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Aren't all modern programming languages Turing complete?



Turing completeness is actually 1. easy to achieve (even accidentally) and 2. undesirable in many circumstances (it makes code hard to analyse and process by machines and the semantics, what you really meant, get lost in the noise).

There's a reason there's no way to express loops and varibles in HTML, for example. That's the principle (or rule) of least power at work:

http://www.w3.org/2001/tag/doc/leastPower.html

Also see:

http://en.wikipedia.org/wiki/Turing_tarpit

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Turing machines are Turing complete.

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Yes. But that's irrelevant. You need to think carefully about how a UTM runs other TM's programs, about interpreters/compilers, and what one is doing when one writes out by hand design patterns instead of your language handling them.

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