A better place for philosophy

A while back I started a new blog called "I Wish to Blog Deliberately" (corny name but accurate in its account). With this new blog I intended to write on philosophical topics and keep more practical discussions focused at MQRL. Aside from being just a collection of philosophical discussions, its creation was important because I was concerned that MQRL might become diluted with esoteric discussions if I were I to maintain only one blog.

However, since that time I've rarely contributed to IW2BD; but my temperament lately has been philosophical and I need an outlet for it. As a result, I'm beginning to post again to IW2BD. I've also been motivated by the observation that my writing is much better now such that I may write coherently on topics such as teleology and ethics. This has arisen in no small part because my writing and thinking has improved as I explored ideas at MQRL.

So, if you're interested in what I have to say, pay IW2BD a visit. I plan on making no changes to MQRL and will continue its theme of the practicalities and execution of science from an academic standpoint.

And if you're really, really interested, e-mail me sometime at kyle.m.douglass@gmail.com. I'd love to hear from you.

Are there better indicators for causality than correlations?

In a recent post concerning the use of analytics to do science, I hypothesized that the notion of cause-and-effect is an ill-suited tool for describing the effects of input parameters on complex systems. In other words, cause-and-effect are ideas associated with models and many complex systems do not readily admit description by models. Now, to give fair warning, I have had no formal training in complexity or dynamical systems analysis, so most of what I write on these topics is an exploration of the relevant concepts to further my understanding--a sort of self-teaching, if you will.

I was therefore pleased to read the current thesis by Mark Buchanan in Nature Physics about work from dynamical systems theory concerning ways of determining causation in a complex system. He references an article from this year's Science journal (Science 338, 469-500; 2012) that contains an example of a model for the interaction of two species. The model consists of two equations for the population of each species that contains coupling parameters linking the two populations. Despite the fact that the population of each species affects the other, the populations are uncorrelated in the long run because the model goes through times of correlation, anti-correlation, and no correlation.

This is an example of the maxim "causation does not imply correlation." (Of course, many of us with scientific training have been chided endlessly about the maxim's well-known converse.) On the face of it, this example seems to support my idea about causation.

However, the main focus of Buchanan's article is about finding descriptors for causation beyond correlations. As he states:

Correlation alone isn't informative, nor is the lack of it. Might there be more subtle patterns, beyond correlations, that do really signify causal influence?

He mentions two major works, one old and one new, that address this question. The old one, introduced by Clive Granger in 1969, states that two variables are causally-linked if including one in a predictive scheme improves prediction of the other. The new work addresses problems with this idea and is somewhat technical, but it is capable of solving the problem of two populations mentioned above and one outstanding problem in ecology concerning the population of two species of fish.

I think now that my earlier conclusion about causality was wrong. I thought that a correlation needed to exist for there to be a causal link between two system parameters. Though I was paying heed to "correlation does not imply causation," I was ignorant of its converse, "causation does not imply correlation." Thus, causation can be an important concept for complex systems; we may only have to find better indicators than correlations.

Data-centric science - Correlation and causation

Yesterday I defined a model as a description that involves a cause-and-effect relationship between phenomena. In contrast, a data-centric approach to science looks only for correlations between data sets to answer scientific problems. This approach relies on very large data sets to come to accurate conclusions.

After thinking about yesterday's post I realized that there is a relationship in my arguments to the common admonishment "correlation does not imply causation." This fallacy is most often made when complex systems made of many interconnected parts are involved, such as in human health. Statements like "taking vitamin C tablets will cause me to not get sick" and "eating vegetables prevents me from getting cancer" are statements about cause-and-effect. As we have been taught again and again, though, taking vitamin C tablets may only decrease the chances that I get sick.

So here is the dichotomy that I was looking for: model-based science is useful in simple systems for which I may make cause-and-effect statements. Data-centric science is more useful for complex, coupled systems for which causality is a poor descriptor.

This is certainly a new way of thinking. Depending on the complexity of what we are observing, we should either employ or abandon causality as a means of interpretation.

Data-centric science - What is a model?

Chris Anderson's The End of Theory: The Data Deluge Makes the Scientific Method Obsolete suggests that models may no longer be necessary to solving scientific problems due to the large amount of data now contained in databases across the globe. Rather, looking for correlations between events may be enough to solve these problems.

I'm going to assume that the article's title is an overstatement; not all scientific problems may be solved with a data-centric approach. Some are very well suited to this method, however. To discern between these types of problems, I think it's necessary to first address the question "what is a model?" After this is answered, I hope to address why models may sometimes be circumvented.

Wikipedia's site on the disambiguation of the word model is quite long. It can mean many things within a scientific context. However, several words continuously appear on this page and its links: description, simulation, representation, framework. More informative (albeit complicated) is the explanation found at the Stanford Encyclopedia of Philosophy. The central question to this post is addressed on this site in Section 2: Ontology. A model may be a physical or fictional object, a description, an equation, or a number of other things.

Based on this information I think it's reasonable to state that a model is an attempt at replicating the behavior of some phenomenon, whether physically or as a result of an application of logical rules. I think further that a model establishes cause-and-effect relationships to do this. For example, Newton's theory of gravity contained the idea that something (gravity) caused the apple to fall. As another example, energy input from the ocean causes (among other things) hurricanes in weather models.

Models satisfy some human desire for causality. I read once (though I don't remember where) that people use reasoning as a coping mechanism for emotionally difficult situations, such as when a loved one dies. Somehow, finding a reason or a cause for things provides us some degree of comfort.

The data-centric approach to scientific problem solving obviates the establishment of a cause-and-effect relationship. Insurance companies don't need to know why married, twenty-something men get in fewer car wrecks than their single companions in order to charge them less. Instead, they only need to know whether this is true.

But other than to make ourselves feel good, why would we need to find a cause-and-effect relationship in the first place? I think that this could be because the ability to make correct predictions is an important part of any model. We make predictions when we're unable to carry out an experiment easily or when we don't have enough data already to answer a question. It is my suspicion that cause-and-effect relationships are central to a model's ability of prediction, though I'm not sure how right now.

So, in summary, a model is a physical or mental construct meant to replicate the behavior of some phenomenon or system. I believe that the main difference between a model-based approach to science and a data-centric approach is that a model-based approach creates a causal chain of events that describe an observation. I don't necessarily see this chain ever ending. Once we determine a cause, we might wonder what caused the cause. And what caused the cause that caused the cause? At some point, data-centric science responds with "Enough! Just give me plenty of data and I will tell you if two events are correlated." That's all we can really hope for, anyway.

Notes: The never-ending chain of causes sounds very familiar to Pirsig's never-ending chain of hypotheses in Zen and the Art of Motorcycle Maintenance. Is there a connection?

Also, I remember E. T. Jaynes arguing in Probability Theory: The Logic of Science that we can't really know an event will occur with 100% probability. This seems to suggest that cause-and-effect relationships do not really exist. Otherwise, we would always know the outcome of some cause. And if they don't really exist but are actually good approximations, then models really are what we've been told since middle-school science: imperfect and intrinsically human attempts at describing the world.

Note, October 25, 2012: I wrote this post late last night after having had a beer with dinner, so my mind wasn't as clear as when I normally write these posts. I realized this morning that the reason for building cause-and-effect relationships is that we can control a phenomenon if we know its proper cause. Many things are correlated, but a fewer number of things is linked by a causal relationship. Therefore, accurate models provide us the ability to control the outcome of an experiment, not just predict it. I don't believe that correlative analytics necessarily allow us to do this.

Being rational with science

There's a cool talk posted at the blog Measure of Doubt that was given recently by one of the blog's authors, Julia Galef. The talk concerns the idea of a straw Vulcan, an idealized character based on Star Trek's race of ultra-logical humanoids. Galef argues that the Vulcans base their actions and decisions on a logic that's popularly perceived as rational, when it is in fact not. This is because she defines rationality in one of two related ways: 1) a method for obtaining an accurate view of reality, and 2) a method of achieving one's goals. To make her argument, she presents five beliefs about Vulcan behavior that are commonly held to be rational and then gives examples from both Star Trek and real life where this behavior has violated her definition of rationality.

I particularly like the second and third items on her list—never making a decision on incomplete information and never relying on intuition—because I find that these are common mistakes that scientists make. For example, suppose some graduate student wishes to setup an experiment that he or she is unsure will work. The student may take one of two courses of action (really there are three, the third being a combination of the first two). The first is to try the experiment and see if the outcome is desirable. The second is to carry out a number of calculations to determine if the desired outcome will be produced, and then perform the experiment. The fallacy occurs when the student attempts to plan too much and wastes time on arduous calculations when the experiment may have consumed less time. This is a case of failing to act simply because he or she did not possess the complete knowledge of whether the experiment would work in the first place.

The example above is irrational by Galef's definition because, in all likelihood, the graduate student would have liked to have obtained a yes-or-no answer to the question "does the experiment work?" in as little time as possible, and sometimes this means running the experiment before fully understanding what the outcome would be. Of course, it takes intuition to determine when it's time to put down the pen and paper and do the actual lab work, and that's why it's rational to rely on intuition.

In a sense, these arguments depend strongly on Galef's definition of rationality, but I see no reason why this isn't a good definition to work with.

Philosophy isn't useful for science? Don't be crass.

Richard Feynman once quipped, "Philosophy of science is about as useful to scientists as ornithology is to birds." Dr. Feynman is one of my scientific heroes, but this quote often tempers my admiration for the man. I respect him because he appreciated what was good in many different things, from the simple aesthetics of a flower to the intricate mathematics underlying quantum mechanics. He was not one to dismiss ideas simply because they were "artsy" or not of pure science. This is why I often puzzle over how he could have made such a statement concerning philosophy.

Without philosophy, I would not be the same scientist that I am, and I would venture that I would not be as good of one, either. Philosophy is the art of critical analysis; the philosophy of science examines the methods and logic that form the foundation of our field. The result of this investigation exposes the mental machinery that powers our work. But this knowledge has also produced a number of practical applications throughout history. The following are two examples.

E. T. Jaynes and R. T. Cox, among others, re-examined the long-held rules of inference. A simple redefinition of probability led to an explosion of techniques for drawing conclusions where information was limited, from signal processing to economics. This is the well known Bayesian revolution. As another example, Henri Poincaré established a daily routine that complemented his work as a scientist. He postulated that the subconscious was at the focal point of discovery, and so he took steps to nurse its well-being. A modern day analog to this is the development of programming philosophies that are intended to increase a software engineer's productivity by tailoring work methods to the structure of the mind.

My justification of philosophy to science was to make a point, but I don't think it was necessary. It is unfortunate that we must always find utility in our work. As I've stated before, science is ultimately a creative process that is powered by our primal nature and instincts. To remove its basis from the romantic mindset and place it solely in the context of practicality is a fallacy. I do science and philosophy because I like to, and no better justification is required than that.

A diverse basis for science

The sum of our experiences, environment, and genetic predispositions form the basis for how we view and interpret the world. This is a principle of many philosophies and helps to explain the broad diversity in human behavior.

The practical view of science is of a rigid structure built upon basic assumptions and prior knowledge. After the proper application of "the scientific method," this foundation leads us to new discoveries. Roughly speaking, the method goes as such: we start from our current state of knowledge, make a hypothesis followed by observations, formulate a proper model that accommodates the data, then draw our conclusions while taking into account the prior information. This outline must follow the rules of logic and not contradict what we already know to be true (and if it does, we place this contradiction under extreme scrutiny until the contradiction is resolved).

This generalization of the scientific method is confounded by the inherent variability in the assumptions from which it starts. In reality, every one possesses a different set of beliefs regarding scientific inquiry. This is exactly analogous to the variety of metaphysical beliefs held by people across the globe. And, just as this variety gives rise to the diversity of people, it leads scientists to different interpretations of theirs and others' work.

Rather than enforce a common basis for the pursuit of science, scientists ought to respect the basic diversity within their own field. Science is more than rote application of a formula; it engages the scientist to the point that discovery becomes an act of self-expression. A study is flavored with the thoughts and feelings of the people involved and can not be separated from them. Once this is understood, we can see that science is a very human endeavor and not the cold, calculated formula known as the scientific method.

When is a conclusion good enough?

I've been doing a lot of reading recently on modern probability theory, Bayesian analysis, and information theory. One of the central tenets of these theories is that any proposition has associated with it a degree of plausibility, i.e. a probability of being true, that reflects the amount of information available. The proposition, "the sky is blue" is extremely plausible since it is based off of daily self-observations and confirmed by others. As another example, I judge the proposition, "thirty million Americans have blue eyes" as plausible based on the knowledge of the current population of the United States and my own observations on the frequency of encountering blue-eyed people. However, this is not as likely to be true as the first statement.

A conclusion in a scientific paper is nothing more than a proposition and thus possesses its own degree of plausibility. The information available to the reader for determining the plausibility of the conclusion is the data presented in the paper and all previously published work on the same topic. Of course, other factors weigh in, such as prejudices for particular theories and affinities or dislikes for the authors on the paper. Temporarily placing these other factors aside, I wonder, "when does a conclusion possess a large enough degree of plausibility to be considered true?"

Of course, a definite answer doesn't exist. No scientific proposition can be true with 100% certainty and it is silly to think that we can even assign a threshold probability for evaluating a scientific paper's correctness. Just imagine a paper successfully passing through the peer-review process so long as it is evaluated to be 78.63% or more true by its reviewers. But the question remains relevant. Science is a culture and every culture has criteria by which it evaluates claims.

In a closely-related post I wrote about the fallacies that workers commit while evaluating other work. But I find it much more difficult to identify the criteria for establishing the truthfulness and quality* of research. Unfortunately, I don't think I'll be able to fulfill my full potential as a scientist until I am capable of doing so.

Note: The problem of defining quality has been approached at great length by American author Robert Pirsig in his popular novel "Zen and the Art of Motorcycle Maintenance." One of his primary arguments is that Quality is actually an undefined construct present at the seminal moment when an observation is made and processed by the brain. People may know if something possesses Quality, but it is inherently undefinable.

The great physicist Subrahmanyan Chandrasekhar gave a famous lecture at the International Symposium in Honor of Robert R. Wilson in April, 1979 entitled "Beauty and the Quest for Beauty in Science." In the second paragraph of the lecture, he quotes Poincaré:

The Scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it; and he takes pleasure in it because it is beautiful. If nature were not beautiful, it would not be worth knowing and life would not be worth living.... I mean the intimate beauty which comes from the harmonious order of its parts and which a pure intelligence can grasp....

It is because simplicity and vastness are both beautiful that we seek by preference simple facts and vast facts; that we take delight, now in following the giant courses of the stars, now in scrutinizing with a microscope that prodigious smallness which is also a vastness, and, now in seeking in geological ages the traces of the past that attracts us because of its remoteness.

Good science is not forced and does not evolve from long hours in the lab and a work-centric lifestyle alone, though I admit that these are necessary to maintain a healthy scientific career. Rather, science is intimately related to one of the most basic of human traits: the impassioned drive to create order out of chaos.

And this is why, despite my affection for Poincaré, I disagree with part of the above quote. Beauty does not exist within Nature because its parts are inherently balanced and "harmonious." Beauty exists as a result of the mind imparting its own structure to random titillations of the senses. Men and women do not render Nature meaningful through physical exertion alone. The reduction of Nature to coherent understanding is the realm of Science.

Notes on Bayesian Analysis

This afternoon I encountered one of those rare moments when I had little to do since I was waiting on input from a number of collaborators, so I read through half of this site on intuitively understanding Bayes' Theorem. Here are some things that I learned or that were made clearer than my previous understanding:

1. The outcome of Bayesian analysis is a modification of the prior (the probability of an event that is known before the analysis) which produces the posterior (the probability of an event given certain conditions and dependent upon the prior).
2. Bayesian analysis requires three pieces of information: the prior and two conditional probabilities (a true positive and a false positive outcome).
3. If the two conditional probabilities are equal, the prior is unmodified and equals the posterior. This is because the result of the test is uncorrelated with the outcome.
4. The degree to which the prior is modified can be described by the concept of differential pressure, i.e. the relative difference between the two conditional probabilities. The process of changing the prior due to differential pressure is known as selective attrition.
5. People use spatial intuition to grasp numbers. Teachers can use this and the idea of natural frequencies to their advantage to teach difficult concepts.
6. Related to number 5, the way in which given information is presented in a word problem (e.g. percentages vs. ratios) will affect the percentage of correct scores.

Is Bayesian analysis related to Kant's a priori and a posteriori knowledge?

Poincaré's Take on Theories

I've always been interested in the ideas of mathematician and philosopher Henri Poincaré. While I have not read any of his philosophical work, his ideas as summarized by others have always resonated with me. Here's an excerpt from the Internet Encyclopedia of Philosophy on Poincaré's thoughts concerning the relationship between observations and theories (italics denote my emphasis).

According to Poincaré, although scientific theories originate from experience, they are neither verifiable nor falsifiable by means of the experience alone. For example, look at the problem of finding a mathematical law that describes a given series of observations. In this case, representative points are plotted in a graph, and then a simple curve is interpolated. The curve chosen will depend both on the experience which determines the representative points and on the desired smoothness of the curve even though the smoother the curve the more that some points will miss the curve. Therefore, the interpolated curve — and thus the tentative law — is not a direct generalization of the experience, for it ‘corrects’ the experience. The discrepancy between observed and calculated values is thus not regarded as a falsification of the law, but as a correction that the law imposes on our observations. In this sense, there is always a necessary difference between facts and theories, and therefore a scientific theory is not directly falsifiable by the experience.

Poincaré did not likely consider systematic errors in the reason for why observations did not match a theory, so it is interesting that a theory that does not match the experimental data precisely is not necessarily wrong.

How does the uncertainty principle tie into this argument?

Absolutes vs. relatives

Though my advisor has stressed this for the entirety of my grad school career, I today finally appreciated the significance of relative measurements over absolute ones.

An absolute measurement is one in which a value is extracted from a data set that is physically important in a particular model. A relative measurement, on the other hand, is one that extracts the effect of varying a parameter amongst two or more data sets.

Model specific parameters are obtained from absolute measurements. Curve fitting is usually performed to find the values of parameters. Alternatively, relative measurements establish relationships between two variables. For example, the reading on a scale will increase proportionally with the mass added on top of it. From this observation, one can infer that weight is linear with mass. A constant, namely the acceleration of a particle due to gravity at the earth's surface, is needed to obtain the absolute value of the weight from a single measurement.

The practical problem with absolute measurements is that they require certain standards to have any significance. At the start of graduate school, I would often puzzle over why a parameter from a curve fitting routine would so often differ from theory. I would often vary different parameters in my calculation and struggle in vain to determine which independent quantity I had measured "wrongly." However, I failed to realize that each measurement was against some standard. A time is measured relative to an internal clock in a circuit; a length is measured relative to a ruler; mass is measured relative to a scale which was calibrated relative to some mass standard.

From the above it seems that the nature of measurement itself is a relative process, and as such a measurement can not be "wrong." If standards differ between two measurements, the measured variable will differ as well. And no one can say which measurement produced the "correct" value. Both conclusions are correct so long as they are logically consistent with how they are derived from the measurement.

I am aware of the definitions of the second and other fundamental quantities, but the definitions are simply agreed to based upon the precision of the measurement that produced the standard. They are arbitrary.

If I have to assert anything from this, it is that I value relative measurements above absolute measurements in scientific papers. Relative measurements reveal physical truths where as absolute ones tell us how well data fit into some theory.

I hope to write more on this in the future once my thoughts have more fully materialized.

A physical standard for time

I've now completed Chapter 2 of Cook's "The Observational Foundations of Physics," my current lunchtime reading. In this chapter, Cook describes a thought experiment in which a beam of caesium atoms is polarized by a strong magnetic field, then enters a region where a strong RF field is applied. Following the RF region, the beam passes through another magnetic field such that atoms whose magnetic dipole moments are not flipped by the RF field are deflected into a beam block. Those atoms that do undergo an electronic transition that is accompanied by a flip of the magnetic dipole moment reach a detector that reports the intensity of the beam. A feedback mechanism adjusts the frequency of the RF field so that the beam intensity at the detector is maximized; in this way, a quantum standard of time is established through the frequency of the RF field that maximizes the atomic beam intensity (you may note the similarity to the Stern-Gerlach appartus).

Cook then proceeds to argue for his thesis, namely that the experiments and observations that are available to us dictate the form of our physical theories. He starts first with the theory. The time-evolution of the caesium atoms is described by the Schroedinger equation. This equation contains a first order time derivative which is a consequence of the wavefunction containing all information about the system at any one point in time. If only one initial condition is required to establish the wavefunction, then it must be first order in time (this is in contrast to the wave equation which is second order in time and whose solution requires an initial condition on the wavefunction and its derivative).

Cook next mathematically defines the operations of the experiment described above, postulating that the two magnetic states of the atoms are described by stationary states of a wavefunction. Using only mathematical arguments derived from the nature of the experiment, he obtains the form of the equations governing the time evolution of the system; the wavefunction is affected by a first order time derivative. This suggests that how we perform experiments determines the form of our theories. The time standard need not be quantum in nature as he repeats the argument for a classical, mechanical oscillator. Again he stresses that once the time standard is set, it is meaningless to ask whether or not its period remains invariant with time, since the standard defines time itself. It is recognized that differences between the same apparatus for establishing the standard exist when the apparatus are spatially separated due to the geometry of spacetime.

These are some of the thoughts I had while reading this chapter:

1. Many times physical theories are developed first and then experiments follow that verify their predictions. Does this fact weaken Cook's argument that experiments shape our theories? If the purpose of theory is to predict experimental outcomes, then why argue for the reverse? Which came first, the chicken or the egg?
2. Cook was careful to explain that his arguments are based on a physical world that is independent of a subjective observer. Still, I wonder how the human perception of time can be reconciled with these arguments. As stated earlier, it makes no sense to ask whether or not the time standard is invariant within the context of observation and theory. But a human can perceive large changes in the period of a slow mechanical oscillator. What is it that acts as an internal time standard for a subjective observer and can it be related to the physical standard?
3. Cook only obtains the form of the equations of motion for the systems he describes. On the other hand, the theories give meaning to his unspecified parameters, such as energy and the unit of electronic charge. What determines how these mental concepts are developed? Energy is a relatively easy concept to understand. Was this why the fathers of thermodynamics used it as a core concept in physics as opposed to some other mental construct?

Notes from "The Observational Foundations of Physics"

Section 1.3, Measurements and Standards, is a continuation of the setup for the arguments for Cook's thesis on how measurement affects the logical structure of physics. First, Cook states that the equations of physics are simply relationships between physical states or quantities. These relationships are congruent to the relationships between observations. I am a bit unclear as to what congruent means here, but aside from that the setup so far seems fairly obvious.

He continues onto a more lengthy discussion of the role that standards play in measurement. Every measurement consists of comparing some quantity to a standard quantity. When measuring the length of an object, for example, one simply compares the object's length to the length of a ruler (the standard). Our system of standards plays a significant role in shaping the nature of physical theories.

What was very surprising is that, traditionally, standards for all physical measurements can be derived from four independent standards: length, mass, time, and current. These standards have since been replaced by other physical constants and quantities, but the number of independent standards has remained the same. For example, length is measured as a ratio between the speed of light in free space to a unit of time, which is derived from a standard of frequency from a certain atomic process.

The standard of voltage comes from the standard of frequency and the Josephson effect with help from another fundamental constant, the ratio of Planck's constant to the unit of electronic charge. Mass currently (as of the book's publishing) escapes a relation to the standard of frequency, but it's conceivable that it could be related to energy, voltage, and current through the quantum Hall effect.

The shift from mechanical standards to electronic and quantum standards has greatly increased the precision with which we can measure physical quantities. It has also changed the nature of our physical theories, Cook claims.

Lunchtime reading: The Observational Foundations of Physics

I have started reading "The Observational Foundations of Physics" by Sir Allan Cook during my lunch breaks. The book's purpose, as Cook states in the first sentence of Section 1.1, "is to attempt to unravel some ways in which the practice of physics determines the form and content of physics and physical theory." In other words, Cook wishes to understand how the practices found in physics affect physical theories and the practices themselves. It is as if there existed a feedback loop such that performing experiments changed not simply the theory used to describe a phenomenon but the nature of theory itself.

Further in Section 1.1, he poses these questions that are central to his analysis:

1. "Why should physics be so effective, and what does that tell us about the world of physics and our ways of gaining knowledge of it?"
2. "Is there a real world that exists independently of whether I or anyone else is looking at it, or are all the ideas I have about a world external to me just the construction of my mind?"

He defers a thorough answer to the second question until the end of the book, but does offer that he believes that most physicists, while working at the bench or on a computer, act as if an external world existed independent of their attention.

Section 1.2 deals with observations and sets many of the premises of his arguments. Observation and experiment are decided to be equivalent. Observations also consist of two aspects: objective and subjective. Of the subjective aspect, only the communal nature of observation is of consequence to his arguments. Science is a social construct and scientists hold great influence over each other such that the act of observation is never truly independent of people other than the experimenter.

Cook goes to some length to explain that physics is empirical, "with observation primary and theory secondary," but he concedes that rarely can observation be performed without some theory underlying the act of observing. He gives the example of reading a voltage from a digital multimeter. The direct observation is of figures on a LCD readout, a consequence of numerous electronic circuits that respond to potential differences between two probes and relates to the potential energy difference of electrons between two points in a circuit. Of course, electrons are theoretical constructs. The theories underlying an observation can in some ways assure an experimenter that the results are telling us something of the real world and not subject to some extraneous errors or misinterpretations. For simplicity, an observation is defined as the operations that lead to a measurement and result in  "raw data." The data is considered "raw" regardless of the complexity of the measurement.

Finally, theories are models of observations, not a model of the real world itself. "I take a theory to be a mathematical realisation of an abstract system that has properties corresponding to those of a set of observations... It is in that sense that I take a theory to be a model of the world of observations, with the implication that there is a more fundamental correspondence than just giving the right answers..." Theory is an abstraction of the real world, not vice versa.

Consistency vs. Accuracy

Here's an interesting footnote from Chap. 3 of Goodman's Introduction to Fourier Optics:

"The fact that one theory is consistent and the other is not does not necessarily mean that the former is more accurate than the latter."

The footnote is in reference to the Kirchhoff diffraction integral which was derived under two inconsistent assumptions for the boundary conditions on the field. Despite these inconsistencies, the theory gives a very good prediction for the diffracted field far from a large aperture.

Kirchhoff's theory is also a good demonstration of the fact that mathematical consistency and exactness does not mean that a theory makes good predictions or can be used to calculate physical quantities. Experimentation must validate a theory's ability to do so.

Kauai

I'm back from my trip to Hawaii (specifically, Kauai). It  was an amazing trip, the first half of which consisted of a hike along the Kalalau Trail to the Na Pali Coast. Before I set out, I established a rule for myself such that I would allow my brain to wander and think on any topic freely and without effort; in this way I hoped to allow my thoughts to constantly cycle in both my conscious and unconscious and eventually settle into some logical structure. Immediately prior to the hike I had been focusing entirely upon my candidacy exam for the better part of two months and had been having difficulties in processing any new information. Vacations are a great time to let things settle in one's brain and make room for more knowledge.

So why talk about any of this? I did at least come to one philosophical realization that I think is worth mentioning. I have for a long time felt that the feeling of complete and total relaxation that accompanies camping after a long day of backpacking is made possible by the extreme effort that a backpacker puts into a hike. In other words, to truly relax one must really work hard. On this particular hike, I realized that there is a reciprocal relationship here: to do quality work, one must really relax. Like I said above, if one's thoughts aren't allowed to settle, then one can't really make the best of his or her time spent working.

On science and faith

Here is an interesting article from Talking Philosophy Magazine. The author discusses the similarity and difference between religions faith and scientific faith. I believe it is often taken for granted that much of what we know about the natural world does not exist in the strict sense; all that we truly know is the outcome of an experiment. Theoretical models, such as the concept of protons and electrons or the theory of gravity, create entities or concepts that don't actually exist in the same way that a ball or dog exists. They are simply mental constructs that are used to explain repeated experimental outcomes and predict future behavior.

Of course, one can always argue that these constructs are "true" in the sense that they are predictive and can be tested as opposed to religious concepts. But I'm not so certain that their predictive powers and testability prove that they exist. "Truth" and "existence" seem to be two separate ideas here. So, in some sense, all of us, whether religious or not, believe in things that don't exist.