In what way is the Antikythera mechanism not a computer? And where did
your 400 years come from?
I understand what you mean, but it was in the last 400y that this machine
took shape. In fact it was Turing that defined it. But he would not be able
to define it if it was not the mathematicians before him. I agree with you
as well, we could go to the roots of mathematics, however even if the
definition of such a machine was so old, it wouldn't be possible to build
it without the technical advantage, so ... I still think my statement is
true. You can argue as long as you will.