The scientific revolution and its child, the scientific method, are often misunderstood in popular treatments of the subject. In my opinion, a large part of this misunderstanding is due to the unstated assumption that there is One Right Way to reason about things, whether science or otherwise. This rigidity is usually unjustified but some schools of thought attempt to present a justification for it, usually couched in terms of the risks of going astray if our reasoning is not lashed to a single, universally accepted method of thinking. In any case, we reject these views as uninteresting for the purposes of this series. There is more than one way to do science correctly. Although the scientific revolution came at great cost and difficulty in Western society, rejection of the old superstitions and past, faulty methods of reasoning does not automatically imply that what superseded them is the One Right Way to do science.
The modern, empirical method has serious limitations. The single, greatest danger of these limitations is that some branches of science are deeply affected by them yet they do not understand their own limitations. Economics, social science and psychology are easy examples of sciences where the limitations of the empirical approach substantially impact the reliability of the reasoning utilized in those sciences, yet the limitations themselves are not well understood. Rather than positing an alternative Right Way to do science, let's build some tools for physical reasoning and add them to our toolbox for thinking. We'll use these tools later in the series.
The importance of physical experiment arises from the unreliability of physical intuitions. Aristotle famously thought that lighter objects fall to the ground more slowly than heavier objects since a feather or a piece of paper falls more slowly than a rock. This intuition is faulty because it neglects the effects of air resistance on an object. In a vacuum, a feather and a rock fall at the same velocity when released at the same time.
Even though our physical intuitions can be faulty at times, the fact of the matter is that physical science is founded on the five senses. If we cannot sense something directly, we build a "detector" that can sense it and transduce it to something that we can sense - sight, sound, etc. The senses of sight and sound are often used for "exact" detection but classification of some chemical substances relies on odor which, by comparison to sight and sound, is less exact. The point is that the detector itself is just an extension of the scientist, who is the measurer. It is always the measurer who measures the world and the instruments he or she uses are just aids to this end.
Detectors with visual readouts - and some detectors with audio notification - are susceptible to detailed analysis by the principles of information theory. We can imagine that our brain garners such and such "bits" of information every time we look at such a detector. We only speak this way about such detectors because we can quantify the amount of information that is available on the detector's readout. In reality, every detector stands in the same relation to the measurer - it is conveying some non-zero amount of information to the mind of the measurer. We will treat this topic in more depth in a later post.
Modern science tends to make a bright-line distinction between subjective and objective knowledge. In scientific literature, the former is sometimes referred to as "sense data" and the latter is usually referred to simply as "data". There are two criteria for a measurement to qualify as objective: (a) it must be repeatable and (b) it must be observer-independent. Note that (a) is actually implied within (b) whenever you are dealing with observations in which the state to be measured is destroyed or perturbed by the act of measuring it [1]. Other kinds of knowledge are presumed to be subjective, pertaining only to the individual.
The objective/subjective distinction is part of a larger philosophical classification of the kinds of knowing that goes back to Kant, and earlier. Knowledge is divided along two dimensions into four classes. The first dimension is analytic knowledge versus synthetic knowledge. Analytic knowledge has to do with knowledge of abstract things - words, ideas, thoughts, numbers, and so on, are all objects of analytic knowledge. Synthetic knowledge, on the other hand, has to do with knowledge of concrete things - dogs, rocks, cars, running, and so on, are all objects of synthetic knowledge. The second dimension is a priori knowledge versus a posteriori knowledge. A priori knowledge has to do with things that are true by reflection alone[2] (or false by reflection alone). A posteriori knowledge, however, has to do with knowledge that arises from interacting with the world. That rocks are solid, while water is fluid, or that the sky is blue are all examples of a posteriori knowledge.
Where things get interesting is when we look at the four categories of knowledge that arise from the combinations of these two dimensions of knowledge - (1) analytic a priori knowledge, (2) analytic a posteriori knowledge, (3) synthetic a priori knowledge and (4) synthetic a posteriori knowledge. A commonly held view is that only (1) and (4) are actual categories of knowing, whereas (2) and (3) are impossible or meaningless. The Austrian school of social science (Menger, Mises, et. al.) holds that synthetic a priori knowledge is possible - this is knowledge about the real world that is true by reflection alone. Such knowledge is possible, the Austrians argue, because of the shared reality of action (choice). In recent decades, there are some mathematicians who have argued for a new discipline in mathematics, called experimental mathematics. The idea is to adopt theorems of mathematics on an evidentiary basis, instead of relying on absolute proof - for example, assuming the unproven Riemann Hypothesis. This approach to mathematics would fall under category (2), analytic a posteriori. The existence of knowledge in categories (2) and (3) tends to blur the line between the objective and the subjective.
If we do not restrict ourselves to categories (1) and (4), our toolbox for physical reasoning gets much bigger. In my opinion, modern science is handicapped by its philosophical commitment to denying the possibility of knowledge in categories (2) and (3). To illustrate the point, let's look at a passage from Ernst Mach's 1915 book, The Science of Mechanics (p. 140), where he introduces a principle of physical reasoning that he calls the principle of continuity and which he particularly notes in Galileo's work.
In all his reasonings, Galileo followed, to the greatest advantage of science, a principle which might appropriately be called the principle of continuity. Once we have reached a theory that applies to a particular case, we proceed gradually to modify in thought the conditions of that case, as far as it is at all possible, and endeavor in so doing to adhere throughout as closely as we can to the conception originally reached. There is no method of procedure more surely calculated to lead to that comprehension of all natural phenomena which is the simplest and also attainable with the least expenditure of mentality and feeling.
A particular instance will show more clearly than any general remarks what we mean. Galileo considers (Fig. 93) a body which is falling down the inclined plane AB, and which, being placed with the velocity thus acquired on a second plane BC, for example, ascends this second plane. On all planes BC, BD, and so forth, it ascends to the horizontal plane that passes through A. But, just as it falls on BD with less acceleration than it does on BC, so similarly it will ascend on BD with less retardation than it will on BC. The nearer the planes BC, BD, BE, approach to the horizontal plane BH, the less will the retardation of the body on those planes be, and the longer and further will it move on them. On the horizontal plane BH the retardation vanishes entirely (that is, of course, neglecting friction and the resistance of the air), and the body will continue to move infinitely long and infinitely far with constant velocity. Thus advancing to the limiting case of the problem presented, Galileo discovers the so-called law of inertia, according to which a body not under the influence of forces, i.e. of special circumstances that change motion, will retain forever its velocity (and direction).
The importance of Galileo's reasoning - this principle of continuity - is that it spans the gap between observation (a posteriori) and pure reason (a priori). Both types of knowledge are required in order to infer the law of inertia in this way. While there are other approaches to constructing the law of inertia (Mach covers some of them, elsewhere) there is something deeply compelling about the reasoning used here. It is my view that this kind of physical reasoning, if used with care, can help us easily derive novel insights into the world without the baggage of more cautious, doubt-riddled approaches. In short, I am arguing that we should not dismiss this kind of reasoning as "mere intuition", even though its conclusion requires us to make a "leap of logic" that cannot be confirmed by physical experiment.
Next: Part 3, What is Information?
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1. If you read literature dealing with quantum phenomena, you can come away with the impression that observer-effects only apply to quantum systems but this is not true. Many psychological problems, for example, are plagued by observer effects - the act of observing someone changes their behavior. There are many other examples of non-quantum (classical) systems in which observation has a perturbing effect.
2. For example, suppose I show you two measuring sticks, one of length 1-meter and another of length 2-meters. Then, I ask you to close your eyes and tell you, "I have another measuring stick of length greater than 1 meter and less than 2 meters. After I arrange the three measuring sticks in order of their lengths from least to greatest, where will the new measuring stick be, relative to the others?" Based on the ordering of the numbers, you know that the new measuring stick will be between the other two measuring sticks, and you know this even before you open your eyes to look. You know it a priori.
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