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You can't tell that from walking around a mere mile. You can barely tell that at all. You certainly can't derive that from first principles without significantly more information.
That's the point. The flat earth model is a good one, for many things. Imagine, if you will, your house. It has walls, and those walls are vertical. For simplicity, let's say that a plumb bob was used, and that therefore the walls are plumb, and the ceiling which joins the walls at right angles is level. Except, it's not. The two plumb bobs are not parallel, and in fact converge. That doesn't matter for your house, because there's no difference at that scale. It's wrong to assume a flat earth, yet we do it anyway in many circumstances because the differences don't add up and aren't apparent.
In your example, if you travel for 1 hour, and at the end are 1 mile away, then you could say you averaged one mile per hour. However, in reality you were above and below that speed at many points throughout the hour. I say your hypothetical does not reflect reality, it merely approximates it locally.
Very interesting. However, I still am curious if 1 mile or 2 miles is a better reflection of the reality of my travel distance, since you said that 1x1=2 is looking at reality rather than avoiding it and retreating into theory.
So by all means, let's look at reality.
You sure can if you're walking uphill.
The problem you’ve presented is not comparable to 1x1, but rather to (1x/y) x (1y), which would equal one in either system.
A better comparison is: you have a property that is 1 mile in length, and 1 mile in width. How large is it? Certainly not 1 mile. Is a response of 1 mile or 2 miles closer to reality?
I think the system we have for math is very useful, but it’s not necessarily cleaving reality perfectly at the joints, and maybe there’s a way it could be.
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It's one mile, but you have very helpfully included units and a divisor.
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