> An imperative program CANNOT be made to do lazy evaluation.

That's not really true, as the execution strategy is not necessarily connected to the programming paradigm. You can create a strict functional language or a lazy imperative language. These are orthogonal dimensions of the design space.

For example:

z = expensive_calculation_take_ten_minutes(); // defer evaluation of z
x = get_user_input(); // strictly evaluate x
y = some_other_thing(x + 3); // strictly evaluate y
if y > 10 {
print(z); // lazily evaluate z, print(z) here
}

There's no reason at all this imperative program must be strictly evaluated. Evaluating z can be deferred until it's clear that it's needed in the print call.

> This is ORTHOGONAL to parallelism and async because each thread must be executed in sync.

It's not really orthogonal, it's a dual. Imperative code can be made to run in parallel by running it on multiple machines simultaneously. But because the imperative model clashes with asynchrony and parallelism, it's much harder to express these concepts in imperative code. It's much easier to express asynchrony in an asynchronous-first language, but in those languages it's harder to express an ordered sequence. Many of the problems I encounter with distributed async programming in imperative languages exist at the boundary between asynchrony and synchrony. The best solution we have today to write async code is to enter a special sync runtime, which needs to exist in order to explicitly support the distributed/async/parallel semantics that imperative paradigm cannot model well. This results in a phenomenon called "function coloring", where only "async colored" functions can only be used in the async code, essentially bifurcating programs into async and synchronous parts.

The notion of "callback hell" should make plain why imperative programming is not the most natural paradigm to model asynchronous communication. Callback hell exists because shoehorning the imperative paradigm into an asynchronous runtime is clunky at best.

> The concept of continuous space has been shown by physics to NOT be the case

But is that understood at an innate biological level? I think not. Human beings, and in particular students of programming, experience their world continuously in time and space. This is why they are surprised that 0.1 + 0.2 != 0.3 in most languages.

> It does not say whether functional syntax is more natural then c-like syntax.

To be clear, Logo is an multi-paradigm Lisp-like language. You can express imperative code cleanly in Logo, and that's how children use turtle graphics. The example is to show you that the c-style syntax is not at all connected to an ability to program at a young age without any concept of either paradigm. Insofar as you are claiming that the c-style syntax is what makes imperative programming biologically innate, the existence proof of Logo must cause you to be wrong at that point, as it has a Lisp-like syntax. If anything, my experience teaching students C shows me that the syntax hinders the learning process (e.g. = vs == and imperative c-style for loops are the source of very many bugs for new programmers).

> You asked for f, they gave it to you.

Right, and you asked for a list and they gave it to you.

> If you asked the child "how do you make lunch"

Throughout your posts, you are treating "here is how I make a sandwich" as programming, while you don't seem to consider "I want a sandwich" as programming. These are both programming. The former is imperative, the later is declarative. If we want to understand whether a young child is capable of imperative programming, we ask them your question. If we want to understand if they are capable of declarative programming, we ask them my question. The question is: which question can they answer first? Child development science tells us it's the declarative program they will be able to express first.

> Your question was demanding a declarative answer. The child gave it to you because you didn't ask for anything else.

Right, indeed. But your question demanded an imperative answer, and that's what you got. My point is that developmentally, children will have the capacity to give you the declarative program long before they can formulate the imperative one. So does that mean we have a biological predisposition to declarative programming? Or maybe there's no such thing as a biological predisposition to any particular paradigm?

> If you reword the question to ask for a temporal answer that flows across the time dimension where each step is dependent on the previous step the child will give you the answer in imperative form rather then functional.

I'll note here that the only temporal notion offered by the imperative paradigm is the notion of an ordered sequence. There are far richer treatments of time in other paradigms, which include temporal operators specifying "as soon as", "before", "after", "until", "whenever", etc. These concepts cannot be expressed directly in imperative paradigms.

The notion of time in most imperative languages I know of is CPU-time, or instruction time. It has little to do with wall time, so appeals to how close imperative programming adheres to an concept of time that's intuitive due to human experience falls short. Indeed, I often experience students frustrated by the inability to cleanly model these concepts in imperative languages.

> Bending your series of instructions on making a sandwich into the do notation of monadic closures of haskell is really trippy, no adult thinks this way, let alone children.

It's interesting that this is how you phrase it, because in my experience children do indeed naturally ask for sandwiches often before they can even describe how they're made. Have you ever seen a kid get mad that the jelly is on the bottom of the PB&J, only to placate them by turning it over? Such a child has no idea how the sandwich is made.

If that means they are using the notation monadic closures of Haskell naturally, it would seem to cut against your argument that this notion is not natural.

> That is why FP is much less intuitive then imperative programming.

To be clear, I'm not saying it is more intuitive. I'm not even mounting a defense of functional programming here. I'm pushing back against the notion that c-style syntax is innately understood at a biological level. In your various posts here you seem to conflate syntax and semantics, which I don't understand because you seem experienced enough to know the difference. Or maybe I'm misunderstanding you, but I feel like you've offered a pretty full-throated argument, so perhaps I'm just not following. But I think we're talking past one another at this point.