Philosophy,  Physics

Properties, Values, and Measurements

One of the problems that has repeatedly bothered me for the last decade is the distinction between physical properties, their measurements, and the values of properties that are discovered during measurement. I have flip-flopped in my understanding of the nature of the problem and what might be a viable solution. I will use this post to describe the problem and what I believe is the best way to resolve it. I will also connect the solution to ideas about the nature of perception and reality in Indian philosophy. But before I begin, let’s take a closer look at how science presently tries to address this issue.

The View in Science

Most people generally believe that both properties and their values are objective—i.e. that they exist in the material objects even when we do not measure them. The measurement of material objects is supposed to reveal their properties just as they exist prior to being measured. For instance, we commonly think that an object has an objective property called speed and a speedometer can be used to measure that property.

The problem with this view is that speed is a measurable property in physics but it is not a physical property because speed is not conserved. Physicists treat only conserved properties as being real (after all, if something is not conserved, then material transformations would change the property and we could not call it real). Thus, for instance, momentum is a conserved property, although speed is not. Momentum includes the ideas of speed, direction of motion, and mass of the moving object. Similarly, while weight is a measurable property, it is not a physical property because the weight of an object would be measured differently on the earth and the moon (the measured value of weight depends on the gravitational pull of earth and moon). Therefore, physicists would argue that the real physical property is mass rather than weight.

Observation vs. Reality

The key point is that all measurements involve a causal interaction between the measuring and the measured systems. The result of the measurement is an effect and while we would like to infer the cause from the effect, this isn’t very straightforward. In the above examples, weight and speed are effects of mass and momentum, respectively; we can measure the effects, but we need a theory to understand whether they are causes. We attribute reality to the causes, but inferring the cause from the effect needs a theory of causality! Thus, it is possible to imagine a theory in which speed and weight are real physical causes, and another theory in which they are merely effects of another cause.

It is clear that there are many more measurable properties than there are physical properties—in any physical theory. Potentially, any measured effect could be directly treated as being a real cause, although whether you treat it that way depends on the theory. For instance, we frequently measure weight and speed, but we do not consider them real in current physics since these properties are not conserved.

When the observer’s state (of motion) is taken into account, the reality of even the physical properties becomes questionable, because the values measured by the observer (in motion) are different. For instance, if the observer is moving, s/he would measure a different speed or direction of a moving object, and thereby attribute a different momentum and mass to it. We can no longer say that the object has a definite mass or momentum, because many possible masses and momenta would be inferred from the perspective of different (moving) observers. We can only say that the different observers would discover the same laws of nature regardless of what they think reality is.

The Nature of the Problem

The problem therefore arises because of two key factors: (1) we don’t know if a measured property is just an effect or also a cause, and (2) even if we fixed the relation between cause and effect, the cause derived from the effect depends on the observer’s state. The former arises due to different theories that might be used to describe observations, and the latter due to variations between different observers who use the same theory.

An everyday intuitive illustration of this fact is that we describe our observations of color, taste, smell, sound and touch in terms of physical properties such as mass, energy, momentum, angular momentum, and physical structure. We don’t treat color, taste, or smell, themselves as real physical properties, although they are measurements. In other words, our observations are effects although not causes and the relation between the cause and effect is theory-laden: a different theory would change the cause-effect relation and thereby whether or not these observations are also viewed as reality.

Given this fact, it seems obvious that what we consider to be a real property depends on our causal theory because a different theory would change the cause and explain the effect differently. We might say that reality is underdetermined by observation; something must be added to observation—i.e. a causal theory—to arrive at reality, and the reality we arrive at depends upon the theory we choose to describe our observations.

Separating Properties from Observations

It is necessary to separate properties—such as speed or momentum—from the observation such as the perception of motion. The properties are supplied by the observer to describe the observation, by imagining a theory of reality. Of course, the theory must predict correctly for it to be consider real, but it is likely that many possible theories will predict equally well—especially if limited domains of experience have to be explained. The possible explanations of an observation reduce as the number of observations required to be explained by the same theory grow. Therefore, theories must be rejected if they cannot explain some observation based on the postulated theories.

For instance, if momentum and mass cannot explain color, taste, or smell, we might have to search for new theories that do explain these observations. This replacement, however, is not very straightforward. Finding a new property that will explain both old and new observations is not always trivial because the causal connection between the reality and its observation itself needs to be revised before the theory predicts correctly. I explored these and other epistemological issues in an older post.

Nevertheless, the mere possibility of postulating different properties to explain observations itself suggests a difference between properties and observations: there are potentially infinitely many properties and observations, and which property best explains which observation (and eventually all the observations) has to be discovered.

Separating Properties from Values

The separation between properties and values is much less controversial. For instance, different objects can have different mass, speed, momentum, or weight values. If nature has to be described parsimoniously, then there must be a small number of properties which could appear in potentially infinite number of values. The fact that everything in the world has some length doesn’t imply a fixed length. Similarly, every property can appear in myriad values in different objects. We can conclude that just as properties and observations are distinct, properties and their values are distinct too.

However, unless you fix the theory—and thereby the properties—you cannot fix the values either. If the property of momentum is real while speed is not, then the values attributed to speed would also be unreal. Conversely, if speed were the real property, then its values would be considered real facts about the world, not just our observations.

We now have a heady problem: we cannot fix the nature of reality (both properties and their values) unless we fix the theory of nature. But theories are something we discover and infer from observation which we suppose tell us about reality. Thus we have a paradox at hand: from a pragmatic standpoint we believe that theories are derived from reality, although in science reality is constructed from the theory. The paradox arises due to a circular dependence between theory and reality. Observation is supposed to fix this problem, but observations can be interpreted in many different ways by different theories thereby changing both the properties and their measured values.

The Separation in Human Perception

It is clear from the above that properties, values, and measurements are different in science. A similar kind of separation exists even in human perception. Our senses are the analogues of measuring instruments, but they only produce phenomena: for instance a detector click or a pointer movement. Whether this click represents the measurement of mass or weight depends on the experimenter who labels the dial on the pointer or the pitch of the click with properties and their values. The same pointer movement on the same dial could, for instance, denote different properties and values.

Similarly, the separation between properties and values also exists in human perception. For instance, the idea of color exists in our minds even when we don’t see red, blue, or green. In this case, the idea of color is the property while red, blue, and green are measured values of that property. Even the idea of redness can be a property and various shades of red would then be interpreted as values of that property.

The key question however is: Does the property of color or redness exist in the external world or only in the mind of the observer? If we say that redness only exists in our minds then the observation cannot be applied back to reality. All observations will now be illusions and our ability to construct reality from these observations—by postulating properties—would be futile because whatever property we imagine in our minds would only be in the mind and not in the external world. Science postulates that some properties (such as length, mass, momentum, etc.) are in the real world while others (such as color, taste and smell) are in the mind. This separation is called the divide between primary and secondary properties and it has no fundamental grounding, given that even many primary properties (such as speed and weight) are actually illusions in science.

The separation between primary and secondary properties also creates great difficulties in explaining the secondary properties as effects of primary properties within a theory (not just as a matter of fact). For instance, we can observe someone’s brain activity when s/he sees redness, and conclude that the brain and the perception are identical. However, there is no way to reduce the redness to the physical properties in a physical theory that relies only on the use of primary properties rather than secondary properties. For instance, nobody has been able to come up with an equation that says that a certain frequency of light is the color red, although empirically we insist on this equivalence.

The only way to address this problem is to reduce perceived properties (i.e. color, taste, smell, tone, pitch, shape, etc.) itself to elementary perceptual properties because this is the only way in which both theoretical and empirical reductions can be achieved. However, this approach to reduction fundamentally alters many key assumptions in modern science.

The Problem of Macroscopic Objects

The problem of perception gets worse when we consider the cognition of macroscopic objects. Historically, when science has described objects, it described fundamental particles. In Newton’s physics, these were just point particles with mass, charge, energy, momentum, angular momentum, position, time, etc. In quantum physics, particles have these and some additional properties like spin, color, etc. The macroscopic objects are supposed to be aggregations of these fundamental particles, but physical theories are unable to describe all their properties because they can only treat the macroscopic object as another particle and therefore its properties as the aggregate of the individual particle properties. Macroscopic objects, however, additionally have structure in them whereby the fundamental particles are distributed and arranged in space and time. There are many possible distributions of fundamental particles subject to the total conserved properties (such as mass, charge, energy, momentum, angular momentum, etc.) being constant. Which of these possible distributions is real, is underdetermined by the the properties of the whole, which creates new problems of indeterminism in science.

To solve these problems of indeterminism, science must add structure or distribution as a new category to its objective description, and this is currently done by assuming that a priori real particles have different locations in space-time. The problem with this approach is where do we obtain the total amount of information required to put each particle in the universe into a definite state? In the real world, we do not suppose that structure emerges automatically from individual particle states. Rather, that the structure exists logically as a design which is then used to create an object. To imagine design, we have to think of the whole object prior to the parts from which it is constructed. This whole exists as an idea, and not a material thing, which entails the reality of the ideas.

Science must now begin in wholes and parts must be derived from that whole, which stands the reductionist thinking on its head. A new approach to reduction must now be found. E.g., if the whole is logically more abstract while the parts are logically more contingent, then we can say that the abstract precedes the contingent, and the contingent reduces to the abstract. However, now we are dealing with a new approach to nature: nature comprises ideas which can be abstract and contingent, and the reduction involves contingent to abstract. This is equivalent to reducing the parts to the whole, but in a wholly new way.

A Linguistic Analogy

This approach has an intuitive counterpart in the expression of meanings whereby an idea is explicated through a structure—a sentence—but the meaning exists even when the sentence does not. The parts of a sentence—the words—can be described partially in terms of their sensual properties, quite like we might sense the shape and size of words and letters. However, the meanings of the words and the order in which they appear within the sentence cannot be explained simply by their shape and size. There is no particular reason why letters must appear in a particular order if the letter is only physical properties; the total physical properties would be conserved even if we redistributed the letters. Likewise, why some such distributions would be forbidden—because they are syntactically and semantically ill-formed—would be inexplicable in a physical theory.

A macroscopic object has many physical properties when the object is broken down into parts. However, the semantic properties of such macroscopic objects cannot be described using a physical view because the physical theory is unaware of the fact that physical objects become symbols of meanings within a collection. If we only study individual objects, the questions of meanings don’t arise, and the theory of nature appears deterministic. However, the theory becomes indeterministic for a collection of objects because physical properties underdetermine particle distributions.

The View from Indian Philosophy

Indian philosophy integrates concepts, observation, and reality in an unprecedented manner. The external reality in this view is also conceptual and not physical: it is produced by the refinement of meanings which reside in the mind. These meanings exist both as individual objects and collections. The idea signifying the collection constitutes a macroscopic object, while the idea signifying the individual particle is the atomic object. The properties of individual objects can be grasped by the senses, but the properties of the collection can only be grasped by the mind. In that sense, the individual objects can be studied by observation of the senses, but object collections need the mind.

The properties of the external world too have to be described in relation to an observer’s senses. This includes sensual perception such as smelling, tasting, seeing, touching, and hearing. If we describe the external world in relation to other objects, the description would be always incomplete. For instance, we can measure the mass, momentum and energy of material objects, which will incompletely specify the taste, smell or color of the object. This incompleteness is theoretical and experimental. That is, we cannot theoretically reduce color and smell to mass and momentum, and therefore our predictions based on mass and momentum will incompletely predict the color and smell. The only recourse is to treat the world objective as redness and sweetness, and then connect them to color and taste in the observer’s senses.

The Inverted Tree of Meanings

Nature, in Indian philosophy, is described as an inverted semantic tree in which the higher nodes are more abstract while the lower nodes are more contingent. We might say that the higher node is the property and the lower node is its value. In this case, color is the property and redness is its value, or taste is a property and bitterness is the value.

The measuring instruments (the senses) are more abstract in this view. From these instruments are created the measurable properties such as color, taste, smell, sound and touch. Each measuring instrument—e.g., the eye—supports many measurable properties such as form, color, size, distance, and direction. These properties are therefore the refinements of the concept of seeing—some information must be added to the idea of seeing to derive the notion of form, color, or size. Each of these properties itself can further be refined—and this refinement represents the values obtained in measurement. For instance, the property of color can be further refined into the values of red, green, and blue, the idea of form can be refined into square, circle, triangle, etc.

Since properties are produced from the refinement of senses, there are infinitely many possible properties. For instance, it is not necessary to divide vision into form and color; it is also possible to think of additional properties that combine and divide form and color in new ways. This means that the vision in every species will not work in the same way—i.e., color and form; it can also involve new properties that we cannot imagine at present. Likewise, the values of these properties would be experienced differently, these values and their properties could be denoted by different words. What appears as being meaningful to us may appear meaningless to someone who sees the world differently, and vice versa.

The Inversion in Thinking

Before we can describe the world, we must postulate a space of properties in which the material objects will be placed. This space is somewhat arbitrary as we have already discussed previously—we can use different properties to describe nature. However, all such spaces must eventually map to our modes of perception—seeing, hearing, tasting, touching and smelling—and therefore they must be refinements of our senses: one particular space of properties is one of the many possible ways in which our perception can be objectified in matter. Therefore, in Indian philosophy, these properties are indeed refinements of the senses. Furthermore, the values of the properties are further refinements of the properties themselves. The observer’s senses are thus logically prior to the material properties, and the properties are logically prior to the objects. These ideas are explored in further detail in my book Sāńkhya and Science.

If we treat the world as primary and the observer as secondary, then the description will always be incomplete: it will work to an extent, but since physical properties cannot completely exhaust the description of macroscopic objects, and our experiences are concerned with macroscopic objects, all theories of microscopic matter will fail when dealing with the macroscopic world. A famous illustration of this problem is Schrodinger’s Cat Paradox where we suppose that since the atomic world is uncertain, the cat must both be dead or alive objectively. Dead and alive are two different distributions of matter, but physical theories cannot distinguish between them because in both distributions total matter and energy is constant. If science only deals in physical reality—i.e., conserved properties—then two distributions are equivalent. To distinguish them in science, we must find a new property by which these can be distinguished. This property is meaning by which one distribution can be called dead and the other one alive.

The Science of the Macroscopic World

The problem of meaning therefore has deep connections to modern science when science is used to describe the macroscopic and not just the microscopic world. The novelty now is that the macroscopic precedes the microscopic. The reduction of micro to macro will always be incomplete, but the reduction of micro to macro can be done, provided both macro and micro are defined as ideas. Quite like complex ideas can be reduced to simple ideas, the macro is simple ideas while the micro is complex ideas. Nature begins in simple ideas and through a gradual process of amplification, complexity is created. A simple example of this process is that an artist draws an outline of the picture before s/he fills in the details. Atoms are the details, which follow the big picture of nature.

In science, sub-atomic particles are simple while consciousness is complex. In Indian philosophy, consciousness is the simplest and sub-atomic particles are the most complex. We can never construct consciousness starting from sub-atomic particles, but we can construct sub-atomic particles beginning from consciousness. In that sense, consciousness is the simplest idea, from which other complexities are created. There are many stages of this complexity creation, and science too must pass through those stages, each time postulating a simpler idea from which other complexities are created. This journey, if the view is correct, will culminate in the idea of a consciousness.