[FOM] Simple Turing machines, Universality, Encodings, etc.

Not wanting to push my luck I'll settle for one question. How did an argument containing such an elementary fallacy get through the filter? Smith gives a series of what I'll call finitary systems each of which runs the computation for a specified number of steps, each simulating its predecessor, then gives a non-finitary system (PDF page 21, Table of Contents page 19) that concatenates the initial conditions of progressively longer computations and runs one of the finitary systems on that concatenation. The non-finitary system is evidently universal, and the program performing the concatenation is equally evidently non-universal. Smith infers from this that the machine checking each of the concatenated initial conditions in turn must be universal. The analogous argument for numbers in place of machines and "infinite" in place of "universal" would be, if x+y is infinite and y is finite then x must be infinite. This line of reasoning works for numbers but not machines. For machines it would show that a linear-bounded automaton (LBA) is universal: a non-universal machine can easily add to the input a string giving in unary the number of steps to emulate the given Turing machine, and a suitable LBA can then run the computation that far without exceeding its linear space bound. As Chomsky showed half a century ago, linear bounded automata are not universal Turing machines. Had I pushed my luck my second question would have been, who has verified this proof that has taught an automata theory course at a suitably accredited institution? Vaughan Pratt