I don't know how I feel about the message "This is optimal!" displaying when you use one NAND gate to build an inverter at level 2. Level 1 forces you to build an NAND gate out of (1) an AND gate, plus (2) an inverter. It feels like it'd be more optimal to just reuse that inverter.
(And then level 3 is an AND gate, the other primitive† you started with...)
† Technically, you start with two primitives, implementing f(a, b) = a ∧ b and g(a,b) = ¬(b ⟶ a). You also get the ability to provide 0 and 1 as fixed inputs, thus ¬a ≡ g(a,1). What you lose after implementing the NAND gate is the ability to provide a fixed 1 input - instead, you are informed that you assume all gates automatically draw from this. Worst of all possible worlds.
Not the person you asked, but the initial point was taking that idea to the extreme. The concept of "one thing" in the NAND case is more extreme (in terms of granularity). No need to be sorry, it's ok.
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?
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".
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.
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:
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?
