The Fabric of Reality David Deutch

part of the fabric of reality. There exist logically necessary truths about these
entities, and these comprise the subject-matter of mathematics. However,
such truths cannot be known with certainty. Proofs do not confer certainty
upon their conclusions. The validity of a particular form of proof depends on
the truth of our theories of the behaviour of the objects with which we
perform the proof. Therefore mathematical knowledge is inherently
derivative, depending entirely on our knowledge of physics. The
comprehensible mathematical truths are precisely the infinitesimal minority
which can be rendered in virtual reality. But the incomprehensible
mathematical entities (e.g. Cantgotu environments) exist too, because they
appear inextricably in our explanations of the comprehensible ones.
I have said that computation always was a quantum concept, because
classical physics was incompatible with the intuitions that formed the basis of
the classical theory of computation. The same thing is true of time. Millennia
before the discovery of quantum theory, time was the first quantum concept.

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11
 
Time: The First Quantum Concept
 
Like as the waves make towards the pebbled shore,
So do our minutes hasten to their end;
Each changing place with that which goes before,
In sequent toil all forwards do contend.
William Shakespeare (Sonnet 60)
Even though it is one of the most familiar attributes of the physical world,
time has a reputation for being deeply mysterious. Mystery is part of the very
concept of time that we grow up with. St Augustine, for example, said:
What then is time? If no one asks me, I know; if I wish to explain it to one
who asks, I know not. 
(Confessions)
Few people think that distance is mysterious, but everyone knows that time
is. And all the mysteries of time stem from its basic, common-sense attribute,
namely that the present moment, which we call ‘now’, is not fixed but moves
continuously in the future direction. This motion is called the 
flow of time.
We shall see that there is no such thing as the flow of time. Yet the idea of it
is pure common sense. We take it so much for granted that it is assumed in
the very structure of our language. In 
A Comprehensive Grammar of the
English Language, Randolph Quirk and his co-authors explain the common-
sense concept of time with the aid of the diagram shown in Figure 11.1.
Each point on the line represents a particular, fixed moment. The triangle ‘ ’
indicates where the ‘continuously moving point, the present moment’, is
located on the line. It is supposed to be moving from left to right. Some
people, like Shakespeare in the sonnet quoted above, think of particular
events as being ‘fixed’, and the line itself as moving past them (from right to
left in Figure 11.1), so that moments from the future sweep past the present
moment to become past moments.
What do we mean by ‘time can be thought of as a line?’ We mean that just
as a line can be thought of as a sequence of points at different positions, so
any moving or changing object can be thought of as a sequence of
motionless ‘snapshot’ versions of itself, one at each moment. To say that
each point on the line represents a particular moment is to say that we can
imagine all the snapshots stacked together along the line, as in Figure 11.2.
Some of them show the rotating arrow as it was in the past, some show it as
it will be in the future, and one of them — the one to which the moving is
currently pointing — shows the arrow as it is now, though a moment later
that particular version of the arrow will be in the past because the will have
moved on. The instantaneous versions of an object collectively 
are the
moving object in much the way that a sequence of still pictures projected
onto a screen collectively 
are a moving picture. None of them, individually,
ever changes. Change consists of their being designated (‘illuminated’) in

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sequence by the moving (the ‘movie projector’) so that, one by one, they
take it in turn to be in the present.
Grammarians nowadays try not to make value-judgements about how
language is used; they try only to record, analyse and understand it.
Therefore Quirk 
et al. are in no way to blame for the quality of the theory of
time that they describe. They do not claim that it is a good theory. They claim
only, and I think quite correctly, that it is 
our theory. Unfortunately it is not a
good theory. To put it bluntly, the reason why the common-sense theory of
time is inherently mysterious is that it is inherently nonsensical. It is not just
that it is factually inaccurate. We shall see that, even in its own terms, it does
not make sense.
…‘time can be thought of as a line (theoretically, of infinite length) on which
is located, as a continuously moving point, the present moment. Anything
ahead of the present moment is in the future, and anything behind it is in the
past.’
FIGURE 11.1 
The common-sense concept of time that is assumed in the
English language (based on Quirk et al., A Comprehensive Grammar of the
English Language, 
p. 175).
This is perhaps surprising. We have become used to modifying our common
sense to conform to scientific discoveries. Common sense frequently turns
out to be false, even badly false. But it is unusual for common sense to be
nonsense in a matter of everyday experience. Yet that is what has happened
here.
Consider Figure 11.2 again. It illustrates the motion of two entities. One of
them is a rotating arrow, shown as a sequence of snapshots. The other is
the moving ‘present moment’, sweeping through the picture from left to right.
But the motion of the present moment is not shown in the picture as a
sequence of snapshots. Instead, one particular moment is singled out by the
, highlighted in darker lines and uniquely labelled ‘(now)’. Thus, even though
‘now’ is said by the caption to be moving across the picture, only one
snapshot of it, at one particular moment, is shown.

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FIGURE 11.2 
A moving object as a sequence of ‘snapshots’, which become
the present moment one by one.
Why? After all, the whole point of this picture is to show what happens over
an extended period, not just at one moment. If we had wanted the picture to
show only one moment, we need not have bothered to show more than one
snapshot of the rotating arrow either. The picture is supposed to illustrate the
common-sense theory that any moving or changing object is a sequence of
snapshots, one for each moment. So if the is moving, why do we not show
a sequence of snapshots of it too? The single snapshot shown must be only
one of many that would exist if this were a true description of how time
works. In fact, the picture is positively misleading as it stands: it shows the
not moving, but rather coming into existence at a particular moment and
then immediately ceasing to exist. If that were so, it would make ‘now’ a 
fixed
moment. It makes no difference that I have added a label ‘Motion of the
present moment’, and a dashed arrow to indicate that the is moving to the
right. What the picture itself shows, and what Quirk 
et al.’s diagram (Figure
11.1) also shows, is the never reaching any moment other than the
highlighted one.
At best, one could say that Figure 11.2 is a hybrid picture which perversely
illustrates motion in two different ways. In regard to the moving arrow it
illustrates the common-sense theory of time. But it merely 
states that the
present moment is moving, while illustrating it as 
not moving. How should
we alter the picture so that it will illustrate the common-sense theory of time
in regard to the motion of the present moment as well as the motion of the
arrow? By including more snapshots of the ‘ ’, one for each moment, each
indicating where ‘now’ is at that moment. And where is that? Obviously, at

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each moment, ‘now’ is that moment. For example, at midnight the ‘ ’ must
point to the snapshot of the arrow taken at midnight; at 1.00 a.m. it must
point to the 1.00 a.m. snapshot, and so on. Therefore the picture should look
like Figure 11.3.
This amended picture illustrates 
motion satisfactorily, but we are now left
with a severely pared-down concept of time. The common-sense idea that a
moving object is a sequence of instantaneous versions of itself remains, but
the other common-sense idea — of the flow of time — has gone. In this
picture there is no ‘continuously moving point, the present moment’,
sweeping through the fixed moments one by one. There is no process by
which any fixed moment starts out in the future, becomes the present and is
then relegated to the past. The multiple instances of the symbols and
‘(now)’ no longer distinguish one moment from others, and are therefore
superfluous. The picture would illustrate the motion of the rotating arrow just
as well if they were removed. So there is no single ‘present moment’, except
subjectively. From the point of view of an observer at a particular moment,
that moment is indeed singled out, and may uniquely be called ‘now’ by that
observer, just as any position in space is singled out as ‘here’ from the point
of view of an observer at that position. But objectively, no moment is
privileged as being more ‘now’ than the others, just as no position is
privileged as being more ‘here’ than other positions. The subjective ‘here’
may move through space, as the observer moves. Does the subjective ‘now’
likewise move through time? Are Figures 11.1 and 11.2 correct after all, in
that they illustrate time from the point of view of an observer at a particular
moment? Certainly not. Even subjectively, ‘now’ 
does not move through
time. It is often said that the present seems to be moving forwards in time
because the present is defined only relative to our consciousness, and our
consciousness is sweeping forwards through the moments. But our
consciousness does not, and could not, do that. When we say that our
consciousness ‘seems’ to pass from one moment to the next we are merely
paraphrasing the common-sense theory of the flow of time. But it makes no
more sense to think of a single ‘moment of which we are conscious’ moving
from one moment to another than it does to think of a single present
moment, or anything else, doing so. 
Nothing can move from one moment to
another. To exist at all at a particular moment means to exist there for ever.
Our consciousness exists at 
all our (waking) moments.

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FIGURE 11.3 
At each moment, ‘now’ is that moment.
Admittedly, different snapshots of the observer perceive different moments
as ‘now’. But that does not mean that the observer’s consciousness — or
any other moving or changing entity — moves through time as the present
moment is supposed to. The various snapshots of the observer do not take it
in turns to be in the present. They do not take it in turns to be conscious of
their present. They are all conscious, and subjectively they are all in the
present. Objectively, there is no present.
We do not experience time flowing, or passing. What we experience are
differences between our present perceptions and our present memories of
past perceptions. We interpret those differences, correctly, as evidence that
the universe changes with time. We also interpret them, incorrectly, as
evidence that our consciousness, or the present, or something, moves
through time.
If the moving present capriciously stopped moving for a day or two, and then
started to move again at ten times its previous speed, what would we be
conscious of? Nothing special — or rather, that question makes no sense.
There is nothing there that could move, stop or flow, nor could anything be
meaningfully called the ‘speed’ of time. Everything that exists in time is
supposed to take the form of unchanging snapshots arrayed along the time-
line. That includes the conscious experiences of all observers, including their
mistaken intuition that time is ‘flowing’. They may imagine a ‘moving present’
travelling along the line, stopping and starting, or even going backwards or
ceasing to exist altogether. But imagining it does not make it happen.
Nothing can move along the line. Time cannot flow.
The idea of the flow of time really presupposes the existence of a second
sort of time, outside the common-sense sequence-of-moments time. If ‘now’
really moved from one of the moments to another, it would have to be with
respect to this 
exterior time. But taking that seriously leads to an infinite
regress, for we should then have to imagine the exterior time itself as a
succession of moments, with its own ‘present moment’ that was moving with
respect to a still more exterior time — and so on. At each stage, the flow of
time would not make sense unless we attributed it to the flow of an exterior
time, 
ad infinitum. At each stage, we would have a concept that made no
sense; and the whole infinite hierarchy would make no sense either.

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The origin of this sort of mistake is that we are accustomed to time being a
framework exterior to any physical entity we may be considering. We are
used to imagining any physical object as potentially changing, and so
existing as a sequence of versions of itself at different moments. But the
sequence of moments itself, in pictures like Figures 11.1—11.3, is an
exceptional entity. It does not exist within the framework of time — it is the
framework of time. Since there is no time outside it, it is incoherent to
imagine it changing or existing in more than one consecutive version. This
makes such pictures hard to grasp. The picture itself, like any other physical
object, does exist over a period of time and does consist of multiple versions
of itself. But what the picture 
depicts — namely, the sequence of versions of
something — exists in only one version. No accurate picture of the
framework of time can be a moving or changing picture. It must be static. But
there is an inherent psychological difficulty in taking this on board. Although
the picture is static, we cannot understand it statically. It shows a sequence
of moments simultaneously on the page, and in order to relate that to our
experience the focus of our attention must move along the sequence. For
example, we might look at one snapshot, and take it to represent ‘now’, and
a moment later look at a snapshot to the right of it and think of that as
representing the new ‘now’. Then we tend to confuse the genuine motion of
our focus of attention across the mere 
picture, with the impossible motion of
something through real moments. It is easily done.
But there is more to this problem than the difficulty of 
illustrating the
common-sense theory of time. The theory itself contains a substantive and
deep equivocation: it cannot make up its mind whether the present is,
objectively, a single moment or many — and hence, for example, whether
Figure 11.1 depicts one moment or many. Common sense wants the present
to be a single moment so as to allow the flow of time — to allow the present
to sweep through the moments from past to future. But common sense also
wants time to be a sequence of moments, with all motion and change
consisting of differences between versions of an entity at different moments.
And that means that the moments are themselves unchanging. So a