Tom Bombadil is one of my favourite characters
in the Tolkien mythology. He is a powerful being who mainly is concerned with
the Nature around him: he can command trees and other things with his voice, he
is married to Goldberry, the Daughter of the River – and not even Sauron’s ring
seemed to have any effect on him. However, at the point of the events in the
Fellowship of the ring, he had restricted his kingdom to lie within certain
boundaries. These are boundaries which he himself has specified, and even
though he seems almost infinitely powerful within these boundaries, he doesn’t
really concern himself with what goes on outside of these boundaries. As we
will see in this blog post, this is very analogous to the discipline of
physics, which also is extremely powerful within its own domain, but which does
not really concern itself with the ongoings outside of these domains.

Tom
Bombadil was unfortunately left out of the movie series by Peter Jackman, so
here is instead an image from the Lord of the rings wiki: a screen shot from lord of the rings online;
added by user Gradivus.

Doesn’t the existence of physical laws lead to
deterministic materialism?

This blog
post is the second in a series of three that is here to lay a first version of
a foundation from which all the other constructions will take off. In the
previous blog post, we made a historical view of how the current situation
appeared, and concluded that the first climax, around 1750-1800, led to the
logical question: “Given the physical laws, and God of the Gaps as an
unnecessary hypothesis – are we not obliged to construct a materialistic and
deterministic worldview?” This question is certainly a valid one, and it needs
to be dealt with properly. There are several reasons why the answer to the
question is no – the physical laws discovered by physics does not necessitate a
materialistic and deterministic worldview – and we will here have a look at two
of these reasons: i) that the current understanding of these laws does not
imply determinism, neither in principle nor in practice, and ii) that physics
operates within certain boundaries that restricts its study object, but that a
worldview should study reality in its entirety.

There is a limit to the predictability: both in
principle and in practice

Let us first take the in principle aspect. This aspect has to do with quantum mechanics,
and means that there is a fundamental limit to how well-determined a prediction
can be, which does not have to do with our computational or measurement
abilities, but with the way the physical universe is structured, according to
our current understanding. As you may be aware of, there are several
interpretations of the equations underlying quantum mechanics, and we will need
to go in to those in more detail in later posts. For now, however, it is enough
to just get a flair of the basic properties of the most well-known
interpretation, which is known as the Copenhagen interpretation. According to
this interpretation, an object – e.g. an electron – is actually not a small
piece of material as we normally think of physical objects (e.g. like a small
little football) but a probability wave. Such a probability wave describes the likelihood that the object is
to be found at different locations, and also the probability that it is to have
any other property of interest, such as energy, momentum, etc. This means that
the particle is not in a single well-determined position, which we can determine
uniquely, but everywhere. In other words, we can only determine its position at
a specific time-point, and after this measurement the position will become
gradually more and more undetermined again – according to the physical laws.
There is also another feature of quantum mechanics that puts a fundamental
limit to how well a system can be determined, and that feature is known as Heisenberg’s
uncertainty principle
. According to this principle, if you determine one
aspect of an object really really well (e.g. the position), that determination
means that some other aspect of the same object (e.g. the momentum) automatically
becomes more undetermined. The above properties taken together mean that the
assertion made around 1750 – that if you could fully determine a system at one
point in time, you could, at least in principle, calculate all future aspects
of that system – no longer is valid, if one considers the latest understanding
of physics. It was valid a valid argument according to the then prevailing
understanding of physics, Newtonian mechanics, but our scientific understanding
has evolved since then. Note that this is one of the several important things
that has happened in this direction science the early 20th century,
which was mentioned in the previous historical review.

Let
us now move on to the in practice
aspect. The reason why it is important to consider this aspect too is that quantum
effects normally only are considered for really small objects (the largest
object that has displayed quantum effects experimentally to date is a 60-carbon
molecule
). When larger objects are considered, quantum mechanics becomes
increasingly more and more equivalent to Newtonian mechanics. Therefore, one
could at this point in the story argue that we still could deterministically
calculate what all future events will be like for all aspects of the world that
we concern ourselves with: the macroscopic events. However, there is then
another aspect that comes into action, and that is the mathematical phenomenon
known as chaos.Image of the Lorenz attractor. It is taken from here (Wikipedia, CC, attribution generic),
but the results can easily be reproduced by anyone knowing how to use e.g. Matlab
or Mathematica.

The feature
of chaos that we need to understand right now is its sensitivity to initial
position uncertainties. The popular science image of this is that the
difference between whether a butterfly flags its wings in Tokyo or not
determines whether or not there a week later will be a tornado in New York. Here
I want to take the chance to refine and improve upon that butterfly image a
bit, since it easily leads to a misunderstanding of what chaos actually means.
To do this, consider the image above, of the Lorenz attractor, which is one of
the most well-studied systems that displays chaos. The image contains two
different simulations, depicted in blue and yellow, and the only difference
between the two simulations is that the place where the simulation starts (at
the cone to the left in each simulation) differs by a small amount. This
difference in where the two simulations starts is much smaller than can be seen
by eye, but after some time in the simulation, the two simulations are clearly
different: they have ended up in different places (the second cone), and, as
can be seen, they have also taken different paths to get there. In other words,
in a chaotic system, even very very small differences in starting positions
will grow over time, and eventually these differences will become so big that
the initial conditions doesn’t matter: one can no longer say where in the
chaotic region the systems started – or, equivalently, no matter how well-determined
the initial conditions are, one can in practice never predict all of the system’s
future. However, with this said, I want to again return to the butterfly
example. As can be seen in the image of the Lorenz attractor, the position becomes
more and more undetermined, and the distance between the two simulated
positions for each given time points grows – but only up to a certain level.
The two simulations are different, but still they lie within the same region in
space. This region is known as the chaotic attractor, and the simulations will
– once they have gotten to this region – never leave it again. In other words,
there is a degree of uncertainty of where the simulation will be (where in the
attractor it will be) but the uncertainty also has a limit (it doesn’t leave
the attractor). For this reason, the butterfly example is perhaps not the best
illustration of a chaotic system: the example relies on the additional
assumption that both the case of a tornado and not a tornado lie within the
same chaotic attractor as the butterfly’s flagging of its wings; such a model has, to my knowledge not been constructed.
However, chaos does appear in living systems, which has been demonstrated in
the latest decades by some of my Danish colleagues, both experimentally and
theoretically.

Let us now sum up this first aspect of the
reasons why materialistic determinism not is a necessary consequence of the
physical laws. First, the results within quantum mechanics mean that there is
an upper limit to how well-determined a system can become: there is an inherent
randomness in all processes. Second, no matter how small uncertainties one
starts with, these will – in the chaotic attractors – grow over time, until the
prediction of the system’s future is completely uncertain (up to the level of
the attractor size). In other words, the latest results of physics show that
what previously seemed like a sufficient condition – the existence of physical
laws – no longer implies determinism: neither in principle nor in practice.

The second argument: about boundaries

To
understand this second argument, we need to dive a little bit more into how
science actually operates. First we will explore the concept of postulates, and
the boundaries that they imply. Then we will shortly examine some examples of
what may lie outside the current boundaries, which will lead us to the left and
right hand sides in Wilber’s four quadrants. We will then return to the
postulates, and see how science moves from them to physical laws, to
predictions and rejections, and we will thereby again arrive at the key insight
that “science does not prove things, but all theories are not equal”.

A set of
postulates is a relatively small set of initial assumptions that a whole theory
is based upon. They could therefore be thought of as axioms, in a mathematical
framework, but postulates also deal with the relationship between the theory
and world. In physics, such postulates have been laid down at various
occasions, and even though that process is not complete, the postulates
typically contains some initial postulated equations, and statements of the
character: the developed theory should be able to explain phenomena that are
reproducible, measurable, interdependent
of the observer, etc. These postulates are then what one uses to derive and
develop all the remaining results, in a process that involves predictions and
experimental tests that will be explained below.

The postulates thus specify the initial
assumptions, and this also includes what
will be studied. In other words, when the physical postulates say that they
should study “measurable, reproducible, observer-independent things”, this is
just like if one would say that “this attempt at a complete theory for biology should
be able to describe all living objects”. This does not mean that there is not
such a thing as non-living objects, and it certainly does not mean that the
success of the theory proves that there isn’t such a thing as non-living
objects. It merely says that non-living objects are – if they exists – not
studied or covered within this theory of biology. In just the same way the
postulates of physics does not say that there isn’t such a thing as
non-measurable, non-reproducible or non-observer-dependent phenomena, and the
success of physics does not prove that there are no such phenomena. The postulates
merely says that if such phenomena does exist, they are not studied or
described within the realms of physics – at least not by a theory of physics
that is based upon those postulates.

Depiction of the 4
quadrants by Wilber, with a focus on the difference between the left and right
hand sides

Let
us now consider some phenomena that would lie outside of the above mentioned realms
of physics, but that still are worthy of studying, and that certainly should be
included in a worldview. To do this, let us consider the above depicted four
quadrants of Wilber, and especially its right and left-hand sides. The
right-hand side of these quadrants are concerned with physical objects, and
physical phenomena, i.e. with physics or things that could be considered as
physics. The left-hand side, on the other hand, is concerned with the inner
subjective thought-experiences of our lives. Often these two sides are just
that: two sides or aspects of a single phenomenon. Consider for instance such a
mundane thing as observing an apple. This could be viewed from a physical
perspective. The apple in itself could be measured with respect to its weight,
color, etc. Also the process of observing could be viewed from a physical
perspective: one could measure the brain activity in the person who is
observing the apple. However, the inner experience of the person who is
observing the apple is not captured, even by such brain activity measurements.
In other words, in the brain scanner one sees the physical representation of
which areas in the brain that is active: but one does not see an apple in the
same way as the person who is observing the able is seeing it. This subjective
experience of the person is something that belongs to the left-hand side of
this phenomenon, and the brain-activity as measured using some technical devise
belongs to the right-hand side of this same phenomenon. This means that the
left-hand side aspect of this experience – or of any studied phenomenon for
that matter – does not fall within the current realms of physics: it is data of
a fundamentally different character.

The two phases of the experiment-analysis
cycle: one of my standard slides when giving scientific lectures.

We are now
ready for the last part in understanding this second argument: the boundary
argument. I already said that the postulates contains some initial equations
and assumptions about the object they are to describe. Just as with
mathematical axioms, these initial statements can then be used to derive a
large number of theorems, which are more complex statements that come as
logical consequences of the initial postulates. In these theorems, which may be
laws of physics, there will often be some unknown constants. To determine these
constants, you need experimental data. We have now introduced the first two
objects in the figure above: the experimental data, and the mechanistic explanations
to these data (which e.g. may be a set of physical laws). In the first phase,
Phase I, one uses the data to determine the values of the unknown constants (if
there are any), and then sees whether the suggested laws can describe the
experimental data. If the theoretical simulations and the experimental data are
sufficiently close to each other, the model is kept, and moves on to Phase II,
and if the agreement between simulations and data is too bad, the suggested
theory is rejected. For the non-rejected statements, one looks for predictions,
that may be tested in new experiments. In this way, Phase I may lead to the
necessity of new theories, and Phase II leads to new experiments, and the above
process is thus a cycle that goes on and on. The reason for this lies at the
heart of what I am trying to convey here: science does not prove things, but all
theories are not equally realistic
. In other
words, what one can say with a high certainty is that a theory has been
rejected, but one can not say that a theory has been proven to be true; there may
always come a new prediction that is wrong when tested experimentally. However,
just because all predictions and affirmative statements in science are
non-proven theories, this does not mean that all predictions and theories are
equal: some of them may have been rejected, because there were experimental
data that they couldn’t describe.

Summing up – and what about the second climax?

With these
insights at place, we are now ready to sum up, and to put all of this together.
First, we have seen that the updated view of what physics actually says implies
that the laws of physics does not necessitate determinism. Second, the other
side of the coin, materialism, also does not follow as a logical and necessary
conclusion from the existence of physical laws, and the reason for that is the
second argument: the boundary arguments. Just because physics has defined
itself as the study of measurable, reproducible, things, this does not mean
that other things does not exist, it only means that e.g. non-measurable things
– e.g. inner experiences and thoughts as
seen by the observer
– not are a part of physics. Third, such subjective experiences
are, nevertheless, an important part of our lives: in fact, they are the only things
that we as humans experience. Therefore, such subjective experiences – our inner
universe – must certainly be dealt with by any complete description of how our
world functions. A worldview must therefore, by necessity, be such a complete
description, which takes all aspects of our lives into account.
In
fact, we do not have a choice: we are all of us making decisions about how
science and physics relate to our own personal experiences, and materialism is only
one of the choices that is compatible with science. Fourth, as I will argue in more
detail in future posts, it would actually be possible to expand the sound
principles of science to include data also from the left-hand side in Wilber’s
four quadrants. Such a science is what Wilber calls broad science. Since such
broad science would explain more data than traditional science, which Wilber
calls narrow science, it would be a superior theory. Therefore, although we
still haven’t seen any details of how broad science, or a more complete
worldview would look, we have now concluded that looking for one would be a
meaningful endeavor, and that it seems like the updated logical conclusion of
looking at the science/worldview relation no longer reads “the necessity of
materialistic determinism”, but “narrow science trumps narrow religion (religion
that e.g. like in some of the fights on evolution stands in opposition to
science), but broad science would trump narrow science – because it would be
able to explain more data

Further reading – and the scientific accuracy/controversy
of these statements

Just as in
the first blog post, I will try to end all sub-sequent posts by links to more
detailed reading, and with some comments of the scientific accuracy in what I
say – including some estimate of the level of controversiality in my
statements. First, regarding more reading, almost all of the statements in this
blog post have been made before, e.g. in the essay that I pointed to
earlier (which is written in a more formal manner, with much more links to
literature), in the book by Ian G. Barbour, and – where already indicated –
in some texts by Wilber. Second, regarding the first argument, which builds on
the understandings within quantum mechanics and chaos theory, I have myself
studied both these theories at a high level – basically to the point of doing
research myself therein – and I do not believe that there are any controversial
statements regarding what the actual physics says. Nevertheless, there may
exist physicists who disagree with me regarding my claims that those results
means that determinism no longer is a necessary conclusion, and I will myself refine this statement in future posts, when we come into discussions on free will. Similarly,
regarding the basic description of how science works, they describe a
relatively standard view of science that goes back to people like Popper.
Again, however, this does not mean that all scientists would agree with me
regarding the importance and soundness of attempting to include data from the
left-hand side in Wilber’s quadrants. But if all people already agreed with
everything I had to say here, this would be a pretty meaningless endeavor.