Mercury - and Mercury, again.

I take it as a given that most western Europeans have never paused to see Mercury in the sky.

If asked, most could not tell you where to look for Mercury (some would now start on the internet.)

If offered a clue: "What about sunrise and sunset?"

Or even more explicit: "What about sunrise and sunset?  Before which or after which?"

Some very few might suggest a deep, shallow mineshaft in daylight - or a full solar eclipse.

Simply: look for Mercury sometimes after sunset in the west or at other times before sunrise in the east.

But why named for Hermes, the messenger?  What are these comings and goings of Mercury while Venus and Apollo's sun-chariot are so much more regular and steady?

And what of the appearance of Mercury?  IF you were to see Mercury with the aid of a telescope, of what might you become aware? [here, see Epictetus]

Suppose that I show you Mercury in a telescope ... here are the variants for this Anschaung that come to mind (and arise if I set up more than one telescope along the road for neighbours and passers-by.)

Subjective: (holding the subjective lens)
  1) 45deg mirror (or 90deg prism)
  2) Amici prism
  3) straight tube extender

Objective
  1) mirror (various overall designs and configurations from simple Newtonian to highly modified)
  2) lens (as in the typical "Galilean" telescope)

Mount
  free-moving (likely a reflector, but also a small refractor on a ball-head mount)
  altitude-azimuth
  German equatorial
  computerized variants of any of the above three

star-gazer
  a digital identifier of the stars, planets and or asterisms at which it is aimed

activity
  hand tracking
  motor-tracking
  the above in combination
 

variants: monocular or binocular options apply in the above to objective, subjective and star-gazer device.

What will be seen: (general characterization)
  reflector - a little fuzzy but with good colour (expecially the planets Mars, Jupiter, Saturn)
  refractor - may be quite sharp image, but may have violet fringe if not using hydrogen filter
What will be seen: (shape)
  The two inner planets, Venus and Mercury, are subject to what might be described as "lunar" phases: they are moon-like in appearance.
 
Sceptic: how do you know it is not a star?
Answer: under magnification it increases in size as a disk: many stars under magnification do not change their "aspect" notably or else may even reveal themselves to be double or even triple stars (and if the tube is tapped lightly, trace clear distinct sinusoidal paths in which each star is clearly distinguished by a fine "parallel" path with the others - a case of movement in observation)
Richer answer: it will visibly have moved against the starry background by tomorrow
Jupiter answer: watch the weather change and moons appear and shadows pass over its face.
 
But not Veuns and Mercury.  Every 16 years Mars displays its ice caps.  But not Venus and Mercury.
 
Where in lies the scientific/social division-of-labor in the apperception of Mercury.
 
The observer tends to need to be coached: "Yes, bigger in the view than the star I just showed you - but how would you describe that shape?  What does it remind you of?"
 
Next task: explain away the violet halo.
 
Next task: explain why the image is inverted up-side down or mirror-reversed.
 
  "See, in this telescope the crescent of Mercury is 'looking down' towards where the sun has set - see?"
 
  "Notice that in this telescope Mercury is 'looking up to the right' but the sun has set down to the left... Let's look at the cresent moon up there in each telecope ... and compare what you see in the scope to what you see with these binoculars ..."
 
And where is the cresent moon if it is just after sunset?  I hope you do not look up, or worse, east ...  And which way is it facing ...
 
Any introductory course in college astronomy should be paired with a course in philosophy.  Ditto for botany.  Chemistry.  Any introductory college course in physics should require one evening learning to look at the night sky.  Otherwise how shall we reply to the attacks on reason, Galileo, naturalism and modernity?  How else shall we defend observation over prejudice if there is no "foundation" in the actual experience of the student?  Next topic: the lunar illusion and the rising full moon.

a note on mathesis in praxis: even the use of the alt-azimuth and the equatorial mounts do not - in use - require mathematics or measurements or numbers or compass points (although the equiatorial mount will be easier to use of faced north and with an angle approximately that of the latitiude of the observer's location.