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File: AMirrorCopied

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----
My latest posts can be
found here:
  * ColinsBlog
----
Previous blog posts:
  * TheOtherOtherRopeAroundTheEarth
  * PhotocopyAMirror
  * ThePointOfTheBanachTarskiTheorem
  * SieveOfEratosthenesInPython
  * FastPerrinTest
  * RussianPeasantMultiplication
  * FindingPerrinPseudoPrimes_Part2
  * FindingPerrinPseudoPrimes_Part1
  * TheUnwiseUpdate
  * MilesPerGallon
  * TrackingAnItemOnHackerNews
  * HackerNewsUserAges
  * PokingTheDustyCorners
  * ThereIsNoTimeForThis
  * PublicallySharingLinks
  * LearningTimesTables
  * GracefulDegradation
  * DiagrammingMathsTopics
  * OnTheRack
  * SquareRootByLongDivision
  * BeyondTheBoundary
  * FillInTheGaps
  * SoftwareChecklist
  * NASASpaceCrews
  * TheBirthdayParadox
  * TheTrapeziumConundrum
  * RevisitingTheAnt
  * TheAntAndTheRubberBand
  * IrrationalsExist
  * MultipleChoiceProbabilityPuzzle
  * RandomEratosthenes
  * WrappingUpSquareDissection
  * DissectingASquarePart2
  * DissectingACircle
  * DissectingASquare
  * AnOddityInTennis
  * DecisionTreeForTennis
  * DecisionTreesInGames
  * AMatterOfConvention
  * DoYouNourishOrTarnish
  * BinarySearchReconsidered
  * TwoEqualsFour
  * TheLostPropertyOffice
  * TheForgivingUserInterface
  * SettingUpRSS
  * WithdrawingFromHackerNews
----
Additionally, some earlier writings:
  * RandomWritings.
  * ColinsBlog2010
  * ColinsBlog2009
  * ColinsBlog2008
  * ColinsBlog2007
  * ColinsBlogBefore2007
********
!!! A Mirror Copied - 2015/08/16

[[[> This page has been _ TaggedAsPuzzles ]]]
So earlier I asked: What do you get when you photocopyamirror?
But the real question, as I then expanded, is not "What do you get?"
but: "Why *must* you get that?"  Can we deduce from first principles,
based only on what a good photocopier must do, what the result will
be?  I claim the answer is "Yes," although there are some who disagree.

Let me explain.

Consider two physical instances of a brochure. They are identical,
except that one is printed on matt paper, the other on glossy. We
would want a photocopier to produce the same result in each case.
We would not want the glossy version to have extra, spurious ghost
images of any kind.

So that means that the glossy surface must not send any extra
light back into the receiver.  The only light bounced back into
the receiver must be from the brochure itself, and not from the
surface.  So we can consider two collections of photons: those
that bounce off the brochure content, and those that bounce off
the glossy surface.

[[[>50 The glossy reflections are "specular", and the reflections
from the non-glossy parts is "diffuse reflection." What we're
arguing here is that a photocopier must be set up to copy the
diffuse reflection and not the specular reflection. ]]]
So the photons from the glossy surface must not affect the final
result - it must be as if they didn't exist.  So any glossy
surface must not result in photons going to the receiver.

But a mirror is the ultimate glossy surface.  That means that
when we photocopy a mirror there must be no photons received
by the copier.

|>>
********> width="20%"
******** width="20%"
A mirror must send no photons to the receiver.
******** width="10%"
******** width="20%"
A totally black object sends no photons to the receiver.
******** width="20%"
********<
<<|

So we deduce that a mirror must look to the photocopier the same
as a totally black object.  Thus photocopying a mirror must result
in a completely black image.

Are you convinced?
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and tell us what you think.
----

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!! Comments

I've decided no longer to include comments directly via the Disqus
(or any other) system.  Instead, I'd be more than delighted to get
emails from people who wish to make comments or engage in discussion.
Comments will then be integrated into the page as and when they are
appropriate.

If the number of emails/comments gets too large to handle then I
might return to a semi-automated system.  That's looking increasingly
unlikely.

********<