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Posts Tagged ‘Philosophy of science’

Dedicated to Johanna[1]

There are two observations about women in physics and mathematics that are at odds with each other. The first is that there are relatively few women in science. In a typical seminar or conference presentation I have counted that just over ten percent of the audience is female. The second is that, despite the relatively few women, they are by no means second-rate scholars. The first person to ever win two Nobel Prizes was a woman–Marie Curie (1867–1924). But I do not have to go far-far away and long-long ago to find first rate women scientists. I just have to go down the corridor, well actually down the corridor and up a flight of stairs since my office is in the ground floor administrative ghetto while the real work gets done on the second floor.  Since women are demonstratively capable, why are there so few of them in the mathematical sciences?

A cynic could say they are too bright to waste their time on such dead end fields but as a physicist I could never admit the validity of that premise. So why are there so few women in physics and mathematics? It is certainly true that in the past these subjects were considered too hard or inappropriate for women. Despite her accomplishments and two Nobel prizes, Madam Curie was never elected to the French Academy of Sciences. Since she was Polish as well as a woman the reason may have been as much due to xenophobia as misogyny.

Another interesting example of a successful woman scientist is Caroline Herschel (1750–1848). While not as famous as her brother William (1738–1822), she still made important discoveries in astronomy including eight comets and three nebulae. The comment from Wikipedia is in many ways typical: Caroline was struck with typhus, which stunted her growth and she never grew past four foot three. Due to this deformation, her family assumed that she would never marry and that it was best for her to remain a house servant. Instead she became a significant astronomer in collaboration with William. Not attractive enough to marry and not wanting to be a servant she made lasting contributions to astronomy.  If she had been considered beautiful we would probably never have heard of her! Sad.

Sophie Germain (1776–1831) is another interesting example. She overcame family opposition to study mathematics. Not being allowed to attend the lectures of Joseph Lagrange (1736–1813) she obtained copies of his lecture notes from other students and submitted assignments under an assumed male name. Lagrange, to his credit, became her mentor when he found out that the outstanding student was a woman. She also used a pseudonym in her correspondence with Carl Gauss[2] (1777–1855). After her death, Gauss made the comment: [Germain] proved to the world that even a woman can accomplish something worthwhile in the most rigorous and abstract of the sciences and for that reason would well have deserved an honorary degree. High praise from someone like Gauss, but why: even a woman? It reminds one of the quote from Voltaire (1694–1778) regarding the mathematician Émilie du Châtelet (1706–1749): a great man whose only fault was being a woman. Fault? And so it goes. Even outstanding women are not allowed to stand on their own merits but are denigrated for being women.

But what about today, does this negative perception still continue? While I have observed that roughly ten percent of attendees at physics lectures tend to be female, the distribution is not uniform. There tend to be more women from countries like Italy and France. I once asked a German colleague if she thought Marie Curie as a role model played a role in the larger (or is that less small) number of female physicists from those counties. She said no, that it was more to do with physics not being as prestigious in those counties. Cynical but probably true; through prejudice and convention women are delegated to roles of less prestige rather than those reflecting their interests and abilities.

My mother is probably an example of that. The only outlet she had for her mathematical ability was tutoring hers and the neighbour’s children, and filling out the family income tax forms. From my vantage point, she was probably as good at mathematics as many of my colleagues. One wonders how far she could have gone given the opportunity, a B. Sc., a Ph. D? One will never know. The social conventions and financial considerations made it impossible. Her sisters became school teachers while she married a small time farmer and raised five children. It is a good thing she did because otherwise I would not exist.

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[1] A fellow graduate student who died many years ago of breast cancer.

[2] Probably the greatest mathematician that ever existed.

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Is science merely fiction?

Friday, February 8th, 2013

Hans Vaihinger (1852 – 1933) was a German philosopher who introduced the idea of “as if” into philosophy. His book, Die Philosophie des Als Ob (The Philosophy of ‘As If’), was published in 1911, but written more than thirty years earlier. He seems to have survived the publish or perish paradigm for thirty years.

In his book, Vaihinger argued that we can never know the true underlying reality of the world but only construct systems which we assume match the underlying reality. We proceed as if they were true.  A prime example is Newtonian mechanics. We know that the underlying assumptions are false—the fixed Euclidean geometry for example—but proceed as if they were true and use them to do calculations. The standard model of particle physics also falls into this category. We know that at some level it is false but we use it anyway since it is useful. Vaihinger himself used the example of electrons and protons as things not directly observed but assumed to exist. They are, in short, useful fictions.

Vaihinger’s approach is a good response to Ernst Mach’s (1838 – 1916) refusal to believe in atoms because they could not be seen.  In the end, Mach lost that fight but not without casualties.  His positivism had a negative effect on physics in many ways was a contributing factor in Ludwig Boltzmann’s (1844 – 1906) suicide.  The philosophy of ‘as if’ is the antithesis of positivism, which holds closely to observation and rejects things like atoms which cannot be directly seen. Even as late as the early twentieth century, some respectable physics journals insisted that atoms be referred to as mathematical fictions.  Vaihinger would say to proceed as if they were true and not worry about their actual existence. Indeed, calling them mathematical fictions is not far from the philosophy of ‘as if’.

The ideas of Vaihinger had precursors. Vaihinger drew on Jeremy Bentham’s (1748 – 1832) work  Theory of Fictions. Bentham was the founder of modern utilitarianism and a major influence on John Stuart Mill (1806 – 1873) among others.  ‘As if’ is very much a form of utilitarianism: If a concept is useful, use it.

The idea of ‘as if’ was further developed in what is known as factionalism. According to fictionalism, statements that appear to be descriptions of the world should be understood as cases of ‘make believe,’ or pretending to treat something as literally true (a ‘useful fiction’ or ‘as if’).  Possible worlds or concepts, regardless of whether they really exist or not, may be usefully discussed. In the extreme case, science is only a useful discussion of fictions; ie science is fiction.

The core problem goes back at least to Plato (424/423 BCE – 348/347 BCE) with the parable of the cave (from The Republic). There, he talks about prisoners who are chained in a cave and can only see the wall of the cave.  A fire behind them casts shadows on the wall and the prisoners perceive these shadows as reality since this is all they know. Plato then argues that philosophers are like a prisoner who is freed from the cave and comes to understand that the shadows on the wall are not reality at all. Unfortunately, Plato (and many philosophers after him) then goes off in the wrong direction. They take ideas in the mind (Plato’s ideals) as the true reality. Instead of studying reality, they study the ideals which are reflections of a reflection. While there is more to idealism than this, it is the chasing after a mirage or, rather, the image reflected in a mirage.

Science takes the other tack and says we may only be studying reflections on a wall or a mirage but let us do the best job we can of studying those reflections. What we see is indeed, at best, a pale reflection of reality. The colours we perceive are as much a property of our eyes as of any underlying reality. Even the number of dimensions we perceive may be wrong. String theory seems to have settled on eleven as the correct number of dimensions but that is still in doubt. Thus, science can be thought of as ‘as if’ or fictionalism.

But that is far too pessimistic, even for a cynic like me. The correct metaphor for science is the model. What we build in science are not fictions but models. Like fictions and ‘as if,’ these are not reality and should never be mistaken for such, but models are much more than fictions. They capture a definite aspect of reality and portray how the universe functions. So while we scientists may be studying reflections on a wall, let us do so with the confidence that we are learning real but limited knowledge of how the universe works.

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I like talking about science. I like talking about religion. I even like talking about the relationship and boundaries between the two. These are all fascinating subjects, with many questions that are very much up for debate, so I am very pleased to see that CERN is participating in an event in which scientists, philosophers, and theologians talk together about the Big Bang and other questions.

But this quote, at least as reported by the BBC, simply doesn’t make any sense:

Co-organiser Canon Dr Gary Wilton, the Archbishop of Canterbury’s representative in Brussels, said that the Higgs particle “raised lots of questions [about the origins of the Universe] that scientists alone can’t answer”.

“They need to explore them with theologians and philosophers,” he added.

The Higgs particle does no such thing; it is one aspect of a model that describes the matter we see around us. If there is a God, CERN’s recent observations tell us that God created a universe in which the symmetry between the photon and the weak bosons is probably broken via the Higgs Mechanism. If there is not, they tell us that a universe exists anyway in which the symmetry between the photon and the weak bosons is probably broken via the Higgs Mechanism. It doesn’t raise any special questions about the origins of the universe, any more than the existence of the electron does.

There are many interesting philosophical questions to ask about the relationships between models of scientific observations on the one hand, and notions of absolute Truth on the other. You can also talk about what happened before the times we can make scientific observations about, whether there are “other universes” with different particles and symmetries, and so on. Theologians and philosophers have much to say about these issues.

But in regard to searches for the Higgs boson in particular, the people we need to explore questions with are mostly theoretical physicists and statisticians.

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How is that for the ultimate claim in the ultimate[1] essay in this series? Science: mankind’s greatest achievement. Can there be any doubt? In the four hundred years since science went mainstream, we have learned how the universe works, changed our conception of man’s place in it, and provided the knowledge to develop fantastic technology. We have big history: the inspiring story of the universe beginning with the primordial big bang and creating order out of chaos through self-interaction, and finally life arising and evolving in our corner of the universe. We have developed models that describe the universe on the largest visible scales down to sub-atomic sizes: astronomy, biology, chemistry, cosmology, medicine, physics, psychology, animate, inanimate, eater, and eatee. The models form a mosaic that overlap and interlock to form a seamless whole.  An amazingly complete picture. There is still much to know, but let us take credit as scientists, that much is known. And yes, we should be glad to be living in a time when so much is known.

However, science has two short-comings[2]: it does not offer the illusions of certainty or purpose.  I once came across a last will and testament that began: I commit my body into the ground in the sure and certain knowledge it will be restored to me on the judgement day. Ah, for sure and certain knowledge. Well, the judgement day has not come yet so we do not know if his sure and certain knowledge was valid, but the resurrection of the body is much less prominent in Christian apologetics than it used to be.  When it comes to knowledge, science promises less but delivers more than its competitors in philosophy or theology. I would take Isaac Newton (1642 – 1727) over Rene Descartes (1596 – 1650), Immanuel Kant (1724 – 1804), Thomas Aquinas (1225 – 1274), or William Paley (1743 – 1805) any day of the week and all together.  Their certain knowledge has largely vanished, but Newton’s uncertain and approximate knowledge is still being used in many practical applications. Ask any mechanical engineer.

In the Hitch Hiker’s Guide to the Galaxy, Douglas Adams (1952 – 2001) introduces the total perspective vortex. It was created by a husband whose wife keeps telling him to put things in perspective. However, when anyone looked in the vortex, they realized how utterly insignificant they were in the vast stretches of the universe and invariably went insane and died. This proved that if life is going to exist in a Universe of this size, then the one thing it cannot afford to have is a sense of proportion. Ah yes, the human need for importance and purpose. I guess the best science can come up with for a purpose is entropy[3] generation. I am not sure that is any worse than what I had heard from a Christian apologist who claimed we were created by God to worship him. Personally, I would never worship that narcissistic a God.

Despite its shortcomings, perceived or real, science has a tremendous track record. But the best is still to come. Let us not make the mistake of the late nineteenth century physicists who thought all the important questions had been answered.  There are things that enquiring minds still want to know: What, if anything, was there before the big bang? How do you combine gravity and quantum mechanics? Is there a solution for global warming that is politically acceptable? Are there room temperature superconductors? How did life begin? How intelligent were the Neanderthals? How does the mind work? The last strikes me as the most interesting question: the final frontier[4].  It has the potential to open up a whole new front in the conflict between science and religion, or science and philosophy.  But it is interesting nonetheless. Answering these questions and others will take clever theoretical approaches, clever experiments, and clever approaches to funding. However, the techniques of science are up to the task.

But what is science? In the final analysis, it is a human activity, an exercise of the human mind. We construct models and paradigms because that is how our minds and brains have evolved to deal with the complexities of our experiences. Thus, the nature of science is tied closely to the last question asked above: How does the mind work? Ultimately, how science works and indeed, the very definition of knowledge, are questions for neuroscience and the empirical study of the mind.

I am taking a break from blogging for the rest of the summer but may have some more blogs in the fall. I have run out of interesting things to say (no snide comments that that happened a long time ago). I would like to thank people for their many comments. They have been quite informative. To receive notices of future posts, if and when they occur, follow me on Twitter: @musquod.

 


[1] That is the LP in the language of effective field theorists (LP=last post, not long playing as you old timers thought).

[2] Humility is not one of them.

[3] Entropy generation is the driving force behind evolution.

[4] Sorry Star Trek fans, it is the mind, not space.

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The contentious relation between science and religion is the topic of this, the penultimate[1] post in the current series.  Ever since science has gone mainstream, there have been futile attempts to erect a firewall between science and religion. Galileo got in trouble with the Catholic Church, not so much for saying the earth moved as for suggesting the church steer clear of scientific controversies.  More recently, we have methodological naturalism (discussed in a previous post), a misidentification of why the supernatural is absent from science. Then there is the: science cannot answer the why question—but it can when it helps make better models (also discussed in a previous post). For example, why do beavers build dams? This can be answered by science. And there is the ever popular non-overlapping magisteria (NOMA) of Stephen J. Gould (1941 – 2002).  NOMA claims that “the magisterium of science covers the empirical realm: … The magisterium of religion extends over questions of ultimate meaning and moral value.”

The empirical realm covers not just what can be directly observed but what can be implied from what is observed. For example, quarks, and even something as well-known as electrons, are not directly observed but are implied to exist. That would also be true for citizens of the spirit or netherworld. If they exist, they presumably have observable effects. If they have no observable effect, does it matter if they exist or not? Similarly, a religion with no empirical content would be quite sterile, i.e. would prayer be meaningful if it had absolutely no observable effects?

Moral issues cannot be assigned purely to the religious sphere. The study of brain function impacts questions of free will and moral responsibility. Disease and brain injury can have very specific effects on behaviour, for example, a brain injury led to excessive swearing in one person. What about homosexuality? Is it biological or a lifestyle choice? Recent research has indicated a genetic component in homosexuality, thus mixing science with what some regard as a moral issue. Finally, what about when life begins and ends? Who decides who is dead and who is alive? And by what criteria?  Scientific or religious? This has huge implications for when to remove life support. The bigger fight is over abortion and the question of when independent life begins. Is it when the sperm fertilizes the egg? That is a scientific concept developed with the use of the microscope. That simple definition has problems when there are identical twins where the proto-fetus splits in two much later than at conception. In the other direction, both the sperm and the egg can be considered independent life. After all, the sperm has the ability to leave the donor’s body and survive for a period of time. The arguments one hears regarding when independent life begins are frequently an ungodly combination of scientific and theological arguments.

In the end, there is only one reality, however we choose to study or approach it.  Thus, any attempt to put a firewall between different approaches to reality will ultimately fail, be they based on science, religion, or philosophy.  At least the various religious fundamentalists recognize this, but their solution would take us back to the dark ages by subjugating science to particular religious dogmas. However, it does not follow that religion and science have to be in conflict. Since there is so much variation in religions, some are and some are not in conflict with any particular model developed by science. Still, it should be a major concern for theology that something like religion has not arisen naturally from scientific investigations.  While there are places God can hide in the models science produces, there is no place where He is made manifest. And it is not because He is excluded by fiat either (see the essay on methodological naturalism referenced above).

One should not make the same mistake as Andrew Dickson White (1832 –1918) in setting science and religion in perpetual hostility. He was a co-founder of Cornell University and its first president. He was also embittered by the opposition from the church to the establishment of Cornell as a secular institute. The result was the book: History of the Warfare of Science with Theology in Christendom (1896); a polemic against Christianity masquerading as a scholarly publication. This book, along with History of the Conflict between Religion and Science by John William Draper (1811 – 1882), introduced the conflict thesis regarding the relation between science and religion and said it is perpetual hostility. Against that, we note Newton, Galileo, and Kepler were all very religious and much science was done by clergymen in nineteenth century England. White’s book, in particular, has many problems. One is that the very opposition to change is cast as science versus religion rather than recognizing a lot of it as simple resistance to change. Even science is not immune to that—witness the fifty year delay in the acceptance of continental drift. The historical interplay between science and religion is now recognized to be very complex with them sometimes in conflict, sometimes in concord, and most commonly, indifferent.

If we take a step back from the results of science and its relation to particular religious dogmas, and look instead at the relation between the scientific method and theology, we see a different picture. Like science and western philosophy, science and theology represent competing paradigms for the nature of knowledge.   Science is based on observation and observationally constrained models; Western philosophy on rational arguments; while theology is based more on spirituality, divine revelation, and spiritual insight. This is, in many ways, a more serious conflict than between scientific results and particular religions. Particular religions can change, and frequently have changed, in response to new scientific orthodoxy, but it is much more difficult to change one’s conceptual framework or paradigm. Also, as Thomas Kuhn (1922 – 1996) and Paul Feyerabend (1924 – 1994) pointed out, different paradigms tend to be incommensurate. They provide different frameworks that make communication difficult. They also have conflicting methods for deciding questions, making cross-paradigm conflict resolution difficult, if not impossible. Hence, there will be tension between science and theology forever, with neither dominating.

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[1] NLP in the notation of effective field theorists.

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The Myth of the Open Mind

Friday, June 22nd, 2012

The race of truly open-minded people is long extinct: To be open minded, I will suspend belief that that tawny blob over there is a leopard. Pounce, chomp, chomp. Even today, natural selection is working to remove the truly open minded from the gene pool: To be opened minded, I will remove any judgment of whether jaywalking and texting at the same time is a good or bad idea. Splat, crumple, crumple. As I said, the race of truly opened minded people is long extinct, if it ever actually existed.

You may complain that I am misrepresenting the concept of open-mindedness. That is probably true. When most people accuse someone of being closed-minded, they mean little more than that the person does not agree with them. Be that as it may, in general, the related concepts of open-mindedness and freedom from preconceived ideas are vastly overrated. But what about in science? Surely in science it is necessary to keep an open mind and eliminate preconceived ideas?  Perhaps, but here is what Henri Poincaré said on the topic:

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, for example, use language, and our language is necessarily steeped in preconceived ideas. Only, they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.

Let’s look at this in a bit more detail. Consider his statement: would it make every experiment fruitless. I have served on many review panels and refereed many proposals. Not one of them was free of preconceived ideas or was truly open minded. I guess such a proposal would begin: To be open-minded to all points of view and to avoid preconceived ideas and prejudice we have used a random number generator to choose the beam species and energy. As I say, I have never seen a proposal like that, but I can easily imagine how it would be treated. Not kindly. Review committees are notoriously closed-minded. They demand that every proposal justify the work based on the current understanding in the field.  The value of an experiment depends on how it relates to the current models in the area. The experiments at the Large Hadron Collider (LHC) are given meaning by the standard model of particle physics. Every experiment at TRIUMF has to be justified based on what it will tell us, how it fits into the nuclear models.

What about the acceptance of new ideas? Surely, there, we have to be open-minded. Certainly not! Extraordinary claims require extraordinary proof. This is not a statement of open mindedness. The idea here goes back at least to Pierre-Simon Laplace (1749 – 1827): The weight of evidence for an extraordinary claim must be proportioned to its strangeness. We saw this closed mindedness play out recently with respect to neutrinos traveling faster than the speed of light. The initial claim was roundly rejected; the proponents criticized for publishing such a preposterous idea. In this case, the closed-minded people were correct
(they frequently are) as it was subsequently found that there was an experimental error.

Even if we wanted to be, we could not be open-minded. Frederick II (1194 – 1250) is said to have carried out an experiment were he had infants raised without people talking to them to see what the natural language was. What he found was that infants treated this way died. Even independent of that experiment, we know most children are talked to and pick up language and other preconceived ideas from their caregivers. As Poincaré said, language is steeped in preconceived ideas.  A truly open mind free from preconceived ideas is an impossibility.

Continuing Poincaré’s quote: Shall we say, that if we cause others [preconceived ideas] to intervene of which we are fully conscious, that we shall only aggravate the evil? I do not think so. I am inclined to think that they will serve as ample counterpoises — I was almost going to say antidotes. They will generally disagree, they will enter into conflict one with another, and ipso facto, they will force us to look at things under different aspects. This is enough to free us. He is no longer a slave who can choose his master. If you like, we should choose our preconceived ideas and choose them wisely. Then we are in charge, not them.

Open mindedness and freedom from preconceived ideas are only positive in small doses. One has to be open-minded enough to accept the next breakthrough, but not so open-minded as to follow every will-of-the-wisp.  The real genius in science is in knowing when to be open-minded and when to be as stubborn as a mule. It is in knowing which ideas to hold onto and which one to discard.

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Many years ago when I was in a grade-eight math class, I was sitting looking out the windows at the dinosaurs playing. Ok, despite what my daughter thinks, I am not quite that old. What I was looking at was planes circling around in the distance. It turns out that a plane had crashed. It was a Handley Page HPR-7 Herald 211 operated by Eastern Provincial Airlines and all eight people on board were killed.  Now, it is sometimes claimed that science cannot explain the past. It’s even argued that historical sciences like paleontology, archeology, and cosmology, somehow use different methods of discovering the past, than say, determining the reason of a plane crash and that is again different from the method for discovering the laws of nature.  In reality, the methods are all the same.

I suppose, in response to the plane crash, people could have sat around and made predictions for future plane crashes but instead they used science to try to discover the past—what had caused the plane to crash. In this case it turned out to not be so difficult. The Aviation Safety Network describes the cause thus: Failure of corroded skin area along the bottom centre line of the aircraft beneath stringer No.32 which resulted in structural failure of the fuselage and aerial disintegration. This was found out by a metallographic examination which provided clear evidence of stress corrosion in the aluminum alloy. The planes of this type that were remaining in service were repaired to prevent them from crashing as well.

The approach to understanding why the Eastern Provincial Airline’s plane had crashed followed a similar approach to any other plane crash: you analyse the debris, gather records from the black box and whatever other information is available, and construct a model for what happened. You test the model by making predictions for future observations; for example, that corrosion will be found on other planes of the same type.  This sounds very much like the standard scientific method as proposed originally by Roger Bacon (1220 – 1292) and followed by scientists ever since: observe, hypothesize, test, rehypothesize, and repeat as necessary.

The same technique is used for any reconstruction of the past, be it plane crashes, the cause of Napoleon’s death, archeology, paleontology, evolution, and cosmology. The cause of Napoleon’s death is quite interesting as an exercise in forensic science. The original cause of death was suggested to be gastric cancer. But that is too mundane a cause of death for such an august figure. So the conspiracy advocates went to work and suggested he was poisoned by arsenic. How to test? Easy look for arsenic in samples of hair. Well, that was done and arsenic was found. Case closed? Not quite. Were there other sources of arsenic than deliberate poisoning? Yes, the wall paper in his room had arsenic in it. Also further investigation revealed that he had been exposed to arsenic long before he went to St. Helena.  In support of the caner hypothesis his father also died of stomach cancer.  The current consensus is that the original diagnosis was correct. He died of stomach cancer. But notice the play of events: hypothesis—arsenic poisoning, testing—look for arsenic in hair samples, refine hypothesis—check for other sources of arsenic, etc. We can see here the classic process of science being played out in reconstructing the past.

We can continue this technique into the more distant past: When did humans evolve? Why did the dinosaurs die out? How did the earth form? How did the solar system form? What if anything preceded the big bang? All of these questions can be tackled using the standard methods of science. Observations of present tell us about the past, counting tree ring tells us when the tree started to grow.

The interplay between what might be called natural history and natural laws is very intricate. We must interpret the past in order to extract the natural laws and use the natural laws to interpret the past. All our models of science have, explicitly or implicitly, both an historical and a law component. In testing a model for how the universe works—ie to develop the laws—we conduct an experiment. Once the experiment is finished, it becomes history and interpreting it is historical science.  For example, why did the OPERA experiment claim to see faster than light propagation for neutrinos? Or is the bump seen in searches for the Higgs boson real or an artifact of the detector? Those investigations are as much forensic science as trying to decide why Napoleon died or the dinosaurs went extinct.  Thus, all science is historical and sometimes, quite explicitly. Einstein abandoned the cosmological constant based on an alternate model for the history of the universe, namely that it is expanding rather than static.

So, we have science as a unified whole, encompassing the past, present, and future; the natural laws entangled with the natural history. But what about the dinosaurs I did not see out of the math-room windows? We can be quite sure they did not exist at that time and that Fred Flintstone did not have one as a pet (a saber-toothed pussy cat is another story). The study of evolution is much like that for plane crashes. You study the debris, in the case of evolution that “debris” includes fossils and the current distribution of species.  Consider the fossil Tiktaalik roseae, a tetrapod-like fish or a fish-like tetrapod, that was found a few years ago.  One can engage in futile semantic arguments about whether it is a fish, or a tetrapod, or a missing link, or whether it is the work of the devil. However, the significant point is that a striking prediction has been confirmed by a peer-reviewed observation. Using evolution, a model of fossil formation, and a model of the earth’s geology, a prediction was made that a certain type of fossil would be found in a certain type of rock. Tiktaalik roseae dramatically fulfilled that prediction and provides information on the fish-tetrapod transition.

The cause of plane crashes, Napoleon’s death, evolution, and the extinction of dinosaurs can all be explored by using the same empirically-constrained model-building techniques as the rest of science.  There is only one scientific method.

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“Give it to me—the real news”
“So I will”
“Well, Dadamashay, let me see what skill you have. Tell me the big new news of these days, making it ever so small.”
“Listen”[1]

When, I was a graduate student, somewhat after the time of the Vikings in long boats, my thesis supervisor, Prof. Bhaduri[2], took me with him when he went on sabbatical to Copenhagen, a Mecca for nuclear physics at that time.  When we were leaving there, his officemate gave him a small Mickey Mouse figurine so he would know what kind of physics to work on. Well another man might have been angry, And another man might have been hurt, But another man never would have[3] stressed during his seminar that he was using a Mickey Mouse model. A yes, Mickey Mouse science, the simple model or calculation that brings out salient features that are all too often lost or obscured in the complete calculation.

We all know what big science is: the big detectors at the Large Hadron Collider (CMS has a 12,500 ton steel yoke) or the Super-Kamiokande (50,000 tons of water). That is big science. Even theoretical physics does big science: the massive calculations of lattice quantum chromodynamics (QCD) or the nuclear shell model. Now, there have been attacks on big science, either the LHC or lattice QCD, as being inherently evil because they are so big. Would you believe, even books written on the topic? I strongly disagree with that view. Large science is an essential part of science. Big is needed to answer the questions we want answers to. However, there is more to science than that. We need the little to complement the big, the simple to complement the complex. As a post-doc, I was returning from a somewhat annoying conference with Gerry Brown[4] (b. 1926), one of leading nuclear physicists of that generation, when he turned to me in exasperation and said that people did not realize how many hours of computer time went into his simple estimates. There is an interesting concept: using computer time to justify simple estimates, simple complementing the complex. The purpose of computing is insight, not numbers[5] and the simple Mickey Mouse models are essential in generating that insight—even when they are justified by complex calculations.

The simple models are useful in a number of ways. First, they are useful in checking the results of complex computer calculations.  I have learnt through bitter experience never to believe the result of a computer calculation until I have “understood” them (and not always then). That is, until using some simple model or estimates, either explicitly or implicitly, I can reproduce the main trends of the results. In trying to do that, I have frequently found errors. Never trust a number you do not understand.

Second, we want to understand what aspects of the model are important in reproducing the results and which are coincidental.  Scientific models are designed to predict future observations, but which aspects of the model are crucial to that endeavour. It is through the use of simple models that we can most easily explore the dependencies of the results on the assumptions.  We calculate some nuclear cross-section. Is that bump significant? What, if anything, does the location of the bump tell us? What about the turn up near threshold? Is that an artifact? We want to know more than merely if the calculation fits the data. It is here that the simple models come in. They give us the insight into how the models can be improved and what assumptions are not necessary and can be eliminated.

Finally, and most importantly, it is the simple models that allow us, as people, to understand the results. It is not just for the layman that we need the simple models, but for the expert as well. A prime example would be the non-relativistic quark model. Its success calculating the properties of the excited states of the proton was touted as proof of the quark model but all it tested was the symmetries built into the calculations. The simple approximations to the non-relativistic quark model revealed it pretentions. But as a Mickey Mouse model, the non-relativistic quark model gave us insight into QCD that would have been difficult if not impossible to obtain otherwise.

I suppose one could hook up the computers directly to the experiments and have them generate models, test the models against new observations and then modify the experimental apparatus without any human intervention. However, I am not sure that would be science.  Science is ultimately a human activity and the models we produce are products of the human mind. It is not enough that the computer knows the answer.  We want to have some feeling for the results, to understand them. Without the simple models, Mickey Mouse science, that would not be possible: the big news made ever so small.

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[1] Quoted from Rabindra Nath Tagore (1861 – 1941) in Fables. Also used as an inscription in R.K. Bhaduri’s book: Models of the Nucleon.
[2] A scholar and a gentleman.
[3] With apologies to Harry Chapin and the song: The Taxi.
[4] No, not the California politician.
[5] Quoted from Richard Hamming (1915 – 1998) 

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There is this myth that science is exact. It is captured nicely in this quote from an old detective story:

In the sciences we must be exact—not approximately so, but absolutely so. We must know. It isn’t like carpentry. A carpenter may make a trivial mistake in a joint, and it will not weaken his house; but if the scientist makes one mistake the whole structure tumbles down. We must know. Knowledge is progress. We gain knowledge through observation and logic–inevitable logic. And logic tells us that while two and two make four, it is not only sometimes but all the time. – Jacques Futrelle, The Silver Box, 1907

Unless, of course, it is two litres of water and two litres of alcohol, then we get less than four litres. Note also the almost quaint idea that science is certain, not only exact, but certain. We must know. The view expressed in this quote is unfortunately not confined to century-old detective stories, but is part of the modern mythology of science. But in reality, science is much more like carpentry. A trivial mistake does not cause the whole to collapse, but I would not like to live in a house built by that man.

To the best of my knowledge, there has never been an exact calculation in all of physics. In principle, everything in the universe is connected. The earth and everything in it is connected by the gravitational field to the distant quasars. But you say, surely that is negligible, which is precisely the point. It is certainly not exactly zero, but with equal certainty, it is not large enough to be usefully included in any calculation. I know of no terrestrial calculation that includes it. Even closer objects like Jupiter have negligible effect. In the grand scheme, the planets are too far from the earth to have any earthly effect. Actually, it is not the gravitational field itself which is important but the tidal forces which are down an additional factor of the ratio of the radius of the earth to the distance to the planet in question. Hence, one does not expect astrology to be valid. The art of the appropriate approximation tells us so.

Everywhere we turn in science we see the need to make the appropriate approximations. Consider numerical calculations. Unless you are calculating the  hypotenuse of a triangle with side of 3 and 4 units, almost any numerical calculation will involve approximations. Irrational numbers are replaced with rational approximations, derivatives are replaced with finite differences, integrals with sums, and infinite sums with finite sums. Every one of these is an approximation—usually a valid approximation—but never-the-less an approximation. Mathematical constants are replaced by approximate values. Someone once asked me for assistance in debugging a computer program. I noticed that he had pi approximated to only about six digits. I suggested he put it in to fifteen digits (single precision on a CDC computer). That, amazingly enough, fixed the problem. Approximations, even seemingly harmless ones, can bite you.

Even before we start programing and deciding on numerical techniques, it is necessary to make approximations. What effects are important and which can be neglected? Is the four-body force necessary in your nuclear many-body calculation? What about the five-body force? Can we approximate the problem using classical mechanics, or is a full quantum treatment necessary? Thomas Kuhn (1922 – 1996) claimed that classical mechanics is not a valid approximation to relativity because the concept of mass is different. Fortunately, computers do not worry about such details and computationally classical mechanics is frequently a good approximation to relativity. The calculation of the precision of the perihelion of Mercury does not require the full machinery of general relativity, but only the much simpler post-Newtonian limit. And on and on it goes, seeking the appropriate approximation.

Sometimes the whole problem is in finding the appropriate approximation. If we assume nuclear physics can be derived from quantum chromodynamics (QCD), then nuclear physics is reduced to finding the appropriate approximation to the full QCD calculation, which is by no means a simple task. Do we use an approximation to the nuclear force based on power counting, or the old fashioned unitarity and crossing symmetry? (Don’t worry if you do not know what the words mean, they are just jargon and the only important thing is that the approximations lead to very different looking potentials.) Do the results depend on which approach is used, or only the amount work required to get the answer?

Similarly, in materials science, all the work is in identifying the appropriate approximation. The underlying forces are known: electricity and magnetism. The masses and charges of the particles (electrons and atomic nuclei) are known. It only remains to work out the consequences. Only, he says, only. Even in string theory, the current proposed theory of everything, the big question is how to find useful approximations to calculate observables. If that could be done, string theory would be in good shape. Most of science is the art of finding the appropriate approximation. Science may be precise, but it is not exact, and it is in finding the appropriate approximation that we take delight.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod.

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This essay was motivated by a question from an engineering colleague. It would be presumptuous to say “friend,” as scientist and engineers are in a state of “friendly” rivalry, however, not to the extent as with arts. I once saw a sign in an engineering department hallway that read: Friends do not let friends study arts. Be that as it may, my colleague’s question was why scientists do not show the same order in all their work as they show in writing papers. That question I will attempt to answer in this essay.

Engineering is far older than science, being perhaps the second oldest profession, dating back at least to the building of the pyramids (Imhotep from the 27th century BCE is the oldest named engineer) and Stonehenge and probably back to when the first club was engineered.  Stonehenge is amazing as it was probably built without the documentation that is the hallmark of modern engineering practice. Unfortunately, that means we do not know what the initial requirements[1] were and this has led to much futile speculation as to its purpose.

Science and engineering are sibling disciplines, frequently mentioned together and have much in common. The main similarity is that they both deal with the observable universe and are judged by their ability to make correct predictions regarding its behaviour. For example, that the Higgs boson will be found at the Large Hadron Collider (LHC) or that the building will not collapse in an earthquake. Secondarily they use similar techniques, placing high importance on analytic reasoning, to the extent that Asperger’s syndrome is sometimes called the engineer’s disease. The relation between Asperger’s syndrome and engineers or scientists may be an urban myth but it does indicate the relation of extreme analytic thought to both science and engineering. The solution to problems in both relies on the same problem solving skills, analytic thinking and mathematics. Do not let anyone tell you that either does not require a high degree of intellectual activity.

Science and engineering rely on each other. Behind every engineering project is a great deal of science, from the basic understanding of Newtonian mechanics in the building of a bridge to the advanced materials science in the construction of a cell phone. Actually, the cell phone is a good example of all the science needed: it depends on Newtonian mechanics (the construction of the cell phone towers), quantum mechanics (the operation of the transistors), classical electromagnetism i.e. Maxwell’s equations (the propagation of the signal from the tower to the cell phone), materials science (almost all the cell phone itself), and general and special relativity (the GPS timing that is necessary in some cell phone technologies).

Equally, science is beholden to engineering. From simple things like the buildings that house scientific equipment to complicated things like the ATLAS detector at the Large Hadron Collider (LHC). Making a building may seem simple but, as I see with the new ARIEL building at TRIUMF, nothing is simple and even something as basic as a laboratory building relies on engineering expertise. The ATLAS detector is another story. Its size and complexity are a marvel of engineering virtuosity. Back to TRIUMF, the IEEE has recognized the TRIUMF cyclotron, commissioned in 1974 and the main driver for much of TRIUMF’s science program, as an Engineering Milestone. Even the slide rule I used back in ancient history as an undergraduate[2] was an engineering achievement.

Despite the close relationship between science and engineering the two are different. The difference can be summarized in this statement: “In engineering you do not start a project unless you know the answer while in science you do not start a project if you know the answer.” Engineering is based on everything being predictable; you do not start building a bridge unless you know you can complete it. In science, the purpose of a project is to answer a question to which the answer is currently unknown. For example, if the properties of the Higgs boson were known, it would not have been necessary to build the LHC. Good engineering practice is based on order but at the center of science is chaos. We are exploring the unknown; great discoveries can come from serendipity. In science, something not working as expected can lead to the next big breakthrough. In engineering, something not working as expected can lead to the bridge collapsing. Advances in science are frequently due to creativity, not following rules.

This difference in perspective leads to very different cultures in the two disciplines. The engineer is much more concerned with process and following procedure. The scientist with following up his most recent hunch—after all, it could lead to a Nobel Prize.  Engineering versus science: order versus creative chaos. This is clearly an oversimplification as there is no clean separation between engineering and science, but it is a good indication of the divergence between the two mindsets. Thus, although engineering and science are closely related and indeed intertwined, the two, in their heart of hearts, are very different; engineering uses science in order to build and science uses engineering in order to explore.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod.


[1] Project management jargon alert: requirements used in technical project management sense.

[2] HP produced the first pocket calculator when I was an undergraduate student.

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