Quantum Diaries

Byron Jennings | TRIUMF | Canada

Read Bio

In Defense of Mickey Mouse Science

Friday, June 1st, 2012

“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.

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

[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)

Tags: Philosophy of science
Posted in Latest Posts | 2 Comments »

Science: The Art of the Appropriate Approximation

Friday, May 25th, 2012

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.

Tags: approximation, Philosophy of science
Posted in Latest Posts | 7 Comments »

Measurement and the New SI Units

Friday, May 18th, 2012

The SI units will be changing again in the next few years. You would think that choosing the units of measurement would be an unemotional topic, but as I recall from Canada’s, only partially successful attempt to convert to the metric system, that is far from the case. I remember one rather irrational editorial on the topic where the writer went on about how the changing definition of the metre was an indication that the people behind the metric system did not know what they were doing. Since this was in an English Canadian paper, he blamed the problem on the French for having blown the original definition. Ignorance profound. The writer would probably have been surprised to learn that the inch is defined as 2.54 centimeters except, of course, in the US where there is a second inch (the surveyor’s inch) defined as 39.37 inches equal one meter. Ah, the joy of traditional measurements. There are at least three different gallons in use, and as for barrels, there are more than you can shake a stick at. However, the petroleum barrel is defined as exactly 158.987294928 litres. I am sure you wanted to know that and don’t forget the last decimal point—the 8 is very important. As far as I can see, the only reason for using the traditional units is familiarity and yes, I still use the inch and foot, but also the kilometer. And I believe it’s also safe to say, that the generation born after the country officially switched, also does the same. That is the joy of living in a country that has half converted to metric.

Measurements tend to be of two types. One is pure numbers like the number of ducks in a row (or in a pond). The other type is the measurement of a number with a dimension. Here we need a standard to compare against; a length of six feet only make sense if we know what a foot is. In other words, we have a standard for it. Thus, the need to define units so different people can compare their results, and when we buy a hogshead of beer, we know how much we are getting.

Editorial writers will have another chance to rant in a few years as the General Conference on Weights and Measures is set to change the definitions of the basic metric or Standard International (SI) units again—this time, not the metre but the kilogram and other units. The history of how the definition of the units have changed over time is quite interesting, involving not just changing technology but also changing tastes. The original metre was defined in terms of the distance from the equator to the North Pole. But this could not be determined sufficiently accurately, so the standard was shifted to a physical artifact; a rod kept in Paris with two marks on it. This was then shifted to the wavelength of light from a certain atomic transition and finally, to fixing the speed of light. Similarly, for time, the second went from being defined in terms of the length of the day to being defined in terms of the frequency of an atomic transition. There is a trend from defining the units in terms of macroscopic quantities—the size of the earth, the length of day, the length of a bar—to microscopic quantities, or more specifically, atomic properties. There is a simple reason for this, namely that it is in atomic systems that the most accurate measurements can be made. Unfortunately, it also makes the unit definitions esoteric and detached form everyday experience. Everyone can identify with the length of a foot, but it is not immediately clear what the speed of light has to do with distance. Telling my daughter it takes five nanoseconds for light to travel from her head to her foot doesn’t do much for her. There is also a trend, partly aesthetic, towards defining the base units by fixing the fundamental constants of nature.

A fundamental constant of nature, like the speed of light, starts it life as something that relates two apparently unrelated quantities. In the case of the speed of light, it is time and distance. But then over time, it comes to be just a way of relating different units for measuring the same thing. Indeed, time units are sometimes used for distances and vise versa. This even happens in everyday life, such as when the distance from Vancouver to Seattle is given as three hours, meaning, of course, an average travel time. But in science, the relation is more definite and defining the metre in terms of the speed of light makes it explicit that the fundamental constant, the speed of light, is just a conversion factor from one set of units to another, from seconds to metres (1 metre = 3.3 nanoseconds).

The new proposal for the base SI units continues this trend of defining units by fixing fundamental constants. The degree Celsius is now defined in terms of the properties of water—the so called triple point. In the proposed new system, it will be defined by fixing a fundamental constant, the Boltzmann constant. The Boltzmann constant relates degrees to energy. At the microscopic level, i.e. in statistical mechanics, temperature is just a measure of energy and the new definition of the degree makes this explicit. Again, a fundamental constant turned to a conversion factor between different units—degrees and joules. The case of the kilogram is more subtle. It is currently defined by a physical artifact—the standard kilogram stored in Paris. The new proposal is to determine the kilogram by fixing the fundamental constant; Planck’s constant. This is another example of a fundamental unit becoming just a conversion factor between different units, in this case between time and energy units, or equivalently distance and momentum units.

As a theorist, this new set of units makes it nice for me as I like to use what are called natural units in my calculations. These are given by setting the speed of light (c), Planck’s constant (ħ), Boltzmann’s constant (k) and π all equal to 1 (OK, usually not π, but I did see that legitimately done once). An interesting side effect of the new units is that they all have exact conversion from these natural units. There is another set of natural units called Planck units which are defined in terms of the gravitational strength and the strength of the electromagnetic force. (In the proposed change, the charge of the electron is used to define the electromagnetic units.) Ultimately, those may be the most elegant units but we are nowhere close to having the technology to make them the bases of the SI units.

Naturally, any change of units has the naysayers coming out of the woods. One of the criticisms of the new units is that, since the fundamental constants are fixed by definition, we can no longer study their time dependence. To some extent, this is true. For example, with the current definition of the kilogram, Planck’s constant changes every time atoms are lost or gained by the standard kilogram. This change will be lost with the new units. This illustrates the absurdity of asking if a fundamental constant changes in isolation. All that is meaningful is if the constant has changed with respect to some other quantity with the same dimensions. The new choice of units makes this explicit, which is a good thing.

There is much more to the new choice of units than I can cover here and the interested reader is referred to the relevant web pages: http://www.bipm.org/en/si/new_si/ , http://royalsociety.org/events/2011/new-si/ , or http://en.wikipedia.org/wiki/New_SI_definitions .

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.

Posted in Latest Posts | 4 Comments »

Science and Engineering: vive la Différence

Friday, May 11th, 2012

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 27^th 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.

Tags: Engineering, Order versus creative chaos, Philosophy of science
Posted in Latest Posts | 11 Comments »

In Defense of Jargon

Friday, May 4th, 2012

Jargon, even the name has a harsh ring to it. Can anyone but an author love a title like[1]: Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case? “How can anyone take science seriously when it uses so much jargon?” said the teamster[2] as he told his helper to fasten the traces to the whiffletree and check the tugs and hames straps. Jargon is everywhere and not unique to science. While you may not understand what the teamster is talking about, my father would have understood instantly and then gone to get a jag of wood.

But back to jargon. To the uninitiated the above title, like the teamsters words, seems like so much gobbledygook. But to the initiated, those working in the field, it is a precise statement and easily understood. Trying to put the title, or the teamster’s words, in a form understandable to the layperson would have been a fool’s errand. In making it understandable to a more general audience, the precision would have been lost and we would probably never have gotten that jag of wood. That would have been unfortunate as Nova Scotian winters can be cold.

One of the principles of all good writing is to tailor the communication to the intended audience. When I am helping put together a report for TRIUMF, the instructions to the authors always includes a statement about the intended audience. Even then, the good authors frequently ask me to make the description of the intended audience more precise. Life gets more complicated when a document has more than one intended audience. Then it is necessary to have a layered document where introductory sections are understandable by an intelligent layperson while the later sections are directed at the specialist. One is reminded of the old joke about the structure of good seminar: The speaker starts at a low level understandable by anyone and then as the seminar progresses he becomes more technical and less understandable so that by the end, even the speaker does not know what he is talking about. Well, perhaps that is getting a little too carried away, but one can error on either side, by making the writing too technical for the audience or not technical enough.

Similarly, the reader has to realize that the writing may not be directed at him or her. We, as people with technical expertise, have to be careful not to judge non-technical writing too harshly because it does not capture all the subtle nuances we are aware of. Including them would lose the layperson. It is a fine line between not confusing the layman and misleading him. When I am reading an article directed at a general audience, on a topic I am an expert in, I find I have to translate the layman’s language back to the technical language before I can understand it. That is as it should be.

Conversely, in fields we are not experts in, we should not criticize technical writing as being too filled with jargon. This latter mistake is made frequently by politicians and commentators who criticize technical writing due to ignorance. Few have the wisdom of the former Canadian Prime Minister, Pierre Elliot Trudeau, who said on opening TRIUMF, “I do not know what a cyclotron is, but I am glad Canada has one.” It is a rare politician who has the confidence to admit ignorance. As an undergraduate student, I picked up a copy of Rose’s book: Elementary Theory of Angular Momentum. That is when I learned one should be leery of books with elementary in the title[3]. If that is an elementary book, I would hate to have to read an advanced one. It is a good book but I, at that stage in my career, was not the intended audience.

Words only have meaning within the context they are used. When used with a person possessing a similar background, the context does not have to be spelled out. Thus, in conversation with a colleague I have worked with for some time a lot is understood without being stated explicitly. Jargon speeds up communication and makes it less prone to misunderstanding. On the other hand, with people who are not acquainted with the field, we have to spell out the background assumptions and suppress the details that are only of interest to the expert.

In the end, it is quite unfortunate that jargon has been abused and hence has received a bad name. In technical writing, jargon or technical terms are not only acceptable but necessary. So press on and employ jargon—but only where appropriate.

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] First title on the lattice archive the day I checked to get an example.

[2] The kind that drives horses.

[3] Books with elementary in the title are usually advanced while those with advanced in the tile are usually elementary.

Tags: Jargon, Philosophy of science, Wiffletree
Posted in Latest Posts | 4 Comments »

Is Science Consistent with Evolution?

Friday, April 27th, 2012

The evolutionary argument against naturalism

Alvin Plantinga (1932), professor emeritus of philosophy at the University of Notre Dame, is a leading theistic philosopher and opponent of evolution. He has proposed an intriguing, and specious—yet non-the-less intriguing—argument against evolution. It is intriguing for several reasons: First, because on the face of it, it is plausible. Second because it is typical of a whole class of specious arguments. Finally, because it highlights the difference between how scientists and philosophers approach a problem.

The argument runs as follows: The naturalist can be reasonably sure that the neurophysiology underlying belief formation is adaptive, but nothing follows about the truth of the beliefs depending on that neurophysiology. In fact, he’d have to hold that it is unlikely, given unguided evolution, that our cognitive faculties are reliable. It’s as likely, given unguided evolution, that we live in a sort of dream world as that we actually know something about ourselves and our world (original emphasis). In other words, if people in fact evolved, they could not trust their cognitive faculties to give them the truth and hence, do science. He goes on to argue that it is only possible to trust our cognitive faculties if people are created in God’s image.

It is amusing that unbelievers argue the opposite; namely that the existence of a God means science is impossible since he/she/it could override the rules of nature at will and there would be no reason to assume constant laws. Both are correct to this extent: Absolute knowledge is impossible,[1] independent of God’s existence. But back to Plantinga’s argument; it hinges on the concept of truth, or equivalently, reliability. But what is truth? A profound question—or a meaningless one. The difference between profound and meaningless is often vanishingly small.

At one level, the idea of truth is simple: Does the testimony of the person on the witness stand agree with what happened? Or perhaps the simpler question: Does the testimony agree with what the person thinks happened? The second is a less stringent requirement. But from this simple concept, the grand metaphysics concept of TRUTH ™ is generated. Whatever this grand metaphysical concept is, science is not concerned with it. Is it TRUTH ™ that colds are caused by viruses? The reductionist, at least if he believes in string theory, would say no. Colds, like all other phenomena, are caused by how strings vibrate in eleven dimensions. Viruses are just a wimpy low-energy approximation to the real TRUTH ™.

In science, we build models for how the universe works, which usually have a limited range of validity. Think of classical mechanics which is only valid for velocities much less than the speed of light. Is classical mechanics the TRUTH ™? No, certainly no, it fails in various places. But it is certainly useful. Science is a natural extension of the model building the unconscious mind does all the time, which is necessary for us to survive in a hostile world. The surprising thing is not that beings who evolved created science, but rather, that they did not do it sooner. Plantinga’s problem is that he does not understand what science is or how it works—seeking effective models rather than the TRUTH ™, whatever that may be. He should have known better, since by the Duhem-Quine thesis, no model can be falsified. Arguing that the current models have deficiencies is never enough. You have to provide better ones with more predicative power.

In the same manner that Plantinga’s argument relies on the grand metaphysics concept of TRUTH ™, many arguments in philosophy rely on similar word definitions. A prime example is the ontological agreement for God’s existence. First proposed by Anselm of Canterbury (1033 – 1109), the argument goes as follows: Define God as the greatest possible being we can conceive. If the greatest possible being exists in the mind, it must also exist in reality. If it only exists in the mind, a greater being is possible—one which exists in the mind and in reality. Note that his argument hinges on the definition of greatest. My daughter believes that anything, no matter how great, can be made greater by being pink. Thus the greatest being is pink. If I define non-existence as being greater than existence,[2] the ontological argument becomes an argument for God’s nonexistence. Evil is another word that is frequently made into a grand metaphysical concept, EVIL™, and used to justify various philosophical positions. The concept of actions I do not like is then taken a step further and personified in the concept of the devil.

While our concepts and word definitions may reflect reality, they do not constrain it. In the end, models founded on observation take precedence over philosophical arguments based on word definitions and phenomenologically unconstrained speculations. If such philosophical arguments disagree with scientific models, so much the worse for them. Thor showing up for Thursday afternoon tea at the Empress Hotel would make all arguments regarding his existence moot[3]. One observation is worth a thousand philosophical arguments.

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] See The Limits of Science.

[2] See Ecclesiastes chapter 4 for why this definition may be reasonable.

[3] You can tell it is Thor because he would be carrying a large hammer and one of the goats pulling his chariot would be limping.

Tags: Duhem-Quine, evolution, Philosophy of science, Plantinga, truth
Posted in Latest Posts | 12 Comments »

The Role of Mathematics and Rational Arguments in Science

Friday, April 20th, 2012

Mathematics is a tool used by scientists to help them construct models of how the universe works and make precise predictions that can be tested against observation. That is really all there is to it, but I had better add some more or this will be a really short essay.

For an activity to be science, it is neither necessary, nor sufficient, for it to involve math. Astrology uses very precise mathematics to calculate the planetary positions, but that does not make it science any more than using a hammer makes one a carpenter (Ouch, my finger!). Similarly, not using math does not necessarily mean one is not doing science any more than not using a hammer means one is not a carpenter. Carl Linnaeus’s (1707 – 1778) classification of living things and Charles Darwin’s (1809 – 1882) work on evolution are prime examples of science being done with minimal mathematics (and yes, they are science). The ancient Greek philosophers, either Plato or Aristotle, would have considered the use of math in describing observations as strange and perhaps even pathological. Following their lead, Galileo was criticized for using math to describe motion. Yet since his time, the development of physics, in particular, has been joined at the hip to mathematics.

The foundation of mathematics itself is a whole different can of worms. Is it simply a tautology, with symbols manipulated according to well defined rules? Or is it synthetic a priori information? Is 2+2=4 a profound statement about the universe or simply the definition of 4? Bertrand Russell (1872 – 1970) argued the latter and then showed 3+1=4. Are the mathematical theorems invented or discovered? There are ongoing arguments on the topic, but who knows? I certainly don’t. Fortunately, it does not matter for our purposes. All we need to know about mathematics, from the point of view of science, is that it helps us make more precise predictions. It works, so we use it. That’s all.

I could end this essay here, but it is still quite short. Luckily, there is more. Mathematics is so entwined with parts of science that is has become its de facto language. That is certainly true of physics where the mathematics is an integral part of our thinking. When two physicists discuss, the equations fly. This is still using mathematics as a tool, but a tool that is fully integrated in to the process of science. This has a serious downside. People who do not have a strong background in mathematics are to some extent alienated from science. They can have, at best, a superficial understanding of it from studying the translation of the mathematics into common language. Something is always lost in a translation. In translating topics like quantum mechanics—or indeed most of modern particle physics—that loss is large; hence nonsense like the “God Particle”. There is no “God Particle” in the mathematics, only some elegant equations and, really, considering their importance, quite simple equations. One hears question like: How do you really understand quantum mechanics? The answer is clear, study the mathematics. That is where the real meat of the topic and where the understanding is—not in some dreamed up metaphysics-like the many worlds interpretation.

Closely related to mathematics are logical and rational arguments. Logic may or may not give rise to mathematics, but for science, all we require from logic is that it be useful. Rational arguments are a different story. Like mathematics, they are useful only to the extent they help us make better predictions. But that is where the resemblance stops. Rational arguments masquerade as logic, but often become rationalizations: seductive, but specious. Unlike mathematics, rational arguments are not sufficiently constrained by their rules to be 100% reliable. Indeed, one can say that the prime problem with much of philosophy is the unreliability of seemingly rational arguments. Philosophers using supposedly rational arguments come to wildly different conclusions: compare Plato, Descartes, Hume, and Kant. This is perhaps the main difference between science and philosophy: philosophers trust rational arguments, while scientists insist they be very tightly constrained by observation; hence the success of science.

In science, we start with an idea and develop it using rational arguments and mathematics. We check it with our colleagues and convince ourselves using entirely rational arguments that it must be correct, absolutely, 100%. Then the experiment is performed. Damn—another beautiful theory slain by an ugly fact. Philosophy is like science, but without the experiment[1]. Perhaps the real definition of a rational argument, as compared to a rationalization, is one that produces results that agree with observations. Mathematics, logic, and rational arguments are just a means to an end, producing models that allow us to make precise predictions. And in the end, it is only the success of the predictions that count.

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] I believe this observation comes from one of the Huxelys but I cannot find the reference.

Tags: mathematics, Philosophy of science
Posted in Latest Posts | 11 Comments »

The Argument from Design

Friday, April 13th, 2012

Central to the scientific method is a process for deciding between conflicting models of how the universe operates. It is very instructive to apply this process to the argument from design for the existence of a higher intelligence in the universe. The argument from design is commonly associated with William Paley (1743 – 1805) and for those who like big words, is also called as the teleological argument for God’s existence. A counter argument is given in Richard Dawkins’ book: The Blind Watch Maker. The basic argument from design is, however, much older than Paley; it goes back to the ancient Greeks. Needless to say, Dawkins’ book has failed to lay the argument to rest. If one checks the current state of the arguments on the topic[1], they typically are of the form: Anyone who does not recognize design in the universe is in denial, and the counter argument is: Those who see design in the universe are delusional. Needless to say, neither argument is particularly convincing. So what can the scientific method add to resolving the impasse? Quite a bit actually.

Let’s begin by looking at the actual form of the argument. It was stated succinctly by Cicero (106BCE – 43 BCE): When you see a sundial or a water-clock, you see that it tells the time by design and not by chance. How then can you imagine that the universe as a whole is devoid of purpose and intelligence, when it embraces everything, including these artifacts themselves and their artificers? This analogy was expanded upon, most famously, by Paley (quoted from the Wikipedia):

[S]uppose I found a watch upon the ground, and it should be inquired how the watch happened to be in that place, I should hardly think … that, for anything I knew, the watch might have always been there. Yet why should not this answer serve for the watch as well as for [a] stone [that happened to be lying on the ground]?… For this reason, and for no other; namely, that, if the different parts had been differently shaped from what they are, if a different size from what they are, or placed after any other manner, or in any order than that in which they are placed, either no motion at all would have been carried on in the machine, or none which would have answered the use that is now served by it.

So what about the watch and how do we know that it was designed? We begin with one of the mantras of this series of essays: The meaning is in the model. To understand the watch and its creation, our mind, either consciously or unconsciously, develops a model for its origin. The watch is deduced to have to been made by humans, not by non-human agencies, and humans do things by design. Thus, by a two-step process we arrive at design. Now, the watch is fairly obvious, but what about that pointed rock on the ground? Is it due to design or natural causes? Is it simply a broken rock or is it an arrow head? Here the question of design is strictly one of if it was made by humans or not. If the indications on the rock show signs of human manufacture it is considered due to design, and if not, then accident.

The typical theist would claim that the universe and everything in it is designed. Thus, we cannot do the comparison of something designed to something that was not designed; a technique that was useful in deciding if the watch was humanly designed or not. So how do we tell if something is designed or not? Use the methodology from science, of course.

In science, there are two distinct steps with any model: first the model must be constructed, and then it must be tested. Model construction is a creative activity and does rely on analogy and pattern recognition. Thus, in the initial stage, the argument from design is on good grounds. Now for the crux of the matter: the crucial test is neither how good the analogy is, nor how striking the apparent pattern, but rather if the argument from design passes the tests of parsimony and also makes successful predictions for observations. The scientific method defines three criteria for judging models: the successful description of past observations, the ability to make correct predictions for future observations, and simplicity. Being able to describe past observations is just the price to play the game, and with sufficient ingenuity, can usually be done. The definitive test of a scientific model is the ability to make predictions for novel phenomena. By predictions, I mean definite predictions that can be falsified. Not the kind of predictions made by Nostradamus that after the fact can be claimed to have been fulfilled, but rather definite predictions that can be tested, like it will rain tomorrow at TRIUMF between 3:00 and 4:00 pm.

Finally, there is simplicity. Yes, there is always simplicity or parsimony. By simplicity, I mean the elimination of assumptions that do not help the model make predictions. Today, common descent for living things is pretty much established and is mainly challenged by gross violations of the simplicity principle. A prime example is the omphalos hypothesis of Phillip Gosse (1810 – 1888). He stated that the world was created six thousand years ago, but in a manner that cannot be distinguished from one that is much older. As pointed out in a previous essay, that hypothesis can only be eliminated by an appeal to parsimony. As for design, natural selection is one way of generating the design of living things without the need for external intelligence and, at least at the small scale, natural selection is observed to be happening. So, can an external intelligence as suggested by the argument from design, or the idea of intelligent design, add anything useful to this? Or can they both be eliminated, like the omphalos hypothesis, by the appeal to parsimony? The challenge to the proponents of the argument from design (and similarly for intelligent design) is to make precise testable predictions, not postdictions, that distinguish it from natural selection.

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] This post was partly motivated by such an exchange on Huffington Post.

Tags: intelligent design, Paley, Philosophy of science, The argument from design
Posted in Latest Posts | 9 Comments »

The Role of the Crucial Experiment

Friday, April 6th, 2012

The idea of a crucial experiment that decisively confirms a model goes back at least to Francis Bacon (1561 – 1626) who used the term instantia cruci. Later, the term experimentum crucis was coined by Robert Hooke (1635 – 1703) and used by Isaac Newton (1642 – 1727), in particular with regard to his theory of light. Alternatively, Pierre Duhem (1861 – 1916) strongly disagreed with the possibility of crucial experiments. Somewhat in anticipation of Thomas Kuhn’s (1922–1996) paradigms, Duhem realized that scientific theories or models do not stand alone, but rather come coupled with auxiliary assumptions. Was what Galileo saw through the telescope features of the heavens, or only of his telescope, as some of his detractors claimed? One has to consider the combined heavens-telescope system to decide. When the detector is as complex as the ATLAS detector at CERN the question is even more apropos.

Karl Popper (1902 – 1994) refined the idea of the crucial experiment to one that falsifies a given model. But the Duhem-Quine hypothesis, a variation of Duhem’s idea, makes the point that falsification, at least in its naïve form, falls victim to same holistic argument: we can never test a single model in isolation. So is the idea of a crucial experiment just a will-o-the-wisp that vanishes on more careful evaluation?

We can think of many examples: Sir Arthur Eddington`s measurement of the bending of star light by the sun, the discovery of high-temperature superconductors, the measurement of the three degree microwave background, the Michelson–Morley experiment, and so on. Did none of these play a critical role in the history of science? I would suggest they did, but not in the simple manner suggested by Bacon or Popper.

Consider the Michelson–Morley experiment in 1887. Scientists did not do a Chicken Little impersonation and run around claiming the sky was falling or, in this case, that Newton (Newton`s laws of motion) and Maxwell (electromagnetism) were wrong. Rather, they started trying to understand what the explanation could be. This led to ideas like ether drag (the earth entraining the ether) or Lorentz-Fitzgerald contraction (the idea that objects shorten in the direction of motion). The latter idea was developed and expanded upon by Lorentz and Poincaré who developed the math for special relativity. Einstein claimed he was unaware of the Michelson–Morley experiment, but he was certainly aware of Lorentz`s early attempts to understand that experiment. Thus, the Michelson–Morley experiment started a chain of events that inexorably lead to special relativity, not in one easy step, but eventually and inevitably. If special relativity had been proposed thirty years sooner, it would have been treated as a curiosity like the Copernicus model when it was first proposed.

As another example, consider the measurement of the bending of light by the sun. The general theory of relativity and classical mechanics differ by a factor of two. Eddington`s 1919 experiment gave a result closer to general relativity and hence contributed to the early acceptance of general relativity (not that people are not still trying to test it; that is as it should be). A more striking example was the discovery of the three-degree kelvin cosmic microwave background. Before then, there were two models, both with strong support: the steady-state model and the big bang model. While the microwave background was a big boost for the big bang model, the solid state model did not give up without a struggle. There were various attempts to describe the microwave background in the solid state model but they were too little too late. Like the Michelson–Morley experiment, the discovery of the microwave background started a chain reaction that led to the acceptance of one model and the rejection of another.

Perhaps the best way of thinking of crucial experiments is not that they prove (that ugly word) one model better than another, but that they serve as a catalyst. Or perhaps, one can think of a super-cooled fluid that when slightly disturbed, suddenly solidifies. The same phenomenon is seen with people. A group are sitting at lunch and when one gets up to go and they all go, but only if the circumstances are right. Consider the discovery of the J/Ψ particle. The time was right and the background had been prepared so that when it was discovered, the particle physics community solidified around the quark model. Similarly, you can consider Galileo turning his telescope on the heavens as providing the catalyst for the acceptance of the heliocentric model.

Like models, experimental results do not exist in isolation. Rather, they build on each other and are given meaning by the prevailing models. The role of crucial experiments should be seen in relation to that milieu. They do not single handedly overturn or confirm the status quo, but rather, start chains of events that lead to or act as tipping points for the establishment of new paradigms. Thus, crucial experiments do exist but not in the naïve manner envisioned by Bacon, Hooke, or Popper.

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.

The idea of a crucial experiment that decisively confirms a model goes back at least to Francis Bacon (1561 – 1626) who used the term instantia cruci. Later, the term experimentum crucis was coined by Robert Hooke (1635 – 1703) and used by Isaac Newton (1642 – 1727), in particular with regard to his theory of light. Alternatively, Pierre Duhem (1861 – 1916) strongly disagreed with the possibility of crucial experiments. Somewhat in anticipation of Thomas Kuhn’s (1922–1996) paradigms, Duhem realized that scientific theories or models do not stand alone, but rather come coupled with auxiliary assumptions. Was what Galileo saw through the telescope features of the heavens, or only of his telescope, as some of his detractors claimed? One has to consider the combined heavens-telescope system to decide. When the detector is as complex as the ATLAS detector at CERN the question is even more apropos.

Consider the Michelson–Morley experiment[W1] in 1887. Scientists did not do a Chicken Little impersonation and run around claiming the sky was falling or, in this case, that Newton (Newton`s laws of motion) and Maxwell (electromagnetism) were wrong. Rather, they started trying to understand what the explanation could be. This led to ideas like ether drag (the earth entraining the ether) or Lorentz-Fitzgerald contraction (the idea that objects shorten in the direction of motion). The latter idea was developed and expanded upon by Lorentz and Poincaré who developed the math for special relativity. Einstein claimed he was unaware of the Michelson–Morley experiment, but he was certainly aware of Lorentz`s early attempts to understand that experiment. Thus, the Michelson–Morley experiment started a chain of events that inexorably lead to special relativity, not in one easy step, but eventually and inevitably. If special relativity had been proposed thirty years sooner, it would have been treated as a curiosity like the Copernicus model when it was first proposed.

Perhaps the best way of thinking of crucial experiments is not that they prove (that ugly word) one model better than another, but that they serve as a catalyst. Or perhaps, one can think of a super-cooled fluid that when slightly disturbed, suddenly solidifies[W2] . The same phenomenon is seen with people. A group are sitting at lunch and when one gets up to go and they all go, but only if the circumstances are right. Consider the discovery of the J/Ψ particle. The time was right and the background had been prepared so that when it was discovered, the particle physics community solidified around the quark model. Similarly, you can consider Galileo turning his telescope on the heavens a��s��

Tags: crucial experiment, Hooke, Philosophy of science, Pierre Duhem, Popper
Posted in Latest Posts | Comments Off

The Agrostic Principle

Friday, March 30th, 2012

In honour of the season.

As I drive to and from work in Vancouver, I notice that even in winter, the grass is green. In the spring, people are out fertilizing their lawns and in summer watering them (even when they are not allowed to)—mollycoddled grass! They are now even putting grass on the top of buildings. You would almost think that Vancouver exists for the benefit of grass. But it is not just Vancouver; we have wide areas of the world devoted to grass, from bamboo to grain. You would think the world was created for the benefit of grass. After all, the earth is just the right distance from the sun to allow grass to flourish. Farther from the sun, it would be cold and arid like Mars. Closer to the sun it would be hot and sterile like Venus. Thus, we have what is known in the trade as the acrostic[1] principle: the philosophical argument that observations of the physical universe must be compatible with the preferred status of grass.

As just mentioned, the earth is just at the right distance from the sun for grass to flourish. But it goes beyond that. Carbon is a major component of grass. However, the creation of carbon in stars depends critically on the existence of an excited state in carbon, known as the Hoyle state, with exactly the right energy. If that state were not there, there would be no carbon and hence no grass. The horror of it! Just think, no grass. And it all depends on having the nuclear state at just the right energy.

The Hoyle state is not the only coincidence necessary for the existence of grass. If the fundamental constants of nature, things like the fine structure constant or the gravitational constant (big G) were slightly different, the universe would not support the existence of grass. There are two solutions to this problem. One is to assume that there is an intelligent designer with an inordinate fondness for grass who fine-tuned the universe so grass could exist. Now, there is a minority opinion that it is not grass that he is fond of, but rather beetles (coleoptera) and that he only created grass as a source of feed for beetles. After all, there are the order of a million species of beetles. But as I just said, the coleopteric principle is distinctly a minority position, but we should be open minded.

The other explanation of the fine tuning of the universe is based on the idea of the multiverse. This is the idea that many different universes exist with all possible values of the physical constants and that we are in the one in which grass is possible. Again, note the preferred role of grass. The evidence for this scenario, at the present time, is no stronger than that for the existence of the coleopterophillic intelligent designer.

Now one might ask what role consciousness and intelligence have in all this. The answer to that is fairly self-evident. The main role of consciousness and intelligence is the development of civilization, and the main role of civilization is the development of agriculture. It should be obvious to even the most obtuse reader that the main purpose of agriculture is to permit grass to more effectively compete with trees. Just think of the extent to which farmers have replaced forests with grassland. The bringing of European “civilization” to North America had as its main effect, the replacement of forest with grassland. It had some unfortunate side effects, like the creation of the United States of America, but what is more important—people or grass?

As further evidence of the agrostic principle, I note that it provides the only possible explanation for the existence of golf courses and cricket pitches. The very idea of grown men or women hitting a ball with a club to prove their virility is silly. Now artificial turf may be considered as evidence against the agrostic principle, but artificial turf seems to be a passing fad. In just 13 years, between 1992 and 2005, the National Baseball League went from having half of its teams (6 of 12) using artificial turf to all of them – now up to 16 – playing on natural grass. As for football (soccer), artificial turf is widely banned. Enough said.

The agrostic principle also highlights flaws in ancient Greek philosophy. Plato believed that the “good” was contemplating his ideals or ideas. That is incorrect; the greatest good is cultivating and contemplating grass. Like Euclid’s postulates, that should be self-evident. That the smoking of grass is the greatest good is a corruption of Epicurus’s teaching. Rather, he was the first of the new atheists. The Sophists, on the other hand, where the first post-modernists and believed that it was impossible to decide if contemplating or smoking grass was the greatest good. After smoking a few joints, the latter is probably true. Socrates believed that nothing could be learned from nature. Perhaps if he had spent more time cultivating and contemplating grass, he would not have been compelled to drink hemlock. However, Aristotle may have been onto something with his final cause or teleology. Evolution shows its bareness by failing to recognize that consciousness and intelligence arose due to the teleological purpose (final cause) of helping grass compete with trees. This is probably the best example of the need for Aristotle’s final cause that can be found in nature. Unfortunately, Aristotle starting worrying about essences rather than cultivating and contemplating grass. Thus, the Greek civilization decayed. And my wife wants me to replace the lawn with a garden. The end of western civilization is in sight.

The agrostic principle has some naysayers. Douglas Adams gives the example in his Hitch-hikers Guide to the Galaxy of the puddle which observed how well it fitted the hole it was in and concluded that the hole and the universe where created expressly for its benefit. It was consequently quite surprised and distressed when it evaporated. Imagine; the gall of Adams using satire to attack the agrostic principle. Now, of course, the properties of the hole can be deduced from the properties of the puddle, but this should not be used to infer the universe was not created for the sole benefit of the puddle. Some people have followed the example of Adams’s puddle and claimed that since humans nicely fit a hole in the universe, the universe was created for their benefit (this is sometimes call the anthropic principle). These people will probably be surprised when humans go extinct. The superiority of the agrostic principle to the anthropic principle is shown by the observation that while homo spaiens have existed for about 200,000 years, grass tickled the feet of dinosaurs over sixty million years ago. And grass will probably still exist after humans have, through sheer stupidly, destroyed themselves and have been replaced by a group with less intelligence and more wisdom, perhaps the coleoptera.

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] From the Greek word ἄγρωστις for grass.

Posted in Latest Posts | 5 Comments »

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Latest Posts

Byron Jennings | TRIUMF | Canada

Search:

Blogs

People

Laboratories

Latest Posts

Follow

A project of the Interaction Collaboration

Blogroll