Well, I have one issue/question about this statement.
Turing-completeness would be a measure of computational equivalence, but that -- and I don't know if this is the right way to phrase it -- that is not the same as "presentational" equivalence.
A modern computer program does computations, but also displays them a certain way and TM's are silent on how you display the results of the computation. (To drive the point home, under no circumstances could Turing's ticker tape machine ever light up a single pixel on a screen.)
So, if you had an infinitely fast actual Turing Machine with infinite memory, you could tell me where the video game should go, and how the web page should render and what the regression visualization would look like, but not actually show it to me.
Ordinarily this is a pedantic argument to make but in the case of a GUI it is not. The GUI has to actually encode literally an infinite number of options to display the data in addition to computing it. This is particularly important for video games for instance.
So, I think you could have a theoretically complete Turing Machine and still not do the things that a modern computing language does.
Turing-completeness would be a measure of computational equivalence, but that -- and I don't know if this is the right way to phrase it -- that is not the same as "presentational" equivalence.
A modern computer program does computations, but also displays them a certain way and TM's are silent on how you display the results of the computation. (To drive the point home, under no circumstances could Turing's ticker tape machine ever light up a single pixel on a screen.)
So, if you had an infinitely fast actual Turing Machine with infinite memory, you could tell me where the video game should go, and how the web page should render and what the regression visualization would look like, but not actually show it to me.
Ordinarily this is a pedantic argument to make but in the case of a GUI it is not. The GUI has to actually encode literally an infinite number of options to display the data in addition to computing it. This is particularly important for video games for instance.
So, I think you could have a theoretically complete Turing Machine and still not do the things that a modern computing language does.