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Posts Tagged ‘Philosophy of science’

This essay makes a point that is only implicit in most of my other essays–namely that scientists are arro—oops that is for another post. The point here is that science is defined not by how it goes about acquiring knowledge but rather by how it defines knowledge. The underlying claim is that the definitions of knowledge as used, for example, in philosophy are not useful and that science has the one definition that has so far proven fruitful. No, not arrogant at all.

The classical concept of knowledge was described by Plato (428/427 BCE – 348/347 BCE) as having to meet three criteria: it must be justified, true, and believed. That description does seem reasonable. After all, can something be considered knowledge if it is false? Similarly, would we consider a correct guess knowledge? Guess right three times in a row and you are considered an expert –but do you have knowledge? Believed, I have more trouble with that: believed by whom? Certainly, something that no one believes is not knowledge even if true and justified.

The above criteria for knowledge seem like common sense and the ancient Greek philosophers had a real knack for encapsulating the common sense view of the world in their philosophy. But common sense is frequently wrong, so let us look at those criteria with a more jaundiced eye. Let us start with the first criteria: it must be justified. How do we justify a belief? From the sophists of ancient Greece, to the post-modernists and the-anything-goes hippies of the 1960s, and all their ilk in between it has been demonstrated that what can be known for certain is vanishingly small.

Renee Descartes (1596 – 1960) argues in the beginning of his Discourse on the Method that all knowledge is subject to doubt: a process called methodological skepticism. To a large extend, he is correct. Then to get to something that is certain he came up with his famous statement: I think, therefore I am.  For a long time this seemed to me like a sure argument. Hence, “I exist” seemed an incontrovertible fact. I then made the mistake of reading Nietzsche[1] (1844—1900). He criticizes the argument as presupposing the existence of “I” and “thinking” among other things. It has also been criticized by a number of other philosophers including Bertrand Russell (1872 – 1970). To quote the latter: Some care is needed in using Descartes’ argument. “I think, therefore I am” says rather more than is strictly certain. It might seem as though we are quite sure of being the same person to-day as we were yesterday, and this is no doubt true in some sense. But the real Self is as hard to arrive at as the real table, and does not seem to have that absolute, convincing certainty that belongs to particular experiences. Oh, well back to the drawing board.  

The criteria for knowledge, as postulated by Plato, lead to knowledge either not existing or being of the most trivial kind. No belief can be absolutely justified and there is no way to tell for certain if any proposed truth is an incontrovertible fact.  So where are we? If there are no incontrovertible facts we must deal with uncertainty. In science we make a virtue of this necessity. We start with observations, but unlike the logical positivists we do not assume they are reality or correspond to any ultimate reality. Thus following Immanuel Kant (1724 – 1804) we distinguish the thing-in-itself from its appearances. All we have access to are the appearances. The thing-in-itself is forever hidden.

But all is not lost. We make models to describe past observations. This is relatively easy to do. We then test our models by making testable predictions for future observations. Models are judged by their track record in making correct predictions–the more striking the prediction the better. The standard model of particle physics prediction of the Higgs[2] boson is a prime example of science at its best. The standard model did not become a fact when the Higgs was discovered, rather its standing as a useful model was enhanced.  It is the reliance on the track record of successful predictions that is the demarcation criteria for science and I would suggest the hallmark for defining knowledge. The scientific models and the observations they are based on are our only true knowledge. However, to mistake them for descriptions of the ultimate reality or the thing-in-itself would be folly, not knowledge.

 



[1] Reading Nietzsche is always a mistake. He was a madman.

[2] To be buzzword compliant, I mention the Higgs boson.

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A colleague of mine is an avid fan of the New York Yankees baseball team. At a meeting a few years ago, when the Yankees had finished first in the American league regular season, I pointed out to him that the result was not statistically significant. He did not take kindly to the suggestion. He actually got rather angry! A person, who in his professional life would scorn anyone for publishing a one sigma effect, was crowing about a one sigma effect for his favorite sports team. But then most people do ignore the effect of statistical fluctuations in sports.

In sports, there is a random effect in who wins or loses. The best team does not always win. In baseball where two teams will frequently play each other four games in a row over three or four days, it is relatively uncommon for one team to win all four games. Similarly a team at the top of the standings does not always beat a team lower down.  As they say in sports: on any given day, anything can happen. Indeed it can and frequently does.[1]

Let us return to American baseball. Each team plays 162 games during the regular season. If the results were purely statistical with each team having a 50% chance of winning any given game, then we would expect a normal distribution of the results with a spread of sigma=6.3 games. The actual spread or standard deviation for the last few seasons is closer to 11 games. Thus slightly more than half the spread in games won and lost is due to statistical fluctuations. Moving from the collective spread to the performance of individual teams, if a team wins the regular season by six games or one sigma, as with the Yankees above, there is a one in three chance that it is purely a statistical fluke. For a two-sigma effect, a team would have to win by twelve games or by eighteen games for a three-sigma effect. The latter would give over 99% confidence that the winner won justly, not due to a statistical fluctuation. When was the last time any team won by eighteen games? For particle physics we require an even higher standard–a five sigma effect to claim a discovery. Thus a team would have to lead by 30 games to meet this criterion. Now my colleague from the first paragraph suggested that by including more seasons the results become more significant.  He was right of course. If the Yankees finished ahead by six games for thirty-four seasons in a row that would be five-sigma effect. From this we can also see why sports results are never published in Physical Review with its five-sigma threshold for a discovery–there has yet to be such a discovery. To make things worse for New York Yankees’ fans they have already lost their chance for an undefeated season this year.

In other sports the statistics are even worse. In the National Hockey League (NHL) teams play eighty-two games and the spread in win-loss expected from pure chance is sigma=4.5. The actual distribution for last year was 6.3 sigma. The signal due the difference in the individual teams’ ability is all in the 1.8 sigma difference. Perhaps there is more parity in the NHL than in Major League Baseball. Or perhaps there is not enough statistics to tell. Speaking of not telling. Last year the Vancouver Canucks finished with the best record for the regular season, two games ahead of the New York Rangers and three games ahead of the St. Louis Blues. Only a fool or a Vancouver Canucks fan would think this ordering was significant and not just a statistical fluctuation. In the National Football League last year, 14 of the 32 teams were within two sigma of the top. Again much of the spread was statistical. It was purely a statistical fluke that the New England Patriots did not win the super bowl as they should have.

Playoffs are even worse (this is why the Canucks have never won a Stanley Cup). Consider a best of seven game series. Even if the two teams are equal, we would expect that the series would only go four games one in every eight (two cubed[2]) series.  When a series goes the full seven games one might as well flip a coin. Rare events, like one team winning the first three games and losing the last four, are expect to happen once in every sixty-four series and considering the number of series being played it is not surprising we see them occasionally.

Probably the worst example of playoff madness is the American college basketball tournament called, appropriately enough, March Madness. Starting with 64 teams or 68 depending on how you count, the playoffs proceed through a single elimination tournament. With over 70 games it is not surprising that strange things happen. One of the strangest would be that the best team wins.  To win the title the best team would have to win six straight games. If the best team has on average a 70% chance of winning each game they would only have a 12% chance of winning the tournament. Perhaps it would be better if they just voted on who is best.

But you say they would never decide a national championship based on a vote. Consider American college football. Now that is a multi-million dollar enterprise! Nobel Laureates do not get paid as much as US college football coaches. They do not generate as much money either. So what is more important to American universities–sports or science?

In the past, the US college national football champions were decided by a vote of some combination of sports writers, coaches and computers. Now that combination only decides who will play in the championship game. The national champion is ultimately decided by who wins that one final game. Is that better than the old system? More exciting but as they say: on any given day anything can happen. Besides sports is more about deciding winners and losers rather than who is best.

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[1] With the expected frequency of course.

[2] Not two to the fourth power because one of the two teams has to win the first game and that team has to win the next three games.

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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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