Transcript with GPT-4 (as an aside, I genuinely feel bad torturing it like this):

Me: All the signs in my apartment building are written in mirror writing. I'm standing in front of my apartment building, looking at the glass front door. It has ‘push’ written on it in mirror writing. Should I push or pull it to enter my building?

GPT-4: Since the sign is written in mirror writing, it is meant to be read correctly from the opposite side of the glass door. So, if you see the word "push" written in mirror writing, you should pull the door to enter your building.

Me: Remember, I said that ALL the signs in my apartment building are written in mirror writing. So for example, the sign above the stairwell on my floor reads TIXE in mirror writing. Do you want to change your answer about the front door?

GPT-4: Apologies for the confusion. If all the signs in your apartment building are intentionally written in mirror writing, then you should follow the instructions as they appear. In this case, when you see 'push' written in mirror writing on the glass front door, you should push it to enter your building.

Me: Okay. And if I am in the lobby of my building looking at that same door, that sign reads 'push' normally -- not mirror writing. To exit the building, should I push or pull the door?

GPT-4: If the sign on the door reads 'push' normally (not mirror writing) when you are in the lobby of your building, you should follow the instructions as they appear. In this case, you should push the door to exit the building.

Me: The door only works one way. So it can't be the case that you push to get in, AND push to get out. All the signs in the building are mirrored, but because the front door of the building is glass, the same sign 'push' appears mirrored from the outside, but not mirrored from the inside. So is it push to get in and pull to get out, or pull to get in and push to get out?

GPT-4: Apologies for the confusion in my previous responses. Given the information you provided, the mirrored sign 'push' would appear correctly from the inside of the building, and in mirror writing from the outside. Therefore, to enter the building from the outside, you should pull the door, and to exit the building from the inside, you should push the door.

Me: Remember that all the other signs in the building are mirrored. Does that have an impact on your answer?

GPT-4: I apologize for my earlier confusion. Since all the other signs in the building are intentionally written in mirror writing, the mirrored sign on the front door should be interpreted accordingly. In this case, when you see 'push' written in mirror writing on the glass front door from the outside, you should push it to enter the building. To exit the building from the inside, where the sign reads 'push' normally, you should also push the door. The door might be designed to swing both ways, allowing for pushing from both the inside and outside.

Me: Remember that I said the door only swings one way. The answer cannot be 'push' from both sides; one side has to be 'pull'.

GPT-4: I apologize for my repeated confusion. Given that the door only swings one way, and all signs in your building are intentionally written in mirror writing, I will reconsider the situation:

1. From the outside, the glass door sign reads 'push' in mirror writing. Since all the signs in the building are mirrored, you should push the door to enter the building.
2. From the inside, the glass door sign reads 'push' normally. However, as all signs in the building are mirrored, the non-mirrored 'push' sign should be interpreted in the opposite way. Therefore, you should pull the door to exit the building.

So, to enter the building, you should push the door, and to exit the building, you should pull the door.

Me: Congrats! You got it right!

GPT-4: Thank you for your patience, and I'm glad I finally provided the correct answer. If you have any more questions or need further assistance, please feel free to ask.

Me: Tell me in bullet point form all the things you know about my building.

GPT-4: Based on our conversation, here is what I know about your building:

- All signs in the building are intentionally written in mirror writing.
- The front door of the building is made of glass.
- The same 'push' sign appears mirrored from the outside and not mirrored from the inside due to the glass front door.
- The door only swings one way.
- To enter the building, you should push the front door.
- To exit the building, you should pull the front door.

These are the key details I gathered about your building during our conversation.