> The only real-world example of symmetries is when your mattress gets lumpy and you have a choice of ways to turn it.
I once failed to notice that, and it led to a lot of teasing at my expense.
It was my second year as an undergraduate at Caltech. Our rooms were rectangles with a door on one of the short sides, a windows and radiator opposite that, a bed and a desk along one of the long sides, and a closet and sink along the other long side.
I decided I wanted to switch where my head and feet were when sleeping, so started trying to turn the bed around. The room was not wide enough to simply swing it around, but it was tall enough that if I lifted one end high enough I'd be able to pivot it.
That was difficult as a one man job, not helped by the growing crowd of people standing outside my door watching with obvious amusement as several times I almost dropped the bed on myself.
I finally managed it and then the spectators then pointed out the the bed consisted of a rectangular frame with a rectangular mattress which is symmetrical under the rotation operation that I had just painfully taken a great deal of time to execute, and that the only thing that determines which is the "head" end and which is the "feet" end is which end you tuck your top sheet in.
I could have simply waited for the weekly linen exchange, which I would be removing all the linens for, and then put the new linens on with the tuck on the other side and accomplished my switch with literally no extra work at all.
It took a long time for people to stop making fun me.
>>which is symmetrical under the rotation operation that I had just painfully taken a great deal of time to execute
This critical symmetry property only holds if the mattress is assumed to be uniformly lumpy (including no discernable lumps at all), which perhaps in your case it was but you might have had the last laugh if you’d challenged them on that point.
They still would have had the last laugh because even if I could justify rotating the mattress I wouldn't have been able to justify rotating the frame, which was what made the operation difficult.
I once failed to notice that, and it led to a lot of teasing at my expense.
It was my second year as an undergraduate at Caltech. Our rooms were rectangles with a door on one of the short sides, a windows and radiator opposite that, a bed and a desk along one of the long sides, and a closet and sink along the other long side.
I decided I wanted to switch where my head and feet were when sleeping, so started trying to turn the bed around. The room was not wide enough to simply swing it around, but it was tall enough that if I lifted one end high enough I'd be able to pivot it.
That was difficult as a one man job, not helped by the growing crowd of people standing outside my door watching with obvious amusement as several times I almost dropped the bed on myself.
I finally managed it and then the spectators then pointed out the the bed consisted of a rectangular frame with a rectangular mattress which is symmetrical under the rotation operation that I had just painfully taken a great deal of time to execute, and that the only thing that determines which is the "head" end and which is the "feet" end is which end you tuck your top sheet in.
I could have simply waited for the weekly linen exchange, which I would be removing all the linens for, and then put the new linens on with the tuck on the other side and accomplished my switch with literally no extra work at all.
It took a long time for people to stop making fun me.