[nivertech]

> From another point of view, do you not think a prairie dog has ever asked another prairie dog, "how many foxes are out there now?" with the other looking and replying "None! All clear!"?

  type PrairieDogFoxCount = NoFoxesAllClear | SomeFoxes 1..5 | TooManyFoxes

  type CrowCount = Some 1..5 | UpsideDown 5..1

  type HumanProgrammerCount = 0..MAXINT

  type HumanMathematicianCount = 0..∞

My point is: "No Foxes - All Clear" is not the same thing (the same level of abstraction) as 0.

> From a third point of view, humans are natural, so everything we do appears in nature.

using this definition everything is Natural, including fore example Complex numbers, which is obviously incorrect, and thus invalidates yr argument

> From a fourth point of view, all models are wrong, but some models are useful. Is it more useful to put zero in the natural numbers or not? That is: if we exclude zero from the natural numbers, do we just force 90% of occurrences of the term to be "non-negative integers" instead?

all models are wrong, but some are really wrong

If all u care is the length of the terms, i.e. "Natural" vs "non-negative integers", then what's wrong with 1-letter set names, like N, W, Z ?

I think the usefulness of including 0 into the set of natural numbers is that it closes the holes in various math theories like [1,2]

1. https://en.wikipedia.org/wiki/Peano_axioms

2. https://en.wikipedia.org/wiki/Set-theoretic_definition_of_na...

[feoren]

> using this definition everything is Natural, including fore example Complex numbers, which is obviously incorrect

No, that's not "obviously incorrect", nor does it invalidate my argument: that is my exact argument. Complex numbers appear in electromagnetism, in exactly the same sense of "appear", as whole numbers appear in herds of sheep. Which is to say, it's the simplest and most useful model of the situation. And what's more natural than one of the four fundamental forces of nature? And the weak & strong nuclear forces have even more esoteric math structures appearing in their most parsimonious models as well.

> "No Foxes - All Clear" is not the same thing (the same level of abstraction) as 0.

In your model. In my model, it is the same thing. All models are wrong; some models are useful. Which one is more useful? Almost always, the one with 0 as a natural number. What about this:

    type PrairieDogFoxCount = NoFoxesAllClear | JustOneFox | ACoupleOfFoxes | SeveralFoxes 3..5 | ManyFoxes

I can make any model as complex as I want; that does not prove some other model wrong.

[SideQuark]

> using this definition everything is Natural, including fore example Complex numbers, which is obviously incorrect, and thus invalidates yr argument

Except you’re wrong here; should we thus call your argument “obviously incorrect”?

Complex numbers are natural; they’re fundamental in quantum mechanics. Ever since Schrödinger’s equation fundamentally required them for time evolution of states, physicists (and philosophers) wondered if they could be removed. Recent experiments say “no.” QED and QFTs are the most precise theories known in all of science.

https://physicsworld.com/a/complex-numbers-are-essential-in-...

[nivertech]

No doubt they're useful to explain some theories, but did someone observed in the Nature 6-4i apples or -7+3i particles?

[SideQuark]

They’re more than useful: they’re required, hence the research demonstrating it that I linked. That you don’t understand it doesn’t mean the rest of science is at your level of ignorance on the topic.

Your repeated, willful ignorance on a topic, especially when shown to you, is why you have such low understanding of the incorrect claims you make.

Take a moment and learn. Then maybe you’ll not repeat claims shown to be wrong.

[nivertech]

I never agreed or disputed whether they're required or not, what I asked was whether they (complex numbers) were ever observed in Nature

[SideQuark]

Yes, they have been observed in the same rigor as any number you claim has been observed. If you’d spend a moment and read instead of repeated willful ignorance, you’d learn something.

Now go do your homework. Attaching idiot phrases like complex apples is as stupid as claiming we don’t see radio waves so they can’t exist or that matter cannot be mostly empty space because you can stack books.

Your limited imagination, understanding, and unwillingness to learn, even when given a source and phrases to look into, doesn’t apply to those scientists that have done the work.

[nivertech]

> Yes, they have been observed

Any references?