Genady

If we accept that -1 and +1 are additive inverses, and if we want to keep the distributive property of multiplication, then it appears that we don't have a choice but make (-1)×(-1)=+1. Here it goes: (-1)×(-1)=(1-2)×(-1)=1×(-1)-2×(-1)=(-1)-(-1)-(-1)=(-1)+(+1)+(+1)=+1 QED

Regardless of being a root of +1, -1 is a label for the additive inverse of +1. How come we use the same label?

https://www.amazon.com/Quantum-Field-Theory-Standard-Model/dp/1107034736/?tag=pfamazon01-20

https://www.amazon.com/Gravitation-Charles-W-Misner/dp/0691177791/?tag=pfamazon01-20

I agree. For example, why i/-1 and not -i/-1?

Beyond the crash event, the geodesic will coincide with the worldline of the Sun (the red line).

What is there to consider? What does make this scenario interesting or non-trivial? It is just a graph of \(x=x(t)\) function with \(x\) and \(t\) axes flipped.

This will manifest in the shape of the wavy curve. It will be flatter farther from the Sun and steeper closer to it.

The horizontal coordinate on the graph is projection of the asteroid position on the direction of the major axis. A geodesic is a line in spacetime, i.e., in four dimensions. To illustrate it in two dimensions, one needs to take a projection.

On a scale of an asteroid orbit shown, the Sun is considered at rest relative to the orbit center.

I think it is for a general ellipse, including circle. I don't see what makes it limited to circle.

I think it is for an elliptical orbit.

The horizontal axis here is some x, e.g., ellipse's major axis. The vertical axis is time. The wavy line is the orbit.

I understand that the OP question is about ontogeny of organism with a genetic disorder. What I don't understand is, what would make one to think that

This is a good summary. +1

Just like Russian! (I know it's OT.)

Got it. +1

I'd say that the basic operations are ascend/descend-by-one. Then to ascend/descend-by-two you just ascend/descend-by-one twice, to ascend/descend-by-three you ascend/descend-by-one three times, etc. To ascend/descend-by-zero you then ascend/descend-by-one zero times, i.e., you don't move. I think it is not difficult to swallow that to ascend/descend-by-(-1) you descend/ascend-by-one, to ascend/descend-by-(-2) you descend/ascend-by-two, etc.

This is one of the recurring themes in this thread, e.g.,

OK. We can use the "× -1" label to get from positives to negatives. How do we come to use the same label to get from negatives to positives?

It is not so in the grown-up's algebra, but might be a good order for learning. However, there seems to be a logical gap there: To introduce negative numbers it uses multiplication by -1, but where does the -1 come from if there are no negative numbers yet?

Ah, I see. IMO, adding and subtracting numbers do not reflect physical moving of objects but rather reflect ways of counting them.

I don't understand. The example, 4-(-6), is neither a) nor b), I think.

Then, I think, they always have a multiplicative identity, but when p is prime, they are fields, as then each element has a multiplicative inverse.