[Cryptography] paragraph with expected frequencies

[John Denker]

On 12/21/2017 04:05 PM, Robin Wood wrote in part:
> 
> Oh well, was worth a try.

I suggest that "oh well" is not the message you should
be sending to your student.  A better message would be:

  Noise on the data is not the enemy.  Noisy data is
  not a mistake;  it is the nature of the beast.  It
  is natural and wholesome.

This concept is already understood by any kid old
enough to play Go Fish, or Clue, or any other game
of imperfect information.  You need to have a
strategy that is robust against statistical
fluctuations in how the cards turn up.

Similarly, any kid that is old enough to play
sports, or even rock-paper-scissors, knows that
you ought not run the same play every time.
There is value in /intentional/ randomness on
your side, i.e. a mixed strategy.  Also, once
again, you need a strategy that is robust
against random behavior by the other side.

Recommendation:  Play the hand you are dealt.  Take a
sample of generic text and do the frequency analysis.
  a) there will be noise, i.e. statistical fluctuations
  b) even so, the signal-to-noise ratio is quite high,
   for any reasonable sample-size.

Also:  Not the first lesson, but useful on a later
turn of the pedagogical spiral:  Don't pay attention
just to the high-frequency counts.  Sometimes the
low-frequency counts are quite informative also.
For example, if a hypothetical partial decrypt causes
the /qz/ bigram to crop up with high frequency, you
know something's wrong.

In the real world, there is very often more than one
right answer to any given question.  The idea that
there must be one almighty Right Answer is rather
widely taught in school these days, e.g. in connection
with high-stakes multiple-guess tests, which IMHO is
a scandal and an outrage.