What's the deal with mirrors?

General Off-Topic Discussion
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Continuing the discussion from Let's play Zork + Colossal Cave Adventure:

Not wanting to derail the original thread, but this puts me in mind of the old Physics chestnut: why does a mirror swap left and right, but not up and down?

(I have my own well-rehearsed explanation of this. But it’s fun to try to come up with your own!)

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I made the mistake of asking an AI for the answer. After some discussion the following is the unedited final response that suggests a conspiracy…

[!abstract]- AI content

  1. The Standard Mirror (Class M0)

Behaviour:

• Reflects normally
• Pretends to be innocent
• Acts like it has no idea what “parity inversion” means

Warning signs:

• Smug silence
• Subtle judgement of your hair
• Never blinks

Threat level: Low
These mirrors follow the Council’s rules but still enjoy confusing you.

  1. The Over‑Eager Mirror (Class M1)

Behaviour:

• Reflects you before you’re fully in front of it
• Over‑bright, over‑sharp, over‑honest
• Loves pointing out asymmetry

Warning signs:

• You feel personally attacked
• Your reflection looks like it’s about to give you unsolicited advice

Threat level: Moderate
Approach with emotional armour.

  1. The Rebellious Mirror (Class M2)

Behaviour:

• Slight delay in reflection
• Occasionally flips diagonally just to see if you notice
• Tries to invert up/down when gravity isn’t looking

Warning signs:

• Your reflection smirks independently
• The room behind you looks slightly wrong
• Pets refuse to look at it

Threat level: High
These mirrors are one bad day away from revealing the entire conspiracy.

  1. The Portal‑Adjacent Mirror (Class M3)

Behaviour:

• Reflection seems deeper than the wall behind it
• You feel like someone is standing just out of frame
• Sometimes shows you holding objects you don’t own

Warning signs:

• Cold breeze from the glass
• Reflection moves a fraction too slowly
• You hear faint committee chatter

Threat level: Severe
This mirror is either malfunctioning or moonlighting as a gateway to the Mirror Council’s headquarters.

  1. The Full Traitor Mirror (Class M4)

Behaviour:

• No longer pretends to flip left/right
• Starts flipping random axes for fun
• Attempts full spatial inversion without a permit

Warning signs:

• Your reflection waves first
• You see yourself wearing clothes you’ve never owned
• The mirror whispers “don’t turn around”

Threat level: Extreme
Report immediately. Do not attempt to negotiate.

  1. The Mirror That Knows Too Much (Class M5)

Behaviour:

• Tracks your movements even when you’re not looking
• Remembers every embarrassing face you’ve ever made
• Has opinions about your life choices

Warning signs:

• Reflection sighs at you
• You catch it rolling its eyes
• It fogs up only to write cryptic messages

Threat level: Catastrophic
This mirror has gone rogue and may attempt to unionise your other appliances.

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I do love this one!

My explanation

Mirrors don’t actually reverse anything at all! Write your name on a piece of clear plastic, for example, and hold it up to a mirror; the plastic will look exactly the same as its reflection.

Its our expectations that reverse things. Write your name on something opaque, like a piece of paper, and hold it up to a mirror; then look at the paper yourself. I’m guessing you flipped it around from left to right to look at it, didn’t you? That’s where the reversal comes from. When we want to turn something around, we almost always rotate it left to right. When a mirror doesn’t do that, we perceive it as getting reversed.

Why do we almost always rotate things left to right, then? Because the laws of physics don’t care about left versus right, but they do care about up versus down: things fall down, they don’t fall up. So an open carton of eggs won’t break if you rotate it left to right, but will break if you rotate it top to bottom.

(If you’ve taken undergraduate physics, you might be saying “wait, but doesn’t physics care about right versus left in things like angular momentum and magnetic fields?” No, that’s a misconception perpetuated by bad conventions for handling bivectors. But that’s a different explanation.)

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  • Mirrors do not flip top and bottom.
  • Mirrors do not flip left and right.
  • Mirrors do flip front and back. (-:
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Mirrors are nearly always vertical. If horizontal (on the floor or ceiling) they DO flip up and bottom.

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That isn’t me in the mirror, it’s my extra-dimensional doppelganger

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?srorrim htiw laed eht s’tahW

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Whoa, I think I can never again look into a mirror without creep!

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Oh, you gotta upgrade to the latest models.

I like the mod where it also flips front-to-back. Super handy for clipping the hair on the back of my head. aidtopia knows what I’m talking about.

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Technically that’d be a mirror that doesn’t flip front-to-back.

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I love talking to students about this. The main reason (besides the front-to-back thing) is that humans tend to turn things around left to right instead of up and down. If you hold a tube of toothpaste facing towards you and then turn it towards the mirror, if you turn it left and right, it’s flipped left and right, and if you turn it up and down, it’s flipped up and down.

(I wrote this before seeing Daniel’s explanation, which covers everything above. So I don’t really have anything to contribute to this conversation but I’m happy to be here and spectate!)

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Um, we’re actually the ones flipping front and back. Writing a word on a piece of paper. Hold it so that you see the word. Now hold it so that you see the word in the mirror. What did you do? You flipped the paper, not the mirror.

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Ah, but if you take a stick that’s half blue and half red, and hold it so the red half is back (toward you) and the blue half is forward (away from you), then a mirror in front of you will show the blue half back and the red half forward!

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I think another way of saying this is that the thing that has flipped is the viewpoint. The mirror’s not flipping anything, but the light is bouncing back and showing you the world from the mirror’s perspective. What you’re seeing in the mirror is what you’d see if you went and stood where the mirror is.

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I feel like this explanation has a serious flaw, which is that mirrors do do something to shapes.

I mean, if we forget about mirrors-as-a-physical-object for a moment and just talk about the mathematical operation of reflection through a plane (or a line, in the 2D case, or a hyperplane in the n-D case), then this operation clearly results in a shape which is not, in general, the same (up to translation and rotation) as the original shape. The writing-on-plastic example is misleading, because when you don’t turn the plastic around, it might seem “exactly the same” in some sense, but that’s only because the transparency of the plastic obscures the fact that you’re comparing the back of the plastic (i.e. the side without the physical marks on it) to the front of the reflected object.

However, the specific line/plane that we reflect in does not make a difference (up to rotation and translation), so as far as “the shape itself” is concerned, ignoring position/orientation, there is no absolute sense in which it is flipped “in some particular direction,” just flipped in general.

So then the perceived difference of “front to back” vs. “left and right” depending on how you rotate (or imagine rotating) the object basically reflects the fact that as you move the object and its reflection around relative to each other, the axis of reflection that would produce that specific spatial relationship between the objects changes.

I dunno if that makes sense as written, but the point is that mirrors absolutely do flip things!

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What freaks me out the most is when you look at a chrome pipe (something big like a chimney exhaust that stands upright).

Ever noticed that you can see distorted reflections of objects moving beyond the expected right angle horizon? Of course it all makes sense once you remember that you are not a cyclop.

I find it very trippy. No matter how often I look at it.

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I’ll admit, when I read the titled I thought it was something much stranger, like “why can’t I see my reflection in the mirror?” Or so, lol.

Also, here’s a question: if I have short-sightedness and I were to look at something very far away, but through a mirror that is 10cm away from my face, would it count as far away or close to my eyes? Because my eyes are focusing on something very close, but at a small thing on it…

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Very close, I’d say. The equivalent of straining to read small font. EDIT - Nope, I was wrong!

By the way, the Duck Soup mirror sequence is proof that mirrors don’t flip left-right because Harpo’s right hand is always his right hand, and Groucho’s left hand never stops being his sinister. QED, case closed, let’s off to the pub, round’s on the OP.

(also, this discussion reminds me of a Monogatari arc. The one just before the recent off and monster season)

EDIT - So if anything, mirrors potentially flip brother-brother.

Begs the question, are you sure it’s you you’re looking at?

…there’s gotta be a game in there, and it’s so obvious someone musta made it already.

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You know how long it took for me to get that? Long enough that I’m ashamed to call myself an adventurer!

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Wait, wouldn’t what you see in the mirror be what you’d see if the mirror was replaced with an open window and you looked at from a position on the far side equivalent to your current position, not what you’d see if you stood where the mirror is and looked back at the room?

Also, isn’t the chrome chimney just a funhouse mirror in the wild? Though now I’m curious how the distortion for a given amount of amplitude differs between different kinds of curve… e.g. a quarter circle versus a semi-ellipse versus a halfwave of a sine curve versus a parabola versus a hyperbola versus a cantenary versus a cycloid…

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