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In the last couple of weeks, I've been using Hermite Polynomials in my work. I won't go into what they are (look them up here if you like) suffice to say that they are one of many contributions to mathematics from Charles Hermite (1822-1901), who was himself one of  many french mathematicians whose work has laid a foundation for much of modern theoretical physics. A physicist would generally know these polynomials (when modulated by a gaussian function ) as the solutions to the 1-dimensional quantum harmonic oscillator, although that's not why I'm using them. 

The 1-dimensional quantum harmonic oscillator problem is a textbook problem that gets inflicted on generations of students. I remembering suffering the algebra that went with it. At the University of Waikato, we save our second year students the algebra by just talking about the solutions, but then spring it on them in third year. For those who like that kind of thing, it's an interesting analysis, but for those that don't, it really is quite horrible. 

Perhaps that is what motivated Paul Dirac to come up with (in my opinion) a really elegant complementary approach to solving the 1-dimensional quantum harmonic oscillator problem. While his approach is easily found in text-books, what I haven't been able to track down is a description of how he came up with it. The same seems to be true of many of the analyses that get wheeled out to students. While they look clean and tidy when presented now, I'm left with the question "How did they come up with this?". That tends to be overlooked in favour of the end product. Did Dirac spend weeks pondering over this, thinking "there must be a better approach - the symmetry between p and x in this equation should surely be exploitable somehow...", was it a sudden revelation, did he try twenty different approaches till something worked, or what? My text books don't say. 

What Dirac did was to reformulate the problem in terms of 'raising' and 'lowering' operators. He realized the problem as a ladder of energy-levels, and showed rather elegantly that these energy levels were equally spaced. Moreover, some rather neat operators, that he defined, could move a quantum state 'up' or 'down' the ladder. That's a very creative way of looking at the problem, and has been taken much further since then. For example, when analyzing problems with many electrons (which generally means just about anything electronic) we can now formulate the problem in terms of operators that create and destroy electrons. Whether electrons really are being created and destroyed is a moot point, but the formulation is a neat one that helps us to analyze what is going on. Theoretical physicists consider it a really useful 'tool' of the trade, even though the history behind its construction tends to be overlooked when we teach it. 

So what is the point of me telling you this? Well, it's about teaching. Just how do you teach creativity, especially in something that is, on the face of it, as tedious as physics. Physics isn't actually tedious (if it were I wouldn't be sitting here writing this) but we do tend to make it unnecessarily so at times. I wonder whether that's because that's the easiest path to take for undergraduate teaching. At PhD level and beyond, there's some really creative research going on, but do our undergraduates really see this? Likewise, from what I've seen at school science fairs, there's some great creativity at primary and intermediate school level, but that then vanishes late in secondary school in favour of 'content'. Somehow, we tend to smother out creativity and elegance in favour of 'something-that-gets-the-job-done.'  But truly great physicists, Dirac included, have never 'just-got-the-job-done'. 

Open-ended projects are a way to go (and we manage to some extent to do this with our engineering students), but, as many readers know, we run into trouble with time, the need to prepare students for exams, fitting in with timetabling requirements, and so forth. The problem may go much deeper than we think - indeed, does the whole secondary and tertiary education structure smother-out creativity from students (at least in physics)? 

And with that, have a creative Christmas, and Happy New Year to you all!  I'll be heading southward next week to the Canterbury hills - a part of the country I haven't been to before. 

 

 

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I've been reading a paper by Majorie Darrah and others (full reference below) on the use of 'virtual labs' in Undergraduate Physics. At Waikato (along with lots of other universities) our first year physics students carry out laboratory sessions to help them learn physics concepts and practical skills. If you are someone who has run a first-year laboratory class, you'll be well aware that these things are costly and time-consuming. If they're not done well, they become an expensive way of wasting everyone's time. 

Recently, there's been a lot of work on 'virtual' laboratories. These are laboratory sessions that aren't 'hands-on', but simulated on a computer. There are some pretty sophisticated ones out there. At our last NZ Institute of Physics conference, David Sokoloff, one of our keynote speakers, talked about some of these. The computer software allows a student to do pretty-much whatever would be done in a laboratory, but without the university having to purchase, set-up and maintain the expensive equipment. (And, from the student's perspective, they are not constrained as to when they carry out the 'lab'). 

So, do they work? I don't mean does the software work, but does the virtual lab give the same benefit to the student as undertaking a real lab. In other words, do the students achieve the same learning outcomes? To test this, Darrah and her colleagues worked with 224 students at two universities. They were put into three groups - one group did the traditional hands-on labs in a laboratory, one group did the hands-on labs AND the virtual labs, and the third group did just the virtual labs. Their learning was tested with a quiz after the lab , an assessment of the student's written lab report, and  tests. 

So what was the result? They found no difference between the groups. One of the universities conveniently carried out a test assessment both before and after the lab sessions and found that all groups improved as a result of the labs, be they real or virtual. That is certainly an encouraging result for the likes of Sokoloff, and those budget-pressed universities with lots of students to push through first year university physics. The problem of doing laboratory work has been one of the reasons why MOOCs for science and engineering have been fairly slow to get going, However, it may be reasonable to do away with this, if good virtual labs can be prodcued. 

But, there is a but. It's a big but in my opinion, and one that, surprisingly, the authors fail to comment on. Their post-lab assessment of learning was based on a written test of the physics theory concepts that were covered in the lab. In other words, they were testing how well the laboratory (real or virtual) supplemented the teaching of physics theory done in lectures and elsewhere. What they weren't testing were practical laboratory skills (e.g. how to wire up a circuit, track down problems with the apparatus, carry out experiments in a controlled manner, etc.) These are all important skills for a physicist. If universities as a whole shifted towards virutal labs in first year, where does that leave students in learning these other skills? The paper doesn't comment. What I'd like to see is the same study done, but the students afterwards given a laboratory test - put them in a real lab and get them to do a real experiment, assessing some practical learning outcomes. Then what happens? It would be nice to try it out - but it will take a bit of organizing (not least acquiring some virtual labs and convincing my colleagues that it is a good idea.) So don't expect a response from me soon.

Darrah, M., Humbert, R., Finstein, J. Simon, M. & Hopkins, J. (2014). Are virtual labs as effective as hands-on labs for undergraduate physics? A comparitive study at two major universities. Journal of Science Education Technology 23:803-814. doi 10.1007/s10956-014-9513-9 

 

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Benjamin has recently acquired a 'new' book from Grandma and Grandad: Mr Archimedes' Bath (by Pamela Allen - here's the amazon link - the reviews are as interesting as the content). The story-line is reasonable guessable from the title. Mr Achimedes puts water into his bath, gets in, and the water overflows. What's going on? So we've been doing some copycat experiments - not by filling the bath right up and having it slosh all over the bathroom floor (Waipa District Council - you can rest easy about water usage)  but filling up rather more sensible-sized containers and dropping objects in.

Archimedes principle is actually a little more involved than simply saying that putting an object in the water will raise the water level. It says that the weight of water displaced is equal to the force of buoyancy acting on the object.  This picture summarizes it. That is, if an object of 2 kg floats, then 2 kg of water will be displaced. If an object is unable to displace enough water for this to be the case, it will sink. That still should be pretty easy to get, especially if you've done some experimenting. However, it can still be the basis of some really hard questions. I had one in my third year  physics exams at Cambridge. In our 'paper 3', as it was called then, the examiners had free reign to ask about ANYTHING that was on the core curriculum from any of our years of study - plus ANYTHING that was considered core knowledge for entry into the degree (which meant basically anything at all you were taught in physics or general science from primary school upwards). This paper was feared like anything - it was basically impossible to revise for*. 

Here is a question then, as I recall it from the exam.

An ice cube contains a coin. The ice completely surrounds the coin. The cube is floating in a container of water.  The cube melts. Does the water level rise, fall, or stay the same? 

Think carefully before answering. 

Now, the icecube melting question is one that is often banded about. A floating icecube will displace its own mass of water (so says Mr Archimedes). When it melts, this water will occupy the 'space' that is displaced by the cube. Consequently, the water level will stay the same. A practical example of this is in the estimation of sea-level rises due to global climate change. When the ice floating on the Arctic Ocean melts, it does not cause a sea-level rise, since it is already displacing its own weight. However, the icecap on Greenland will cause a sea-level rise as it melts, since it is currently not displacing any of the sea (since it is sitting on land.) 

However, that is not the question that is asked. Our icecube has a coin inside it. What difference does it make? Well, the icecube-and-the-coin will still displace its weight of water since it floats. However, when the icecube melts, the coin sinks and no longer displaces the same amount of water as it did when it was frozen into the cube. Therefore the water level falls. That's quite a subtle application of Archimedes principle. After the exam, a group of us sat arguing about it, till we collectively worked out what the right answer was (see - exams can be good learning experiences!). Unfortunately, at this point I realized my answer was wrong. Even still, I managed to get out of the degree with a first-class honours, so I couldn't have done too badly on this exam overall.

*The other question I remember from this paper is 'What is Cherenkov Radiation?' I didn't have a clue what Cherenkov radiation was when I sat the paper - I made up some waffly words and wrote them down and almost certainly received zero for the question.'  Later, one of my friends found a single, incidental sentence in a handout that was given out by our nuclear physics lecturer that identified what it was. That's how nasty this exam was. 

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Today the University of Waikato is hosting a group of local secondary physics teachers. We've had an entertaining morning, with some sharing of ideas. As part of this, Rob Torrens, who teaches our large first-year engineering papers, talked a bit about life as a first-year engineering student. How does the school to university transition work? (or not.)   On a non-technical front, he talked about the need for students to begin to take some responsibility for their own learning. If you fail to submit an assignment, it might be a little while before it's noticed and acted on.  At university there's no 'bell' to tell you that you need to be at your next lecture - there may indeed be no-one even telling you to get out of bed in the morning. It's easy fall off the radar if you're not motivated. 

On a technical front, Rob talked about some of the skills developed at university that are new to many students. Mathematical modelling is one. He used the example of 'mass balance' in an industrial process. If you are drying grain, you put damp grain into your drier and extract dry grain from the end; this is achieved by drawing in dry air from outside, heating it up, passing it over the grain, and expelling the damp air. Mass balance says that mass isn't created or destroyed in the process. But how is that represented for this particular process. There isn't a 'grain-drying mass-balance'  formula in most engineering text books. Students need to work it out for themselves. The mass of what goes in must equal the mass of what goes out, so:

M_grain_in + M_air_in = M_grain_out + M_air_out

We have an equation that we've constructed, just by thinking about the physical principles involved. Throw in some more consideration about the amount of water air can hold (and therefore what M_air_out - M_air_in can be, and we can find out useful things, like how much air we need to draw into the machine for each tonne of grain that goes through it. We've started the process of mathematical modelling. 

This is a skill aligned well with what the Physics Scholarship exam is about - where students need to think carefully through physics concepts before drawing from mathematical equations. 

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As we all know, a scientifically-minded toddler plus a piece of technology can lead to unexpected results. This is the result of Benjamin playing with a retractable steel tape measure at the weekend. How we came to break the case apart I don't know, but the results are pretty (the cellphone shot in poor light doesn't do justice to the artwork): 

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I like the koru-shape made by the end. The measure has curled itself into a complicated form rather reminiscent of a protein structure, with sections of helices and straighter lengths. Although the mechanisms are different (protein structure has a lot to do with the intricaces of chemical bonding) the physical process is similar -  the structure works itself to a local minimum of energy. Just how this happens  is all rather complicated from a physics perspective. Perhaps the most obvious example of twists of this form is in telephone cords. The phenomenon has even lent its name to a type of structure seen in thin films - the 'telephone cord buckle'. Unfortunately Benjamin didn't give me any warning about what was going to happen - otherwise I'd have filmed it (and he would probably have retreated to a safe distance - the whole unravelling was pretty energetic). 

BUT...since Karen is an occupational therapist and has accumulated large numbers of free tape measures as corporate freebies in her career, we could maybe spare a few for high-speed filming.

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The Engineering Design Show is currently in full swing here, with the competitions for the various design projects. The white-line followers kicked off proceedings. They were pretty impressive, with all but one team successfully being able to follow the (very squiggly) line without mistakes. There were traps to confuse the robots - the line got thinner and thicker, crossed over itself, had abrupt corners and so on, but the robots were well programmed and coped with this easily. The winning group was impressive indeed. They had some very carefully optimized control parameters, meaning that the robot was (a) really straight and fast on a straight-line section but also (b) precise round the turns, slowing down just enough to take each turn at about the right speed. I think anyone would struggle to get something going quicker than this one. 

On show at the moment are the third year mechanical engineering students who have designed a pin-collecting machine. The idea is that the vehicle pulls still pins (about 5 cm in length, maybe 5 mm in diameter) out of a board - the one that collects all the pins in the quickest possible time and drops them back in the collecting bin is the winner. The most striking conclusion from this exercise is the emphasis on the old adage "To finish first, first you must finish". A good proportion of the entries have died part way through the process - pins have jammed the mechanisms, the motors have failed, or, in one disappointing case, the machine collected the pins in lightning quick time and then failed to go back to deposit them in the collecting bin. Also, we've seen one machine disqualified for being downright dangerous - its first run saw it pulling pins out of the board and firing them across the room causing spectators to beat a hasty retreat. 

But the winner (or so it looks) has pushed their luck to the limit.  The "...first you must finish" line is actually not quite correct. More accurate would be to say "...second you must finish. First, you must start". They've admitted to putting 5 volts over a motor rated at 3 volts in practice just before the event, and frying the motor. They then had to hurridly locate a replacement and install it while the competition was in progress. Missing their first two rounds, they appeared looking hot and sweaty just in time for their run in round 3 out of 4 and simply destroyed the rest of the competition. (Presumably it won't be long before they destroy their new motor too, but it's survived long enough to win, according to the rules, and that's what counts.)

Overall the design show has been great fun to be a part of and has really demonstrated the skills that the students have acquired. Well one everyone involved!

Postscript 29 October 2014: We're a hit with the Waikato Times!

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Yesterday I read a neat little report by one of our final year engineering students. As part of her final year project, she'd been looking at misconceptions in first-year students' thinking about electromagnetism. Learning about electric and magnetic fields isn't easy. For one thing, you can't actually see them. Therefore it's not at all obvious how something influences them. It's not like learning mechanics  - where you can swing pendulums of different lengths and see for yourself the effect it has on the period of oscillation - these fields are invisible and therefore some indirect way of probing them is required. That adds its own problems. 

Most of the problems identified by the student weren't terribly surprising. The theory of electromagnetism is full of horrible cross-products, which are a mathematical oddity in themselves* (try to read the Wikipedia article on them - I bet you won't get very far). It's hard relating experiment to theory when the theory is a struggle to grasp. Many misconceptions relate to whether fields and currents lie parallel or perpendicular to each other, and which generates a force and which doesn't. 

But one problem that was identified by the research (based on formative tests) was the slap-dash approach to terminology. Many students used terms such as 'magnetic field', 'B-field', 'flux', 'force', 'current', extremely loosely. They have very specific, and different meanings, and they are not interchangable.  I heard a case of this in the lab today - a student talked to me about the force of the wire, when he meant the current in the wire. I think there are two questions here: 1. Using terminology loosely may simply be a consequence of not understanding what the terminology is trying to describe, and therefore is a symptom of  deeper problems with grasping the concepts. Alternatively, 2. The slopiness in using terminology may actually be the root cause of some of the students problems. How can you explain something if you're not using words correctly? - you end up confusing yourself. I'm writing a journal article at the moment - and it's obvious that the process of putting down my thinking on paper, in a precise manner that someone else can follow, does wonders for cementing my own understanding of it (or, sometimes, exposing my own lack of understanding of it when I thought I had grasped it.) 

It wouldn't surprise me if both cases formed a feedback loop (vicious circle) where lack of understanding leads to poor use of terminology, which in turn prevents students acquiring the right understanding. I feel like a little research project is brewing here for next year...

*Cross-products would cease to be an oddity if we put them where they belong - in the dustbin. They are a consequence of a desparate attempt to represent areas as vectors. If we recognized areas for what they actually were - areas (or bivectors) - and worked with geometric algebra, physics theory would become so much easier. But, alas, we are stuck with historical conventions that are probably too far ingrained to break. 

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A few weeks ago I commented on a task our second year software-engineering students are doing: building robots to follow a white line with the Lego 'Mindstorm' kit. It's been entertaining watching their various attempts and their design selections. Most groups have pretty-well optimized their robot now, and there's some final tweaking going on, ahead of our Engineering Design Show at the end of semester.

There's a fine line between an excellently-performing robot and a disaster. To be fair to the students, they haven't come across control theory yet, so for them to identify what's going on when the robot veers off sideways and accelerates into the wall is often not easy. There's been one common problem that the groups have been tackling, namely instability in their tracking. 

Most groups are using two sensors to look for the white line. Crudely speaking, if the robot veers off to the right, the left-hand sensor will cross the line, the robot will 'realize' this, and turn to the left. Conversely, if it goes too far to the left, the right-hand sensor crosses the line and the robot will respond by turning right. But getting the control system stable isn't as straightforward as that. 

If the robot doesn't turn hard enough, what happens is that it fails to get round corners. It goes off the line completely, so that neither sensor now sees the line, and then it's doomed. However, if it turns too hard, it can over-adjust, so that it now veers off the line on the other side. What can happen now is an oscillation: the robot drifts off to the left - so it then corrects and moves hard to the right - but it goes too far right and now it needs to turn hard back left, and so on. 

We can end up with the robot either wiggling along a perfectly straight line, or worse, having it progressively over-correct until the corrections become so large it loses the line completely. The former is an example of a 'limit cycle, or attractor' - a systems-theory term for a stable but possibly rather complicated oscillation. 

More amusing this morning was the poor robot that ended up going in every-decreasing circles. Just what was happening with it I'm not sure, but it veered off the line, did a large diameter circle, and continued in a circlular orbing, but gradually speeding up and reducing its diameter. It ended up spinning on the spot with the left-wheel on maximum forward speed and the right-wheel on maximum reverse speed. This is another (and more entertaining) example of a limit cycle - once it had got into the spinning state, that was where it was going to end up. 

Preventing these things is a bit easier when you know some control theory (see here for example) and can apply the negative feedback in a sensible manner - but we teach them that later. For now, it's about the design process (and the entertainment value). 

 

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In the last few weeks holes have been popping up all over Cambridge. They are being dug by 'ditch-witches'  - pieces of machinery designed for making small-diameter tunnels for cabling - as part of the installation of fibre-optic cables for the much vaunted ultra-fast broadband. A ditch-witch is about the ultimate in machinery-obsessed-toddler heaven. We've been avidly following their movement around the Cambridge streets, or at least the youngest member of our family has. They went down our street about seven weeks ago, and since then have been tracking southwards. I'm tempted to slip a GPS locator beacon on them and then write a ditch-witch locator app to help all those stressed parents cope with constant demands to find them.

So, Sunday saw Benjamin and I get on the bicycle and go on a ditch-witch hunt. (We're going on a ditch-witch hunt... We're going to catch a BIG one...we're not scared...). And, much to my relief, we found them, resting quietly on Thompson Street. 

But this entry isn't about ditch-witches or diggers or cranes or other large pieces of machinery, it's about what we saw on the way. On the front lawn of one house, there was a teenage boy practising 'barrel walking'. He was standing on a barrel, and rolling it forward and backwards around the garden. He was obviously reasonably skilled at this since he had some pretty good control of where he was going. 

An interesting observation is that to get the barrel to roll forwards, the rider has to walk backwards. That must feel a little disconcerting. To get the barrel (and you) moving forward at say 2 km/h, you have to walk backwards at 2 km/h . That's because the bottom of the barrel, in contact with the ground, is instaneously stationary, so if the centre is travelling at 2 km/h forwards, the top of the barrel must be going 4 km/h forwards relative to the ground. In order for you to go at the pace of the centre, 2 km/h forwards (and stay on top), you therefore need to go 2 km/h backwards with respect to the top of the barrel. In terms of mathematics: your speed relative to the ground = 2v - v = v, where the 2v is the speed of the top of the barrel, the  '-v' is the speed of you relative to the barrel, and the 'v' is the speed of the centre. Go it?

That kind of relationship crops up quite a bit in physics. I've talked about a case before - when a satellite in orbit loses energy because it hits air molecules, it speeds up. Uh! How does that work? It's because, as it loses energy, it drops to a lower orbit, one with less potential energy. But lower orbits have higher orbital speeds. It turns out that the loss in potential energy is exactly double the gain in kinetic energy. That is, if the satellite loses 100 J of energy, It's made up of a gain of 100 J of kinetic energy and a loss of 200 J of potential energy. It's another '2 - 1 = 1' sum. 

There's also the neat but confusing case of a parallel plate capacitor at constant voltage. Let's say a capacitor consists of two large flat plates, a distance of 1 cm apart. The plates are maintained at constant voltage of say 12 V by a power-supply (e.g battery). This means that the plates have opposite charge, and so attract each other. (To hold them at constant distance, you have to fix them in place somehow). Now, consider pulling those plates apart. Since they attract each other, it is clear that you have to do work on the system to do this. One might therefore expect that the energy stored in the capacitor has gone up. But no. Do the calculation, and you'll see that the energy goes down. (Energy stored = capacitance times voltage squared, divided by two. The voltage stays the same, and since the capacitance is inversely proportional to plate separation, increasing the separation will decrease the stored energy.) Uh! Where does the energy go then? In this case, you have to consider the power supply. What happens is that you are putting energy back into the battery, by causing a current to flow backwards through it. It turns out in this case, that the work you need to do is exactly half the energy that goes to the power supply. The other half comes from the loss in energy stored in the capacitor. So, if we put in 10 J of energy, we lose 10 J of stored energy in the capacitor, and we gain 20 J of energy in the power supply. So, again, we have the '2 - 1 = 1' sum. 

So, for every kilojoule of energy burned by the ditch-witch, doe the toddler also burns a kilojoule, thus meaning 2 kilojoules of heat end up in the air?  (As neat as it would be if that were true, I don't think the actual figures will come close). 

 

 

 

 

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The 'Science' news hitting the media at the weekend was Guilio Ruffini and Alvaro Pascual-Leone's demonstration of 'telepathy'. There's been a lot of media coverage on this - for example the neat little interview of Ruffini on the BBC's 'Today' programme.

Their article on this can be read here. It's not a long one, and, for a piece of science, I reckon it's pretty clearly described. 

But, I'm afraid, you can forget The Chrysalids - the messages sent from India to France are of a rather more humble nature. But the science behind it is great. 

Essentially, the work has linked together two existing technologies, via the internet. The first is long-established - namely monitoring of the electroencephalogram (EEG). If you place electrodes on the surface of your scalp, you can detect electrical signals that originate from the electrical behaviour of the neurons in the cortex of your brain. The signals aren't large, just a few microvolts, but they are fairly easy to pick up. I get students doing it in the lab. Different kinds of brain activity lead to different signal patterns. A 'thinking' brain has lots of small amplitude, fast activity, whereas someone in deep sleep shows an EEG pattern that has a large, approximately 1 Hz cycle to it. The two patterns are very different. EEG is routinely used for monitoring sleep patterns and as a tool for an anaesthetist to monitor the depth of anaesthesia in their patient - one wants to make sure the patient is well anaesthetised, but on the other hand one doesn't want to head into Michael Jackson territory. The EEG can help. 

So the EEG is a way of 'reading' the state of the brain. To go from an EEG recording to working out what the subject is thinking about is a long, long way off, if indeed it's possible at all, but one can certainly say something about the brain state. 

If EEG is about reading the state of a brain, then the other technology, transcranial magnetic stimulation (TMS), does the reverse. This is rather newer, and our understanding of it is much poorer (I'm involved with a TMS research project at the moment).  In TMS, pulses of magnetic field are applied to the brain. The effect depends on what area of the brain the pulse is applied to, and in what orientation. At a simple level you can make an arm 'twitch' by applying the pulse to the correct part of the motor cortex. I've seen this done at the University of Otago (on a brave summer student of mine). In Ruffini's work, they used the magnetic pulse to 'create' the perception of a flash of light by stimulating the visual cortex. The subject 'sees' the light, even though there's no such flash on the retina, since the sensory circuits in the cortex that usually interpret what's going on on the retina are activated remotely. 

So what did the experiment do? The person in India sending the message imagined a particular activity (hand or foot movement), and their EEG changed depended on whether they imagined the hand or foot. A computer interpreted the EEG, decided on which it was, and communicated with the computer in France. The French hardware system then zapped the human receiver in such a way as to either trigger the flash or not trigger the flash. The receiver then reported orally whether they'd seen a flash. In this way the 'message' (a string of 1's (hands) and 0's (feet) ) has been sent from one to another without using the senses of the receiver. 

In that sense this is telepathic. The receiving person had no communication with the transmitting person in a visual, oral, or any other way. True, one might ask, why didn't they just phone/Skype/email each other to send the message, and of course you wouldn't want to communicate with your family members overseas with an EEG/TMS system. But that's not the point. The point is that it is a great demonstration of science. 

Will it lead to small telepathic headsets? Rather than fuss with phones and email, we could just have a conversation with anyone in the world just by thinking about it. (You'd want to be sure you'd switched it off afterwards!)  Don't get excited - we're not in Chrysalids territory yet. That's a long, long, long, long way off. But it is good science. 

 

 

 

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