Calculus and the Infinitesimals: 'The Ghosts of Departed Quantities'

 

In this  episode of Adrian Moore's 'A History of Infinity' (BBC R4, 2016), the subject is the nature and development of the calculus. It begins with the observation that to divide zero by zero, or zero into anything at all, makes no sense. If you know anything about the calculus, it is clear what is being talked about in this episode, but the way it is discussed is lacking in the kind of precise description you might expect. 

A train is used as an illustration. Travelling a distance of sixty miles over an hour means that the train had an average speed of sixty miles an hour. However, the train might have been travelling at a much higher speed for half of the journey, and have been delayed by signal failure during the second half of the journey. So if you measure the distance travelled and the speed at a particular point in the journey, the result may be misleading. If the time period measured is very short, say close to zero, and the distance travelled is close to zero, then you will know nothing useful about how fast the train is going, and how long it will take to complete its journey.  

Calculus enables the accurate measure of quantities which are subject to change (which is why the inventor of the calculus as we know it today, Isaac Newton, referred to it as ‘Fluxions’). The episode makes clear how important the development of the mathematics of change has been ever since, and that much of the modern world depends on the use of calculus. The term ‘integration’ makes no appearance in this episode. 

Much of the rest of the programme discusses the invention of calculus, and the bitter dispute which arose between Isaac Newton and the philosopher Leibniz, who developed a similar approach to the mathematics of change quite independently. Newton appears to have begun to develop the mathematics for ‘fluxions’ early on – perhaps as early as the 1660s. The chronology is not clearly established, but Leibniz may have developed his version some ten years later. 

Newton did not publish any information about the mathematics involved in the calculus until many years later, preferring to share a few details with his friends and colleagues. Newton was aware of Leibniz and his work, not least because he too was a member of the Royal Society. Eventually he wrote to Leibniz with some limited details of the calculus (Moore suggests that Leibniz could not have understood these details since they were in code). Newton became aware that Leibniz had developed similar mathematics to deal with change, and a long dispute ensued, mostly conducted via intermediaries. Leibniz was often travelling, and so correspondence sometimes took months to reach him. Newton launched attacks on the integrity of Leibniz, accusing him of plagiarizing his ideas. Leibniz was bemused by his attacks and the force with which they were made. But Newton had decided that Leibniz was his enemy, and that was that.

Eventually it was proposed that a report be prepared by the Royal Society to establish who had the prior claim to the invention of calculus. This sounds fair, except that the President of the Royal Society wrote the report, and the President was Isaac Newton. As Moore says, ‘not Newton’s finest hour’.

The philosopher George Berkeley makes another more substantial appearance in this episode, since he wrote a criticism of what he called ‘the analysts’ (The Analyst: a Discourse addressed to an Infidel Mathematician (1734)). His criticism was based on the general lack of rigour with which calculus was often used at the time, and argued that scholars who attacked religious and theological arguments for lack of rigour were being similarly careless. The criticism revolves around the limitations of the technique already  mentioned, when the quantities and measures chosen are too small to produce intelligible results.

The most famous quotation from this book describes infinitesimals as ‘the ghosts of departed quantities’. The book seems to have been aimed particularly at the mathematician Edmund Halley, who is reported to have described the doctrines of Christianity as ‘incomprehensible’, and the religion itself as an ‘imposture’. Moore references the fact that the technique of the calculus lacked technical rigour until the early nineteenth century, until the idea of the limit was introduced (in fact Cauchy, and later Riemann and Weierstrass redefined both the derivative and the integral using a rigorous definition of the concept of limit. But that is another story). 

Moore concludes the episode by saying that:

precisely what such precision and rigour show, is that the calculus can be framed without any reference to infinitely small quantities. There is certainly no need to divide zero by zero. What then remains is a branch of mathematics, which is regarded by many, in its beauty, depth and power, as one of the greatest ever monuments to mathematical excellence.

'Shar Kishati' and The Cult of Eternity

This is part of a chapter from the draft of The Sacred History of Being which was under way in 2004. The chapter did not make it through to the final version which was published in November 2015, though I did write about the same things in the published version, in slightly different terms. I had moved on considerably in those eleven years.

Trying to separate out key aspects of Greek and Mesopotamian models of Reality, as I did here,  was something of a methodological conceit, and the discussion of the hypothetical core of the ancient understanding of Reality as something which might be separated from everything else,  doesn't mean that such a hypothetical core existed apart from the rest of the religious and theological implex of ideas which constituted Greek and Mesopotamian religion. The point of the exercise was to explore what was actually essential to that implex of ideas, and to get a better understanding of why it was important to the functioning of the ritual universe in both Greece and Mesopotamia.

So this text should be understood as a snapshot of how I was approaching the ancient data, and the different points of view I was exploring, as part of the study in 2004.

Essentially what I called in this text the 'Cult of Eternity' revolves around the 'Doctrine of Totalities', which is mentioned in connection with Pythagoras, is described by Plato, mentioned by the Neoplatonists, and is also referenced in a Nag Hammadi text. We know the doctrine was known in Babylon, and it is possible that Pythagoras learned of it while he was there. It is in fact a logical modality, though currently it is not recognised as such. It can be argued that this logical modality underpins the entire intellectual edifice of Mesopotamian thought, and much of the philosophical thought in ancient Greece, from Pythagoras onwards.

I have taken the liberty of re-Englishing some of the text, but the argument is as it was.

Thomas Yaeger, October 17, 2016

Defining the Cult

Why characterise the beliefs of some elite groups in Greece and
Mesopotamia as cultic, rather than considering them simply as elite groups
functioning within the social and institutional structures of these cultures?

The reason for this is quite simple: the belief system of these elite groups is at variance
with aspects of the more broadly based belief system of the culture in which the cult is
embedded. The cult in question enshrines a pattern of belief which is shared by a small
and influential group; it has great meaning for that group, and it informs
almost every aspect of their lives. It has all the characteristics of
individuated cults – liturgy, ritual, festival, sacred objects and images, etc. It
also has a secret at its core, which is often a feature of individuated cult*1.

It is not strictly a secret society however – or at least we have no reason to
believe that it functioned entirely in secret. This does not mean that it functioned in
public – rather that it functioned as an elite club, occasionally admitting new members,
according to merit. Thus, it would be possible for individuals outside the group to
know something of its existence, and perhaps to know individuals who belonged to the
group, as well as perhaps knowing the time and place of ritual, etc. But these individuals
would not know any significant detail of the cult, either in terms of practice or belief.*2
 It is a secret society however in terms of it having secret aims and beliefs, and a
restricted membership.

Its function was religious. The detail of what was involved and the belief
system which underpinned this activity is the focus of this study.
In essence what we have uncovered is a way of thinking of some
importance in history. It underpins the historical development of many
ancient religions, even if it is not itself older than these religions, or is not
native to the region in which the religions grew up.

It needs a name, if we are not always to be returning to the details of its nature
and influence in order to indicate its involvement. I have decided to call this
phenomenon the ‘Cult of Eternity’, since it is clear that emulation of the nature
of eternity is the principal goal of this school of thought: the source of the cult is
the understanding of the importance of invariance above all else, and the members
of the cult are focussed on eternity. Eternity is a concept which all important
religions - of which we have knowledge - have.

We are not talking here about an organisation with physical and intellectual
continuity across both time and the geography of the ancient world when
we talk about the ‘Cult of Eternity’: what we are talking about is a way of
thinking which might have been transmitted by contact between elite groups
over large geographical distances, but which, alternatively, might as easily
come to exist at a certain place and time whether or not such actual contact
has occurred. If it can arise as a notion spontaneously in the mind of one
man, then it has arrived within the culture in question.*3

If it subsequently informs the theological and religious structures of that culture,
then that form of cultic belief is of importance to the understanding of that culture,
and its dynamics.

It must be understood as a cult in the sense that it involves a shared set of beliefs,
understandings, and practices belonging to a small group within ancient cultures.*4
The true nature of these cultic beliefs were not understood – and perhaps not even
 suspected outside of members of the royal court, and some parts of the priesthood.

Notwithstanding the fact that we can often trace the ideas of the cult in the
art and literature and language of a culture, where elements associated with
the cult have shaped the outward form of the institutional religion, the
nature of the core ideas of the cult, then as now, make it very unlikely that
any but a small group of people with control of the political and religious
hegemony could hold these beliefs.

The Pattern of Belief

What is the essential nature of this cultic belief? It can be stated quite
simply, though its difficult passage through history has been as a
consequence of the fact that its essential nature it is so easy to miss, and to
lose, without any sense that something important has been lost.

It is lost when the understanding that the doctrine enshrines images which
are understood as recollections of the ur reality, turns into the notion that the
images themselves, whether in ritual or narrative or poetic form, represent
the matter of the cult, rather than pointers and paths to the real goal of the
cult.

In essence the central belief of the cult is that reality itself is utterly
transcendent of all the characteristics and properties of earthly existence.
The divine, as a consequence of this understanding, is understood as
entirely beyond our human ability to grasp, except in terms of a crude
inversion of the categories normally employed in our understanding. This
idea of reality is conveyed and referred to by means of a number of images
– these may be actual images, through descriptions of images, through
ritual, through narrative, and through mythic and poetic constructs.

One of the key concepts of this cult is the distinction between the secular
and the eternal. Most of the desirable (and as Robert Graves might say,
‘nostalgic’) characteristics of reality are imaged in the idea of the eternal. It
does not move, does not participate, but simply is itself. The moving image
of eternity, which we have seen is of central importance in the Greek
version of the doctrine of the cult, is the one which does participate in
generation, which does move. Significantly, it is itself described as an
image, since it, along with all the elements of secularity within the moving
image, is an approximation, a metaphor to the all but indescribable and
unreachable.

The second aspect of this pattern of belief in a completely transcendent ur
reality, is that there are certain areas of earthly reality which are closely
connected with the ur reality. These areas are the limits or boundaries of
things. A characteristic of a limit or a boundary is that it is the place where
something passes into something else. In this place, the utter limit of
something is no longer what it is, but is the place between what that thing
was (whatever it was) and the thing which is beyond. In other words, the
boundary or limit is a no-man’s-land in terms of categorical understanding.
In consequence, it resembles very strongly the nature of the divine.

Why this Pattern?

Why do these properties of both the ur reality and of boundaries and limits
have such importance for those involved in the cult? Because the ur reality
is the place of generation, the place of the ur decisions – the principal
separations and divisions of eternity, the place of ultimate completion – the
ur of all and everything. Like the soil of the original home of a tribe, packed
into its ritual altar, its ‘first earth’, eternity is the place and condition of
resort when change, joining, sundering, enhancement, and judgement are
required. The devotee of the cult can, by means of its rituals and discipline,
both travel there, and bring eternity to the here and now.

The tribe need not have a theory of being to know the importance of ‘first earth’,
and it is not necessary for there to be a theory of being behind the existence and
importance of the practice. However it is clear that the concept of an ur
reality has abstracted to the nth degree many of the simpler notions which
occur to man, and brought them together, as Solon suggested to Croesus, ‘to
arrive at the proper time and agree’.*5 Where we find many clues to the
existence of this abstracted and rarified vision of the other in one or several
cultures, we cannot ignore these clues without damaging our capacity to
understand the cultural processes at work.

One of the problems which historians face in studying the ancient world is
the problem of studying patterns of belief which, are full of the practice of things
which have become reprehensible or meaningless - magic, witchcraft, divination
and sacrifice. To the modern scholar, these are credulous beliefs, without
foundation in anything which makes sense to the rational mind, and so the
historian is expected to have no sympathy wth the patterns of thought involved -
beyond that necessary to explore the social and cultural dynamics of these beliefs
in the material under examination. It is of course perfectly possible to write an excellent
study of a belief system without the writer sharing that belief system, but, for the
sake of professional credibility, it is important that objectivity – the ‘not sharing’ in
the belief system under study – is visible and public. Hence there is a tendency for
historians to avoid as far as possible discussion of beliefs and the intellectual undertow
of ancient practice, and where they find it necessary to engage with it, they usually
describe rather than analyse.

The difficulty of a historian is therefore very great, if we attempt to bring in
from the cold the common practice of the ancient world, and its intellectual
origins within a pattern of cultic belief and ritual. If it is more like what we understand
 than we (formerly) understood, and belongs to the known tradition of understanding
the world in terms of the relationship between being and the world of becoming,
then a danger emerges that the work involved might seem like a rehabilitation rather
than an objective study.*6

Who would be safe? The objectivity of a discipline can mean that the object of
study is preferred lying dead on the dissecting table, rather than as something whose
whole nature requires study as a living thing: the object is studied as an ‘it’ rather than as
 a ‘thou’. Where its dynamics are explored, these are often framed within modern
models of the forces at work in social structures, since these are the product of rational
discussion over many decades, and give us the tools and approaches to understand social
dynamics.

But is this really adequate as an approach? The cultures of the ancient world once lived,
and it is important to look at them as living things, driven by by their own will and
concerns. Looking at these cultures as supported and vivified by the powerhouse of a
theory of Being allows us to understand what it is that shapes them, and to understand
the connections between that powerhouse and more distributed and diffuse practices and
phenomena.*7

The cult itself is sustained by the inner logic of its belief system. Based on the
understanding of the importance of the concept of the eternal, it shares
serveral features with the religion in which it functions as the intellectual
core, supplying access to the functional aspects of the ur reality. Serving in
this way, it has a technical language, and technical logic. Much of this, particularly in
the fine detail, is lost to us within Mesopotamian culture, and we must also use non-textual
evidence as part of the recovery technique. But sometimes it peeps out at us, utterly
 inexplicable within the now traditional modes of interpretation which are applied to
near eastern  civilisations.

One example of this is the Akkadian phrase ‘Shar Kishati’, which was applied to Assyrian
Kings in the 1st Millennium B.C.E. The phrase literally means: ‘King of
Totality’. This makes very poor sense outside of the context of a cultic model
for the importance of the king – the phrase does not specify the nature or context of
the totality – whether it is to be understood as a totality of nations, of peoples, or even of
the world.

Within the context of a cult which has the pursuit of eternity at its core, the epithet
makes perfect sense: totality is one of the ways in which eternity may be
spoken of, since the eternal is the undivided and undifferentiated ur reality,
before the creation, the moving image of the same. The phrase ‘King of the
Four Quarters’ similarly does not refer (except where made explicit) to
earthly power and hegemony. The ‘four quarters’ refer to a division of the
ur reality or totality made by the cult, in which the properties of kingship
are defined in terms of different images of his transcendence over the
world.

These images are connected with the bull, the ram, the eagle, and
man. Other combinations of images are possible, and  found, but these
four are the principle ones. Very often aspects of these animals are brought
together in images of the King and of the sages, so that the leg of the king is
overmuscled to invoke the strength of the bull; his cloak is feathered in
order to invoke the power and clarity of vision of the eagle*8, and he wears
a torque around his arm whose ends are marked with ram’s heads, a
favoured animal for the purposes of enquiry by divination. The human part
of the quartet represents intelligence and the rational part of the soul.

That this totality of the four quarters is something to which limits and
borders are closely associated is clear from the fact that the quartet of
images is often combined in the sacred winged bulls, found situated within
the limits of palaces and temples, marking the gateway between the
precincts of the palace or temple, and the outside secular world of movement
 and change.

Notes -

1 We are familiar with the existence and importance of the indivuated Greek cults,
which eventually assumed an enormous importance in the later Roman Empire.
Herodotus sometimes mentions these cults, but makes offhand references to the
nature of the rites performed in thse ceromonies, saying ‘those who have experienced
 them will know what I mean’. The details were secret from the uninitiated. We do not know
about the details of the cult of the Great Gods, the Kabiroi at Samothrace, on account of
this reticence on the part of Herodotus. As for Mesopotamian cults, we know that the whole
religious edifice functioned more or less as an assemblage of individuated cults. Those in
the lower levels ofsociety were simply not admitted to cult buildings at all, far less being
admitted to worship or to participate in ritual. So far however, it has not been considered as a possibility that the whole thing was held together by a cult which might be restricted to an
even smaller group, initiated into a cult whose ideas reflect a different kind of
intellectual picture of the world

2 Of course there are exceptions to this rule. The journalist Richard Carlile gained access to
Masonic ceremonies and documents in the early years of the 19th century, and wrote
extensively about this cult. Though he was pilloried for his efforts at the time, it was not
long before his ‘Manual of Masonry’ was being used in preference to official texts by the
members of the craft – indeed, one of the two copies I own has clearly been marked by
someone learning the rites of the craft.

3 The question of the routes by which the ideas of the cult have moved around is
nevertheless interesting, and in some instances it is possible to point at likely nodes
of contact and exchange. However this question is beyond the scope of this book.

4 I have defined the belief in the importance and efficacy of eternity as a cult for two
principal reasons. The first is that this belief is clearly necessarily confined to a small
group or network of individuals, for the simple reason that the nature of some of the
beliefs belonging to the cult would be anathema to the wider population. Talking of a
divine nature which has none of the properties of earthly existence could easily be
misunderstood as atheism. The second reason for defining this pattern of belief as cultic is
that, during the first millennium B.C. E., the belief system was more often than not
accompanied by cult ritual.

5 Those who invite for example the pre-eminent anthropologist of the ancient
world, Walter Burkhert, as keynote speaker to a conference on the subject, are perhaps
 unconsciously exhibiting similar behaviour to tribal elders who place ‘first earth’ at the
core of their cultic life.

6 We are familiar with the Platonic tradition, which, through a number of twists and
turns, is more or less continuous as a body of ideas in the west during the past two
and a quarter millennia. It isn’t a tradition which is continuously active, in that it is not always worked within, and sometimes it has lain fallow. However we can trace a continuous tradition
based on the original Platonic corpus all the way from classical Greece to modern times.
And sometimes this tradition has actively shaped institutions and patterns of belief.

Examples of the powerful influence of this tradition include the neo-Platonist writings, the
take-up of Platonic ideas within the court and intellectual life of the Italian Renaissance,
and its particularly fertile influence in the English Renaissance of the late sixteenth
century. What is being suggested here is that a similar pattern of tradition existed in the
ancient world before Plato, and that the Platonic writings, rather than instituting something
entirely new, refashion an existing tradition of arcane cultic ideas, passed on largely
through oral means, within small and select groups within institutions which offer a
conducive and receptive environment for these ideas. Plato therefore is one highly important
node in the tradition, particularly because he is deliberately trying to pass on a body of ideas being threatened by a wholly secular view of the world.

7 If it is faulty to approach ancient societies which are replete with magical practice as
supported by a theory of being which informs much of the detail of its belief and practice,
then we will find out our error soon enough: we will find no evidence to support the claim
which is not inexplicable by other means. Some of the key pieces of evidence in this book
have no explanation in terms of existing interpretative schema: they are not treated as
evidentially significant, even when they clearly absorbed much of the ancient economy, as
well as the time and intellectual focus of the elite of the society in question.

8 Most probably the feathered cloak also is intended to conjure the idea of the king
functioning in another world, as the eagle can exist on land, but has its true existence
 in the air

The Irrationality of Atheism

[This is one of twenty-one essays in the book Man and the Divine, published in August 2018. The book is available in ePub format from leading retailers of eBooks, such as Barnes & Noble, Blio, Kobo, Itunes, Inktera, Smashwords, etc. Information about Man and the Divine can be found here]

The word atheism is constructed from the Greek word for God, ‘theos.’ God was spoken of by Plato as ‘ho theos,’ meaning ‘the god’. With the addition of the Greek privative particle, we have ‘atheos’, meaning ‘no god,’ or ‘godless.’

So, one might imagine that the derived term ‘atheism’ is a legitimate pair with ‘theism,’ the one indicated the idea of no god, and the other the idea of God. You can be inclined to one or the other according to your disposition, your culture, or your education. Both are apparently rational concepts, and both can be used in rational argument.

It is peculiar that Plato spoke of the creator of the world (though the actual work of the creation was done by the demiourgos, in order that there should not be too much of the divine about the world) as ‘the God’, which seems to imply a single divinity. The Greeks were polytheists, with a large pantheon of gods, and many stories about the gods’ lives and relationships. They paid divine honours to them at their birthplaces and their shrines, and sacrificed to them. So the idea of ’ho theos’ needs to be explained. I will return to this interesting question later in this post.

Atheism, in the sense of not believing in god or the gods, or giving the idea of them any credence, is an idea which is very old. The people who ransacked ancient tombs and holy places in antiquity, did not show reverence to those places, their contents, or the gods who were honoured by them.

It is easy to understand how the idea that the gods or divinity were not in any sense real might have come about. We do not see them, and we do not see them act. We do not hear them talk, or give advice. They are altogether invisible to mortal man. What we have are stories about them, places venerated as the place of their birth, and their holy sites. All of which could have been made up by the priests who honour them, and maintained the divine cults. Their images in wood, metal and stone were made by mortal craftsmen, after the pattern of the descriptions of the divine in poetry and myth. Many of these divine cults had become extremely rich over centuries of patronage by rich benefactors and many pious pilgrimages to their shrines. The show spoke of unimaginable wealth. But the gods themselves were nowhere to be seen.

So an intelligent individual might come to the conclusion that the pomp and circumstance of holy ritual and temple life, most of which took place behind closed doors, was a fiction devised by the priestly cults, in order to maintain their own wealth and power.

This is one side of the story – the part which it is easy for us to understand. The cults create stories and images around the idea of the gods, and gain power and prestige for themselves and their gods. The intelligent individual does not know anything of the mechanics or the purpose of the fiction. He simply has no reason to treat the divine as something real.

Some other intelligent individual, having been at one time a neophyte in one of the divine cults in the ancient world, will have known something of the details of the fiction. But as a disbeliever in the reality of the gods, it does not matter to him what there might be to understand. His mind is made up. The complexity of the myths and rituals mean nothing, and suggest nothing to him which he would benefit from knowing.

Of course, it is possible to object to the reality of the gods, while holding to the idea that a single god is real. This view might be arrived at by a form of logical argument, along the lines of: only God is real, everything else is illusory. This is the view that the author of the Book of Enoch took. In which case the apparent and iconoclastic atheism of the individual is actually the extreme expression of the idea that there can be only one God.

In this case, everything apart from the idea of a single god, apparently divorced from the whole of the physical creation, and the representation of other aspects of the divine through sculpture, ritual and cult, is illusory and false. The representations might be ascribed to the work of demons, who strive to distract us from our proper purpose, which is to pay due honour to the one god.

The point I’m making here is that we have to be clear about what is in the mind of those who appear to be atheists. There are those who think that there is no such thing as the divine, and that the very idea of the divine is a fictional presence in the world, created by those who are credulous, or who are cynically exploiting the credulity of the majority of mankind (or both). Most modern atheists are of this kind.

Those who did not understand the origin and function of the various divine cults in the ancient world, and rejected them, but who embraced the idea of a single god, were not atheists. They were simply against the plurality of the gods. They too could destroy temples, shrines and statues of the gods, but had the notion of a purer ‘cultus deorum’ in their heads.

We can describe these individuals as monolaters or monotheists, though they are not the same. The monolaters follow one god, however they arrived at the notion. Their single god does not need to have a philosophical aspect, by which its singleness is put beyond question. Monotheism however does imply the presence of a degree of philosophical debate around the uniqueness of god. In the Book of Malachi for example, Jehovah is presented as saying ‘I do not change’. So the Hebrew god is beyond a political and tribal conception.

Returning as I said, to the question of Plato’s term for God, ‘ho theos’, it is clear that his conception of God is purely philosophical, as we might expect. He is described by his master Socrates (himself accused of impiety towards the Gods) as having ‘no form, shape or colour’, and we know from other parts of Plato’s work that ‘ho theos’ has a nature which is beyond change. His nature is transcendent of all the categories of experience and understanding.

Plato is writing about a God who is in fact Reality itself, in that the properties and attributes of his god are identical with the properties and attributes of his understanding of transcendent reality. We cannot see it, measure it, and it has no presence in the secular world as itself. It would be easy to jump to the conclusion that this conception of Reality is equivalent to the conception of a nothingness, a void, and an absence. This conclusion would be foolish: I’ve written elsewhere of the notion of Reality as a plenum, as something which is undefined and unlimited, and which is beyond the conception of something which is absent. Absence implies presence, and transcendent Reality is beyond both absence and presence.

Atheism can mean many things, but ordinarily it means the lack of a belief in God. Or rather the lack of a belief that God has some form of existence, or the property of being something which is real, as opposed to a figment of the human imagination. But consider, if the definition of God is Reality itself, and not an entity which just occupies some part of the universe and has powers and properties attributed to it, then the atheist is in effect denying the reality of a transcendent reality, which lies behind all the phenomena of the universe, its laws, its properties, and its very existence.

Atheists do not deny the existence of the world, its laws and properties: they just argue that the concept of God is not required to accept the world, and to have an understanding of it. They are of course at a loss to explain how the world came to be, and why it should have come into existence. They have no explanation for physical existence of anything, and no explanation for the existence of spatial dimensions and the phenomenon of time. These are not important questions for atheists in general, since the important point for them is that they are not credulous people, and not people who put their faith in the fictions which are promoted by most formal and informal religions, particularly in the modern west.

But if God is Reality itself, then to deny the reality of God is effectively to deny the reality of the world and everything in it. In which case even the illusion of the physical world can never be properly accepted or explained. Atheism itself is therefore a form of privation, in which nothing can make sense beyond the casual acceptance of physical reality, and about which no great questions can or should be asked, and where even the laws of the universe are the way they are for no reason that might be understood.