Archives for category: Bertrand Russell

Events rather than things

The West has, from the Greeks onwards, been ‘object-based’ as opposed to ‘event-based’ at any rate with regard to natural philosophy. The only prominent Western thinker to have seriously supposed that matter, and thus by implication the entire physical universe, was inherently unstable and might conceivably disappear into thin air, i.e. revert to the nothingness from which it came, was Descartes. But, being a believer ─ a deist at any rate ─ like practically everyone else of his time, Descartes was able to bring God into the picture  to save not just appearances but (physical) reality itself. Descartes would have had a much larger audience in India than in Europe and Stcherbatsky states that a remark of Bergson’s summarizing Descartes’ theory, once translated into Sanskrit, “sounds just like a quotation from a Sanscrit text” (Note 1).
But the resounding success of the Newtonian paradigm firmly based on the concepts of matter, force and motion silenced such mystical sounding speculations. It is only in the 20th century that we find natural philosophers, or ‘scientists’ as they now consider themselves, talking about ‘events’ as such at all. Einstein’s theory of Special Relativity (SR) concern ‘events’ ─ “occurrences that every observer would agree took place such as an explosion” as the author of a textbook on Relativity defines them ─ rather than things and a good deal of SR is taken up with the (ultimately insoluble) problem of ordering events so as to plot the operational range of causality. Bertrand Russell remarks :“From all this [‘all this’ being a discussion of Relativity] it seems to follow that events, not particles, must be the ‘stuff’ of physics. What has   been thought of as a particle will have to be thought of as a series of events. (…) Thus ‘matter’ is not part of the ultimate material of the world, but merely a convenient way of collecting events into bundles.” (Note 2)
But Russell  does not follow up this particular line of thought mainly because of his misguided belief that mathematics was essentially an extension of logic. A sceptic and a rebel with respect to so many leading dogmas of his time, Russell was not the main to question the dogma of continuity which is so deeply embedded in Western mathematics.

Fields
As for Einstein, his basic philosophic position is not easy to determine but seems to have been, at least during his middle period, that ‘fields’ were the primary reality. Ultimately everything was part of a single ‘Unified Field’ which was continuous, and ‘matter’ was merely “that portion of the field which is particularly intense“. This is, of course, incompatible with the basic assumption of Ultimate Event Theory, namely that reality is made up of discrete bundles of ultimate events. However, these ‘observables’ can be viewed as disturbances of an underlying, invisible, all-pervading substratum which is continuous, somewhat in the manner that ripples or foam are discrete disturbances of a fluid that is continuous (or at any rate appears so to us). So there is, conceivably, an underlying ‘continuous’ entity after all (as David Bohm for one believed) but such an entity, source and origin of All That Is is not directly observable and thus does not properly speaking fall within the remit of science.

Space-time ultimates
Whitrow, in one of his numerous books on time, advances the idea of a minimal unit of time, the chronon, and suggests a plausible value based on the diameter of an elementary particle divided by c the speed of light. This was the first time I came across the idea in a Western writer. Whitrow also has some useful comments to make on the illogicality of calculus which always treats time and motion as continuous variables but, like Russell, he does not pursue this line of thought.
More recently, in his very remarkable book, A New Kind of Science, Stephen Wolfram writes:
The only thing that ultimately makes sense is to measure space and time taking each connection in the casual network to correspond to an identical elementary distance in space and elementary distance in time. One may guess that this elementary distance is around 10 (exp -35) meters , and that the elementary time interval is around 10 (exp -43) seconds.”    (p. 520)
        He draws the conclusion :
“Whatever these values are, a crucial point is that their ratio must be a fixed speed, and we can identify this with the speed of light. So this means that in a sense every connection in a causal network can be viewed as representing the propagation of an effect at the speed of light.”
        This certainly is a crucial point but I would prefer to see this fixed space-to-time ratio as simply defining the operation of causality, i.e. it is a speed barrier which no effect propagated from one ultimate event to another can exceed, or even attain (Note 2).
More recently still, Lee Smolin writes:
“If space and time consist of events, and the events are discrete entities that  can be counted, then space and time themselves are not continuous. If this is true, one cannot divide time indefinitely. Eventually we shall come to the elementary events, ones which cannot be further divided and are thus the simplest possible things that can happen. Just as matter is composed of atoms,  which can be counted, the history of the universe is constructed from a huge  number of elementary events” Lee Smolin, Three Roads to Quantum  Gravity p. 41-2  Phoenix Paperback Edition.
      However, Lee Smolin  writes in another place:
“A causal universe is not a series of stills following on, one after the other. [Why not?] There is time, but there is not really any notion of a moment of time. There are only process (sic.) that follow one another by causal necessity.”  (Ib. p. 55)

Process

Lee Smolin thus, seemingly, pins his faith on ‘processes’ rather than ‘ultimate events’, whereas, for me, a process is simply a tightly connected chain of  events : in UET, it is the constituent ultimate events that are fundamental, not  the ensemble.
Also, Lee Smolin, reverting to a conception of Leibnitz, dispenses with the independent existence of what I call the Locality :“There is no meaning to space that is independent of the relationships among  real things in the world. Space is not a stage which might  be empty or full [Why not?], onto which things come and go. Space is nothing apart from the things that exist; it is only an aspect of the relationships that hold  between things.” Ib.  p. 18
I don’t see this. Rather, if anything at all happens (and seemingly ‘something’ does), then it must happen somewhere and this ‘somewhere‘ must seemingly already in some sense exist, even pre-exist, otherwise nothing could happen because there would be nowhere where it could happen. Smolin even goes so far as to attack the very idea of Space-Time possessing a ‘structure’ and declares, quite incorrectly as far as I can make out, that this never was Einstein’s conception. From my point of view, reducing Space-Time to ‘relations’ is throwing out the baby and keeping the bathwater. What Smolin views as the fictitious entity, ’empty space’, I see as the underlying reality while ‘relationships among real things in the world‘ are not even a secondary reality : in my book, they are still farther down the actuality scale, coming well after the ‘real things’ Smolin refers to (i.e. ultimate events).

Causal Set Theory
Causal Set Theory, a contemporary version (or extension?) of General Relativity that is, in this country, chiefly promoted by Professor Fay Dowker, is  the most appealing of contemporary cosmological theories because it maintains that ‘Space-Time’ is fundamentally discrete ─ “This reasoning [concerning the physics of Black Holes] leads us to the conclusion that every region of spacetime (and not only the horizon of a black hole) should be fundamentally discrete”. The quotation comes from Causal Set Theory as a Discrete Model for Classical Spacetime by F. Soss Rodriguez of Imperial College, London. This very professional article is available free on the Internet, or was when I downloaded it. It is not, however, for the general reader since it requires extensive knowledge of topology, logical theory and the mathematics of GR. Much more approachable is Introduction to causal sets: an alternative view of spacetime structure by David D. Reid, also available on the Internet.

A Contemporary Theory of Events?
Although Causal Set Theory is committed to discreteness, it is not essentially a theory of events and their interactions. On the other hand, A Formal Ontological Theory Based on Timeless Events by Gustavo E. Romero from the Instituto Argentino de Radioastronomia of Buenos Aires really is a genuine event-based physical theory, the first that I have come across from a contemporary thinker.
Although the author says at the beginning “I assume as background knowledge the predicate calculus, set theory, semantics, and real analysis”, the text is just about approachable by the general reader, at least in parts. The author covers much of the ground that I have laboriously been exploring since I first conceived of Ultimate Event Theory after reading Stcherbatsky’s great book, Buddhist Logic. Romero specifically mentions Buddhist thinkers as the leading promoters of the ‘event-based’ paradigm, admirably summarizing their position as
The whole world [for them] is an inter-dependent storm of events that, here and there, cluster giving the illusion of stability and delivering the illusion of being”.
Although the confident use of symbolic logic gives this paper a style and concision that I can at present only envy, there is a danger that the crucial philosophic issues ─ and by implication, physical issues as well ─ are not sufficiently highlighted. My main disagreement as far as I can see is as follows. The author quite rightly distinguishes between the Universe, U, which is “the composition of all things” and the World, W, which is “the composition of all actual events and processes”. Also, he writes, quite properly, Events do not change, they simply are”.
        However, he goes on to declare, “The totality of events is changeless, otherwise there would be an event not included in the totality, which is absurd”. But this is not in the least absurd! Unless, of course, one believes, as I suspect Romero does, that, as I put it, “Everything that can have occurrence already has occurrence”. This is indeed the view of Barbour, the author of The End of Time, and many others and is implicit in the Block Universe version of General Relativity (which is the current orthodox theory of Space/Time inasmuch as there is one). That Romero adheres to this view is shown by his defining the World as “the composition of all actual events and processes” ─ the weasel word being ‘actual’. Hopefully, not all possible events are also actual; for if they were/are there is “nothing new under the sun” and as far as I am concerned there would be no point in living.

Einstein and Time

Einstein, towards the end of his life, did indeed come to believe that ‘past, present and future’ were “a stubbornly persistent illusion“as he put it and he was serious enough about this to mention it in a latter of soi-disant sympathy to the widow of one of Einstein’s longest friends, Besso, on the event of the latter’s death. Nonetheless, there is evidence that Einstein was much troubled by the implications.
Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something essentially different from the past and future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation” (Note 3)
It is ironic that the Western thinker who first placed events rather than things under the spotlight, namely Einstein, was also the man who dealt a devastating, possibly lethal, body blow to the renascent event-paradigm. For Einstein initiated a re-examination of the concept of simultaneity and his ponderings ended up by establishing that the term has little or no meaning on a universal scale. That there are events that are not unambiguously ‘ordered in time’ ─ the so-called ‘space-like’ events of SR ─ led on eventually (sic) to the idea that “everything is simultaneous”, for that is what the Block Universe theory implies. For there is ‘no before and after’, only a sickly ‘eternal present’. Such a conception is, just possibly, ‘correct’ physically speaking but is utterly unacceptable psychologically: it would make nonsense of all our social institutions (especially laws) and inherited ways of thinking. It is far worse than the ancients’ blind belief in fate, for the latter only implied that certain events were predestined and unalterable, not that all of them were.
S.H.  4/12/19

Note 1. More specifically, Stcherbatsky quotes Bergson (Creative Evolution p. 23-24) as writing, “the world of the mathematician deals with a world that dies and is reborn at every instant, the world which Descartes was thinking of when he spoke of continuous creation”. Stcherbatsky comments, “This idea is quite Buddhistic and…put into Sanscrit… sounds like a quotation from an Indian text” (Buddhist Logic, footnote p. 109).
Quite why Bergson should have thought  that the mathematician’s world was instantaneous is unclear; certainly the world of Euclidian geometry is not in the least ephemeral, on the contrary it views shapes sub specie aeternitatis which is why Plato endorsed it so emphatically. Bergson was perhaps thinking of differential equations which model physical changes over increasingly smaller intervals of time, but, even here, continuity rather than discontinuity is the name of the game.

Note 2. It is traditional, but by no means obligatory, to identify the actual speed of light with this ‘maximum transmission speed‘ for all physical or informational processes. Quite possibly, light, likewise other speedy particles such as neutrinos, approach but do not actually reach this speed, which allows us to attribute to them a small mass. Today, the consensus seems to be that the neutrino does possess a small mass. To my mind, nothing material can have strictly zero mass: this is a contradiction in terms. A strictly massless particle is certainly impossible in Newtonian physics since it would have absolutely no capacity to resist any attempt to change its state of rest or constant rectilinear motion ─ it would be the ultimate puff-ball.

Note 3.  From Carnap, Intellectual Autobiography  (quoted Smolin).  “Moreover,” Smolin adds, “Einstein was not satisfied by Carnap’s reply and repeated that “such scientific descriptions cannot possibly satisfy our human needs; that there is something about the Now which is just outside the realm of science” ”       Smolin, Time Reborn p. 91-2

 

 

 

In the last Post I introduced what I called the ‘Classic Theory of Causality’ which would seem to be based on the four following assumptions :

  • 1.    There exists a necessary connection between certain pairs of events, and by extension, longer sequences;
  • 2.    The status of the two events in a causal pair is not equivalent, one of the two is, as it were, active and the other, as it were, passive or acted upon;
  • 3.    The ‘causal force’ always operates forwards in time, it is transmitted from the earlier event to the later;
  • 4.    All physical occurrences, and perhaps mental occurrences as well, are brought about by the prior occurrence of one or more previous events.

           Actually, the four assumptions listed, necessary though they are, do not suffice to distinguish the post-Renaissance Western theory of causality (CTC)from earlier beliefs and theories. Further restrictions are required to eradicate the remaining vestiges of magical pre-scientific thinking. The most important of these principles seem to be :
1.    The No Miracle Principle
2.    The Principle of Spatio-Temporal Continuity
        3.    The Principle of Energy
4.    The Principle of Localization
5.    The Mind/Body Principle
6.    The Principle of Parsimony

 (1.) No Miracle Principle

By ‘miracle’ I mean an event brought about by a supernatural agency, by someone or something considered to be outside or beyond the physical universe.
Practically all belief systems prior to the seventeenth and eighteenth centuries included some appeal to supernatural beings, although advanced monotheistic systems had reduced these agencies to a single all-powerful one. The ‘new philosophy’ of Descartes and Galileo still required God as a ‘Prime Mover’ and there was some debate as to whether His intervention in the day to day working of the universe was needed. Leibnitz strenuously denied this, arguing that the contrary opinion was ‘blasphemous’ since it implied that God had been unable to make a perfectly functioning universe in the first place. Newton, for his part, found himself obliged to give God a small role in keeping the celestial machinery in working order, for example by stopping stars getting too close together. But by the early nineteenth century, mathematicians had so successfully improved on Newton’s schema that Laplace, when berated by Napoleon for writing a long book on the universe without mentioning its Creator, famously replied, “I had no need of that hypothesis”.
The most important feature of what we know as the ‘Enlightenment’ was the exclusion of the supernatural from the physical world : all physical events were explicable according to mechanical laws (and in principle all mental events as well). This attitude had certain immediate social benefits, leading for example to the prohibition of trials for witchcraft in France and Russia ─ since sorcery was an ‘imaginary crime’ ─ and to a certain degree of religious tolerance. It did, however, imply total determinism : all events were caused by previous events and in ways that could be predicted by way of Newton’s Laws, at least in theory. There was thus no place for free will and  there were no ‘chance events’.

 (2.) The Principle of Spatio-Temporal Continuity.  

This Principle is sometimes called the Law of Transmission by Contact. It is the celebrated prohibition of ‘action-at-a-distance’ that is held to mark the line of demarcation between magic and science. In magical belief systems the possibility of action at a distance is implicitly accepted : I can perform a rite here which will, say, cause the death of an animal or person several miles away. And I can perform a rite now which will cause it to rain tomorrow. According to classical scientific thinking, the only way I can produce an effect some way off is by some sort of chain reaction.
This Principle was assumed by Newton though he was embarrassed by the undoubted fact that his Law of Universal Attraction seemed to violate it, since the gravitational impulse was propagated ‘instantaneously’ throughout the entire universe. This incidentally was the main reason why continental scientists, while accepting Newton’s terrestrial mechanics, rejected his gravitational theory as being much too far-fetched.
Einstein in his Special Theory of Relativity also assumed the Principle and made it rather more precise by stating that no message, or causal impulse, could be transmitted at a speed faster than that of light. Since the speed of light in a vacuum is known, and believed to be fixed for all time, this put a serious restriction on the effects that any action of mine, or anyone else, could have : whole chunks of the universe were condemned to follow quite different destinies with no possibility of interaction between them simply because they were too far away from each other.
Einstein was such a firm believer in the principle that he remained to his dying day deeply unhappy about Quantum Mechanics  because QM seemed to involve a sort of ‘telepathic’ connection between distant particles — the term was used by Einstein himself  (Note 1).
Despite Quantum Mechanics, most of us still assume the complete validity of the principle. If I want to get from A to B, I have to traverse ‘the space’ in between : if it really were possible to ‘leap-frog’ in this way being seen miles away minutes before a crime would not constitute an alibi. Contemporary physics has found it necessary to deduce (or invent) ‘virtual particles’ that carry force between neutrons and to propose that there are ‘gravitons’ that carry gravity : all this essentially because of the Principle of Spatio-Temporal Continuity.

(3.)  The Principle of Energy  

The Principle may be stated thus :

All effective action on or in the world requires an energy source.

           This is a (deliberately) vaguer and more general version of the 1st Law of Thermo-dynamics which states that the total amount of energy within a closed system remains constant.
We are familiar with the feeling of ‘being drained’ when we have concluded an exhausting task : it is as if something has been taken from us. What is this something? Not seemingly anything we can touch or see.
Newton did not deal in ‘energy’ : the term only entered the vocabulary of physics in the nineteenth century and even then with some hesitation (Note 2). Strictly speaking, ‘energy’ is ‘Potential Work’, and Work is ‘the first integral of Force with respect to Distance’. But few people, even professional scientists, envisage energy in this way. The 19th century scientific and technological concept of energy fitted in well with a much more primitive notion, that of an immaterial ‘power’ that  is all around us and can be harnessed by man, what the Polynesians called mana, the North American Indians wakanda and the ancient Chinese ch’i.
Why “can’t you get owt for nowt?” Essentially, because of the Principle of Energy : if you want results, you must expend energy, either yours or someone else’s. Even money only brings about changes in the world  because it enables one to command machines or persons to do your bidding, and both persons and machines wear out.
Why are scientists sceptical about Uri Geller’s alleged ability to bend spoons by touching them? Because of the Principle of Energy. Although the human body does contain electro-magnetic energy, the source is too feeble to bring about such effects directly. Most so-called occult phenomena involve a violation of the Principle of Energy which is why the present society, rightly or wrongly, dismisses them out of hand — a well-known physicist of the time damned Professor Taylor for even investigating Uri Geller.

(4)  The Principle of Localization
 

This Principle does not, as far as I know, appear explicitly in the writings of any thinker, ancient or modern : it is nonetheless extremely important. Put crudely, it is the claim that everything must be somewhere. As such, this is a very restrictive requirement indeed — too restrictive perhaps. Where are all these gods, spirits, demons that obsessed and terrified ancient man?  Where are the “thrones, principalities and powers” of which Saint Paul speaks?  In the past they could be safely relegated to unexplored parts of the Earth, or to the sky. But we, having been to many of these places and taken photographs of them, know that these beings are not to be found there and, if astronomers are to be believed, there is not much place for them on distant galaxies either since the same set of natural laws are applicable everywhere in the universe. So, according to the Third Principle, these alleged beings must either be ‘nowhere’, or ‘in people’s heads’.
The Principle of Localization, or a natural extension of it, also stipulates that an entity cannot be in more than one place at a time, i.e. the possibility of multi-localization is explicitly denied. This makes all the ‘voyages’ of seers, shamans and other visionaries ‘imaginary voyages’, not real ones. It is basically because of the Principle of Localization that scientists and rationalists do not take to the idea of a ‘Group Mind’ or ‘species mind’ — for where exactly are these collective entities?  To be sure, ‘entities’ like ‘the nation’ or ‘the government’ are not precisely localized either, but they are, physically speaking, in the last resort made up of human beings who are localizable.
Quantum Mechanics, of course, does not verify the Third Principle since, prior to an ‘act of measurement’, an elementary particle does not (according to the orthodox interpretation of the theory) have an exact position, it is ‘all over the place’. But this is one of the main reasons why Quantum Mechanics is so worrisome.

(5.) The Mind/Body Principle  

The Fourth Principle may be stated thus : 

          The mind (inasmuch as it exists at all) is confined within the bounds of the body, and can only bring about changes in the world via the body, or an extension of the body.

The Fourth Principle is really nothing but a special case of the First combined with the Third — for the mind, if it exists, must be somewhere.
For many physicists and psychologists mind is just a handy word : only the brain exists. Dr. Susan Blackmore, for example, writes : I want to emphasize that comnsciousness cannot do anything. The subjectivity, the ‘what it’s like to be me now’ is not a force, or a causal agent that can make things happen” (The Meme Machine p. 238).

Dr. Blackmore does not believe in the ‘self’ or a controlling mind but even people who are prepared to accept that there are such things are usually not prepared to accept that the mind can be separated at will from the body, can ‘have a life of its own’, so to speak.  When a burglar ties up a man’s hands and feet, and gags him or her, the burglar feels pretty confident that the victim will be unable to send for help. Why does he believe this? Because of the Fourth Principle.
A certain Zen exercise tells you to “Stop that ship on the distant ocean”. Science considers such a feat to be impossible. Why? Because of the Fifth Principle.
Not all persons and societies subscribe to the Fourth Principle — indeed I am not sure that I subscribe to it myself. The young child imagines that it can affect the world around it simply by an act of will and most early societies were firm believers in the power of Mind over Matter. “Hopi attitudes,” writes Whorf, “stress the power of desire and thought. To the Hopi one’s desires and thoughts influence not only his immediate actions but the whole of nature as well” (Whorf, Language, Thought and Reality).
The radical dualism which we inherit from the Greeks (rather than the Jews) goes right back to shamanism which has been described as mankind’s earliest religion (Note 3). In trance the shaman’s body remains on the floor of the hut in full view, but his ‘spirit’ travels far away. Contemporary people who claim to have had OBEs (Out-of-the-Body-Experiences) — and there are plenty of them — clearly do not accept the Mind/Body Principle. Such people claim, for example, to have seen themselves (or rather their bodies) undergoing surgery, and have described what went on. Official science takes a dim view of such claims — why? Because of the Fifth Principle.

 (6.)  Occam’s Razor or the Principle of Parsimony 

One version of the principle is  Entities are not to be multiplied without necessity though, according to Bertrand Russell, Occam did not say this but did say something rather similar which, translated, goes It is pointless to do with many what can be done with less.  In other words, keep it brief when it comes to assumptions.
This principle is completely different from all the others : not only it can’t be proved or disproved, but we would still use it even if we knew it to be wrong. When Occam was formulating this very important principle, most people in Europe believed in the reality of spirits, angels, succubi and all sorts of non-corporeal entities. The existence of these ‘entities’ could hardly be disproved, and indeed they have crept back again in a disguised form as ‘aliens’ and inhabitants of the unconscious, but enough was enough and there was, understandably, a pressing need to sweep the whole lot of them away and start again. However, the theory that appeals to less entities or assumptions is not necessarily the right one : Quantum Mechanics and Relativity are vastly more complex than Newtonian Mechanics but they are also more accurate.
Suffice it to say that the Principle of Parsimony or Occam’s Razor is something we can’t do without, true or not.

S
ummary

It is remarkable that all these laws are essentially negative in character. They can be summed up as

CTC 1     No Miracles and No Chance Events
CTC 2     No Leapfrogging with Space and Time
CTC 3     No Action without an Energy Source
CTC 4     No Entity without a place
CTC 5     No Physical Change caused by Mind alone
CTC 6     No Unnecessary Entities

 These Six Principles are hardly ‘self-evident’ and, in the last resort, their validity depends on their usefulness. Since they have been  the intellectual background to the greatest technological change in history ─ or, at least since invention of agriculture ─ there must be something in them. But there is no ‘reason’ to believe that they are the be all and end all, and plenty of reasons to believe that they are not.  I am outlining them here as a preamble to my own tentative views within the framework of Ultimate Event Theory and to see how my own theory of causality differs, which it does. The chief difference is that I envisage causality not as a matter of logic but as a force, perhaps the most fundamental force of all since without it physical reality would be entirely chaotic while it manifestly is not.

What about Free Will ?

Our society believes, broadly speaking, that adult, sane human beings are responsible for their actions and, in consequence, can be justifiably applauded and/or rewarded for certain acts, likewise justifiably reproved and punished for certain others.  However, it is becoming increasingly ‘scientifically correct’ to disbelieve in free will completely though, curiously, this seems not to have the slightest effect on scientists’ and rationalists’ actual behaviour which is more or less the same as everyone else’s — sometimes worse. Most scientists keep their scientific and private lives completely separate ─ a very convenient arrangement, also a pusillanimous one.  Dr. Blackmore, however, discussing this very point writes “I cannot divorce my science from the way I live my life.  If my understanding of human nature is that there is no conscious self inside, then I must live this way” (The Meme Machine  p. 242) . The ancient Greek philosophers took their philosophy very seriously indeed. Diogenes believed in the simple life and so slept in a tub (actually a large amphora). It is said that one sceptical Greek philosopher was drowning in a quagmire and appealed to another wandering by to help him, but the latter took no notice. The first philosopher survived and allegedly complimented the other on being consistent in his rational selfishness.              SH  17/10/12

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Note 1  One can escape from the conclusion [that the quantum theory is incomplete] only by assuming thatb either the measurement of S(1) ‘telepathically’ chamges the real situation of S(2) or by denying independently real situations as such to things that  which are spatially separated from each other. Both alternatives appear to me enirtely unacceptable” (Einstein, Autobigraphical Notes

Note 2  See Jennifer Coopersmith’s remarkably interesting and scholarly work, Energy, the Subtle Concept (OUP).

Note 3  See the fifth chapter of E.R. Dodds, The Greeks and the Irrational