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When I was at school, and introduced to magnetic fields in a quantitative sense (that is, with a strength attached to it), I remember being told that the S.I. unit of magnetic flux density (B-field) is the tesla, and that 1 tesla is an extremely high B-field indeed. Ha! Not any more. Last Friday night  I got to see a MRI machine in action - at Midland MRI at Waikato Hospital - this particular one is a 3 tesla affair. One of my PhD students was making some measurements with it. It needed to be at night - such is the demand for MRI scans we'd never get to play with it during the day. But well worth extending my day's work for. 

Now, what does 3 tesla do? First you are advised to check pockets very carefully and remove keys and the like. No pacemakers? Good. Now enter the room. Interestingly, I didn't really 'feel' anything until very close to the machine - then there was just a hint of something slightly 'odd'. Things a little tingly, but nothing really significant. 

Two events, however, confirmed that there was a sizeable field indeed. First, my belt unbuckled by itself. That prompted a quick retreat outside to take that off, before bits started flying through the air. Then our host demonstrated what 3 tesla does to a sheet of aluminium. 

It's important to remember that alumunium is not ferromagnetic. It is not attracted by a magnet. But it is, most certainly, very conductive. When a conductor moves through a magnetic field, electric currents are induced. These in turn generate magnetic fields, which are such that they oppose the movement. This is Lenz's law. Consequently there is a force felt by the conductor that opposes its motion. And at 3 tesla, that's some force. You can stand the sheet of alumnium on its end. Normally, you'd expect it to fall over, pretty quickly. But not at 3 tesla, it doesn't. Very, very slowly, it topples, taking several seconds to move from vertical to horizontal. I could feel the effect of Lenz's law by trying to flip the sheet over. It was like trying to turn a rapidly spinning gyroscope. Pretty impressive stuff. 

You can see a movie of this experiment (not ours, I should add), here. 

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I've just given a couple of lectures on special relativity to a class of first years. It's clear that grasping the key ideas is going to take some time. The results are so far removed from everyday experience that there is a certain air of bewilderment in the classroom. Here's an example of what I mean. 

Suppose two students are travelling on skateboards, both at 10 km/h, but heading towards each other. In the frame of reference of one, what is the velocity of the other? 

The answer is simple: Add up the speeds - one sees the other coming at a speed of 20 km/h. 

Now make the skateboards a little quicker. To be precise, make them both travel at 0.8 times the speed of light. Now what does one of the skateboarders experience?

Our immediate reaction might be to say 0.8 + 0.8 = 1.6  -they see the other approaching at 1.6 times the speed of light. But that would be wrong. At high velocities, it just doesn't work that way. The correct answer would be (from the Lorentz addition formulae) 0.98 times the speed of light. That is hard to grasp. There are at least two reasons. First, we never experience skateboards going at 0.8 times the speed of light, so the question is not physically meaningful. Secondly, it is so far removed from our physical experience it just doesn't make any intuitive sense. 

One can do the correct relativistic calculation on our first example - two skateboarders each heading at 10 km/h (or 9.26 billionths of the speed of light). This time we end up with 19.999 999 999 999 998 3 km/h. It is little wonder that calling it 20 km/h is an approximation that works for us! Putting it in context - if we travelled at this speed for an hour (thereby covering 19.999 999 999 999 998 3 km), we would be about 2 picometres short of 20 km. That's something much less that the size of an atom (but rather larger than the size of a nucleus). Little wonder we get away with calling it 20 km without any trouble. 

A consequence of special relativity is that time and space are 'relative' - meaning that different observers will disagree on the time between two events, and the distance between two events. This is measurable - put an atomic clock on an aircraft and one on the ground, and fly the plane around for a few hours. On landing, the two clocks will be different, showing that time has been experienced (very slightly) differently. 

There is, however, one very readily measurable consequence of relativity - one for which we are all familiar. That is magnetism. Magnetic fields and electric fields are part of the same entitiy. Just as observers will disagree on the time and distance between two events, so two different observers will disagree on the strengths of magnetic and electric fields in a system. A magnetic field becomes an electric field to a different observer. The reason we experience magnetic fields at all is down to the extreme neutrality of matter - the number of electrons and protons in a sample of material being incredibly well balanced. I didn't try to explain that one - but it makes a nice bit of analysis for third-years. 


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I just love the word 'obfuscate'. It means (in my words) to take something that is perfectly clear, and render it incomprehensible. As in "Using the word 'obfuscate' in a sentence will obfuscate its meaning". 

I say this because I've just been reading an article on which (clearly) a statistician has been let loose - thus rendering an otherwise wonderful article incomprehensible - at least in places. Now, I'm not saying that the statistical analyses aren't necessary, rather that in my opinion the article would be much more readable if most of the statistics were presented neatly in an appendix, rather than being liberally splatted across the second half of the article. I mean, seriously, how many of us actually know what the "Kaiser-Meyer-Olkin measure of sampling adequacy" involves, what "Bartlett's test of sphericity" is (something FIFA use to assess the roundness of a football, maybe?), or what "Mahalanobis' Distance statistic" measures?  Or am I just dumb in this regard?

That aside, the article I think is a little gem (though it's not often such a blatant apostrophe error finds its way into a journal title, especially one in pedagogy):

C.D. Smith, K. Worsfold, L. Davies, R. Fisher & R. McPhail. Assessment literacy and student learning: the case for explicitly developing students [sic] 'assessment literacy'. (2013). Assessment & Evaluation in Higher Education, 38(1), 44-60.

Here the authors talk about the need to educate students in what assessments are there for and how to interpret them. The over-arching message is clear (that is, unobfuscated).  With reference to Francis (2008)*, they say

...first-year students in particular are likely to over-rate their understanding of the assessment process and ... there is a disjuncture between what they think they are being assessed on and what the marking criteria and achievement standards require of them

The authors go on to describe a simple intervention - a workshop in which students get to undertake peer discussion on examples of submitted work - and how they shape up against the marking criteria. Such an intervention results, I believe  (the paper is rather obfuscated here), in a good improvement in the quality of  students' submissions in a similar assignment. In particular, two areas show marked improvement.

First, students develop the ability to judge for themselves what makes a good response to an assignment. By implication, then, it means they develop the ability to judge the quality of their own work. That is a skill required by any professional. Imagine you have an electrician do some work in your house and she's unable to say for herself whether she's done a good job of it. A frightening prospect!

Secondly, students develop the idea of 'assessment for learning' (as opposed to assessment of learning), that is, they can see that they are able to learn while doing the assignment, Moreover, they begin to grasp that assignments can be set with the very purpose of developing student learning as opposed to simply providing a summative measure - in other words their lecturers are using the assessment process in a carefully considered manner with the primary purpose of achieving student learning. 

Also increased, though not by as much, was student understanding of the actual assessment at hand, and their desire to put effort into the assessment. 

All this has me thinking about what we commonly ask on physics assignments, tests and exams, and whether the students really know what we mean. The answer, I am sure, is 'no'. We use words and phrases such as "show that...", "evaluate...", "discuss..." and "from first principles..." These might be clear to experienced physicists, but I wonder whether  students find them not unobfuscating. 

Time for a bit of research. 

*R. A. Francis (2008). An investigation into the receptivity of undergraduate students to assessment empowerment. Assessment & Evaluation in Higher Education 34(4), 481-489. 

P.S. Thank you to Dorothy Spiller of our Teaching Development Unit for drawing my attention to thie Smith article. 

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There's no hiding my conflicts of interest here. I'm on the New Zealand Institute of Physics 2015 conference organizing committee. I'm also the NZIP treasurer. And I'm a staff member at the host organization.  So, to contribute to the New Zealand physics community's biennial event  in Hamilton on 6 - 8 July, click on this link. 

But why? Pick from the following

a. Because you get to meet colleagues and actually talk with them. 

b. Because you get to hear and discuss first hand about some of the exciting physics work that goes on in New Zealand

c. Because you get to meet, talk to, and learn from Eugenia Etkina, who is one of the most honoured and respected physics educators in the US. She's researched in particular student learning through practical experiments, and how to maximize it. But also she's looked at the modern physics curriculum more generally. And she'll be here with us to share it all. 

d. Because you get to celebrate the International Year of Light (which, by the way, was designated by UNESCO following lobbying from a handful of countries including New Zealand)

e. Because you get to experience practical examples of Bessel Functions.  (You may need to click here for an explanation). 

So, no excuses. See you in The Tron in July. 


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In the last few years I've been experimenting with the way I test our 3rd year mechanical engineering students in their 'Dynamics and Mechanisms' paper. I've chosen this paper because (a) it has more than a handful of students, and (b) I am in charge of it. When  I've suggested to my peers that I do something similar with other papers I teach on (but not in charge of) a "Don't you dare" tends to ring out rather clearly in response. So Dynamics and Mechanisms it has to be. 

I've tried 'tests you can talk in', with mixed success. This year, I tried an oral test. That involved giving every student a personal, fifteen minute interview. I had the idea from an article I read which talked about the problems with traditional written assessments, and discussed other possibilities* It's not a new article, but then universities have a lot of inertia, so it's no surprise that the troublesome written assessment still seems to stand as the perceived 'gold-standard' for assessment at university. 

But an oral test was a big risk for several reasons.  First, I had to declare what form the test would be on the paper outline (an official summary of what the paper involves) well in advance of it starting. This meant that I didn't know how many students they'd be, and how much work it would involve. I was expecting, based on previous years, something around forty students. I watched in horror in the week before semester as the student enrolments climbed well beyond this. In the event I had 55 interviews to do, last week and early this week. That was a high workload, fitting all that in amongst my other lectures and commitments. That said, preparing and marking a written test is a pretty demanding exercise time-wise as well. But I wouldn't want to repeat the exercise with a bigger class. 

Then I had to convince students that this was actually a reasonable thing to do. I spent an entire lecture session on discussing how the test would run. It was the best attended of any of the lectures in this paper! If that's not proof that students are motivated by assessment, I'm not sure what is. The feedback I've had so far has been mostly positive, which is reassuring, although there are some things that in hindsight I could have got better. 

Then, what if it all fell apart? What if I were sick? (I had no back-up plan here). Or students, for whatever reason, got the wrong idea of what was required? (I had given them a task to do beforehand which we'd talk about as part of the interview).   In the end, there were no such problems, but there could have been.  

So how did students do? I've had a number of positive comments (plus some negative ones) relating to how students felt that the oral test actually got them better prepared and engaged with their learning beforehand than a written test would. That was part of the plan! Also, from my point of view, I got to learn just what it was that the students had learned. The breadth of the learning took me by surprise. My first question to all of them (which they were expecting, because I'd told them) was "tell me about something you've learned in this paper". I had my own pre-conceived ideas about what they'd all choose, but I was wildly mistaken. Between them the students covered just about the whole paper, sometimes in accurate detail, including bits that I thought I'd glossed over. Aspects that I thought were really difficult were in fact grasped really well. Conversely, when I started to ask some probing questions, some things that I thought were straightforward, proved to be mis-understood. That feedback to me is more useful than years' worth of student appraisal questionnaires, and that reason alone is enough for me to view the oral tests as a success.

So what happens if I get 70 students next year?

*Biggs, J. (1999) Teaching for Quality Learning at University (pp. 165-203). Buckingham, UK: SRHE and Open University Press.

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While there is some great fiction out there, one really shouldn't try to learn much physics from it. One case in point, which I am forced to listen to over and over by the youngest member of our house, is the story of the Three Little Pigs. 

I'm not talking here about the relative merits of various building materials for construction of houses. Straw, wood and brick all have their place. I refer to the rather rapid boiling of the pot of water that the Third Little Pig puts on the fire when the wolf comes knocking at the door. 

In the version of the story that we have on CD, thw wolf, fresh from his succesful huffing- and puffing- of the straw and wood houses, arrives at the home of the Third Little Pig, where  the First and Second Little Pigs have taken refuge. A house made of brick. The door is locked in his face. No problem for the wolf - or so he thinks. A little more huff and puff and this one will be blown in to.  But this time he's mistaken. The house stands still. The angry wolf now resorts to plan B. He puts safety regulations aside and climbs onto the roof of the house, with the intention of gaining ingress via the chimney. 

Time for the third Little Pig to move quickly. He gets a fire going, puts a wolf-sized  pot of water on in, and gets it boiling - just in time, as the wolf drops down the chimney. This version of the story ends with the wolf fleeing in pain (rather than cooked) and the Three Little Pigs jubilant. 

Actually, the story doesn't end, because Benjamin now pushes the button on the CD player to play it again. And again...

Now, just how much power does the Third Little Pig have at his disposal to boil a wolf-sized pot of water in the time taken for a wolf to climb up onto the roof and head down the chimney. The wolf is in a foul mood, so he's not going to hang around. Let's say it's going to take him  minute for this task. A wolf-sized pot might be around 100 litres in size. If it's full of water at about room temperature, this 100 litres of water has to gain 75 degrees Celsius in just 60 seconds. 

One litre of water takes 4200 joules of energy to raise its temperature by 1 degree C. That's called the 'specific heat capacity'. To raise 100 litres by 75 degrees, we therefore need 4200 times 100 times 75 = 31 500 000 joules. This happens in sixty seconds - thats about half a million joules per second. 

What does that mean? One joule per second is one watt of power. So here we have about 500 kW of power - a kW (kilowatt) being a thousand watts.  

This is something pretty substantial. If you've watched the disc on your electricity meter spin around, you'll know that it's rotation rate is a measure of your power consumption. Usually 200 revolutions equals 1 kWh of energy. Do the maths and you'll find that 1 revolution per second (a seriously high domestic consumption) equates to 18 kW of power.  500 kW equates to about 30 revolutions per second. Dizzy stuff.  

If the Little Pigs were relying on electricity they'd be needing to upgrade their mains connection. But they are using wood. Consumer NZ tells me that efficient, domestic wood-pellet fires can produce about 10 kW of power. To hit the 500 kW range, the pigs obviously have a sizeable one indeed. 





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I can't help thinking that the West Indies team got their run chase strategy wrong on Sunday night. They had a tricky task ahead of them. One might say the problem was one of their own making, judging from the rubbish that they served up to Guptill to hit at the end of tne New Zealand innings, but that was in the past. The fact was they had to chase down 393 in 50 overs. How does a team go about doing that?

I would have thought that the obvious answer was 'in the same way that the opposition made it'. In other words, keep the scoreboard turning over nicely in the early stages, but without taking excessive risks, and then, with the wickets in hand (especially Gayle's), hit the accelerator at the end. Rather than taking 50 overs to reach the target, they looked like they were trying to do it in 40. It was never going to work. You can contrast this to the calm manner in which Sri Lanka reached England's 300+ score in the group stages. Nothing flash, no excessive risks, they just ticked the board over just short of the required run-rate, and then with wickets in hand they pushed on at the end to win easily. No fuss, no stupid shots. They knew exactly what was needed, and they achieved it. 

A school of thought says, other things being equal,  it's much better to bat second in a limited overs match, because you know exactly what you have to do. It clarifies your batting strategy: Choose whatever strategy maximizes your chances of reaching the target score within 50 overs. Yes, there are other considerations, our friends Duckworth and Lewis being one, but let's put those aside for the moment.  You have 10 wickets and 50 overs, and a target score. You only need to beat that target by 1 run on the last ball, with one wicket left.  What strategy will maximize your chance of success?

The team batting first has a much less defined problem. They don't know what a winning score is. True, they'll have some feel of what one will be, given the ground, the quality of opposition, the state of the pitch and so on, but fundamentally, they don't know what score is going to be good enough. For example, a team could probably secure a moderate score (let's say 280) with 80% probability, by batting conservatively. Or they could aim for a larger score (say 350) by taking more risks. They might get there with a probability of 25%,  but then there's the possibility (maybe also 25%) they crash out on the way and end up with something more like 250. What  should they do? Which strategy is better? 

It's viewed as a criminal offence if the team batting first fails to bat out its 50 overs. If it's all out beforehand, it has obviously taken too many risks. But also, one could say its a criminal offence if they end up with just a handul of wickets down. In that case they haven't been taking enough risk. Balancing all that up, a typical strategy for a team batting first is to go at a moderate rate to start with, and slowly increase the rate as wickets allow. It seems to have stood the test of time. 

It is possible to make this a bit more mathematical. What a team needs to do is to maximize its score, subject to the constraints that a. it only has 50 overs, and b. it only has 10 wickets. Since the rate of fall of wickets is certainly related to the scoring rate (the higher the runs-per-over, the higher the risk, usually, and the higher the wickets-per-over) we can write down some equations for the situation. [You'll be relieved to hear I won't try to do those here].

It turns out to be is an optimization problem, of which there are many in physics. We can tackle many of them with the Euler-Lagrange equation.  For example, what shape does a chain have when it hangs under its own weight? Take a chain of length 2 metres, secure the ends to posts 1.5 metres apart. The chain clearly sags in the middle, but what shape is the resulting curve?  The chain hangs in such a way as to minimize its gravitational potential energy, subject to the constraint that it has a constant length and that it has to start and end at fixed points. One can put this in equation form and solve for the shape. The resulting curve is called a 'catenary'. 

Certainly, if one could write down the rate of loss of wickets as a function of scoring rate, wickets lost already and other factors, we should be able to have a go at tackling the cricket scoring rate problem. Given the degree of professionalism of the sport, it wouldn't surprise me if that has actually been done by someone. I imagine it would be a closely guarded secret.






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A mathematician can say what he likes... A physicist has to be at least partly sane

J. Willard Gibbs 

What is it that makes a physicist sane (if only in part)? Everything has to be related back to the 'real world', or the 'real universe'. That is, a physicist has to talk about how things work in the world or universe in which we live, not some hypothetical universe. That's how I think of it, and I know, having done a bit of research with some of my students, a lot of them think the same way. That's not to say mathematicians don't have a lot to say about this universe too. It's just that the constraints on them are somewhat less. 

Another way of looking at it is that physicists work with dimensioned quantities. Most things of physical relevance have dimensions. For example, a book has a length, width and thickness. All of these are distances, and can be measured. The unit doesn't matter; we could use centimetres, inches or light-years - but the physical size of the object is determined by lengths. Also, the book has a mass (one could measure it in kilograms). It might find its way onto my desk at a particular time (measured, for example, in hours, minutes, seconds, millennia or whatever). Perhaps it is falling at a particular velocity - which describes what distance it travels in a particular time. All of these things are physical quantities, and they carry dimensions.

One of my pet hates as a physicist is reading physics material in which the dimensions have been removed. You can do this by writing lengths in terms of a 'standard' length, but then only quoting how many of the standard length it is. So we might talk about lengths in terms of the length of a piece of A4 paper (which happens to be 297 mm); a piece of A2 paper has length 2 standard-lengths, and an area of 4 standard-areas. The problem really comes when the discussion drops the 'standard-length' or 'standard-area' bit and we are left with statements such as a piece of A2 paper has a length of 2 and an area of 4.  It is left to the reader to work out what this actually means in practice. A mathematician can get away with it - she can say what she likes, but not so the physicist. 

Here's a question which illustrates the point? What is the length of a side of a cube whose volume is equal to its surface area? The over-zealous mathematics student blunders straight in there: Let the length be x. Then volume is x^3, and surface area is 6 x^2 (the area of a face is x^2, and there are six on a cube). So x^3 = 6 x^2 ; cancelling x^2 from both sides, we have x=6.  Six what? centimetres, inches, furlongs, parsecs? The point is that the volume of a cube can never be equal to its surface area. Volume and area are fundamentally different things. 

The Wikipedia page on 'fundamental units' , along with many text books, blunders in this way too. The authors should really know better. (Yes, I should fix it, I know...) For example:

A widely used choice is the so-called Planck units, which are defined by setting ħ = c = G = 1

No, NO, NO!  What is wrong with this? How can the speed of light 'c' be EQUAL to Newton's constant of Gravitation 'G". They are fundamentally different things. The speed of light is a speed (distance per unit time), Newton's constant of gravitation is... well.. it's a length-cubed per mass per time-squared. It's certainly not a speed, so it can't possible be equal to the speed of light. And neither can be equal to 1, which is a dimensionless number. What the statement should say, is that c = 1 length-unit per time-unit; and G = 1 length-unit-cubed per mass-unit per time-unit squared. 

However, doing physics can be more complicated that this. A lot of physics is now done by computer. In writing a computer programme to do a physics calculation, we almost always don't have explicit record of the units or dimensions in our calculations. Our variables are just numbers. It's left to us to keep track of what units each of these numbers is in. Strictly speaking, I'd say it's rather slack. It would be nice to have a physics-programming language that actually keeps track of the units as well. However, I'm not aware of one. (If someone could enlighten me otherwise, that would be fascinating...) Otherwise, I'll have to have a go at constructing one.

What's prompted this little piece is that I've been reviewing a paper that has been submitted to a physics journal. The authors have standardized the dimensions out of existence, which makes it awfully hard for me to work out what things mean physically. Just how fast is a speed of 1.5? How many centimetres per second is it? While that might be an answer their computer programme spits out, the authors really should have made the effort of turning it back into something that relates to the real world. In a mathematics journal, they might get away with it. But not in a physics journal. At least, not if I'm a reviewer...



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Further to my last post, here's a very accessible discussion on some of the physics related to 'the arrow of time'. Maybe, just maybe, Benjamin has the right idea after all...


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Benjamin is now two-and-two-thirds, or near enough. As ever, his grasp of physics continues to improve.  In the last few weeks, he has been picking up the idea of time. 

We have a large (more accurately, LARGE) analogue clock on the wall of our lounge. He's watched me take it off the wall, change the battery and move the hands to a new position when it started to run slow. It's clear to Benjamin that what the hands do on the clock is related to the time of day, although just how I think is some way off.  Over the weekend he wanted me to read him a book, but didn't want me to get it for him. He shoved me away, and rather matter-of-factly said "Daddy stay there. Poppet will get a story." Then he turned to get the book, but quickly came back to me and added "I'll be back at half-past-four. See you soon." And off he went to get his favourite book (which, as ever, is about excavators and other large machines). 

That was just one of those amusing moments you get with a young child. But another 'time' incident was rather more interesting. Karen was out, and Benjamin was somewhat upset over her absence. I was trying to reassure him that she would be back. "She'll come home at about half-past-eight". Benjamin looked at the clock longingly and said "Daddy change the clock so it's time for Mummy to come home". 

Now there's a thought! Wouldn't it be great if we could just manipulate time by turning the hands of the clock? So, somehow, if we changed what the clock says, then the time of day would actually change. Does Benjamin think that this is how it actually is? Maybe. It would be useful if it were true - extended weekends, short work days; one could cut hours of a plane trip to Europe by taking the clock with you. 

While it might work for science fiction writers, unfortunately that's not how time works for us. While the clock and time are intimately linked, it is time that controls the clock, not the other way around. We are stuck with progressing through time at the rate of one second every second. 

That makes time a rather strange concept from a physics perspective. Unlike space, where we are free, more or less, to move to any point in it, we don't have that option with time. We can only move forward in it, and only move forward at the same rate - one second every second. The past is forever behind us; and the future is always unknown. Physicists call this the 'Arrow of Time'. It points one way: forward. 

Special Relativity makes it more interesting still. The way time works for you may not be the same as it works for me. If I were to get on a Really Fast Spaceship and travel close to the speed of light for a while, then return to earth, I would be noticeably younger than my identical twin brother. (I actually DO have an identical twin, by the way.)  Not only would the clock in my spaceship be telling me less time had past, I would have actually aged less. From my point of view, I might have been gone for two weeks; from yours, I might have been gone ten years. But even so, each of us will still have perceived time as travelling at one second every second. Forward. 

What about real time-travel - going back in time. Just maybe physics permits this to happen. That's in the realms of General Relativity and Quantum Gravity and involves some really big masses indeed. Matt Visser's work at Wellington might give us some pointers here. But the summary of it is: Don't expect a such a time-machine to be built in Benjamin's lifetime, even if he does prolong it indefinitely take the battery out of our lounge clock.






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