Computing,  Mathematics,  Philosophy,  Physics

Information, Uncertainty and Choice

In the previous post, I described how modern science employs two contradictory ideas—possibility and choice—although in practice only one of them can be used, resulting in incompleteness. An example of that incompleteness is that quantum theory describes the world as a possibility which needs to be completed by a choice, although that choice cannot be reduced to that possibility. The predictions of the theory therefore are probabilistic, and we cannot predict the next event or observation. This post explores how a new way of thinking can reconcile the contradiction between possibility and choice—when both possibility and choice are treated as information. Possibility is now missing or incomplete information, and choice is a partial or complete overcoming of that uncertainty.

The Mind-Body Problem in Quantum Physics

In the standard interpretation of quantum theory, possibility and choice are mutually inconsistent categories. The material world is a possibility of different observations and the selection on this possibility represents a choice. John von Neumann called the possibility as “matter” and choice as “consciousness”. The implication of that interpretation is also that we cannot reduce possibility and choice into a single logically consistent theory, because matter and consciousness cannot be described within the same theory. We also cannot logically reduce one to the other since any attempt to do so would produce a contradiction. However, if we keep them as two distinct material entities, then this naturally results in an incompleteness.

possibility-choice-problem

John von Neumann provided an unsatisfactory solution to this problem by insisting that the choice provided by consciousness is a different kind of “process”, which has been subsequently interpreted to mean that consciousness is different from matter, and somehow acts on matter in a way that cannot be explained in science. Effectively, this entails that scientific predictions will forever be incomplete. Niels Bohr too had similarly argued earlier that we have reached a limit to describing nature completely in physics, and that we cannot but choose only this description.

The Solution to the Mind-Body Problem

What if we are not limited to the current kind of description? What if we could find another description in which choice and possibility don’t remain mutually contradictory but mutually consistent? This alternative is possible if we treat both possibility and choice as information. Possibility is missing information, and choice completes that missing information, by adding information. Until a choice is made, the world is objective, although due to missing information it does not produce sensations. When this missing information is added, the objective world which earlier could not be observed becomes observable.

The point is that the contradiction between possibility and choice is easily resolved by changing the material ideology from the current materialist dogma where the material world—if it exists—must be observable. When this dogma is replaced by information, the world can be objective, although not perceivable. The amount of information perceivable, when a choice is made, is far greater than the amount of information passed through a choice. Therefore, to explain the observation we must suppose that the information  we did not previously perceive also existed objectively, although was not sensually perceivable. How this information can be perceived opens up doors to new kinds of perception in science, where we see the world in a new way although not through the senses.

In this approach, the mind is the possibility and the body is the choice. They are both information which interacts according to a different set of rules. The world prior to observation exists objectively as abstract information which we call the “mind”. When more information is added to this abstraction, an instance of that abstraction is created. We perceive this instance, but we also know in quantum theory that this is not the only instance we could perceive. For example, the same wavefunction can be represented through a different basis. In other words, there is an objective reality, but it must be instantiated to be perceived.

An example will be useful here. Consider the idea of a “car” and the instances of “car”. The idea of a car is definite, and yet it allows the possibility of being instantiated into many distinct types of cars and individual cars. In the same way, the quantum wavefunction is a definite state, when described as information. The measurement choice on this wavefunction is the act of instantiating that idea into a definite observation. Just as a meaning can be expressed through different sentences, similarly, the quantum wavefunction can be converted into a physical instance of that meaning.

The probability description of quantum theory is therefore unnecessary. The world is a possibility but not a probability. It is the possibility of an idea being converted into instances of that idea. That conversion involves a causal interaction, which science cannot currently explain. The probability is not a permanent feature of reality. However, possibility is a permanent feature of reality because the world exists in an abstract form. A quantum theory that changes the material ideology will discard probability, without discarding possibility. Ideas would now be possibilities of instantiation.

The mind-body problem is unsolvable in Cartesian metaphysics, because these two are described as substances which cannot interact except through a force between them. It is also unsolvable in classical physics where matter is real physical objects, and the theory is conceptually complete without the mind; adding mind to an already complete theory adds no value and appears superfluous. It is unsolvable in current quantum theory because it makes choices entirely inconsistent with possibilities. This problem is, however, eminently solvable if both possibility and choice are treated as information.

The Role of Information

Possibility and choice don’t have to be contradictory ideas if possibility was abstract information, which is completed by adding contingent information. The material world can exist as incomplete information, which means that something must be added to this world to complete its state. Unless this information is added, the extent of incompleteness represents the uncertainty in its state—which we call possibility.

Given any uncertain state, we can add to it many kinds of information, thereby compensating for its incompleteness. This is precisely what we do while performing a measurement. It is also what we do while observing the world through the senses and mind, when we supply an interpretation of the world. The world presents to us sensations gathered by the body, and these are then given an interpretation by the mind, thus creating a perception. The interpretations are judged to be true or false based on some beliefs or axioms about the world. These beliefs are owned by the observer as their intentions. And this intent rests upon a moral view of good and bad.

Each observer thus tries to complete the incompleteness in matter by the choice of an interpretation, judgment, intention, and morality. And each observer thereby produces a different experience and we are living different lives by completing the incomplete material world in different ways. If the body and mind are both described as information, then their interaction is not causally problematic. It is, however, problematic if body and mind are described as two kinds of substances.

Observation vs. Measurement

Many materialists will like this idea of mind-body reduction. But there are reasons why this reduction isn’t what materialists currently think, and the reason is knowledge representation. In any observation, the observer perceives the world, and represents the information about the world. In a representation, one object is the symbol of another. This is not expected of physical theories, where each object only describes itself, and the outcome of measurement is a property of the measuring instrument. Knowledge representation brings two kinds of important shifts to this view of matter: (1) matter involves a hierarchy of types, and (2) matter refers to other material objects.

When your eyes see the world, the eyes represent the dimensions of color, form, and size, while the world represents the values of color, form, and size. For instance, the world might be redness of color, squareness of form, and a specific length denoting size. By definition, ‘color’ is more abstract than ‘red’, ‘form’ is more abstract than ‘square’, and ‘length’ is more abstract than ’10 meters’. We can say that the dimensions of a measurement are conceptually more abstract than the values on that dimension. The dimensions define the ‘space’ and the values represent ‘locations’ in the space. This has a very simple implication: while performing an observation, the observer’s senses are conceptually more abstract than the objects they measure. The senses are the dimensions and the objects are values. Conceptually, the senses are therefore ‘higher’ than the objects they measure, although this ‘height’ is conceptual hierarchy.

Materialism discards this conceptual hierarchy and presumes that the measuring instrument is of the same type as the measured object. This was true in classical physics, where the measuring and measured instruments were material objects of the same kind. We just called a particular object a measuring instrument—e.g. a meter or a clock—but any object could be the standard of measurement. This symmetry between measuring and measured instruments in classical physics has now been broken in quantum theory. Now, measuring and measured systems are indeed of different types: the measured system is incomplete information, and the measured system completes that uncertainty through a choice. This problem seems unintuitive in the context of materialism or classical physics, but is easily understood if we treat quantum measurements as observations.

What is the difference? In a measurement, all objects have the same type. In an observation, the observer’s senses are conceptually more abstract than the measured objects. If we try to reduce the observer’s senses to the objects, we create a contradiction. If we keep them as two types of entities, we create incompleteness. But if we join them as dimensions and values, there is no contradiction. However, we now have a surprising conclusion: the observer’s senses, or the measuring instrument, is not an object in the same space as the things it measures. The senses are rather the space in which the object is given a location; the senses are the dimensions in which objects are values.

Choice and Possibility Revisited

If you measure the number 10, the measurement is incomplete unless you know the type of property that you measured—e.g. length vs. time. Similarly, if you have a property but no value, again, the knowledge is incomplete, unless you also have a specific value of the property. There are thus two kinds of information that we ordinarily call the dimension and the value. The dimensions are the ideas or the “mind” and the values are the physical values or the “body”. Both mind and body are incomplete individually, not just in the specific case of living beings but even in all material objects.

In measurement, the measuring instrument represents the dimension and the measured system represents the value. In an experience, the mind denotes the dimensions and the body represents the value. They are therefore both incomplete without each other. However, the dimension is logically prior to the values, and the values are created within the dimension. In that sense, the dimension must exist before values can exist. In short, the mind must exist before the body can exist.

The measuring and the measured systems are therefore not the same kinds of entities. Rather, the measuring instrument is conceptually more abstract than the measured instrument. The measuring instrument denotes the dimension, in which the measured system is given a value. In the quantum 2-slit experiment, for example, the battery of detectors represents the dimension, while quantum objects arriving at the battery of detectors represent the values. They are not the same kinds of entities, but under the physical interpretation we think of both as objects and hence values.

The problem of choice and possibility can be resolved if the measuring instrument was treated as a dimension rather than values. If the dimension is length, then the value is position. However, if the same dimension is color, then values are different hues of color. Thus, simply by reinterpreting the dimension as a different type of property, we can change the meaning of a value: the value becomes a color instead of a  length. This means that the problem of observation need not be reduced to some specific physical properties—e.g. length. Observations can also detect color, taste, smell, etc. if the extension of a measuring instrument was interpreted as a different kind of property dimension. This entails that extension in space is not merely a physical property called ‘length’. Rather, the same extension can also denote color, shape, taste, sound, touch, or smell.

The mind therefore need not be a different kind of substance. It also need not be treated differently than a measuring instrument, if only the measuring instrument—as an object—represents a dimension. Ordinary measuring instruments such as meters, clocks, and weights, represent different dimensions, although they are, in one sense, simply material objects. The human body too can be an object and a dimension. The latter represents the novelty in modern science where ordinary objects represent both a value and a dimension, and this novelty has begun to have a bearing on the theory: the theory is incomplete unless we incorporate these two ideas. These two ideas are not mutually inconsistent in principle, although they become mutually inconsistent if we treat objects only as values.

Matter as Symbols of Properties

An ordinary meter has the property of length and a value of length. The meter symbolizes the property of length through a specific value. Individually, both length and value are possibilities, and therefore incomplete. Together, they complement and complete each other. This makes ordinary objects symbols of properties. The “physical” part of the symbol is its value, and the “conceptual” part of the symbol is the property. A meter has both the physical and the conceptual; the conceptual in the case of length is ‘hidden’ from our vision because we attribute this property to the underlying space, and not to the object itself. This attribution is problematic because if all objects in space only have length, then how are some objects symbols of mass or temperature? Clearly, if one instrument measures weight and the other one measures heat, then we have to attribute the properties of those objects to space too.

The problem in science is that we are measuring properties like “mass” but we are not placing the objects in a “space” whose dimension is “mass” (it is notable that mass has become a property of space in relativity theory, although not a dimension like other properties; this ‘dimension’ is rather presented currently as the ‘curvature’ of space). Similarly, we measure temperature using a thermometer, but the thermometer does not exist in a space whose dimension is temperature. All objects exist in the same space, but they are supposed to indicate different properties. If length is a property of the space, then why are mass and temperature not properties of space?

This idea is incomprehensible unless we dramatically increase the dimensions in the space—allowing a unique dimension for each kind of property—which would be conceptually unproblematic, although it will violate the empirical fact that there are only three dimensions in space. The only alternative resolution to this problem is that the objects themselves are both dimensions and values, and each object represents a different dimension or property. A long black table therefore has the dimension of a “furniture” and a value of a “table”, a dimension of “length” and a value of “long”, a dimension of “color” and a value of “black”. This idea can be understood only when objects are not merely in space; rather, they are also the dimensions of space. This new kind of space is hierarchical instead of linear.

The Notion of Hierarchical Space

A hierarchical space has infinite dimensions, although all these dimensions are physically accommodated within three cardinal directions. Take your ordinary house address for example. Your house has a number or value, which is defined in relation to a dimension—a street. The street has a name, which is defined in relation to a dimension—a locality. This locality has a name in relation to a city, which has a name in relation to a state, which has a name in relation to a country.

All these entities—from your house to your country—are both values and dimensions. They are dimensions in relation to the less abstract entity, and values in relation to a more abstract entity. Therefore, two observations have to be performed to know both the value and the dimension. These observations detect complementary aspects of the object. An object becomes a concept when there are many other objects which are given values in relation to the first object. For instance, a meter is an individual object, unless other objects are measured in relation to the meter, at which point it becomes a concept. Mind and body are therefore different aspects of all entities, although they are not identical because two separate observations or measurements are needed to express them.

They would be identical if both could be revealed in the same measurement, or one could be reduced to the other—i.e. if you knew one, you could compute the other. If mind and body involve two separate measurement relationships, then they both exist simultaneously, and yet are not identical.

Conclusion

The problem of possibility and choice represents not a contradiction but a new way of looking at the world as symbols. The symbols are inadequately described in current science because we disregard the conceptual properties in objects, which are indispensable during measurements, because the measuring system represents a conceptual dimension. Since we don’t admit concepts as material entities in science, we must push the measuring instrument out of the measurement process and consider it a “choice”, when the measuring and measured systems only need to represent dimension and value.

The dimension and value are both information but they are not the same kind of information. The value is defined in relation to the dimension, and if that dimension is a value in relation to another dimension, then we must construct a hierarchical space of many dimensions and values.