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Originally Posted by adysav
This wouldn't be a sphere.
You can mathematically describe any object, but simplifcations are often used because.. they're simpler.
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Of course it would be a sphere! As a three-dimensional object the sphere would have to be constructed of something. Carbon atoms are just as good as anything else.
And yes, we use mathematics to describe objects, but the mathematics are irrelevant to the object. These simplifications are simple for us, not intrinsically. From a distance the Earth resembles a sphere (or an Oblate Spheroid if you prefer). For its inhabitants, most of the time, this macro-shape of the Earth is irrelevant. To us it is a collection of valleys, mountains, composite parts and different elements. For us to treat it as a sphere would often be useless. It is simpler to treat it as a bunch of component parts.
Consider, where do you live?
Apt. 2B, 1313 Mockingbird Lane, Scranton, Pennsylvania, United States of America, North America, Northern Hemisphere, Planet Earth, Sol System, Milky Way, etc... All of these answers are accurate, but only one is a meaningful answer to the question depending on who is asking and for what purpose. None of them are a universal truth, they all depend on the relationship of the person asking the question.
Try using mathematics to answer that question. You will still have to come up with arbitrary marks for a person to understand.
12 feet from the front door, or 600 Kilometers from the Washington Monument, or 42 degrees North Latitude, whatever. It's all dependent on the parties involved. There is no universal truth there, only a descriptive method for use between parties that have some frame of reference.
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OK, what about dogs, such as mine, that have not been trained to count, but if you mess up and give them the wrong number of treats, they bitch at you until you add in the missing ones.
They've not been trained to count, yet they know about quantity.
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There's no reason dogs can't learn to count. But of course, we taught it to count, didn't we? It didn't discover it on its own. On its own, your dog probably wouldn't know it wants 5 milkbones, rather it would want enough milkbones to fill its stomach. It's the total mass of milkbone that matters to the dog, not the number of treats. Consider predatory animals in nature. They don't care if they take down 1 or 2 gazelle to feed. If the first gazelle is plump and its stomach is full, then its done for the day. But if the total amount of gazelle-age the animal has consumed is not enough to satisfy itself then it will take down a second gazelle. Not because it cares about the number it eats, but rather because it needs more stuff.