I think it is articles like this one which are misleading. The Turing Machine was never “built” because it is just a class of machines, i.e. particular machines are of the Turing Machine class, Turing-complete. Because the class of machine has an infinitely long “tape”, then finite machines can be created “under” it, or in that domain. Turing literally devised a method to create machines with a specific name, a number, and compute that number. Each and every one of your computers could be formalized to have a specific number, even if extremely large. Therefore, each of your computers are Turing Machines, unless of course you can show that you can run a program that the class of Turing Machines cannot.<p>Edit: I think the surest example of this is in the term “binary”. When you compile a C program, you get an executable binary. Literally, you have a file of ones and zeroes. Well, that’s just an extremely large number in binary, exactly the same as the binary string “100001” being “33” in decimal.