Well, that's the problem: we can't reproduce it.
Which was my whole point. Universal Turing Machines can't be produced either yet most of theoretical computer science is predicated on it. Many well-educated but otherwise foolish people forget that UTMs don't exist and are qualitatively different than what we can produce. A similar story exists with respect to closed systems and thermodynamics. Engineering often assumes closed systems for its equations when no such thing exists -- the errors get buried in engineering fudge factor.
It is dangerous to assume that just because an assumption is pervasive that it has a real existence in our universe. Pervasive myths in many fields of endeavour exist because they have utility, NOT because they are factual in any given instance. For many purposes myth is cheaper than fact, and if there is no harm there is no foul.
You need to learn what is "fact" (to the extent that such things exist) and what is "pervasive myths treated as fact because they have utility". Just because a concept is useful does not imply that it is a real thing in our universe. This may not affect most people in their day to day lives too often, but if you want to get down to brass tacks you have to know the difference.
Well... The processing mechanism is straightforward to produce, but that infinite tape is the real b**ch.
But for a real tour de force, check out this Turing Machine built using Conway's game of Life. (Short background on Conway's game of Life can be found here.) Who would have believed that a grid operating under such a simple ruleset (originally conceived as just an idle amusement) would contain enough richness of behavior to enable the existence and operation of a full Universal Turing Machine? And who would have thought that a handful of subatomic particles would contain enough richness of behavior as to enable the existence of biological life?
This does not mean that the errors are ignored or that one fails to estimate them. It means that they are accounted for as best one can. It's is important to keep an explicit account of the fact that there is an error and some estimate of its magnitude.
"Well, that's the problem: we can't reproduce it. "
allow me to requalify that for you.
"Well, that's the problem: we haven't reproduced it yet."
so now, whats the problem?
hypothetically speaking, we cant achieve Absolute 0 either, yet we're getting so close, it's frightening. (somewhere in the 1/12% range if i recall correctly)
just because we haven't reached it doesnt mean it does not/cannot exist.
here's one for you to think about as well though:
We have a concept of the abstract, yet we have nothing around us that we would have learned "abstract" from. where, precisely, did our understanding of "non-existance" come from? how do we dissociate this from "un-existance"?
and of course, a twist on my first big point in the thread:
if we have not seen (nor been able to replicate) "life" from simple matter.... where, still, did we come from? fine, evolution got us to this stage. what got us to live in the first place?