[thaumasiotes]

Right, the person I asked is claiming that NAND is two things. You appear to have responded as if you disagree with my comment while not actually disagreeing with any part of it.

What did you think I meant by this question?

>> In what conceivable sense is "doing a logical and" one thing while "doing a logical nand" isn't?

[Skgqie1]

Sorry, I will try to make it more clear.

NAND is more complex than AND, in the sense that it is more expressive than AND (having functional completeness which AND does not).

Similarly, it can be built from other less complex operators (AND and NAND).

If you're taking "One thing" to the extreme, in terms of the granularity or complexity of that "one thing", NAND is not as granular or simple as AND - and therefore isn't taking it to as far "to the extreme".

[thaumasiotes]

What's the argument that AND is less complex than NAND? It's true that NAND has completeness and AND doesn't, but so what? What you can build from something is not a measure of how complex it is. You measure complexity in terms of what it takes to describe something.

[TylerE]

It seems naively obvious to me that a(b(x)) is more complex than b(x). Practically tautology.

[thaumasiotes]

You have to justify why you've chosen the particular starting point. NAND isn't defined as being "first you do AND, and then you negate it". It's defined like this:

    +---+---+-------+
    | a | b | a ↑ b |
    +---+---+-------+
    | 0 | 0 |   1   |
    +---+---+-------+
    | 0 | 1 |   1   |
    +---+---+-------+
    | 1 | 0 |   1   |
    +---+---+-------+
    | 1 | 1 |   0   |
    +---+---+-------+

AND is defined like this:

    +---+---+-------+
    | a | b | a & b |
    +---+---+-------+
    | 0 | 0 |   0   |
    +---+---+-------+
    | 0 | 1 |   0   |
    +---+---+-------+
    | 1 | 0 |   0   |
    +---+---+-------+
    | 1 | 1 |   1   |
    +---+---+-------+

You may notice that they are almost exactly the same.

> It seems naively obvious to me that a(b(x)) is more complex than b(x).

This is just obvious gibberish; if you define b(x, y) = x & y and a(x) = ~x, then you can say "I think a(b(x, y)) looks more complex than b(x, y)", but how do you respond to "when c(x, y) = x ↑ y, I think c(c(x,y), c(x,y)) looks more complex than c(x,y)"? The two claims can't both be true!

Everything, no matter how simple, can be described as the end of an arbitrarily long chain of functions. So what?