more on symbolic knowledge

30/01/2017

In an earlier article, we asked ‘what is knowledge?’ Here we shall explore the nature of knowledge further.

As previously discussed, knowledge is a symbolic model of something else. To construct such a model, we need symbols. In natural languages, these symbols are words, typically rather loosely defined. In science, the symbols are technical terms which are, ideally, rigorously defined. Either way, the definition of a symbol is a curious business.

One way to define what a symbol represents is to point to it in the real world. If someone were to ask the meaning of the word ‘car’, I could point to a car and state, ‘This is a car.’ Note that to define the word rigorously by pointing, I would have to collect all the cars in existence (including past and future cars) and state that everything in this set is a car and nothing else is a car. Of course that is impractical, and for natural languages, we make do with a few examples and assume that we are all going to extrapolate the full meaning in roughly the same way. Science, on the other hand, demands rigour, so pointing at things is typically not of much use.

Apart from pointing at things, a symbol can be defined in terms of other symbols. This leads to a rather odd characteristic of almost all symbols: a symbol cannot stand alone. In itself, it is devoid of meaning. Its meaning is almost always in reference to other symbols, which in turn are meaningful only in relation to yet more symbols. Let’s consider a few examples.

What is a car? This question can actually be answered in different ways. One way is to refer to a more general symbol: a car is a type of vehicle. It would then be desirable to define what attributes distinguish a car from other vehicles: a car is a vehicle designed to transport a small number of people. Sometimes a definition can be made in the opposite way, by enumerating sub-types, for example a vehicle might be defined as a car or a bus or a lorry or a motorbike…

So far, we’ve considered definitions with regard to sets of objects. There are other sorts of definitions though. One is structural: a car is comprised of a chassis and an engine and some wheels… With such a definition, there also needs to be some definition of how the parts are connected to one another. Another approach is a functional definition: A car is a machine designed to transport people along roads.

There are other flavours of definitions too. One refers to the historic causes leading to the thing: an oak tree is a plant which has grown from an acorn. The opposite of this is to state what is going to become of something: an acorn is a seed which, after germination, grows into an oak tree.

Regardless of the flavour, any definition of a symbol is relational. The meaning of a symbol is determined by how it relates to the meaning of other symbols. This inter-dependence of symbolic meaning has many ramifications.

One consequence of symbolic inter-dependence is that totally abstract languages and models can be constructed, that are formally disconnected from the material world. Pure mathematics is the quintessential example of this. This sort of abstraction is thinking at its best: honest thinking in its own domain, that doesn’t pretend to be a direct reflection of reality.

In an abstract model, truth is determined by whether a statement follows syntactic rules and can be proved to be consistent with other statements known to be true in the model. The proofs themselves have to follow strict logic, which itself forms part of the model. This type of system requires some foundation statements – axioms – which are not in themselves proven. Everything else is derived logically from the axioms. In mathematics, the need for axioms is accepted without any debate; it's obvious that some foundation is needed. In the non-scientific arena, we also need foundation beliefs which are, in themselves, unproven. Oddly, some scientists seem to think that this invalidates all knowledge derived from one’s core beliefs. A more accurate view is simply to accept that the truth of knowledge is dependent on the truth of the core beliefs. A mystic is someone who sees all this and simply accepts that no knowledge can be shown to be truthful in any strictly meaningful sense. Everything is fundamentally unknowable.

A century or so ago, it was assumed that mathematics could be made formally complete. It was believed that a mathematical system could be defined where everything was internally consistent and that any mathematical statement could, in principle at least, be proved to be either true or false. This is the sort of rigour that a scientist is always striving for. Unfortunately for rigour, Gödel proved that any formal system that is powerful enough to be of any use is, fundamentally, incomplete. By incomplete, it is meant that it is always possible to construct a valid statement in a formal language which cannot by proved to be either true or false. Even a formal system has paradox as a characteristic: there are statements which are both true and false at the same time. Or they can be interpreted as neither true nor false. Or it can be said that their truthfulness is undecidable. In any case, we now know that it is not possible to construct a formal system that is logically complete in the way that had previously been assumed. Despite this, everyone (including scientists) continues to use maths because it’s practical and works as long as one steers clear of the paradoxes. This practical approach is reminiscent of the acceptance of scientific theories that have singularities, discussed in a previous article.

I’ll leave it at that for this article, though the mind has that intangible feeling that there is more to be said on this topic…

the understanding of a mystic

29/01/2017

In preceding articles, we’ve looked at the scientific approach to knowledge. In this piece, we’ll outline the perspective of a mystic.

A mystic believes that life is fundamentally a mystery, that ultimately it cannot be understood through rational thinking. Within this broad definition, there is a range of beliefs – various flavours of mystics. Here we’ll look at some of these beliefs and flavours.

One flavour of mystic does not deny rational knowledge (including scientific knowledge). However, all rational understanding is seen as a secondary phenomenon, only approximately modelling reality. Such a mystic basically has the same world view as a scientist. The only difference is that the mystic likes to spend a lot of time feeling the mystery of the moment, whereas a scientist likes to spend a lot of time finding and improving the models that describe the moment. The difference is where the passion lies, rather than a difference of belief.

A stronger flavour of mystic, and one which is more at odds with the endeavours of science, claims that existence is fundamentally acausal. In other words, this moment is seen as arising spontaneously, not dependent on what has gone before and not relevant to what will come next. With this belief, the strong causality claimed by science is seen as something of a distraction with, at best, some sort of rough heuristic truth value. This acausal belief leads the mystic to be even more focussed on the present moment. Why bother thinking about the past or the future when the past is finished, no longer relevant even to this moment, and the future is yet to come, not determined by the present moment? Basically, thinking about the past or the future is seen as missing the point.

This acausal view has some ramifications. Not only does it lead to the mystic being focussed on the present moment, it also simplifies the moment considerably. Our thought patterns are almost always dancing between the past (memories) and the future (predictions). One could say that the whole purpose of thinking is to predict the future based on memories triggered by present sensations. Dropping the obsession with making predictions, thinking is effectively redundant, and the conscious experience becomes focussed on direct perception of the senses in the moment.

Curiously, even if thinking in symbols (words) is not happening, there can still be an emotional response to the moment. For example, whilst simply looking at a flower there can be a feeling of beauty and love. All of this can happen without any thoughts as words. The reason that a mystic is passionate about living moments in this way is that without the distraction of thoughts, these emotional responses are felt much more intensely. There is a wonderful intimacy in looking at a flower with full awareness, yet without thoughts. With such direct perception, our awareness is on the reality, or as close to it as our sense organs will allow, rather than on our model of reality. And reality is somehow more juicy, more alive, than any model.

Although causality is one of the basic assumptions of science, there are situations in which even science has to admit that strict causality no longer applies. One example of this is those quantum events which occur spontaneously, such as a pair of entangled particles coming into existence out of nothingness. It is an acausal event, fundamentally unpredictable by scientific modelling, and yet science concedes that it happens. So at least at the quantum scale, acausality is a reality for some events.

Bear in mind also that science asserts that everything is made out of fundamental particles, that quantum physics is the reality that underlies everything. It follows that any acausal events at the quantum level introduce a degree of acausality at larger scales. Another way of stating this is that all our knowledge of larger scale phenomena is, strictly speaking, statistical knowledge, rather than of a deterministic nature.

Another example where science must acknowledge an acausal event is where there is a singularity in time. The big bang might be the only example of this. However, given that science understands that everything that has happened in the universe has been a consequence of the big bang, there is a sense in which existence as a whole is acausal.

Returning to the mystic, another understanding is that deeper truths about reality can be encountered through direct conscious experience, without recourse to thoughts. This is really why mystics meditate or practise other disciplines. There is an understanding that there is a route to uncovering truth which does not involve making a mental model of things. Such a mystical truth exists only in the moment it is being experienced. Afterwards the mystic might try to put the truth into words but that is already a movement away from the truth. For this reason, the words of mystics often have a very poetic feel to them.

One particular truth that the mystic might experience is the non-separation of all that is. More specifically, it is possible to have the direct experience of no separation between oneself and whatever one is perceiving. The apparent duality between the observer and the observed can disappear.

Once one has experienced for oneself the reality of non-duality, then the dualistic description of things is seen as a consequence of symbolic thought, rather than being a fundamental characteristic of reality. In other words, reality is a continuous energy field and it is the use of symbols which necessitates an arbitrary dividing up of that continuous field. Science (along with all other symbolic knowledge) can only exist with an imposed dualism. The use of symbols creates the appearance of duality.

Although most scientists would probably take issue with the mystic’s assertion of non-duality, there are hints of it in science. As mentioned in a previous article, the fact that making an observation affects the state of a quantum system means that the observer and the observed are not as cleanly separated as a scientist might like. Another example, at the grander scale of things, is that the local warping of the space-time continuum is affected by all matter in the universe. The warping of space-time in turn affects how things behave locally. So, strictly speaking, all behaviour locally is dependent on everything that exists. With such total inter-dependence, is it meaningful to think of things as separate?

Here we’ve looked at a few aspects of the world view of a mystic and made some comparisons with the scientific view. In some later articles we will consider some questions which are problematic for science, where the perspective of the mystic seems to be undeniable.

what does science create?

27/01/2017

From the previous articles, we can see that what science creates is a model of the material world.

In practice, there are many models, each concerned with one aspect of the world around us. In some cases, it is demonstrated that these models are compatible with one another and in other cases this is assumed to be the case without formal proof. Occasionally, a pair of the generally accepted models are known to be incompatible. One example of this at present is the incompatibility between general relativity and quantum theories.

Incompatibilities between models, or other difficulties such as singularities, serve as a reminder that scientific theories are always a work in progress. The standard model in quantum physics, for example, is understood to be the best model that we’ve come up with so far. That is not to say that it is the last word in the matter. In a sense, every scientific theory is of an interim nature, valid until a better model is found.

This is not a defect of the scientific method. On the contrary, it is its main strength. Scientific knowledge keeps getting better and better because of it. Sometimes these improvements are incremental, when an existing model is adjusted to honour some observations that did not fit with the old version. In other cases, a whole new theory comes into being which overturns completely the knowledge in that realm. The two great twentieth century physics theories – relativity and quantum theory – are both in this category.

There is a sense in which a scientific theory is never strictly proven to be true. A hypothesis can often be shown to be false: a single inconvenient observation is enough to do that. As we cannot actually observe every particle in the universe, at every point of time, we can never be 100% certain that a scientific theory is true. We can only say that it is extremely probable, if it accords with all known observations, when many observations have been made.

So, science is creating an ever-more-accurate set of models of the material world. What it is not providing is an absolute truth.

implications of invariance

26/01/2017

As mentioned in an earlier article, science is identifying patterns which are invariant in time and space. This allows scientific assertions to be tested by different people at different times and places. This requirement of invariance creates one limitation to the scientific method.

If a phenomenon is not invariant, it is not amenable to scientific description. In other words, if something happens a particular way only once, or strictly randomly, or only in specific regions of space, the scientific method cannot be applied.

Some scientists believe that all phenomena are invariant, so the difficulty will not arise. However, there is no particular reason why everything in the universe should behave consistently. It is an unscientific belief that things are such. Note that it might be the case that everything behaves consistently. We just don’t know that. And we can’t know that in a scientific sense. It is an unprovable hypothesis, ie. a belief.

This highlights one of the difficulties of science. Sooner or later, we always reach a point of belief – irrational belief. A theist believes in god. A scientist might believe that all phenomena are invariant. They are both irrational beliefs.

When a scientific theory mostly holds true but is known to fail in a particular situation, that situation is labelled a singularity. One example of a singularity is the centre of a black hole, where the mathematics of the general theory of relativity break down. The theory seems to work everywhere else in the universe, so it’s quite useful, but it doesn’t apply in a black hole. So, the fabric of space-time does not quite behave with invariance. Some people simply gloss over this issue, whilst other scientists understand that the theory is therefore incorrect and will eventually be replaced with something better, just as relativity theory itself replaced Newton’s laws of motion.

A black hole is an example of a singularity in space. Scientists also know that there is at least one singularity in time, namely the moment of the big bang. Physics describes things quite well from a time soon after the big bang; very soon indeed after the big bang. At present, I believe that theory has got a handle on things from a time of about 0.000000000000000000000000000000000000000001 seconds after the bang. Considering that was 13 or 14 billion years ago, most of time is covered, so again the theory is very useful. Like in the case of black holes, though, it is known to break down in that first fraction of a second. With further research, the theory might be developed to cover time even closer to the big bang. However, it seems unavoidable that the actual moment of the big bang will always remain a singularity.

Quantum physics has raised some other challenges for the scientific method. One is the uncertainty principle, which states that the position and momentum of a particle cannot both be determined precisely at the same moment. This is a fundamental characteristic of the quantum world, rather than merely a restriction due to current technical capabilities. To put it another way, physics has ascertained that there is a fundamental limit to how precisely we can know the state of things.

To complicate things further, in quantum physics a particle exists as a probabilistic wave function until it is observed. At the moment of observation, the wave function collapses and the particle’s attributes become decided. It is not that we are simply ignorant of the attributes until observation; rather, the particle actually exists in a probabilistic form, with all possible attributes, until the moment of observation. This means that the act of observing phenomena is not passive; making the observation actively affects the state of things. Strictly speaking, this means that no knowledge is purely objective, and yet objectivity is one of the foundations of the scientific method.

The behaviour of things at the quantum scale raises another significant difficulty regarding invariance: Quantum events can occur at random times. For example, an individual radioactive decay event occurs randomly, which means that it violates the requirement to be invariant in time. As with the uncertainty principle, it is not that we are simply missing some measurement which would tell us when the event will happen. Rather, the timing of the event is genuinely random and, fundamentally, cannot be predicted. Quantum physicists handle this difficulty by resorting to statistics. These random events collectively follow well defined probability distributions. Again, this allows the theory to be very useful, even if there are some specific things it cannot (and will never be able to) predict.

So quantum theory has declared that some things are fundamentally unknowable. Another word for things that are fundamentally unknowable is mystery. A mystic is someone who believes that the whole of existence is fundamentally a mystery. Given that the big bang is a fundamental singularity and that quantum physics underlies the whole of existence, it turns out that physicists are actually mystics!