ‘has occurrence’ for me, it must ‘have occurrence’ for everyone else whether they realize it or not, since the occurrence of an event is not something subjective — or so I firmly believe. Generally, in Relativity, it is the order in time of two events that may be different for different observers, not the occurrence of the events themselves. (Terms such as ‘observer’ and ‘order in time’ clearly are not going to have the same meaning in Eventrics as in physics or normal speech but it would be foolish to forbid oneself using them altogether at this stage in the game. Such terms will eventually be precisely defined.)
Irrevocability and Direction of Occurrence
If we have something that can change, develop and so on, there is the possibility of intervening: we can remodel a project, educate a person, arrest a process. But with respect to an ultimate event, none of this is possible, there is no ‘time’ to intervene. Either an ultimate event does not have occurrence, i.e. is not, or it has occurrence on a single spot of the Locality, a spot that cannot a ccept another inhabitant. An ultimate event is thus final, irrevocable, and, since procedure for disposing of ultimate events has been suggested, it will remain as it is forever.
This is the Irrevocability Principle
An ultimate event cannot be altered or obliterated.
This means that past events are in some sense still there — for they have not been obliterated — even if we have no access to them.
There is and can be, moreover, only one direction involved, that leading from non-occurrence to occurrence. There is no converse procedure, no way of ‘dis-occurring’ ultimate events. In consequence, the sum total of occurrent ultimate events can thus only increase or remain constant (the next principle stipulates that it cannot remain constant). This is the equivalent of the ‘Principle of Entropy’ in Eventrics.
Dominance
Why are we so sure that the sun will rise tomorrow? Why doesn’t everything just grind to a halt? Why doesn’t the ‘universe’ disappear overnight?
Rather few western thinkers have given serious attention to this issue, Descartes being an honourable exception (4).
For some reason the West, at any rate in recent times, has always assumed that stability and continuity are the rule rather than the exception : there is always ’something’ that carries on whether it is Nature or amorphous matter or the Christian soul. In our daily lives, we assume without a moment’s thought that events will give rise to other events : ‘Every event has a cause’ is mirrored by the conviction that ‘Every event is a cause of at least one other event’. This attitude is comparatively recent : so-called ‘primitive man’ was apparently often beset by the recurring anxiety that darkness might last for ever, spring never return. He had expectations, of course, but not our blithe confidence.
The peculiar property which events have and which enables them to bring about new events will be called Dominance. The concept is somewhat broader than that of ‘necessary causal relation’ and the term has been chosen to emphasize the (in general) asymmtrical nature of the rapport between ’cause‘ and ‘effect’.
Dominance, if it exists at all, is clearly a meta-physical (beyond the physical) property, which is why it has worried certain thinkers. Consistently empirical thinkers such as Hume denied that it exists while Wittgenstein wrote melodramatically, “the causal relation is a superstition”. For all that, a world without causality is unthinkable, more fantastic than world without matter, and Hume himself admitted that he felt otherwise when he was playing billiards (5). While Buddhist thinkers dismissed matter (and soul) as illusory, they retained belief in ‘Dependent Origination’, a sort of cosmic force of causality.
Dominance may be viewed as an invisible influence exerting itself between events, a force somewhat analogous to the force of attraction. But one should beware of taking such an analogy too far since attraction is exerted between co-existing bodies and exerted in both directions simultaneously, whereas Dominance is usually, though not necessarily invariably, one-directional. (Someone to whom I exposed these ideas even suggested that ‘dominance’ is more basic than events themselves (cf. ‘energy’) and that events and things were just ‘carriers of dominance’.)
However it is to be conceived, the purpose of the concept is to provide an explanation (or at least a rationalization) of the apparent fact that all phenomena seem to give rise to other phenomena : once it has been commenced, the game of life is never-ending. Hence the Principle of Dominance
Every ultimate event gives rise to at least one other ultimate event.
This principle does not stipulate that all events must have arisen in this way : it remains a possibility that there are ultimate events which do not have predecessors, that have acquired their dominance from a source other than that of occurrent ultimate events.
Anticipating later developments, we can make a distinction between active ultimate events (those which still have dominance and can thus give rise to other events) and those which have lost this power and are thus inactive or inert. Also, there are seemingly ultimate events whose dominance is dormant, the equivalent of seeds which only germinate in special conditions. However, these are special cases which will be dealt with when and if necessary : for the moment all ultimate events will be assumed to have dominance unless stated otherwise.
This concludes the list of essential preliminary assumptions about events.
Notes
(1.) The Greek sophist, Gorgias, is supposed to have maintained in his book Nature or the Non-Existent
(a.) that nothing exists; (b.) that if anything did exist it could not be known; and (c.) that if anything about such a ‘thing’ could be known, this knowledge could not be communicated.
One notes that even Gorgias finds it necessary to pull back from his original sweeping assertion that there is nothing.
(2.) During Newton’s lifetime there was considerable scepticism amongst continental scientists about Newton’s ‘Force of Gravity’ or ‘Universal Attraction’, most people preferring Descartes’ rival vortex theory. Centuries later, the eminent French scientist, Duhem, decided that ‘force’ must be banished from physics and actually wrote a Théorie Physique which dispenses with the term/concept. ‘Force’ has in fact largely disappeared from contemporary physics but only to be replaced by the even more metaphysical concept of ‘energy’ which, literally, is nothing more than ‘potential work’, i.e. work that can be done by a physical system but which is not actually being done. Thus a boulder at the top of a hill has ‘potential energy’ because it can be made to do work if it is toppled over, and a moving object has kinetic energy since it can be made to do work by putting something in its path. The expansion of the energy concept to cover pretty well the whole of physics is a development which only goes back to the mid nineteenth century.
(3.) The only artistic movement of importance in the west which has placed the ephemeral at the centre of its attention is Impressionism which was directly influenced by the arrival of Japanese prints in the west. The term ‘impression’ was originally pejorative : the momentary sensation or ‘impression’ was not considered worthy of the serious painter’s attention, whereas for Japanese and Chinese painters, especially those influenced by Zen Buddhism, the first impression was likely to be nearer to the truth since it was as yet unmediated by human rationalization.
(4.) Plato, who advanced the idea that “all knowledge is recollection”, was probably right to believe that, in some areas, we “know more than we think”. In such cases, the best strategy is to bring to the light of day deep-rooted feelings and intuitions which one can only assume to be based on memories, whether individual or trans-personal. The idea that the world is a sort of kaleidoscope where nothing remains the same for more than an instant comes up frequently in Eastern religion and philosophy, not only in Buddhism.
(5.) Keith Devlin, in his pioneer work on ‘the logic of meaning’, writes, “It seems to me that there is nothing for it but to take as fundamental the relation of one event causing another” (Devlin, Logic and Information p. 184).
Likewise, Campbell quotes work down by Leslie and Keeble who “believe that a distinct mechanism in the brain….operates independently of general knowledge and reasoning, so that whatever an infant does not know about the world, at least she knows that events have causes” (Campbell, The Improbable Machine p. 221).
Sebastian Hayes