Question: I was just reading an e-book and saw this sentence which really confused me:

[![enter image description here](https://i.stack.imgur.com/CuYCV.png)](https://i.stack.imgur.com/CuYCV.png)

"Played twice as fast as written" - This isn't what cut time actually means right, or are there situations where cut time means exactly that?

I thought cut time is basically just 2/2 time signature, but the speed would still depend on the bpm and the note durations...

Answer: 
That sentence "Played twice as fast as written" indicates that someone must have a misunderstanding. Someone who probably thinks that quarter notes are supposed to be played at a certain speed. That person would need more knowledge and experience with both tempo markings and different kinds of time signatures.

I suppose you could say that in the beginning when you learn your first note values and make your first exercises with the values you do get used to think of quarter notes as indicating some basic speed. You need to crawl before you can walk so to speak. But you certainly better learn to walk before you write a work book on the matter.
Adding to the other answers, I played in a group for a few years that liked to take music "a bit" faster than normal, for stylistic purposes, and we would often count 4/4 music in 2 (or 3/4 music in 1) because it was just easier for our leader to count off the tempo (from the piano, often by nodding) when counting at a slower pace and not give herself whiplash. But even if we were counting 4/4 in two, we still played it as if in 4/4 (giving it 4 beats per measure instead of two).

Of cousre, this was the same band leader that would ask us to play in the style of "bad 80's rock music", so perhaps she wasn't always giving us instructions in the most formal music theory lingo possible (although she did know her theory as well).

The problem I have with "played twice as fast as written" is that it ignores the stylistic difference of 4/4 played twice as fast as 2/2. For beginners, this may not matter as much, but it is still there, and we shouldn't confuse them.