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Posts Tagged ‘Philosophy of science’

Not all philosophy is useless.

Friday, December 5th, 2014

In this, the epilogue to my philosophic musing, I locate my view of the scientific method within the landscape of various philosophical traditions and also tie it into my current interest of project management. As strange as it may seem, this triumvirate of the scientific method, philosophy and management meet in the philosophic tradition known as pragmatism and in the work of W. Edwards Deming (1900 – 1993), a scientist and management guru who was strongly influenced by the pragmatic philosopher C.I. Lewis (1883 – 1964), who in turn strongly influenced business practices. And I do mean strongly in both cases. The thesis of this essay is that Lewis, the pragmatic philosopher, has had influence in two directions: in business practice and in the philosophy of science. Surprisingly, my views on the scientific method are very much in this pragmatic tradition and not crackpot.

The pragmatic movement was started by Charles S. Peirce (1839 – 1914) and further developed by Williams James (1842 – 1910) and John Dewey (1859 – 1952). The basic idea of philosophic pragmatism is given by Peirce in his pragmatic maxim as: “To ascertain the meaning of an intellectual conception one should consider what practical consequences might result from the truth of that conception—and the sum of these consequences constitute the entire meaning of the conception.” Another aspect of the pragmatic approach to philosophic questions was that the scientific method was taken as given with no need for justification from the outside, i.e. the scientific method was used as the definition of knowledge.
How does this differ from the workaday approach to defining knowledge? Traditionally, going back at least to Plato (428/427 or 424/423 BCE – 348/347 BCE) knowledge has been defined as:
1) Knowledge – justified true belief
The leaves open the question of how belief is justified and since no justification is ever 100% certain, we can never be sure the belief is true. That is a definite problem. No wonder the philosophic community has spent two and a half millennia in fruitless efforts to make sense of it.

A second definition of knowledge predates this and is associated with Protagoras (c. 490 B.C. – c. 420 B.C.) and the sophists:
2) Knowledge – what you can convince people is true
Essentially, the argument is that since we cannot know that a belief is true with 100% certainty; what is important is what we can convince people of. This same basic idea shows up in the work of modern philosophers of science with the idea that scientific belief is basically a social phenomenon and what is important is what the community convinces itself is true. This was part of Thomas Kuhn’s (1922 – 1996) thesis.

While we cannot know what is true, we can know what is useful. Following the lead of scientists, the pragmatists effectively defined knowledge as:
3) Knowledge – information that helps you predict and modify the future
If we take predicting and modifying the future as the practical consequence of information, this definition of knowledge is consistent with the pragmatic maxim. The standard model of particle physics is not knowledge by the strict application of definition 1) since it is not completely true; however it is knowledge by definition 3 since it helps us predict and modify the future. The scientific method is built on definition 3). The modify clause is included in the definition since the pragmatists insisted on that aspect of knowledge. For example, C.I. Lewis said that without the ability to act there is no knowledge.

The third definition of knowledge given above does not correspond to what many people think of as knowledge so Dewy suggested using the term “warranted assertions” rather than knowledge: The validity of the standard model is a warranted assertion. Fortunately, this terminology never caught on. In contrast, James’s pragmatic idea of “truth’s cash value”, derided at the time, has caught on. In a recent book “How to Measure Anything,” on risk management, Douglas W. Hubbard spends a lot of space on what is essentially the cash value of information. In business, that is what is important. The pragmatists were, perhaps, just a bit ahead of their time. Hubbard, whether he knows it or not, is a pragmatist.
Dewey coined the term “instrumentalism” to describe the pragmatic approach. An idea or a belief is like a hand, an instrument for coping. A belief has no more metaphysical status than a fork. When your fork proves inadequate to the task of eating soup, it makes little sense to argue about whether there is something inherent in the nature of forks or something inherent in the nature of soup that accounts for the failure. You just reach for a spoon . However, most pragmatists did not consider themselves to be instrumentalists but rather used the pragmatic definition of knowledge to define what is meant by real.

Now I turn to C.I. Lewis. He is alternately regarded as the last of the classical pragmatists or the first of the neo-pragmatists. He was quite influential in his day as a professor at Harvard from 1920 to his retirement in 1953. In particular, his 1929 book “Mind and the World Order” had a big influence on epistemology and surprisingly on ISO management standards. One can see a lot of the ideas developed by Kuhn already present in the work of C.I. Lewis , for example, the role of theory in interpreting observation. Or as Deming, influenced by Lewis, expressed it: “There is no knowledge without theory.” As a theorist, I like that. At the time, this was quite radical. The logical positivists took the opposite tack and tried to eliminate theory from their epistemology. Lewis and Kuhn argued this was impossible. The idea that theory was necessary for knowledge was not new to Lewis but is also present in the works of Henri Poincaré (1854 – 1912) who was duly reference by Lewis.

Another person Lewis influenced was Willard V. O. Quine (1908 – 2000), although Quine and Lewis did not agree. Quine is perhaps best known outside the realm of pure philosophy for the Duhem-Quine thesis, namely that it is impossible to test a scientific hypothesis in isolation because an empirical test of the hypothesis requires one or more background assumptions. This was the death knell of any naïve interpretation of Sir Karl Popper’s (1902 –1994) idea that science is based on falsification. But Quine’s main opponents were the logical positivists. Popper was just collateral damage. Quine published a landmark paper in 1951: “Two Dogmas of Empiricism”. I would regard this paper as the high point in the discussion of the scientific method by a philosopher and it reasonably readable (unlike Lewis’s “The Mind and the World Order”). Beside the Duhem-Quine thesis, the other radical idea is that observation underdetermines scientific models and that simplicity and conservatism are necessary to fill the gap. This idea also goes back to Poincaré and his idea of conventionalism – much of what is regarded as fact is only convention.

To a large extent my ideas match well with the ideas in “Two Dogmas of Empiricism.” Quine summarizes it nicely as: “The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges.” and “The edge of the system must be kept squared with experience; the rest, with all its elaborate myths or fictions, has as its objective the simplicity of laws.” Amen.

Unfortunately, after the two dogmas of empiricism were brought to light, the philosophy of science regressed. In a recent discussion of simplicity in science I came across, there was neither a single mention of Quine’s work nor his correct identification of the role of simplicity – to relieve the under determination of models by observation. Philosophers found no use for his ideas and have gone back to definition 1) of knowledge. Sad

Where philosophers have dropped the ball it was picked by people in, of all places management. Two people influenced by Lewis were Walter A. Shewhart (1891 – 1967) and Edwards Deming. It is said that Shewhart read Lewis’s book fourteen times and Deming read it nine times. Considering how difficult that book is, it probably required that many readings just to comprehend it. Shewhart is regarded as the father of statistical process control, a key aspect of quality control. He also invented the control chart, a key component of statistical process control. Shewhart’s 1939 book “Statistical Method from the viewpoint of Quality Control” is a classic in the field but it devoted a large part to showing how his ideas are consistent with Lewis’s epistemology. In this book, Shewhart introduced the Shewhart cycle, which was modified by Deming (and sometimes called the Deming cycle). Under its current name Do-Plan-Check-Act (DPCA cycle) it forms the basis of the ISO management standards.

shewhart

The original Shewhart cycle as given in Shewhart’s book.

What is this cycle? Here it is as captured from Shewhart’s book. This is the first place where production is seen as part of a cycle and in the included caption Shewhart explicitly relates it to the scientific method as given by Lewis. Deming added another step to the cycle, which strikes me as unnecessary; the act step. It can easily be incorporated in the specification or plan stage (as it is in Shewhart’s diagram). But Deming was influenced by Lewis who regarded knowledge without the possibility of acting as impossible, hence the act step. This idea has become ingrained in ISO management standards as the slogan “continual improvement” (Clause 10 in the standards). To see the extent Deming was guided by Lewis’s ideas just look at Deming’s 1993 book “The New Economics.” He summarizes his approach in what he calls a system of profound knowledge. This has four parts: knowledge of system, knowledge of variation, theory of knowledge and knowledge of physiology. The one that seems out of place is the third; why include theory of knowledge? Deming believed that this was necessary for running a company and he explicitly refers to Lewis’s 1929 book. Making the reading of Lewis’s book mandatory for business managers would certainly have the desirable effect of cutting down the number of managers. To be fair to Deming, he does suggest starting in about the middle of the book. We have two unbroken chain – 1) Peirce, Lewis, Shewhart, Deming, ISO management standards and 2) Pierce, Lewis, Quine, my philosophical musings . It reminds one of James Burke’s TV program “Connections”.

Popper may be the person many scientists think of to justify how they work but Quine would probably be better and Quine’s teacher, C.I. Lewis, through Deming, has provided the philosophic foundation for business management. Within the context of definition 3) for knowledge both science and business have been very successful. Your reading of this essay required both. In contradistinction, standard western philosophy based on definition 1) has largely failed; philosophers still do not know how to acquire knowledge. However, not all philosophy is useless, some of it is pragmatic.

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This blog is all about particle physics and particle physicists. We can all agree, I suppose, on the notion of the particle physicist, right? There are even plenty of nice pictures up here! But do we know or are we aware of what a particle really is? This fundamental question tantalized me from the very beginning of my studies and before addressing more involved topics I think it is worth spending some time on this concept. Through the years I probably changed my opinion several times, according to the philosophy underlying the topic that I was investigating. Moreover, there’s probably not a single answer to this question.

  1. The Standard Model: from geometry to detectors

The human mind conceived the Standard Model of Particle Physics to give a shape on the blackboard to the basic ingredients of particle physics: it is a field theory, with quantization rules, namely a quantum field theory and its roots go deep down to differential geometry.
But we know that “particles” like the Higgs boson have been discovered through complex detectors, relying on sophisticated electronic systems, tons of Monte Carlo simulations and data analysis. Quite far away from geometry, isn’t it?
So the question is: how do we fill this gap between theory and experiment? What do theoreticians think about and experimentalists see through the detectors? Furthermore, does a particle’s essence change from its creation to its detection?

  1. Essence and representation: the wavefunction

 Let’s start with simple objects, like an electron. Can we imagine it as a tiny thing floating here and there? Mmm. Quantum mechanics already taught us that it is something more: it does not rotate around an atomic nucleus like the Earth around the Sun (see, e.g., Bohr’s model). The electron is more like a delocalized “presence” around the nucleus quantified by its “wavefunction”, a mathematical function that gives the probability of finding the electron at a certain place and time.
Let’s think about it: I just wrote that the electron is not a localized entity but it is spread in space and time through its wavefunction. Fine, but I still did not say what an electron is.

I have had long and intensive discussions about this question. In particular I remember one with my housemate (another theoretical physicist) that was about to end badly, with the waving of frying pans at each other. It’s not still clear to me if we agreed or not, but we still live together, at least.

Back to the electron, we could agree on considering its essence as its abstract definition, namely being one of the leptons in the Standard Model. But the impossibility of directly accessing it forces me to identify it with its most trustful representation, namely the wavefunction. I know its essence, but I cannot directly (i.e. with my senses) experience it. My human powers stop to the physical manifestation of its mathematical representation: I cannot go further.
Renè Magritte represented the difference between the representation of an object and the object itself in a famous painting “The treachery of images”:

magritte_pipe

“Ceci n’est pas une pipe”, it says, namely “This is not a pipe”. He is right, the picture is its representation. The pipe is defined as “A device for smoking, consisting of a tube of wood, clay, or other material with a small bowl at one end” and we can directly experience it. So its representation is not the pipe itself.

As I explained, this is somehow different in the case of the electron or other particles, where experience stops to the representation. So, according to my “humanity”, the electron is its wavefunction. But, to be consistent with what I just claimed: can we directly feel its wavefunction? Yes, we can. For example we can see its trace in a cloud chamber, or more elaborate detectors. Moreover, electricity and magnetism are (partly) manifestations of electron clouds in matter, and we experience those in everyday life.

bubbleplakat

You may wonder why I go through all these mental wanderings: just write down your formulas, calculate and be happy with (hopefully!) discoveries.

I do it because philosophy matters. And is nice. And now that we are a bit more aware of the essence of things that we are investigating, we can move a step forward and start addressing Quantum Chromo Dynamics (QCD), from its basic foundations to the latest results released by the community. I hope to have sufficiently stimulated your curiosity to follow me during the next steps!

Again, I want to stress that this is my own perspective, and maybe someone else would answer these questions in a different way. For example, what do you think?

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Good Management is Science

Friday, October 10th, 2014

Management done properly satisfies Sir Karl Popper’s (1902 – 1994) demarcation criteria for science, i.e. using models that make falsifiable or at least testable predictions. That was brought home to me by a book[1] by Douglas Hubbard on risk management where he advocated observationally constrained (falsifiable or testable) models for risk analysis evaluated through Monte Carlo calculations. Hmm, observationally constrained models and Monte Carlo calculations, sounds like a recipe for science.

Let us take a step back. The essence of science is modeling how the universe works and checking the assumptions of the model and its predictions against observations. The predictions must be testable. According to Hubbard, the essence of risk management is modeling processes and checking the assumptions of the model and its predictions against observations. The predictions must be testable. What we are seeing here is a common paradigm for knowledge in which modeling and testing against observation play a key role.

The knowledge paradigm is the same in project management. A project plan, with its resource loaded schedules and other paraphernalia, is a model for how the project is expected to proceed. To monitor a project you check the plan (model) against actuals (a fancy euphemism for observations, where observations may or may not correspond to reality). Again, it reduces back to observationally constrained models and testable predictions.

The foundations of science and good management practices are tied even closer together. Consider the PDCA cycle for process management that is present, either implicitly or explicitly, in essentially all the ISO standards related to management. It was originated by Walter Shewhart (1891 – 1967), an American physicist, engineer and statistician, and popularized by Edwards Deming (1900 – 1993), an American engineer, statistician, professor, author, lecturer and management consultant. Engineers are into everything. The actual idea of the cycle is based on the ideas of Francis Bacon (1561 – 1629) but could equally well be based on the work of Roger Bacon[2] (1214 – 1294). Hence, it should probably be called the Double Bacon Cycle (no, that sounds too much like a breakfast food).

But what is this cycle? For science, it is: plan an experiment to test a model, do the experiment, check the model results against theCapture observed results, and act to change the model in response to the new information from the check stage or devise more precise tests if the predictions and observations agree. For process management replace experiment with production process. As a result, you have a model for how the production process should work and doing the process allows you to test the model. The check stage is where you see if the process performed as expected and the act stage allows you to improve the process if the model and actuals do not agree. The key point is the check step. It is necessary if you are to improve the process; otherwise you do not know what is going wrong or, indeed, even if something is going wrong. It is only possible if the plan makes predictions that are falsifiable or at least testable. Popper would be pleased.

There is another interesting aspect of the ISO 9001 standard. It is based on the idea of processes. A process is defined as an activity that converts inputs into outputs. Well, that sound rather vague, but the vagueness is an asset, kind of like degrees of freedom in an effective field theory. Define them as you like but if you choose them incorrectly you will be sorry. The real advantage of effective field theory and the flexible definition of process is that you can study a system at any scale you like. In effective field theory, you study processes that operate at the scale of the atom, the scale of the nucleus or the scale of the nucleon and tie them together with a few parameters. Similarly with processes, you can study the whole organization as a process or drill down and look at sub process at any scale you like, for CERN or TRIUMF that would be down to the last magnet. It would not be useful to go further and study accelerator operations at the nucleon scale. At a given scale different processes are tied together by their inputs and outputs and these are also used to tie process at different scales.

As a theoretical physicist who has gone over to the dark side and into administration, I find it amusing to see the techniques and approaches from science being borrowed for use in administration, even Monte Carlo calculations. The use of similar techniques in science and administration goes back to the same underlying idea: all true knowledge is obtained through observation and its use to build better testable models, whether in science or other walks of life.

[1] The Failure of Risk Management: Why It’s Broken and How to Fix It by Douglas W. Hubbard (Apr 27, 2009)

[2] Roger Bacon described a repeating cycle of observation, hypothesis, and experimentation.

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Why pure research?

Thursday, October 2nd, 2014

With my first post on Quantum Diaries I will not address a technical topic; instead, I would like to talk about the act (or art) of “studying” itself. In particular, why do we care about fundamental research, pure knowledge without any practical purpose or immediate application?

A. Flexner in 1939 authored a contribution to Harper’s Magazine (issue 179) named “The usefulness of useless knowledge”. He opens the discussion with an interesting question: “Is it not a curios fact that in a world steeped in irrational hatreds which threaten civilization itself, men and women – old and young – detach themselves wholly or partly from the angry current of daily life to devote themselves to the cultivation of beauty, to the extension of knowledge […] ?”

Nowadays this interrogative is still present, and probably the need for a satisfactory answer is even stronger.

From a pragmatic point of view, we can argue that there are many important applications and spin-offs of theoretical investigations into the deep structure of Nature that did not arise immediately after the scientific discoveries. This is, for example, the case of QED and antimatter, the theories for which date back to the 1920s and are nowadays exploited in hospitals for imaging purposes (like in PET, positron emission tomography). The most important discoveries affecting our everyday life, from electricity to the energy bounded in the atom, came from completely pure and theoretical studies: electricity and magnetism, summarized in Maxwell’s equations, and quantum mechanics are shining examples.

It may seem that it is just a matter of time: “Wait enough, and something useful will eventually pop out of these abstract studies!” True. But that would not be the most important answer. To me this is: “Pure research is important because it generates knowledge and education”. It is our own contribution to the understanding of Nature, a short but important step in a marvelous challenge set up by the human mind.

Personally, I find that research into the yet unknown aspects of Nature responds to some partly conscious and partly unconscious desires. Intellectual achievements provide a genuine ‘spiritual’ satisfaction, peculiar to the art of studying. For sake of truth I must say that there are also a lot of dark sides: frustration, stress, graduate-depression effects, geographical and economic instability and so on. But leaving for a while all these troubles aside, I think I am pretty lucky in doing this job.

source_of_knowledge

Books, the source of my knowledge

During difficult times from the economic point of view, it is legitimate to ask also “Why spend a lot of money on expensive experiments like the Large Hadron Collider?” or “Why fund abstract research in labs and universities instead of investing in more socially useful studies?”

We could answer by stressing again the fact that many of the best innovations came from the fuzziest studies. But in my mind the ultimate answer, once for all, relies in the power of generating culture, and education through its diffusion. Everything occurs within our possibilities and limitations. A willingness to learn, a passion for teaching, blackboards, books and (super)computers: these are our tools.

Citing again Flexner’s paper: “The mere fact spiritual and intellectual freedoms bring satisfaction to an individual soul bent upon its own purification and elevation is all the justification that they need. […] A poem, a symphony, a painting, a mathematical truth, a new scientific fact, all bear in themselves all the justification that universities, colleges and institutes of research need or require.”

Last but not least, it is remarkable to think about how many people from different parts of the world may have met and collaborated while questing together after knowledge. This may seem a drop in the ocean, but research daily contributes in generating a culture of peace and cooperation among people with different cultural backgrounds. And that is for sure one of the more important practical spin-offs.

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Isaac Asimov (1920 – 1992) “expressed a certain gladness at living in a century in which we finally got the basis of the universe straight”. Albert Einstein (1870 – 1955) claimed: “The most incomprehensible thing about the world is that it is comprehensible”. Indeed there is general consensus in science that not only is the universe comprehensible but is it mostly well described by our current models. However, Daniel Kahneman counters: “Our comforting conviction that the world makes sense rests on a secure foundation: our almost unlimited ability to ignore our ignorance”.

Well, that puts a rather different perspective on Asimov’s and Einstein’s claims.  So who is this person that is raining on our parade? Kahneman is a psychologist who won the 2002 Nobel Prize in economics for his development of prospect theory. A century ago everyone quoted Sigmund Freud (1856 – 1939) to show how modern they were. Today, Kahneman seems to have assumed that role.[1]

Kahneman’s Nobel Prize winning prospect theory, developed with Amos Tversky (1937 –1996), replaced expected utility theory. The latter assumed that people made economic choices based on the expected utility of the results, that is they would behave rationally. In contrast, Kahneman and company have shown that people are irrational in well-defined and predictable ways. For example, it is understood that the phrasing of a question can (irrationally) change how people answer, even if the meaning of the question is the same.

Kahneman’s book, Thinking, Fast and Slow, really should be required reading for everyone. It explains a lot of what goes on (gives the illusion of comprehension?) and provides practical tips for thinking rationally. For example, when I was on a visit in China, the merchants would hand me a calculator to type in what I would pay for a given item. Their response to the number I typed in was always the same: You’re joking, right?  Kahneman would explain that they were trying to remove the anchor set by the first number entered in the calculator. Anchoring is a common aspect of how we think.

Since, as Kahneman argues, we are inherently irrational one has to wonder about the general validity of the philosophic approach to knowledge; an approach based largely on rational argument. Science overcomes our inherent irrationality by constraining our rational arguments by frequent, independently-repeated observations.  Much as with project management, we tend to be irrationally overconfident of our ability to estimate resource requirements.  Estimates of project resource requirements not constrained by real world observations leads to the project being over budget and delivered past deadlines. Even Kahneman was not immune to this trap of being overly optimistic.

Kahneman’s cynicism has been echoed by others. For example, H.L. Mencken (1880 –1956) said:  “The most common of all follies is to believe passionately in the palpably not true. It is the chief occupation of mankind”. Are the cynics correct? Is our belief that the universe is comprehensible, and indeed mostly understood, a mirage based on our unlimited ability to ignore our ignorance? A brief look at history would tend to support that claim.  Surely the Buddha, after having achieved enlightenment, would have expressed relief and contentment for living in a century in which we finally got the basis of the universe straight. Saint Paul, in his letters, echoes the same claim that the universe is finally understood. René Descartes, with the method laid out in the Discourse on the Method and Principles of Philosophy, would have made the same claim.  And so it goes, almost everyone down through history believes that he/she comprehends how the universe works. I wonder if the cow in the barn has the same illusion. Unfortunately, each has a different understanding of what it means to comprehend how the universe works, so it is not even possible to compare the relative validity of the different claims. The unconscious mind fits all it knows into a coherent framework that gives the illusion of comprehension in terms of what it considers important. In doing so, it assumes that what you see is all there is.  Kahneman refers to this as WYSIATI (What You See Is All There Is).

To a large extent the understandability of the universe is mirage based on WYSIATI—our ignorance of our ignorance. We understand as much as we are aware of and capable of understanding; blissfully ignoring the rest. We do not know how quantum gravity works, if there is intelligent life elsewhere in the universe[2], or for that matter what the weather will be like next week. While our scientific models correctly describe much about the universe, they are, in the end, only models and leave much beyond their scope, including the ultimate nature of reality.

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[1] Let’s hope time is kinder to Kahneman than it was to Freud.

[2] Given our response to global warming, one can debate if there is intelligent life on earth.

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René Descartes (1596 – 1650) was an outstanding physicist, mathematician and philosopher. In physics, he laid the ground work for Isaac Newton’s (1642 – 1727) laws of motion by pioneering work on the concept of inertia. In mathematics, he developed the foundations of analytic geometry, as illustrated by the term Cartesian[1] coordinates. However, it is in his role as a philosopher that he is best remembered. Rather ironic, as his breakthrough method was a failure.

Descartes’s goal in philosophy was to develop a sound basis for all knowledge based on ideas that were so obvious they could not be doubted. His touch stone was that anything he perceived clearly and distinctly as being true was true. The archetypical example of this was the famous I think therefore I am.  Unfortunately, little else is as obvious as that famous quote and even it can be––and has been––doubted.

Euclidean geometry provides the illusionary ideal to which Descartes and other philosophers have strived. You start with a few self-evident truths and derive a superstructure built on them.  Unfortunately even Euclidean geometry fails that test. The infamous parallel postulate has been questioned since ancient times as being a bit suspicious and even other Euclidean postulates have been questioned; extending a straight line depends on the space being continuous, unbounded and infinite.

So how are we to take Euclid’s postulates and axioms?  Perhaps we should follow the idea of Sir Karl Popper (1902 – 1994) and consider them to be bold hypotheses. This casts a different light on Euclid and his work; perhaps he was the first outstanding scientist.  If we take his basic assumptions as empirical[2] rather than sure and certain knowledge, all we lose is the illusion of certainty. Euclidean geometry then becomes an empirically testable model for the geometry of space time. The theorems, derived from the basic assumption, are prediction that can be checked against observations satisfying Popper’s demarcation criteria for science. Do the angles in a triangle add up to two right angles or not? If not, then one of the assumptions is false, probably the parallel line postulate.

Back to Descartes, he criticized Galileo Galilei (1564 – 1642) for having built without having considered the first causes of nature, he has merely sought reasons for particular effects; and thus he has built without a foundation. In the end, that lack of a foundation turned out to be less of a hindrance than Descartes’ faulty one.  To a large extent, sciences’ lack of a foundation, such as Descartes wished to provide, has not proved a significant obstacle to its advance.

Like Euclid, Sir Isaac Newton had his basic assumptions—the three laws of motion and the law of universal gravity—but he did not believe that they were self-evident; he believed that he had inferred them by the process of scientific induction. Unfortunately, scientific induction was as flawed as a foundation as the self-evident nature of the Euclidean postulates. Connecting the dots between a falling apple and the motion of the moon was an act of creative genius, a bold hypothesis, and not some algorithmic derivation from observation.

It is worth noting that, at the time, Newton’s explanation had a strong competitor in Descartes theory that planetary motion was due to vortices, large circulating bands of particles that keep the planets in place.  Descartes’s theory had the advantage that it lacked the occult action at a distance that is fundamental to Newton’s law of universal gravitation.  In spite of that, today, Descartes vortices are as unknown as is his claim that the pineal gland is the seat of the soul; so much for what he perceived clearly and distinctly as being true.

Galileo’s approach of solving problems one at time and not trying to solve all problems at once has paid big dividends. It has allowed science to advance one step at a time while Descartes’s approach has faded away as failed attempt followed failed attempt. We still do not have a grand theory of everything built on an unshakable foundation and probably never will. Rather we have models of widespread utility. Even if they are built on a shaky foundation, surely that is enough.

Peter Higgs (b. 1929) follows in the tradition of Galileo. He has not, despite his Noble prize, succeeded, where Descartes failed, in producing a foundation for all knowledge; but through creativity, he has proposed a bold hypothesis whose implications have been empirically confirmed.  Descartes would probably claim that he has merely sought reasons for a particular effect: mass. The answer to the ultimate question about life, the universe and everything still remains unanswered, much to Descartes’ chagrin but as scientists we are satisfied to solve one problem at a time then move on to the next one.

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[1] Cartesian from Descartes Latinized name Cartesius.

[2] As in the final analysis they are.

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Since model building is the essence of science, this quote has a bit of a bite to it. It is from George E. P. Box (1919 – 2013), who was not only an eminent statistician but also an eminently quotable one.  Another quote from him: One important idea is that science is a means whereby learning is achieved, not by mere theoretical speculation on the one hand, nor by the undirected accumulation of practical facts on the other, but rather by a motivated iteration between theory and practice.  Thus he saw science as an iteration between observation and theory. And what is theory but the building of erroneous, or at least approximate, models?

To amplify that last comment: The main point of my philosophical musings is that science is the building of models for how the universe works; models constrained by observation and tested by their ability to make predictions for new observations, but models nonetheless. In this context, the above quote has significant implications for science. Models, even those of science, are by their very nature simplifications and as such are not one hundred per cent accurate. Consider the case of a map. Creating a 1:1 map is not only impractical[2] but even if you had one it would be one hundred per cent useless; just try folding a 1:1 scale map of Vancouver. A model with all the complexity of the original does not help us understand the original.  Indeed the whole purpose of a model is to eliminate details that are not essential to the problem at hand.

By their very nature, numerical models are always approximate and this is probably what Box had in mind with his statement. One neglects small effects like the gravitational influence of a mosquito. Even as one begins computing, one makes numerical approximations, replacing integrals with sums or vise versa, derivatives with finite differences, etc. However, one wants to control errors and keep them to a minimum. Statistical analysis techniques, such as Box developed, help estimate and control errors.

To a large extent it is self-evident that models are approximate; so what? Again to quote George Box: Since all models are wrong the scientist cannot obtain a “correct” one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity. What would he have thought of a model with twenty plus parameters, like the standard model of particle physics? His point is a valid one. All measurements have experimental errors. If your fit is perfect you are almost certainly fitting noise. Hence, adding more parameters to get a perfect fit is a fool’s errand. But even without experimental error, a large number of parameters frequently means something important has been missed. Has something been missed in the standard model of particle physics with its many parameters or is the universe really that complicated?

There is an even more basic reason all models are wrong. This goes back at least as far as Immanuel Kant (1724 – 1804). He made the distinction between observation of an object and the object in itself. One never has direct experience of things, the so-called noumenal world; what one experiences is the phenomenal world as conveyed to us by our senses. What we see is not even what has been recorded by the eye.  The mind massages the raw observation into something it can understand; a useful but not necessarily accurate model of the world. Science then continues this process in a systematic manner to construct models to describe observations but not necessarily the underlying reality.

Despite being by definition at least partially wrong, models are frequently useful. The scale model map is useful to tourists trying to find their way around Vancouver or to a general plotting strategy for his next battle. But, if the maps are too far wrong the tourist will get lost and fall into False Creek and the general will go down in history as a failure. Similarly, the models for weather predictions are useful although they are certainly not a hundred per cent accurate. However, they do indicate when it safe to plan a picnic or cut the hay; provided they are right more than by chance and the standard model of particle physics, despite having many parameters and not including gravity, is a useful description of a wide range of observations. But to return to the main point, all models, even useful ones, are wrong because they are approximations and not even approximations to reality but to our observations of that reality. Where does that leave us? Well, let us save the last word for George Box: Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.

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[1] Hence the foolishness of talking about theoretical breakthroughs in science. All breakthroughs arise from pondering about observations and observations testing those ponderings.

[2] Not even Google could produce that.

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Theoretical physics, simplicity. Surely the two words do not go together. Theoretical physics has been the archetypal example of complicated since its invention. So what did Frank Wilczek (b. 1951) mean by that statement[1] quoted in the title? It is the scientist’s trick of taking a well-defined word, such as simplicity, and giving it a technical meaning. In this case, the meaning is from algorithmic information theory. That theory defines complexity (Kolmogorov complexity[2]) as the minimum length of a computer program needed to reproduce a string of numbers. Simplicity, as used in the title, is the opposite of this complexity. Science, not just theoretical physics, is driven, in part but only in part, by the quest for this simplicity.

How is that you might ask. This is best described by Greg Chaitin (b. 1947), a founder of algorithmic information theory. To quote: This idea of program-size complexity is also connected with the philosophy of the scientific method. You’ve heard of Occam’s razor, of the idea that the simplest theory is best? Well, what’s a theory? It’s a computer program for predicting observations. And the idea that the simplest theory is best translates into saying that a concise computer program is the best theory. What if there is no concise theory, what if the most concise program or the best theory for reproducing a given set of experimental data is the same size as the data? Then the theory is no good, it’s cooked up, and the data is incomprehensible, it’s random. In that case the theory isn’t doing a useful job. A theory is good to the extent that it compresses the data into a much smaller set of theoretical assumptions. The greater the compression, the better!—That’s the idea…

In many ways this is quite nice; the best theory is the one that compresses the most empirical information into the shortest description or computer program.  It provides an algorithmic method to decide which of two competing theories is best (but not an algorithm for generating the best theory). With this definition of best, a computer could do science: generate programs to describe data and check which is the shortest. It is not clear, with this definition, that Copernicus was better than Ptolemy. The two approaches to planetary motion had a similar number of parameters and accuracy.

There are many interesting aspects of this approach. Consider compressibility and quantum mechanics. The uncertainty principle and the probabilistic nature of quantum mechanics put limits on the extent to which empirical data can be compressed. This is the main difference between classical mechanics and quantum mechanics. Given the initial conditions and the laws of motion, classically the empirical data is compressible to just that input. In quantum mechanics, it is not. The time, when each individual atom in a collection of radioactive atoms decays, is unpredictable and the measured results are largely incompressible. Interpretations of quantum mechanics may make the theory deterministic, but they cannot make the empirical data more compressible.

Compressibility highlights a significant property of initial conditions. While the data describing the motion of the planets can be compressed using Newton’s laws of motion and gravity, the initial conditions that started the planets on their orbits cannot be. This incompressibility tends to be a characteristic of initial conditions. Even the initial conditions of the universe, as reflected in the cosmic microwave background, have a large random non-compressible component – the cosmic variance.  If it wasn’t for quantum uncertainly, we could probably take the lack of compressibility as a definition of initial conditions. For the universe, the two are the same since the lack of compressibility in the initial conditions is due to quantum fluctuations but that is not always the case.

The algorithmic information approach makes Occam’s razor, the idea that one should minimize assumptions, basic to science. If one considers that each character in a minimal computer program is a separate assumption, then the shortest program does indeed have the fewest assumptions. But you might object that some of the characters in a program can be predicted from other characters. However, if that is true the program can probably be made shorter. This is all a bit counterintuitive since one generally does not take such a fine grained approach to what one considers an assumption.

The algorithmic information approach to science, however, does have a major shortcoming. This definition of the best theory leaves out the importance of predictions. A good model must not only compress known data, it must predict new results that are not predicted by competing models. Hence, as noted in the introduction, simplicity is only part of the story.

The idea of reducing science to just a collection of computer programs is rather frightening. Science is about more than computer programs[3]. It is, and should be, a human endeavour. As people, we want models of how the universe works that humans, not just computers, can comprehend and share with others. A collection of bits on a computer drive does not do this.

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[1] From “This Explains Everything”, Ed, John Brockman, Harper Perennial, New York, 2013

[2] Also known as descriptive complexity, Kolmogorov–Chaitin complexity, algorithmic entropy, or program-size complexity.

[3] In this regard, I have a sinking feeling that I am fighting a rearguard action against the inevitable.

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If there were only one credible interpretation of quantum mechanics, then we could take it as a reliable representation of reality. But when there are many, it destroys the credulity of all of them. The plethora of interpretations of quantum mechanics lends credence to the thesis that science tells us nothing about the ultimate nature of reality.

Quantum mechanics, in its essence, is a mathematical formalism with an algorithm for how to connect the formalism to observation or experiments. When relativistic extensions are included, it provides the framework for all of physics[1] and the underlying foundation for chemistry. For macroscopic objects (things like footballs), it reduces to classical mechanics through some rather subtle mathematics, but it still provides the underlying framework even there. Despite its empirical success, quantum mechanics is not consistent with our common sense ideas of how the world should work. It is inherently probabilistic despite the best efforts of motivated and ingenious people to make it deterministic. It has superposition and interference of the different states of particles, something not seen for macroscopic objects. If it is weird to us, just imagine how weird it must have seemed to the people who invented it. They were trained in the classical system until it was second nature and then nature itself said, “Fooled you, that is not how things are.” Some, like Albert Einstein (1879 – 1955), resisted it to their dying days.

The developers of quantum mechanics, in their efforts to come to grips with quantum weirdness, invented interpretations that tried to understand quantum mechanics in a way that was less disturbing to common sense and their classical training. In my classes in quantum mechanics, there were hand waving discussions of the Copenhagen interpretation, but I could never see what they added to mathematical formalism. I am not convinced my lecturers could either, although the term Copenhagen interpretation was uttered with much reverence. Then I heard a lecture by Sir Rudolf Peierls[2] (1907 – 1995) claiming that the conscious mind caused the collapse of the wave function. That was an interesting take on quantum mechanics, which was also espoused by John von Neumann (1903 – 1957) and Eugene Wigner (1902 –1995) for part of their careers.

So does consciousness play a crucial role in quantum mechanics? Not according to Hugh Everett III (1930 – 1982) who invented the many-worlds interpretation. In this interpretation, the wave function corresponds to physical reality, and each time a measurement is made the universe splits into many different universes corresponding to each possible outcome of the quantum measurement process. Physicists are nothing if not imaginative. This interpretation also offers the promise of eternal life.  The claim is that in all the possible quantum universes there must be one in which you will live forever. Eventually that will be the only one you will be aware of. But as with the Greek legend of Tithonus, there is no promise of eternal youth. The results may not be pretty.

If you do not like either of those interpretations of quantum mechanics, well have I got an interpretation for you. It goes under the title of the relation interpretation. Here the wave function is simply the information a given observer has about the quantum system and may be different for different observers; nothing mystical here and no multiplicity of worlds. Then there is the theological interpretation. This I first heard from Steven Hawking (b. 1942) although I doubt he believed it. In this interpretation, God uses quantum indeterminacy to hide his direct involvement in the unfolding of the universe. He simply manipulates the results of quantum measurements to suit his own goals. Well, He does work in mysterious ways after all.

I will not bore you with all possible interpretations and their permutations. Life is too short for that, but we are still left with the overarching question: which interpretation is the one true interpretation? What is the nature of reality implied by quantum mechanics? Does the universe split into many? Does consciousness play a central role? Is the wave function simply information? Does God hide in quantum indeterminacy?

Experiment cannot sort this out since all the interpretations pretty much agree on the results of experiments (even this is subject to debate), but science has one other criteria: parsimony. We eliminate unnecessary assumptions. When applied to interpretations of quantum mechanics, parsimony seems to favour the relational interpretation. But, in fact, parsimony, carefully applied, favours something else; the instrumentalist approach. That is: don’t worry about the interpretations, just shut up and calculate. All the interpretations have additional assumptions not required by observations.

But what about the ultimate nature of reality? There is no theorem that says reality, itself, must be simple. So quantum mechanics implies very little about the ultimate nature of reality. I guess we will have to leave that discussion to the philosophers and theologians. More power to them.

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[1] Although quantum gravity is still a big problem.

[2] A major player in the development of quantum many body theory and nuclear physics.

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In the philosophy of science, realism is used in two related ways. The first way is that the interior constructs of a model refer to something that actually exists in nature, for example the quantum mechanical wave function corresponds to a physical entity. The second way is that properties of a system exist even when they are not being measured; the ball is in the box even when no one can see it (unless it is a relative of Schrodinger’s cat). The two concepts are related since one can think of the ball’s presence or absence as part of one’s model for how balls (or cats) behave.

Despite our and even young children’s belief in the continued existence of the ball and that cats are either alive or dead, there are reasons for doubting realism. The three main ones are the history of physics, the role of canonical (unitary) transformations in classical (quantum) mechanics, and Bell’s inequality. The second and third of these may seem rather obtuse, but bear with me.

Let’s start with the first, the history of physics. Here, we follow in the footsteps of Thomas Kuhn (1922–1996). He was probably the first philosopher of science to actually look at the history of science to understand how science works. One of his conclusions was that the interior constructs of models (paradigms in his terminology) do not correspond (refer in the philosophic jargon) to anything in reality. It is easy to see why. One can think of a sequence of models in the history of physics. Here we consider the Ptolemaic system, Newtonian mechanics, quantum mechanics, relativistic field theory (a combination of quantum mechanics and relativity) and finally quantum gravity. The Ptolemaic system ruled for half a millennium, from the second to seventeenth centuries. By any standard, the Ptolemaic model was a successful scientific model since it made correct predictions for the location of the planets in the night sky. Eventually, however, Newton’s dynamical model caused its demise. At the Ptolemaic model’s core were the concepts of geo-centrism and uniform circular motion. People believed these two aspects of the model corresponded to reality. But Newton changed all that. Uniform circular motion and geo-centrism were out and instantaneous gravitation attraction was in. Central to the Newtonian system was the fixed Euclidean space time geometry and particle trajectories. The first of these was rendered obsolete by relativity and the second by quantum mechanics; at least the idea of fixed number of particles survived–until quantum field theory. And if string theory is correct, all those models have the number of dimensions wrong. The internal aspects of well-accepted and successful models disappear when new models replace the old. There are other examples. In the history of physics, the caloric theory of heat was successful at one time but caloric vanished when the kinetic theory of heat took over. And on it goes. What is regarded as central to our understanding of how the world works goes puff when new models replace old.

On to the second reason for doubting realism–the role of transformations: canonical and unitary.  In both classical and quantum mechanics there are mathematical transformations that change the internals of the calculations[1] but leave not only the observables but also the structure of the calculations invariant. For example, in classical mechanics we can use a canonical transformation to change coordinates without changing the physics. We can express the location of an object using the earth as a reference point or the sun. Now this is quite fun; the choice of coordinates is quite arbitrary. So you want a geocentric system (like Galileo’s opponents), no problem. We write the equation of motion in that frame and everyone is happy. But you say the Earth really does go around the sun. That is equivalent to the statement: planetary motion is more simply described in the heliocentric frame. We can go on from there and use coordinates as weird as you like to match religious or personal preconceptions.  In quantum mechanics the transformations have even more surprising implications. You would think something like the correlations between particles would be observable and a part of reality. But that is not the case. The correlations depend on how you do your calculation and can be changed at will with unitary transformations. It is thus with a lot of things that you might think are parts of reality but are, as we say, model dependent.

Finally we come to Bell’s inequality as the third reason to doubt realism. The idea here goes back to what is known as the Einstein-Podolsky-Rosen paradox (published in 1935). By looking at the correlations of coupled particles Einstein, Podolsky, and Rosen claimed that quantum mechanics is incomplete.  John Bell (1928 – 1990), building on their work, developed a set of inequalities that allowed a precise experimental test of the Einstein-Podolsky-Rosen claim. The experimental test has been performed and the quantum mechanical prediction confirmed. This ruled out all local realistic models. That is, local models where a system has definite values of a property even when that property has not been measured. This is using realism in the second sense defined above. There are claims, not universally accepted, that extensions of Bell’s inequalities rule out all realist models, local or non-local.

So where does this leave us? Pretty much with the concept of realism in science in tatters. The internals of models changes in unpredictable ways when science advances. Even within a given model, the internals can be changed with mathematical tricks and for some definitions of realism, experiment has largely ruled it out.  Thus we are left with our models that describe aspects of reality but should never be mistaken for reality itself. Immanuel Kant (1724 – 1804), the great German philosopher, would not be surprised[2].

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[1] For the relation between the two type of transformations see: N.L. Balazs and B.K. Jennings, Unitary transformations, Weyl’s association and the role of canonical transformations, Physica, 121A (1983) 576–586

[2] He made the distinction between the thing in itself and observations of it.

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