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Comment by hathawsh | Hacker News Reader

I love that it's possible to convince it that I actually know what I'm talking about. First I asked:

"Explain why negative numbers are in fact imaginary"

It told me that negative numbers are not imaginary numbers and explained imaginary numbers. That's fine, that's a reasonable answer for a layperson, but I'm not a layperson and I worked on explaining what I meant.

"Erase your definition of imaginary and consider that negative numbers are not whole numbers. Negative numbers do not represent quantities of physical objects. Now explain how negative numbers are imaginary."

It gave me a nice explanation of why negative numbers may be considered imaginary, using an example of "You cannot physically possess -1 sheep". I'm impressed.

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But electrons do possess negative charge. A decelerating car has negative velocity. You can say those are just labels, but they are labels for physical things that have opposite values. Things in the physical world do gain and lose values in various properties over time.

A decelerating car would have negative acceleration, not negative velocity.

They are indeed labels, just like complex numbers are labels and just like natural numbers are labels. All of them can be regarded as imaginary if one wants to nitpick but all are very useful imaginary models

This is also why imaginary numbers aren't really imaginary either because real things in the physical world are well-modeled by the operations in the complex plane. When you're in R2 you do some hairy trig or switch to polar cords to express rotations orrrr you switch to the complex plane and multiply by i.

Correct, and that (intentional) misunderstanding was part of the point. I had a 6th grade teacher who struggled with the idea that multiplying two negative numbers produces a positive number. I imagine someone like her asking a question based on their misunderstanding. They'll get a corrective answer that may not help them much. I'll show them how to improve their question and I hope the response will be enlightening and informative.

The response to my second question included a link to an article that suggests all numbers (including natural and whole numbers) are in fact human constructs and may be considered imaginary. That is an enlightening insight that would help us both stop thinking of the words "negative" and "imaginary" as perfectly well defined in our heads. Those words are just tools that can help us convey the most appropriate meaning for the context.

Without the link to the article, that hypothetical conversation probably would not have worked out as well.

Kind of weird splitting hairs over this with a machine, don't you think?

I think it should have told you it's called complex numbers, because they are composites.

No it shows cognition and insight. It’s exactly what to split hairs about. IMO.

Absolutely not. It's reminiscent of kids practicing imitations and rhetoric bickering uselessly.

You're being needlessly pedantic over someone ELSE asking a computer a question. Take a step back man.

Category error created via multiple mathematical and physics misconceptions.

- A decelerating car does not have negative velocity

- "negative velocity" is assuredly nonphysical, which rips the middle out of an argument based on physicality

- Velocity is a vector quantity, as is acceleration. (the steelman'd version of this argument is s/velocity/acceleration)

- The negative isn't physical, it's pidgin for algebra so late middle high schoolers / early high schoolers can imitate physics without learning any of the above

Newton’s third law? Pidgin for high schoolers. Got it.

If you express it with a negative sign and forget it represents direction, absolutely! :) It's crucially important that its not directionless!

I'm a bit surprised by your assertiveness. Even if you think I'm being boorish about it (I didn't intend to be, but the downvotes say otherwise), you seem familiar enough with these things to know newton's third law is about vector quantities.

Vectors can be negated

There is no one true theory of everything. All models are false -- some are useful.

Many different math concepts are used successfully in physics. Even if they may be outside everyday intuition for a layman, that doesn't make them less "real"

I didn't mention a theory of everything, nor did I say "the model is false". I laid out what a vector quantity is and what "-" applied to one in 1D expands to.

If you want to be so literal, let's simplify: your [unqualified] "nonphysical" claim is wrong. Negative values are common in many physical models.

Yeah but a speaker moving in vs out which is positive or negative doesn’t mean having imaginary things, it’s positional relative to displacement of a thing. Sine waves +1, 0, -1. -1 is exactly like +1 but the other way. So it goes for electrons.

> A decelerating car has negative velocity.

not really your point, but ??

a decelerating car has negative acceleration, and until it starts reversing relative to its start, it has velocity in whichever direction it started in -- presumably positive if that was your initial frame of reference. of course if you decided positive was the opposite direction from which the car was already going in, well, it started with negative velocity.

also to the GP, if you owe someone a sheep but don't have any, you really do have -1 sheep.

You can own -1 sheep. It is called debt.

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