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File: NotASpectatorSport

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<<|
----
My latest posts can be
found here:
  * ColinsBlog
----
Previous blog posts:
  * LeftTruncatablePrime
  * TheDoctorAndTheLawyer
  * FourPointsTwoDistancesProof
  * MeetingRonGraham
  * NapkinRingVersusSphericalCap
  * TheFourPointsPuzzle
  * RadiusOfTheEarthPartTwo
  * GrepTimingAnomaly
  * TheRadiusOfTheEarth
  * ThisWorksToCureMyHiccoughs
  * PerhapsWeSavedOne
  * ThinkingAboutMastodon
  * DisappearingTrainsOnVirgin
  * TheIndependenceGame
  * OneOfMyFavouritePuzzles
  * ThinkingAboutRecursion
  * MemorisingTheTube
  * SpikeySpheres
  * SurprisinglyQuick
  * AnUnexpectedFraction
  * YouHaveToAdmireTheirOptimism
  * RepresentativesMatter
  * PythagorasByIncircle
  * APuzzleAboutPuzzles
  * HowNotToDoTwitter
  * Calculating52FactorialByHand
  * SmallThingsMightNotBeSoSmall
  * NotIfYouHurry
  * FactoringViaGraphThreeColouring
  * AnotherProofOfTheDoodleTheorem
  * WhenObviousIsNotObvious
  * GraphThreeColouring
  * TheDoodleTheorem
  * BeCarefulWhatYouSay
  * TheMutilatedChessboardRevisited
  * AMirrorCopied
  * TheOtherOtherRopeAroundTheEarth
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  * ThePointOfTheBanachTarskiTheorem
  * SieveOfEratosthenesInPython
  * FastPerrinTest
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  * FindingPerrinPseudoPrimes_Part2
  * FindingPerrinPseudoPrimes_Part1
  * TheUnwiseUpdate
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  * PokingTheDustyCorners
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  * DiagrammingMathsTopics
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  * TheBirthdayParadox
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  * BinarySearchReconsidered
  * TwoEqualsFour
  * TheLostPropertyOffice
  * TheForgivingUserInterface
  * SettingUpRSS
  * WithdrawingFromHackerNews
----
Additionally, some earlier writings:
  * RandomWritings.
  * ColinsBlog2010
  * ColinsBlog2009
  * ColinsBlog2008
  * ColinsBlog2007
  * ColinsBlogBefore2007
********
One of my university lecturers gave what we all thought were dreadful
lectures.  Muddled, unclear, chaotic, with no discernible thread.  It
took ages to reconstruct and rework the material to a point where we
could attack the problems and old exam questions.

I got nearly full marks on that exam.

Other lecturers were brilliant.  Clear, lucid, entertaining.  But I
didn't get full marks on their exams, because I found it hard to do
the problems, even though I thought I'd understood the material from
the lectures.

I hadn't.

Maths is not a spectator sport.  You need to get involved, otherwise
you're in the situation of someone who has watched a lot of tennis,
but never played.

I used to mock the "it is clear that" phrase when it would then take
two or three pages to show the result. But I learned that having done
the work to show it, I was then equipped to handle the next stage of
the work.  Having the explanation given to me as to why it was "clear"
would not have done that, my understanding would have been meagre and
unsatisfactory, and I would have gradually fallen behind and not been
able to understand what was missing.

So /when/used/properly,/ when used well, when used constructively, the
phrase "it is clear that" and its friends are not there because:

* that's how the game is played (tradition);
  * it excludes the uninitiated/untalented;
  * it's neater to leave out the truth of discovery;
  * it makes the author seem superhuman;
  * there's satisfaction for the reader in understanding the puzzle.

When done properly it's genuinely for more effective communication.

I'm not saying it's always done well - after all, not everyone writes
equally well - and I'm not saying that everyone always has the best
of motives.  But working on what you see as gaps in the presentation
really is the best way to understand the material.

There was an occasion when I said all this, and someone replied:

********> width=15%
******** width=70%
Someone, somewhere will have to work out the combination -
I'm suggesting it is more efficient for it to be the one writer
than the many readers.
******** width=15%
********<

If your purpose is simply to have it written down, then yes. However,
if your purpose is to communicate effectively to the readers, then no.
The "doing" is an essential part of the eventual "understanding".

----

This was prompted by a discussion of "How to Read Mathematics" by
Shai Simonson and Fernando Gouvea.  The article is here:

* http://web.stonehill.edu/compsci//History_Math/math-read.htm

This has been submitted multiple times to Hacker News, and at the time
of writing, the most recent discussion is here:

* https://news.ycombinator.com/item?id=15905048

The comments there repeat similar sentiments time and time again:

* Mathematics writing should be _
    more like computer programs: _
    Complete, and unambiguous.

So much misunderstanding, so many misconceptions.

Another rant, another time.

----

|>>
| |>> <<<< Prev <<<< ---- LeftTruncatablePrime <<| | : | |>> >>>> Next >>>> ---- JustTeachMyChildTheMaths ... <<| |
----
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