teachers, vernier callipers

For the past few sessions, we (erdkinder and I) have been studying about measurements, precision, accuracy, error, terror ad infinitum. As part of this and with a view to addressing the ‘syllabus’ requirements of the eminently (in)evitable X std exams, the children have to study about Vernier Callipers, Screw gauges etc.

Now, I have always been fascinated by this ingenious concept of Pierre Vernier, but I recall that, when I ‘studied’ his wonderful ideas a few decades back, it was quite sad; my illustrious (then) teacher (RIP) ‘covered it’ without a clue, though the concept is fascinatingly simple. Same story got repeated during my baccalaureate studies too. Unfortunately, I realized it only later that all these folks merely taught because they were paid to teach, and NOT because, they loved to teach nor were they men/women who were fascinated by the world of  ideas. May be the reason is that teaching is such an underpaid job, in spite of it being exhausting and sometimes saddeningly thankless, and hence is mostly dominated by folks, who are/were otherwise ‘rejects’ from the ‘system’ – meaning, highly paid cushy jobs; or it may be that it is a sadly negative feedback system in which good folks can’t get in for various reasons – and the folks who are there in the system, have lost all enthu for life. Of course there are exceptions, but then I believe, exceptions only prove the general rule. This is not to say that I did not have good teachers and I have thusly a bunch of axes to grind – I have had my own delightful quota of exceptions but they were mostly outside of the walled gardens of acadummya. heh!

But, by and large, there is so much joy in teaching, learning and being with children (ah, the luxury!) that, if by some magical Poincare inversion, if teaching becomes the highly paid and most respected profession – then… the result would be a deliriously delightful future, what else, but may be am merely dreaming or better still, smoking marijuana!

Now for a commercial break! 🙂

Luckily, all teachers (‘adults’ in montessoriese) in NammaShaale are there because they either love children or love montessori education mode – and mostly & actually it is both,,, It is a pleasure working (and getting workedup) with them. Thank dog for small mercenaries, am not talking about the cutely brattish young fellers and fellerinas at the primary environment, though..

Getting back the rant…

Considering, how important this teachers’ role is in/for the society, it is amazing, but is true in general all over the world, that the status quo continues. Of course there was one significant exception – ‘Soviet’ Russia – which alas or happily so, is no more.

Is the concept ‘water find its level’ applicable and operative here? Would this theory help one understand this breed of abominable know men and women? Would this be the result of parents happily outsourcing the ‘education’ to the schools, as they think that, with transfer of genes (le vice?)  their contribution towards their children is over – except in the case of  buying the new, latest and improved Sony PSP? For all I know, my neighbour’s golden retriever only knows…

Pierre Vernier beckons.  He has been waiting patiently for my rant to end, and I respect him for that too!

The idea of any measurement is to allow to us to have a reasonable take on something to be measured – and that which is possible with predictable accuracy and precision. In a given scale (Ruler, that is – not very despotic, I hope) graduated in centi and millimeters, the minimum measurement (technical jargon: least count) that is possible would be 1 mm; this is also normally called ‘pitch‘ – but I intend queering it. Now, <drumroll> here enters the French man (actually he did this nearly 4oo years back) who decided to use a scale (vernier scale) that had ten divisions that were equal to 9 normal scale (‘main scale’) divisions. Hence each vernier division had a least measurement possibility of 0.9 mm.

Now comes the magic. If these two are brought together / juxtaposed then it is possible to measure lengths accurate to 0.1 mm. The least count of the combination of scales is 0.1 mm! How?

We worked with mere paper strips. I gave the children 2 strips each (some 1 cm x 10 cm – the size does not matter, dinosaurs notwithstanding – but we will call them A and An just to confuse you). One of the strips A was folded into 10 equal parts and marked off appropriately – the other strip An was placed over the first and was reduced/cut-off to measure 9/10ths of A. In other words Lengths of (A/An) = 10/9. An is also folded into 1o equal lengths and is marked off. All reasonably approximate of course.

A = mein skale. An = vernier scale.

Now, if you juxtapose them in such a way  that the markings face each other, Voila – at any point any ONE division mark of An will coincide/align with some division or the other of A – if you move A and An against each other! Yay! There is a picture of it below to befuddle you more!

how to understand 'vernier' using paper strips - you can move them against each other,,,

how to understand 'vernier' using paper strips - you can move them against each other,,, (the newspaper just serves as a background)

From this, it is a small baby step ahead, to understand how the magic works, nothing earthshaking, but beautiful! Of course, the children understood the cutting edge technology with a little bit of steering etc. I am proud of them.

If you are curious about how this concept works or if your engineer neighbore wants to know it, just go ahead and hustle any of our erdkinder. They will be happy to enlighten…

Erdkinder macht frei. Ja.

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  • Reshma  On March 13, 2009 at 1:30 am

    On the question least count is 0.1, wonder if we can apply the same to a different context

    (ramjee sorry ..but can’t help but give a sawaal pe sawaal…)

    If we look a different music styles … can we listen to or practice music by beating drums or setting talas to different speed settings and check when two different pulse meters (or even different talas) meet in harmony? When is the first time they will meet?

  • Ramjee Swaminathan  On March 13, 2009 at 11:07 am

    Interesting thought, dear Reshma. 🙂

    Our Johannes Sebastian Bach has tried all these kinds experiments. If you haven’t already listened to his Musical Offering, Goldberg Variations, Toccata & Fugue in G minor please do. Fascinating.

    If you tweak the tempo settings of two instances of a given musical composition (as in main scale – venier scale combination), it will give rise to repeating crescendoes… in good harmony.

    When will the two movements meet – they will at the least common multiple of the beat/tala sequences (n x m) and thenceforth.

    I STRONGLY recommend that Arnold Schoenberg’s “Theory of harmony” be digested… This man is a genius. I have been hunting for a personal copy for a couple of decades now… It is somewhere in my looong list of books to *own* – what a bourgeois mentality, sheesh! (hint, hint)

    Thanks for asking, it was a great mapping and parallel in other fields.

    Perhaps others would share their thoughts too??

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