The Problem of Measurement in Science – Ashish Dalela

It is commonly assumed that science describes objective facts about the world, which are discovered through measurements of physical properties. The problems in this measurement are generally not understood, and this post describes them, highlighting two key issues of circularity and recursion in the definition of measurement. How these problems are addressed in Indian philosophy is also discussed.

The Scientific Definition of Measurement

Physical theories assume that material objects comprise physical properties, which can be measured using measuring instruments. The result of this measurement is expressed as a numerical value: for instance mass can be expressed as 5 kilograms.

There are, however, some important issues in the definition of the measuring instrument. For instance: How do we measure the measuring instrument to know what its physical properties are? The definition of a measuring instrument is fraught with difficulties because to arrive at this definition we must find a second measuring instrument which measures the first instrument, which then measures the object under measurement. Thus, to define a measuring instrument, we must first measure the measuring instrument, and this quickly leads to an infinite regress in the act of measurement.

Scientists avoid this infinite regress by arbitrarily choosing some material objects as the standards of measurement. For instance, we might choose a pound or a kilogram as the standard of measurement, against which all other measurements of mass would be performed. This frees us from the problem of trying to define the numerical value of a property, but it does not free us from the definition of the property itself.

The Problem in Defining Properties

How do we define physical properties, such as mass? For mass to be an empirical property, it must be defined in relation to a measurement procedure, which in turn requires us to define a standard of measurement, which only represents a numerical value of the property, although not a definition of the property itself.

Science solves this problem by postulating an effect for each property. For example, the property of mass has a gravitational effect by which the mass attracts other masses. For such an effect to be useful in measurement, a law of nature that governs the attraction of masses under gravitational effect must also be defined. For instance, Newton formulated the Law of Gravitation to predict the gravitational attraction of masses.

The law requires a value of the mass to be plugged into the equation of the law to compute the gravitational effect. However, the mass is only measured under the gravitational effect; e.g., the mass on Earth is measured due to the gravitational effect of Earth.

Therefore, mass depends on gravity, and gravity depends on mass. The property of mass is meaningless unless defined in relation to gravity, but gravity is undefined unless mass has been defined. Both mass and gravity are therefore defined circularly.

Recursion and Circularity

All physical measurements in modern science suffer from the two problems of recursion and circularity. The problem of recursion arises because the measuring instrument is also a material object whose properties in turn require more measuring instruments, creating infinite recursion. The problem of circularity arises because a physical property is undefined unless there are some effects, the effects cannot be defined unless the natural law governing the properties is defined, that law cannot work until properties are defined, thereby creating a circular dependence between a property and a law.

The circular dependence means that you can postulate innumerable physical properties, identify arbitrary measuring instruments to supposedly represent these properties, then postulate laws that incorporate these properties, and try to predict. In this prediction, the property, law, and the measuring instruments are arbitrary; only the prediction is real. However, if the law works, we begin to attribute reality to the properties, laws and instruments, although they were arbitrary choices to begin with.

The goal of science, Einstein once said, is to explain the maximum number of facts with the minimum number of assumptions. Since the maximum and minimum are not accurately defined, science is an on-going process of broadening the facts and narrowing the assumptions. However, the limits of this expansion and convergence are not the key problem we are concerned with here. We are concerned with the problem of using recursive and circular reasoning―assuming what you aim to prove.

Dimensions and Locations

While performing a measurement, the measured property (e.g., mass) is necessarily more abstract than the values detected during measurement. The properties being measured are the dimensions of a space while the measured values are the locations on those dimensions. A dimension (such as mass) must be defined before that property is measured in a particular object, and this dimension is of a different type than the values measured on that dimension. Specifically, we cannot define the dimension of mass in terms of the objects which possess mass because the objects are locations on that dimension. To suppose that mass is a real property of matter, there must be a space which contains all the objects, and which has a dimension called mass.

As we add new properties into matter―e.g., charge―additional dimensions must be added into this space. As new properties are formulated, the dimensions of the space also grow. The space of physical properties and its dimensions, however, are conceptual rather than physical. That is, we cannot measure the ideas of mass or charge, although we can measure the values of mass and charge. No scientist can point to a space in the real world whose dimensions are mass and charge because we are just familiar with a three dimensional space, the dimensions of which are not mass and charge.

Given this problem, science reduces the dimensions of a property space to their effects via laws, and reduces these effects to the values being measured. Effectively, through such a reduction, the dimensions of a property space are reduced to locations in that space. What started out as a concept―e.g., mass or charge―now becomes a physical object. Such a reduction, however, leads to the problems of recursion and circularity, as already shown above. To save ourselves from this problem, we must recognize that mass and charge are not physical properties, but concepts. The material objects are being located not in a physical world, but in a conceptual space of properties.

There is a space of three dimensions that we can perceive with our senses, but there is also a space of properties which we cannot perceive, but which must exist beyond this visible space. Such a space is certainly postulated in science when properties are postulated, but to maintain a materialistic flavor, these properties are reduced to objects.

Perception in Indian Philosophy

Indian philosophy describes that there are several “spaces” deeper than the space of objects perceived through the senses. If an apple has the value of redness, then there must be a deeper property of color which cannot be seen, but which must exist before we can speak about redness. Similarly, color is itself not a fundamental property; rather this property is embedded in a deeper space called seeing or sight together with other properties such as form, size, direction, etc. The property of sight too is not fundamental, and it must be embedded in a deeper space of meanings, which are expressed through various sensations. Meanings are embedded in a space of truths, which are embedded in a space of intentions, which are embedded in a space of morals. Ultimately, all this is embedded in a space of consciousness, which sees itself.

We cannot see, taste, touch, smell or hear all these deeper levels of properties, but they must exist if the process of measurement has to be free of the problems of circularity and recursion. Only when an object can measure itself does the value and dimension become identical. The conscious observer is such an object. Its ability to perceive is the dimension, and the result detected during the observation is the value. The logical distinction between dimension and value collapses when something measures itself.

Since material objects cannot measure themselves, the distinction between dimension and value must be maintained in the study of such objects. That distinction in turn leads to deeper and deeper spaces of properties in which the previous property becomes a value. Only when something perceives itself, is the property-value distinction collapsed.

The Necessity of Consciousness

Consciousness is an empirical necessity for science because without observation scientific laws and theories cannot be verified. However, consciousness is also a theoretical necessity for science because the space of physical properties has to be embedded in a deeper space all the way to a space that is its own object.

By neglecting the space of physical properties―and reducing them to objects―science not only creates conceptual difficulties, but also hides several layers of material properties from our vision. Such a science not only has no foundation, but it is also a very limited perspective on the world around us, because while we seem to understand the things that exist, we don’t seem to understand the manner in which we understand.

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