[Jim Moonan]

One . All others are reflections.

[Alexander Givental]

OK, in engineering, problems are often solved by rethinking the initial set up (the solution is then called "invention"). In math, problems are to be considered within the given, and somewhat idealized setting. In particular - no cheap cheating, such as "ah! reflections are not real iPhones", or "there could be other people with iPhones in the room", or "the hand blocks the view", or "in modern art the angles between the walls don't have to be 90 degrees", or "if I close my eyes ..." - no, the situation is meant to be the most natural (and I did see such an installation in a museum), and the question, of course, is about the number of my iPhones I see, including the reflections and the actual one.

Roger, by "both walls" I mean that at the corner of the room, (of course, parts of) the walls and the floor are mirrors - in other parts of the room, some other modern art pieces are positioned.

Allen, my answer cannot be wrong, since I haven't given any one yet. You and Carl gave the same answer, 4, but for different reasons: you - that there are 3 reflections, one in each of x-,y-,z- planes plus the actual iPhone, and Carl - based on the poems.
Carl, could you please clarify how the poem gives 4?

[Orwn Acra]

Two. The "iPhone" in the first sentence and the "iPhone" in the second.

The actual answer though is undefined as is the question.

[Sarah-Jane Crowson]

Oh, I LOVE these kinds of puzzles.

I'd say 'none'. You are holding the iphone and looking in the mirror and the installation. You will see a representation of the iphone, not the phone itself.

(I also usually get them wrong. I still love them though)

Sarah-Jane

(I've just read the thread more carefully - I was in a rush before - and now realise that you don't want the representation answer. I guess then it depends what you are focussing on. Are you holding up the iphone in front of you and deliberately looking for reflections?)

[Jim Moonan]

Is there an absolute "right" answer?
Or is there a "consensus" answer?
Or is the best answer one that takes into account things like the carrier of the iPhone is at the Museum of Modern Art?
Was the mirrored wall and floor an art exhibit? Or part of one?
Was the iPhone held in a certain way as to prevent its reflection in one of the mirrors?

I still stick to my first answer: One (assuming the iPhone is visible in the hand). All the others are reflections.
.

[Roger Slater]

I'll say four. If just two 90 degree walls had mirrors, there would be three. One on each wall, plus a half on each where they join. I'm not sure how the floor would figure in, though. Beyond my puny brain.

[Carl Copeland]

Originally Posted by Alexander Givental

You and Carl gave the same answer, 4, but for different reasons: you - that there are 3 reflections, one in each of x-,y-,z- planes plus the actual iPhone, and Carl - based on the poems.
Carl, could you please clarify how the poem gives 4?

That was my line of reasoning too, along with the repeated “four” in the poem, but I dismissed it as too easy and too superficial a use of the poem. And if you’ve got your camera screen turned on … but that’s “cheap cheating” again. How different math is from philosophy! To say that it’s “cheating” to distinguish image from reality!

[Alexander Givental]

Originally Posted by Orwn Acra

Two. The "iPhone" in the first sentence and the "iPhone" in the second.

The actual answer though is undefined as is the question.

Orwn, you are talking about the word "iPhone" in the formulation of my question, but that's easy - and it wasn't the question.

The actual answer is not less undefined than that to 2+2=? (Most people would say 2+2=4, though there are some unusual situations where that's not true.)

[Alexander Givental]

Originally Posted by Carl Copeland

That was my line of reasoning too, along with the repeated “four” in the poem, but I dismissed it as too easy and too superficial a use of the poem. And if you’ve got your camera screen turned on … but that’s “cheap cheating” again. How different math is from philosophy! To say that it’s “cheating” to distinguish image from reality!

The cheating is in the betting on the ambiguity of the words.
No, the iPhone has nothing to do with the question: when I ask 3rd graders, I draw a girl with a flower and ask how many flowers she sees.

"Four" indeed occurs in the poem, but this is not specific to the poem - any quatrain has 4 lines. To give you a further "poetic" hint:

There is an article by Gasparov about this poem of Usov (mostly he compares the lexicon of the "source" and "translation" to conclude that the mock translation is indeed a translation of the source, and not the other way around) but at the end he praises the poem for the excellent match between form and content.

[Alexander Givental]

Originally Posted by Roger Slater

I'll say four. If just two 90 degree walls had mirrors, there would be three. One on each wall, plus a half on each where they join. I'm not sure how the floor would figure in, though. Beyond my puny brain.

You are right in trying first a simpler problem - with two mirrors instead of three. But isn't a translation akin to a mirror image? In my post, you can easily see at least two such "mirrors" (especially if you imagine the original and the English translation typeset side-by-side as it is done here:
https://math.berkeley.edu/~giventh/v...translator.pdf
But how many "mirror images" (including the source) are there?