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Posts Tagged ‘falsification’

Finding the Higgs boson will have no epistemic value whatsoever.  A provocative statement. However, if you believe that science is defined by falsification, it is a true one.  Can it really be true, or is the flaw in the idea of falsification?  Should we thumb our noses at Karl Popper (1902 – 1994), the philosopher who introduced the idea of falsification?

The Higgs boson, the last remaining piece of the standard model, is the object of an enormous search involving scientists from around the world.  The ATLAS collaboration alone has 3000 participants from 174 institutions in 38 different countries. Can only the failure of this search be significant? Should we send out condolence letters if the Higgs boson is found? Were the Nobel prizes for the W and Z bosons a mistake?

Imre Lakatos (1922 – 1974), a neo-falsificationist and follower of Popper, states it very cleanly and emphatically:

But, as many skeptics pointed out, rival theories are always indefinitely many and therefore the proving power of experiment vanishes.  One cannot learn from experience about the truth of any scientific theory, only at best about it falsehood: confirming instances have no epistemic value whatsoever (emphasis in the original).

Yipes! What is going on? Can this actually be true? No! To see the flaw in Lakatos’s argument, let’s consider an avian metaphor—this time Cygnus not Corvus. Consider the statement: All swans are white. (Here we go again.) Before 1492, Europeans would have considered this a valid statement. All the swans they had seen were white. Then Europeans started exploring North America. Again, the swans were white. Then they went on to South America and found swans with black necks (Cygnus melancoryphus) and finally to Australia where the swans are black (Cygnus atratus). By the standards of the falsificationist, nothing was learned when white swans were found, but only when the black swans or partially black swans were found.  With all due respect, or lack of same, that is nonsense. It is the same old problem: you ask a stupid question you get a stupid answer. Did we learn anything when white swans were found in North America? Yes. We learned that there were swans in North America and that they were white. Based on having white swans in Europe, we could not deduce the colour of swans in North America or even that they existed. In Australia, we learned that swans existed there and were black. Thus, we learned a similar amount of information in both cases—really nothing more or nothing less.  The useful question is not, ‘Are all swans white?’ Rather, ‘On which continents do swans exist and what color are they on each continent?’

Moving on from birds to model cars (after all, the standard model of particle physics is a model). What can we learn about a model car? Certainly, not if it is correct. Models are never an exact reproduction of reality. But, we can ask, ‘Which part the car is correctly described by the model? Is it the color? Is it the shape of the head lights or bumper?’ The same type of question applies to models in science. The question is not, ‘Is the standard model of particle physics correct?’ We knew from its inception that it is not the answer to the ultimate question about life, the universe and everything. The answer to that is 42 (Deep Thought, from The Hitchhiker’s Guide to the Galaxy by Douglas Adams). We also know that the standard model is incomplete because it does not include gravity. Thus, the question never was, ‘Is this model correct?’ Rather, ‘What range of phenomena does it usefully describe?’ It has long history of successful predictions and collates a lot of data. So, like the model car, it captures some aspect of reality, but not all.

Finding the Higgs boson helps define what part of reality the standard model describes. It tells us that the standard model still describes reality at the energy scale corresponding to the mass of the Higgs boson. But, it also tells us more: It tells us that the mechanism for electroweak symmetry break –a fundamental part of the model—is adequately described by the mechanism that Peter Higgs (and others) proposed and not some more complex and exotic mechanism.

The quote from Lakatos, given above, misses a very important aspect of science–parsimony. The ambiguity noted there is eliminated by the appeal to simplicity. The standard model of particle physics describes a wide range of experimental observations. Philosophers call this phenomenological adequacy. But a lot of other models are phenomenologically adequate. The literature is filled with extensions to the standard model that agree with the standard model where the standard model has been experimentally tested. They disagree elsewhere, usually at higher energy. Why do we prefer the standard model to these pretenders? Simplicity and only simplicity. And the standard model will reign supreme until one of the more complicated pretenders is demonstrated to be more phenomenolgically adequate. In the meantime, I will be a heretic and proclaim that finding the Higgs boson would indeed confirm the standard model. Popper, Lakatos, and the falsificationists be damned.

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

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One of the more interesting little conundrums in understanding science is the raven paradox. It was proposed by Carl Hempel (1905 –1997) in the 1940s. Consider the statement: All ravens are black. In strict logical terms, this statement is equivalent to: Everything that is not black is not a raven. To verify the first we look for ravens that are black. To verify the latter we look for coloured objects that are not ravens.  Thus finding a red (not black) apple (not raven) confirms that: Everything that is not black is not a raven, and hence that: all ravens are black. Seems strange: to learn about the colour of birds, we study a basket of fruit.

While the two statements may be equivalent for ravens, they are not equivalent for snarks.  The statement: Everything that is not black is not a snark, is trivially true since snarks do not exist, except in Lewis Carroll’s imagination. However, the statement: All snarks are black, is rather meaningless since snarks of any colour do not exist (boojums are another matter). Hence, the equivalence of the two statements in the first paragraph relies on the hypothesis that ravens do exist.

One resolution of the paradox is referred to as the Bayesian solution.  The ratio of ravens to non-black objects is as near to zero as makes no difference.  Thus finding 20 black ravens is more significant than find 20 non-black, non-ravens. You have sampled a much larger fraction of the objects of interest. While it is not possible to check a significant fraction of non-black objects in the universe, it may be possible to check a significant faction of ravens, at least those which are currently alive.

But the real solution to the problem seems to me to lie in different direction. Finding a red apple confirms not only that all ravens are black but also that all ravens are green, or chartreuse, or even my daughter’s favorite colour, pink.  The problem is that a given observation can confirm or support many different, and possibly contradictory, models.  What we do in science is compare models and see which is better. We grade on a relative, not absolute scale.  To quote Sir Carl Popper:

And we have learnt not to be disappointed any longer if our scientific theories are overthrown; for we can, in most cases, determine with great confidence which of any two theories is the better one. We can therefore know that we are making progress; and it is this knowledge that to most of us atones for the loss of the illusion of finality and certainty.

We do not want to know if: All ravens are black is true but rather if the statement all ravens are black is more accurate than the statement all ravens are green. A red apple confirms both statements, while a green apple confirms one and is neutral about the other. Thus the relative validity of the two statements cannot be checked by studying apples, but only by studying ravens to see what colour they are.  Thus, the idea of comparing models leads to the intuitive result. Whereas, thinking in terms of absolute validity, leads to nonsense:  Here, check this stone to see if ravens are black. Crack, tinkle (sound of broken glass as stone misses raven and goes through neighbor’s window)

We can go farther. Consider the two statements: All ravens are black, and Some ravens are not black. The relative validity of these two statements cannot be checked by studying apples or even black ravens. Rather what is needed is a non-black raven. This is just the idea of falsification. Hence, falsification is just a special case of comparing models: A is correct, A is not correct.

In practice, all ravens are not black. There are purported instances of white ravens. Google says so and Google is never wrong. Right? Thus, we have the statement: Most ravens are black. This statement does not imply anything about non-black objects; they may or may not be ravens.  Curious… this whole raven paradox was based on a false statement and as with: All ravens are black, most absolute statements are false, or at least, not known for certain.

Even non-absolute statements can lead to trouble. Consider: Most ravens are black, and: Most raven are green. So we merrily check ravens to see which is correct. But is it not possible that the green ravens blend in so well with the green foliage that we are not aware that they are there? Rather like the elephants in the kid’s joke that paint their toe nails red so they can hide in cherry trees. Works like charm. Who has seen an elephant in a cherry tree?  We are back to the Duhem-Quine thesis that no idea can be checked in isolation. Ugh. So, why do we dismiss the idea of perfectly camouflaged green ravens and red-nailed elephants? Like any good conspiracy theory, they can only be eliminated by an appeal to simplicity. We eliminate the perfectly camouflaged green raven by parsimony, and as for the red apple, I ate it for lunch.

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

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