• John
  • Felde
  • University of Maryland
  • USA

Latest Posts

  • James
  • Doherty
  • Open University
  • United Kingdom

Latest Posts

  • Andrea
  • Signori
  • Nikhef
  • Netherlands

Latest Posts

  • CERN
  • Geneva
  • Switzerland

Latest Posts

  • Aidan
  • Randle-Conde
  • Université Libre de Bruxelles
  • Belgium

Latest Posts

  • Richard
  • Ruiz
  • Univ. of Pittsburgh
  • U.S.A.

Latest Posts

  • Laura
  • Gladstone
  • University of Wisconsin, Madison
  • USA

Latest Posts

  • Byron
  • Jennings
  • TRIUMF
  • Canada

Latest Posts

  • Seth
  • Zenz
  • Imperial College London
  • UK

Latest Posts

  • Michael
  • DuVernois
  • Wisconsin IceCube Particle Astrophysics Center
  • USA

Latest Posts

  • Emily
  • Thompson
  • USLHC
  • Switzerland

Latest Posts

  • Ken
  • Bloom
  • USLHC
  • USA

Latest Posts

Byron Jennings | TRIUMF | Canada

Read Bio

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.

Share

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.

Share

Is the Understandability of the Universe a Mirage?

Friday, September 5th, 2014

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.

To receive a notice of future posts follow me on Twitter: @musquod.

[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.

Share

Higgs versus Descartes: this round to Higgs.

Friday, August 1st, 2014

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.

To receive a notice of future posts follow me on Twitter: @musquod.


[1] Cartesian from Descartes Latinized name Cartesius.

[2] As in the final analysis they are.

Share

‘Essentially, all models are wrong, but some are useful’

Friday, July 4th, 2014

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.

To receive a notice of future posts follow me on Twitter: @musquod.


[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.

Share

“Theoretical Physics is a Quest for Simplicity”

Friday, June 6th, 2014

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.

To receive a notice of future posts follow me on Twitter: @musquod.



[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.

Share

Mathematics: Invented or Discovered?

Friday, May 2nd, 2014

The empirical sciences, like physics and chemistry, are partially invented and partially discovered. Although the empirical observations are surely discovered, the models that describe them are invented through human ingenuity. But what about mathematics which is based on pure thought? Are its results invented or discovered?

Not surprisingly there are different views on this topic. Some people maintain that mathematical results are invented, others claim that they are discovered. Is there a universe of mathematical results just waiting to be discovered or are mathematical results invented by the mathematician and would disappear, like a fairy tale, when mathematicians vanish in the heat death of universe when all the available energy is used up? Invented or discovered? Perhaps some results are invented and others discovered. There is, however, a third view, namely that mathematics is game played by manipulating symbols according to well defined rules. At some level this is probably true.  All those who prefer Monopoly,® put up your hands!

What are the foundations of logic? Bertrand Russell (1872 – 1970) and Alfred Whitehead (1861 – 1947) tried to derive mathematics from logic. The result was the book: Principia Mathematica (1910), a real tour de force. Their derivation still required axioms or assumptions beyond pure logic and it has been questioned on other grounds. An alternate to this approach is set theory, in particular based on the Zermelo–Fraenkel axioms, with the axiom of choice. And an alternate to that is category theory. Whatever all that is. It is certainly very technical. The quest for foundations of mathematics and even logic, like the quest for the Holy Grail, is probably never ending. But the question remains: Was logic and set (category) theory, themselves, invented or discovered?

Let us look at things more simply. Historically, mathematics probably arose empirically: two stones plus two stones equals one stone plus three stones. Then it was realized that this holds for any tokens, stones, bushels of wheat or sheep.  The generalization from specific examples to the generic 2+2=1+3 could be considered an early example of the scientific method: generalizing from specific examples to a general rule. But one plus one does not always equal two. Consider a litre of liquid plus a litre of liquid. If one is water and the other alcohol, the result is less than two litres if they are put in the same container. Adding one litre of water to one litre of concentrated sulfuric acid is even more interesting[1].

Multiplication is also easy to demonstrate with counters. Division is a bit more problematic but if we think of dividing a bushel of wheat into equal parts the idea of fractions is quite natural. Dividing a sheep is messier. Subtraction however leads to a problem: negative numbers. Naively, we cannot have fewer than zero stones but subtraction can lead to that idea. So were negative numbers invented or discovered? We can finesse the problem of negative numbers by saying that negative numbers correspond to what we owe. If I have minus three stones it means I owe someone three stones.

Thus thinking of stones and bushels of wheat, we can understand the rational numbers, numbers written as the ratio of two whole numbers. The Pythagoreans in ancient Greece would have claimed that is all there is. Then can the thorny problem of the square root of two? This arises in connection with the Patagonian theorem. Some poor sod showed that the square root of two could not be written as the ratio of two whole numbers and was thus irrational. He was thrown into the sea for his efforts[2]. The square root of two does not exist in the universe of numbers discovered using stones, sheep, and bushels of wheat. Is it possible to have square root of two stones? Was it invented to make the Patagonian theorem work or was it discovered?

The example of the square root of minus one is even more perplexing. We can think of the square root of two as an extra number inserted between 1.414 and 1.415. But there is no place to insert the square root of minus one.  So again the question arises: Was it invented or discovered? Perhaps it is best to say it was assumed: Assume the square root of minus one can be treated like a normal number[3] and see what happens. A lot of good things as it turned out but does that mean it exists in any real sense. Perhaps it is just a useful fiction.

Nevertheless, mathematics has developed, discovering or inventing new results. As a phenomenologist, I would say we do not have enough information to assert if mathematics was invented or discovered. If we could contact extra-terrestrial mathematicians, it would be interesting to see if their mathematics was different or the same as ours. If it was different, that would be a strong indication that mathematics is invented. Or less black and white, the difference between terrestrial and extra-terrestrial mathematics would tell us the extent to which mathematics is discovered or invented.

In any event mathematics is a very interesting game, whether based on set theory or category theory, whether discovered or invented, and certainly more profitable than Monopoly®[4] in the long run.

To receive a notice of future posts follow me on Twitter: @musquod.


[1] Do not try this at home.

[2] At least that is the legend.

[3] √(-1)+√(-1) = 2 √(-1) , etc.

[4] On the other hand, oligarchy, as any large multinationals will tell you, is very profitable.

Share

Cosmic Inflation or Are the Photons Messing with Our Minds?

Tuesday, April 1st, 2014

Recently it has been announce that a smoking gun has been found for cosmic inflation but could it instead be the smoking[1] gun for a grand conspiracy, the mother of all conspiracies, the conspiracy theory to put all other conspiracy theories to shame?  You may have your favourite conspiracy theory: the Roswell cover up, who shot JFK, the suppression of perpetual motion machines by the energy companies or the attempt by communication departments to take over the world. As a professor, once said: “Just because you are paranoid does not mean they are not out to get you.” (Followed closely by my second-best piece of advice, “Never trust a communications expert.”) But the conspiracy I am talking about is on a much larger scale, a cosmic scale, the conspiracy of all elementary particles in the universe to use their free will for the sole purpose of messing with the minds of humans and particularly that subclass of humans known as particle physicists[2]. The professor was right to be paranoid.

We hold these truths to be self-evident, that all particles are created equal and endowed by their Creator with free will. Surely you do not question that elementary particles have free will. Consider the muon. It decays at a time if its own choosing.  There is no rule that says when a given muon will decay. It is decided by the muon in its own stubborn way.  But you still claim that only humans have freewill. Why? Could it not be just of part the grand conspiracy of elementary particle to give humans the illusion of freewill? Besides we all know politicians do not have freewill. They just do, as a Pavlovian reflex, what they think will get them the most votes.  Hence the mess the world is in. But I digress.

To explore further: what criteria is there to decide if a given object has freewill? Is it just unpredictability? If so, then Vancouver weather has freewill. We have already decided that politicians do not have freewill. But what about dogs? Are all their reactions Pavlovian conditioning? Most certainly not.  Hence they are better candidates to have freewill than politicians. And what about cats? Cats certainly have will but it is free?  Does the fact cats cannot be herded indicate they have freewill? And cows, do cows have freewill? Does the fact they can be herded indicate they do not have freewill? Or that plant on my window sill beckoning to be watered?  Does it cause its leaves to droop out of the exercise of its own freewill just to annoy me? Possibly (there it goes again). It seems to me the hallmark of freewill is precisely that combination of random and non-random behaviour found in elementary particles and not in politicians. Hence another interpretations of quantum uncertainty, it is just elementary particles exercising their freewill.

You may be surprised that I claimed all particles are created equal. Surely the neutrino and electron have different properties and are not equal. But that is just them exercising their freewill. Those particles we call electrons have decided (note the verb decided) to behave as if they had a given set of interactions while the neutrinos have decided to be behave like they have a different set of interactions. The interactions, themselves, are illusionary created by the particles exercising their freewill. There was probably a grand council meeting at the beginning of time where the grand conspiracy was initiated and the roles assigned to different sets of particles.  Indeed, it may have been that grand council meeting that started time itself.

The freewill of particles also explains the problem of evil. From earthquakes to global warming[3], the evil consequences are due to particle exercising their freewill. This type of evil could only be eliminated by denying particles freewill­–an even greater evil.

Now back to the initial observation about the polarization of photons in the cosmic microwave background. Surely that polarization is not due to gravitational waves but due to photons exercising their freewill to mislead humans. Is it not more reasonable to assume that the measured polarization[4] is due to freewill than to some far distant interaction with gravitons? (Do gravitons even exits? They have never been directly observed.)

This conspiracy theory–just like all conspiracy theories–accounts for all the known facts and cannot be disproved. It therefore must be correct and we have shown conclusively that it is particles, not people, that have freewill and the photons are trying to mess with our minds[5].

To receive a notice of future posts follow me on Twitter: @musquod.



[1] And no, I have not been smoking with the mayor of certain large Canadian city.

[2] Nuclear physicists have always known that something was messing with the minds of particle physicists.

[3] Global warming is due to particles excising their freewill not carbon dioxide emissions.

[4] But beware the Jennings principle: Most exciting new results are wrong.

[5] This is not the perfect particle physics blog because it does not mention the Higgs boson, the LHC or super symmetry. Oops, maybe now it is.

Share

Nobody understands quantum mechanics? Nonsense!

Saturday, March 8th, 2014

Despite the old canard about nobody understanding quantum mechanics, physicists do understand it.  With all of the interpretations ever conceived for quantum mechanics[1], this claim may seem a bit of a stretch, but like the proverbial ostrich with its head in the sand, many physicists prefer to claim they do not understand quantum mechanics, rather than just admit that it is what it is and move on.

What is it about quantum mechanics that generates so much controversy and even had Albert Einstein (1879 – 1955) refusing to accept it? There are three points about quantum mechanics that generate controversy. It is probabilistic, eschews realism, and is local. Let us look at these three points in more detail.

  1. Quantum mechanics is probabilistic, not determinist. Consider a radioactive atom. It is impossible, within the confines of quantum mechanics, to predict when an individual atom will decay. There is no measurement or series of measurements that can be made on a given atom to allow me to predict when it will decay. I can calculate the probability of when it will decay or the time it takes half of a sample to decay but not the exact time a given atom will decay. This lack of ability to predict exact outcomes, but only probabilities, permeates all of quantum mechanics. No possible set of measurements on the initial state of a system allows one to predict precisely the result of all possible experiments on that state.
  2. Quantum mechanics eschews realism[2]. This is a corollary of the first point. A quantum mechanical system does not have well defined values for properties that have not been directly measured. This has been compared to the moon only existing when someone is looking at it. For deterministic systems one can always safely infer back from a measurement what the system was like before the measurement. Hence if I measure a particle’s position and motion I can infer not only where it will go but where it has come from. The probabilistic nature of quantum mechanics prevents this backward looking inference. If I measure the spin of an atom, there is no certainty that is had only that value before the measurement. It is this aspect of quantum mechanics that most disturbs people, but quantum mechanics is what it is.
  3. Quantum mechanics is local. To be precise, no action at point A will have an observable effect at point B that is instantaneous, or non-causal.  Note the word observable. Locality is often denied in an attempt to circumvent Point 2, but when restricted to what is observable, locality holds. Despite the Pentagon’s best efforts, no messages have been sent using quantum non-locality.

 

Realism, at least, is a common aspect of the macroscopic world. Even a baby quickly learns that the ball is behind the box even when he cannot see it. But much about the microscopic world is not obviously determinist, the weather in Vancouver for example (it is snowing as I write this). Nevertheless, we cling to determinism and realism like a child to his security blanket. It seems to me that determinism or realism, if they exist, would be at least as hard to understand as their lack. There is no theorem that states the universe should be deterministic and not probabilistic or vice versa. Perhaps god, contrary to Einstein’s assertion, does indeed like a good game of craps[3].

So quantum mechanics, at least at the surface level, has features many do not like. What has the response been? They have followed the example set by Philip Gosse (1810 – 1888) with the Omphalos hypothesis[4]. Gosse, being a literal Christian, had trouble with the geological evidence that the world was older than 6,000, so he came up with an interpretation of history that the world was created only 6,000 years ago but in such a manner that it appeared much older. This can be called an interpretation of history because it leaves all predictions for observations intact but changes the internal aspects of the model so that they match his preconceived ideas. To some extent, Tycho Brahe (1546 – 1601) used the same technique to keep the earth at the center of the universe. He had the earth fixed and the sun circle the earth and the other planets the sun. With the information available at the time, this was consistent with all observations.

The general technique is to adjust those aspects of the model that are not constrained by observation to make it conform to one’s ideas of how the universe should behave. In quantum mechanics these efforts are called interpretations. Hugh Everett (1930 – 1982) proposed many worlds in an attempt to make quantum mechanics deterministic and realistic. But it was only in the unobservable parts of the interpretation that this was achieved and the results of experiments in this world are still unpredictable. Louis de Broglie (1892 – 1987) and later David Bohm (1917 – 1992) introduced pilot waves in an effort to restore realism and determinism. In doing do they gave up locality. Like Gosse’s work, theirs was nice proof in principle that, with sufficient ingenuity, the universe could be made to conform to almost any preconceived ideas, or at least appear to do so. Reassuring I guess, but like Gosse it was done by introducing non-observable aspects to the model: not just unobserved but in principle unobservable. The observable aspects of the universe, at least as far as quantum mechanics is correct, are as stated in the three points above: probabilistic, nonrealistic and local.

Me, I am not convinced that there is anything to understand about quantum mechanics beyond the rules for its use given in standard quantum mechanics text books. However, interpretations of quantum mechanics might, possibly might, suggest different ways to tackle unsolved problems like quantum gravity and they do give one something to discuss after one has had a few beers (or is that a few too many beers).

To receive a notice of future posts follow me on Twitter: @musquod.


[1] See my February 2014 post “Reality and the Interpretations of Quantum Mechanics.”

[2] Realism as defined in the paper by Einstein, Podolsky and Rosen, Physical Review 47 (10): 777–780 (1935).

[3] Or dice.

Share

Reality and the Interpretations of Quantum Mechanics

Friday, February 7th, 2014

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.

To receive a notice of future posts follow me on Twitter: @musquod.


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

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

Share