because the formal definition of a Turing Machine requires a memory tape of infinite length

skill issue. I could make one

Huh. Functionally, are humans Turing-complete, by that definition?

I mean, human brains can do calculations, even if we do them way slower than computers.

they are not

we have finite memory

if a calculation requires a billion values to be stored in memory simultaneously, a true turing machine could do it but ahuman could not

But also our brains do not do calculations int eh sense that Turing machines do

No, not a human, singular. Humans, collectively.

All the knowledge we accumulate and pass down, as a species. We don't know if the capacity to do that is infinite, but theoretically it could be, right?

humans, collectively, have finite energy

it's a large amount, and we could make a real long tape

but it would not be infinite

not even close

Does a Turing complete algorithm need to operate on a Turing machine, or does it need to simulate a Turing machine

Because I can simulate a Turing machine by just feeding it increasingly long strips of tape

algorithms aren't turing complete, machines are

and you can do that, but you will eventually run out of tape

a machine or system is Turing Complete if and only if it can execute any possible Turing program

and because a hypothetical True Turing Machine would have an infinitely long tape, it can execute programs that a meatspace computer cannot, no matter how sophisticated

for a nice simple example: a program that outputs the first 3↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑3 digits of pi