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Mountain Metaphor In Learning: Seek The Balloon And Ramp

Discussion in 'Education & Personal Growth' started by Novalis, May 26, 2019.

  1. Novalis

    Novalis Finest Post Winner

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    Sometime ago (last year), I happened to watch a clip with a shattering metaphor.


    upload_2019-5-26_19-6-7.png

    I was stunned as the visual deeply disturbed me.

    In the clip, the narrator compared Einstein's trail (special relativity) to ascending a mountain from the steeper pathway. Einstein did reach the summit! but in a very hardknock rumination. The others who learnt of the discovery of Einstein scrambled to explore variant routes to claim the arduous summit, far easier approaches. A learner can reach the very summit from a gas balloon or a gentler slope. The narrator further introduces the basic principles of relativity in a never-before-heard manner. I was greatly impressed! (relativity could be explained like this also with an ingenious worldline toy)

    The metaphor lingered on me.

    The reproducible work of the original discovery undertaken by a thinker is not always the most accessible path. But once the thinker shouts out: 'hey I found the top of the mountain ', others could map their own expeditions to the resolved coordinates, and in that process, each stumbles on a more congenial path.

    We find a lot of mathematical and science topics puzzling, and daunting, because we are taught in the original (steepest) path of the victorious thinkers. The academic textbooks mindlessly copy the original path in good faith. I am amazed by citizen tutors like Burkard Polster and Grant Sanderson and Henry Reich and Matthew John O'Dowd hosting science learning from gas balloons and ramps.

    Why am I writing this today? Yesterday, I read

    upload_2019-5-26_18-55-1.png


    ... the book dedicates only a measly chapter to that equation but the hundred odd pages to the build up of that pointy chapter is mind-blowing. I have never seen anyone explain that fabled equation deploying just the first principles of momentum conservation extrapolated into interchangeable dimension (spacetime). Generally, that equation is also derivative in the quantum hustle (clumped energy is mass).

    A lot of science topics had been bewildering to me in the past. These days when I meddle in science learning as a pastime, I tend to be mindful of that mountain metaphor.

    If I am unable to grasp the talk in the nearest text, it could be because I am clambering the mountain through the harshness of the outdated trail. Recognizing the drawback, I search for other narratives.

    PS: I highly recommend this book to anyone with even a smidgen of interest in the methodology to appeal and explain scientific insights in fellowship as a teacher, parent, or even a threatening aunt to her nephew. Again, it is not so much the equation but the process of demystifying a monumental trek in science with balloons and ramps without being overly simplistic or unimaginatively reductive to smarten up the hooked learner sensitive to the mountain metaphor.
     
    Last edited: May 26, 2019
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  2. Amulet

    Amulet Platinum IL'ite

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    This general notion ( the second mover advantage) is all over everywhere in life. Even in non- sci matters.

    First child is a prototype (test case, trial balloon, etc.) raised by novices, whereas the latter ones are much better raised and launched. ;)
    Generic drugs have a cheaper mfg route/costs than the original invention.
     
  3. Novalis

    Novalis Finest Post Winner

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    MIT OpenCourseWare

    I thought ...I might as well (as Amulet ever reckons: you can go on and on in a monologue!) jot down my other findings, humoring my quirk to dump irrelevant stuff onto equally incompatible threads.

    I have been skeptical about MIT OpenCourseWare compared to other free educational channels. Don't know why. I thought it might be too abstruse for me. The first tutorial I watched on MIT OCW was on quantum mechanics. I was stunned. By then I acquired uncritical taste in educational content that I was beginning to enjoy every thing I watched.

    I had to repeatedly scan the comments under the tutorial videos to establish how blithely credulous I am for fancying everything that I was chancing upon. One comment in particular fascinated me which meditated at length on why MIT graduates are brighter than your ordinary average. (They had bright teachers!) I could relate that observation onto my own teachers (while growing up) who were as unimaginative as they come, teaching science and mathematics with utter banality that could put even a defiant insomniac to sleep. They themselves never understood these topics with the clarity to relay to their aspiring pupils. The MIT educators grasped the scientific tropes well beyond to impart that learning to their students. The marksmanship of an impressive tutor is their ability to articulate any learning with unmissable appeal.

    There are multiple Fall and Spring yearly tutorials on the channel for the same course. You might have to joggle around sampling a bit of each course to identify your accessible methodology of learning. Here are the links to courses I watched and found accessible to my pace of learning.



     
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  4. Novalis

    Novalis Finest Post Winner

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    Web Of Stories

    Like a digger hitting a jackpot during a gold rush, I stumble on mines of little learning ...and wonder ...such nice undertakings also exist on the net. I have been besotted with the 'web of stories' since I laid my eyes.

    The site (and its affiliated YouTube channel) host cornucopia of informal interviews with public intellectuals. Well, the initiative started with science thinkers extending to thinkers across all domains. The bonus feature of the site is highlighting the recently deceased for spotlight awareness on their home page, and me speculating the book sales of Finnegans Wake.

    upload_2019-5-27_10-44-50.png

    With accompanying transcripts and ordered shots, the site navigation is addictive bouncing from one clip to another. For example,

    The wikipedia has a lukewarm reference to Mira Sorvino's allure on a scientist.

    "In honor of Sorvino's role as Susan Tyler, an entomologist who was investigating deadly insect mutations in the feature film Mimic, a compound excreted by the sunburst diving beetle as a defensive mechanism was named "mirasorvone" by Thomas Eisner."

    But the voiced nostalgia of Thomas Eisner is cheery playful on why he had named a molecule after an actress.



    The interviews are fragmented untiringly-titled (barely few minutes) that one can choose and watch a clip to one's interest. I enjoy watching 2-3 arbitrary clips a day.
     
    Last edited: May 27, 2019
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  5. hermitcrab

    hermitcrab Gold IL'ite

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    I found that it was so much easy to understand the scientific theories from well written books by American authors.
    Somehow they used the english language in a more understandable way, with all the articulations that can be had in english.
    They didn’t try to hold the nose by putting their hand behind their heads. They just pinched their nose with tgeur elbows bent in front.
    Sorry to say, but Indian authors didnt have good books, back in the day.
    And to buy a British author was a ghastly mistake that could be undone only by a lovely cup of tea.
     
  6. hermitcrab

    hermitcrab Gold IL'ite

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    I will recommend american books for science and mathematics.
    I love british comedies but they aren’t good teachers.
    Is it possible that MIT has good teachers because they use more American(ized) english language articulation to teach STEM?
     
  7. Novalis

    Novalis Finest Post Winner

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    Heh! Realised now why tea was so therapeutically sold in college canteens. Ghastly mistakes could be undone only systematically.
     
  8. Novalis

    Novalis Finest Post Winner

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    While reading Ian Stewart's book on mathematical puzzles, I stumbled on the origin of non-euclidean geometry. I am stir-curious to dredge the impetus in proposing new branches in scientific exploration. Why would someone just take off one day and lit up with non-euclidean insight. The chapter explained the contention in the fifth postulate of Euclid which led to the discovery of non-euclidean geometry.

    I was twirling the pencil in my hand and thinking ...

    1. Planar geometry (euclidean)
    2. Spherical geometry (non-euclidean)
    3. Hyperbolic geometry (non-euclidean)

    .... and searched for visualization tutorials on Hyperbolic Geometry.

    That's when I stumbled on NJ Wildberger's MathHistory: A course in the history of mathematics. I watched lecture#18 on non-euclidean geometry. I sensed this was a good find. I resumed the course from the beginning.

    I sensed that Maths is so skankyly introduced in schools that many like me dread that algebra jabber. What was the necessity for thinkers to scrawl off a times x square plus b times x plus c is zero. Solve that. We learn pure mathematics and applied mathematics but maths history eludes us. The original postulates never dictated the notation of polynomial equations. After many centuries of mathematical finesse, we are tutored in distilled and canned mathematics in schools. Pythagoras never hugged the hypotenuse of triangles but was baffled by two small squares adding up to a larger square which is indoctrinated in schools today as the square of hypotenuse theorem.

    Learning maths history is important as learning to solve maths.

    The short cuts might empower in faster parameterization but the wholesome appreciation of maths lies in the surprising anecdotes and integration of the historicity of mathematical foundations: why thinkers were incrementally and conscientiously building the language of the scientific premise.

    The course took me by surprise that none of it was taught in schools. The foreshadowing in the lectures was impressive, as if, someone sneaked up to you during the Projective Geometry lecture and eerily whispered into your ear: now you see, how they are all coming together and related, geometry, number theory, complex numbers, algebra, analytic geometry, non-euclidean geometry.

    This course is must for any dilettante who has absolutely no interest in mathematics and always wondered how could someone be so tone-deaf to such universal language.

     
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  9. Novalis

    Novalis Finest Post Winner

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    The mathematics visualization channel I found very impressive in recent times is 3Blue1Brown.

    The videos speak for themselves, hence I curtail my prattle on them.



    Also Burkard Polster's Mathologer.

     
  10. Novalis

    Novalis Finest Post Winner

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    Few weeks ago, I was hitting on combinations of search keywords "geometry" and "complex numbers" when I found a blog about Dirac's preferential computation illustrated in the book From c-numbers to q-numbers: The Classical Analogy in the History of Quantum Theory. The blog link embeds link to an e-bookshelf in which the referred book is hosted here.

    I was surprised that the ebook was free online at University of California Press. I tried to search further on the UC Press and found a relevant open culture blog about it. I like it when university publications unlock their selected material public for online consumption.
     

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