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November 2013 Archives

Something isn't right. Our laboratory facilities contain a couple of Faraday-shielded rooms. The idea is that electromagnetic radiation can't get in (or, for that matter, out). That means mobile phones shouldn't work in there. And they don't. Mine has no reception at all - others in our research group report either no reception or 'one-bar' reception occasionally, and that with the door open. At least, that used to be the case. Then a summer student arrived. With him came an extremely new 4G phone which WORKS JUST FINE inside the Faraday shield with the door closed. Not only that, but the student reports that he gets better reception in the room than at home. THIS IS NOT SUPPOSED TO HAPPEN. 

For sure, we don't expect the room is perfect. It needs to have holes in it, such as letting internet cables through (no wireless reception, obviously) and, a little more importantly, air. But there shouldn't be much radiation at all. In fact, we have two shielded rooms across a corridor from each other - one is used for electrophysiology (where we look at very tiny voltage signals) and the other for simulating lightning strikes on electronic equipment (where voltages are very high). The fact that the lightning experiments don't interfere with the electrophysiology ones shows that it's working. So how does my student's phone get really good reception? This is still a bit of a mystery. 


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Last week I attended a conference on Emergent Learning and Threshold Concepts, here at the University of Waikato. It was a very interesting couple of days. As far as academic conferences go, it was unusual in that it was really cross-disciplinary. We had engineers mixing with physiotherapists, and management consultants with dancers. It certainly was interesting to hear about how other disciplines approach educating their students. A challenge faced by everyone presenting, me included, was to make the presentations accessible to someone with no expertise in the area whatsoever. It was a job that was surprisingly well done. 

I'm not going to mention here what I talked about (you can find it on the ELTC website if you are that interested). Rather, I'll talk about what my colleague Jonathan Scott presented. He's been looking at Threshold Concepts and Learning for a while now and had some observations to make which he cased in terms of thermodynamics. Jonathan had to keep it pretty maths-easy for those in the audience that weren't mathematically inclined (probably most of them) and I think he did a good job. Here's a potted summary of things.  

When we learn something 'thresholdy', things get more ordered in our brain. Pieces of information fit together better. We can see how concepts work, rather than just being pieces of knowledge. Things come into order. In thermodynamics, order is associated with a quantity called entropy. Specifically, something well ordered has low entropy; something with little order has high entropy. Ice has less entropy than water (since its molecules have an ordered structure), but water has less entropy than steam (since even in water there is some degree of ordering among the molecules).  We give entropy the symbol 'S'.  (Actually, I've never stopped to think why it's 'S' for entropy  - Does anyone know?) 

Another key quantity in thermodynamics is heat. Heat is a form of energy. Practically, however, it's not always the best quantity to work with. That's because if we do experiments at constant pressure, which is what the laboratory usually has, gases and liquids expand when they heat up. That means a more useful quantity to work with is enthalpy. It's like heat energy, but it takes into account the fact that things can expand and contract, so the amount of stuff in say a 1 litre volume changes. When ice melts into water, for example, there is a change in enthalpy of the system. We need to put energy into the ice to melt it, which means that the enthalpy of the water is higher than that of the ice. We often give enthalpy the symbol 'H'. 

We can combine the effects of a change in enthalpy and a change in entropy in something called the Gibbs' Free Energy.  We give it the symbol 'G'.  Specifically, it's the enthalpy minus the produce of temperature (T) and entropy - in maths terms G = H - TS.  Now, here's the neat bit. To make a system change its state (e.g. ice into water) the change in Gibbs' free energy needs to be negative. For ice turning to water, we note that the change in entropy is positive (more disorder). The change in enthalpy is also positive. To get the change in G to be negative, we need the temperature T to be large enough. At atmospheric pressure, if T > 0 degrees C, it will happen. If not, it won't.  

What has that got to do with learning. Well, here's Jonathan's analogy. To learn a threshold concept, we need to have a move to more order. But a large, negative change in entropy means -TS is strongly positive and so if this is to happen we need to make the change in H (energy) strongly negative. In other words we need to 'take the heat out' of the system. If the system is 'the student', then this equates to getting the student to do lots of work. (Remember the first law of thermodynamics: Heat and work are equivalent). If a system does lots of work (on something else), it loses heat. A good example is gas from a pressurized bottle doing work as it moves to atmospheric pressure and expands  - the nozzle of the bottle will get cold. The bigger the ordering that is required in one's thoughts, the bigger the amount of work that the student needs to do.  The process is assisted by a lowering of the temperature - a 'cool' environment (as opposed to a hot one with too much going on)  helps the student learn. 

Perhaps all this is taking a physics analogy a bit too far. If we think of the message as being "to get thoughts to order together is actually quite difficult" then it's got merit - that is really what the Threshold Concept environment is about.

Finally, it's been noted that Threshold Concepts, are indeed, a threshold concept. Therefore if you struggle to see what I'm commenting on, you need to do some more work ;-)




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Last week I watched again the highly amusing film "Kitchen Stories". It's hardly a mainstream affair - in fact I feel like editing Wikipedia's meagre entry on it. The scenario is amusing because it's so ridiculous - a group of Swedish scientists is sent off to Norway to observe single men use their kitchens, in order to optimize the kitchen layout for them.  I detected a bit of Norway-poking-fun-at-Sweden in this film (or was it the other way around?) but also quite a lot of everyone-poking-fun-at-scientists-and-their-stupid-studies. 

Observer Nilsson gets the short-straw and has to observe the intensely unco-operative Bjorvik. The observers have been instructed that it is of paramount importance that they do not communicate with their subjects or interact with them in any way. The research is from a positivist perspective - that means the subject 'does' and the observer 'observes'. Any mixing of the two would jepoardise the whole undertaking. 

In protest at this stupidity Bjorvik refuses to do anything in his kitchen. He then decides that if he is being observed, he can observe back, and starts observing Nilsson. There are long periods in this film where nothing else happens. No dialogue, no interaction, just one observing the other. 

What happens from then I'll leave you to find out. Be warned - this is not fast-paced  Indiana Jones-style entertainment.

There are some interesting parallels with science here. An underlying assumption in the 'positivistic' approach is that there is a real reality out there that has no relation to what's looking at it. Doing an experiment on it doesn't change it.  However, just as Nilsson's presence changed how Bjorvik behaved, so it's not always the case in science that we can do this. In some experiments, it is pretty hard to carry out the experiment without fundamentally changing what it is you are experimenting on. The extreme example is quantum mechanics, where it is impossible to observe a system without making a drastic change to it. The observer cannot be isolated from the system.

But even in more classical situations, the issue may still be there. I have a project in which a student is tackling the thorny problem of measuring the electrical conductivity of biological tissue. In order to keep the tissue 'alive' (in the sense that any isolated piece of tissue can be alive), it has to be bathed in a solution that contains what the tissue needs to function. But the solution has an appreciable electrical conductivity itself. If we measure the conductivity of the tissue on its own, it will be dead tissue - but if we measure that of the alive tissue it won't be the conductivity of the tissue alone. Tricky. To measure it, we have to change it. 

It's an issue that's worth more than a passing thought in the design of a good many experiments. 





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At the recent NZ Institute of Physics conference, we were treated to a wonderful description of the earth's magnetic proceses, by Gillian Turner.  What makes up the earth's magnetic field? What effect does it have? How is it changing?

At first glance the magnetic field of the earth is pretty straightforward. There's a magnetic north pole and a magnetic south pole. In fact, the earth's magnetic field looks a lot like what you get from a simple bar magnet. 

But look only a little more closely, and it's clear there's a lot more to it than that. For example, the magnetic south pole is not diametrically opposite to the magnetic north pole. In fact,  both are moving about quite substantially - like a lost polar bear / penguin, depending upon your hemisphere. At sixty-something degrees south, the magnetic south pole currently isn't all that far south at all!

Then there are the reversals in magnetic field, that occur from time to time. We're talking hundreds of thousands of years. But they're not regular, suggesting a great deal of randomness is going on. 

It helps in interpreting what we see to remember that we are observing the field at the surface of the earth. It originates deeper within the earth - in the inner and outer cores. The distance from the centre of the earth is rather important. Why? Because as we move away from the centre, the smaller-scale variations get 'ironed-out' more quickly than the larger-scale variations. The effect is that the large-scale behaviour (i.e. the bar-magnet-like shape of the field) is emphasized at the earth's surface, whereas deeper down it is much less like a bar magnet. 

For those more mathematically inclined, one can see this with multipole expansions. This is a mathematical way of breaking up the description of a shape of an object into different components. One starts with a monopole - how much like a sphere an object is. Then we move on to a dipole moment - this is describing how separation of material along an axis there is.  Next are quadrupoles, then octupoles - each describing finer variations in the shape. So, as an example, a perfect sphere has a monopole moment of 1, and no multipoles of any other type. A rugby ball is quite like a sphere, so it has a high monopole moment. While it's got a preferred direction (its axis) both ends of the axis are the same and so there is no dipole moment. The next term, the quadrupole moment, however isn't zero - it's this moment that describes the bulk of the distortion from a sphere.  The link above gives a nice example of a skittle - it has monopole, dipole and quadrupole moments. 

Now, with the earth's magnetic field, there is exactly no monopole moment. Magnetic field isn't like electric charge - while one can have an isolated 'positive' charge, one can't have an isolated 'north' pole. The leading term for the earth's field is the dipole moment - there's an axis and a distinct split of field on the axis - at one end it points away from the centre, at the other towards the centre.  Now, the interesting thing is how the impact of the moments changes with distance away. The n-th order multipole has a strength that varies as the inverse of distance to the power n plus one. So the field due to a monopole varies as 1/r^2 (where r is distance away), the field due to a dipole varies as 1/r^3, that of a quadrupole as 1/r^4 and so on. As r gets large, the effect of the higher-order (higher n) moments diminishes quickly. Consequently, it doesn't matter what mish-mash of magnetic behaviour one has, at large enough distances away, the field from it  will look like that of a dipole. 

At the boundary between the outer core and the mantle, there is such a mish-mash of magnetic behaviour. A picture from an impressive computer simulation of the field by Glatzmaier and others  is here. At the earth's surface, however, it is much smoother and we see it as approximately a dipole - with a clear north pole and south pole, (very) approximately diametrically opposite. 

But the mish-mash of the field in the liquid outer core isn't the whole story. It's tempered by the solid inner core, which isn't going to change its magnetism so easily. It provides a large inertia against any changes, meaning that flipping the field of the inner core required some extreme behaviour in the outer core. It gets extreme enough just occasionally, and indeed the inner core can then be flipped, but it's not often. Our compasses are still likely to work tomorrow.

Glatzmaier, Gary A.; Roberts, Paul H. (1995). "A three-dimensional self-consistent computer simulation of a geomagnetic field reversal". Nature 377 (6546): 203–209.Bibcode:1995Natur.377..203Gdoi:10.1038/377203a0


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Sorry for no blogging in the last week. I've been away and then had the usual bewildering array of tasks to do when I got back.

So, to kick off again, here's an amusing video of what one can do with robotics. The application is of course silly, but the high-speed image processing and automation certainly isn't. The slow-motion at the end of the video shows just how fast the robot is reacting.


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