Delvo
Дэлво Δε&#
Not yet, but we can bring it closer by adding one more aspect to it: different rates of occurrence for different numbers. Suppose there's some set of things, like a pile of pebbles, for which there's some trait that can be represented by a number, like an individual pebble's mass or roundness or blueness or magnesium content or even just a number somebody painted on each one. Then you count up how many pebbles have each number.Look at the numbers 1,2,3,4,5,6,7,8,9. You can distinguish between high numbers and low numbers.
But that does not mean that there are two mathematical groups of numbers. Wherever you draw the line is an arbitrary choice.
Once you draw the line, you can distinguish mathematically between high and low numbers but they are still arbitrary groups.
With human races it is the same.
Your description of the pebble population would need to depend on how many of each digit were actually there. If it's the same amount of pebbles for every digit, then it's a homogenous population with even distribution. If there's a smooth transition with the fewest pebbles having a 1 or a 9 and the most having a 5, then it's a homogenous population with some kind of centered distribution such as a "normal" or "bell curve" distribution, with something making individual pebbles more likely to be average than much above or below it. If there's a smooth transition with the fewest pebbles having a 9, the most having a 2, and the second-most having a 1 or 3, then it's a homogenous population with a skewed distribution, where something is making individual pebbles more likely to be below average than above it.
So far, we're not dividing anything by drawing any lines. But what if the distribution had two peaks with a dip between them? For example, let's say you counted the pebbles and found that the most common results by far were 3 and 8, the least common were 1 and 9, and the second least common was 6. That population of pebbles is inherently not homogenous but two-grouped, and the "line" between them at 6 is not an arbitrary creation but a part of their reality. It already was this way before you ever saw the pebbles; all you did was find out. It would be nothing but dishonest to refuse to acknowledge this fact (and in real life nobody ever does on subjects that don't have politics or religion involved). Also note that the fact that both groups meet at 6 and an individual pebble whose digit is 6 can't be exclusively placed in one group and not the other changes nothing.
Not really. The distribution of skin colors as actually measured is more complex than that, not only because of racial separation but also because of migration and the delay before natural selection has had time to adjust things upon arrival in a new land, plus the fact that radiation exposure is not strictly latitude-based either. The result is sometimes relatively abrupt breaks (typically at a boundary between two races' regions) and sometimes smooth gradients (typically within a race's geographic region), often not oriented in simple north-south or east-west lines. For example, black people only fairly recently started expanding away from a little area pretty close to or right on the equator, thus spreading very dark skin out into areas that might have been lighter-skinned otherwise and smashing the "gradient" pretty flat in those areas. (It's never been in the nature of widespread species to maintain smooth gradients for long; what happens instead is that a few bubbles somewhere along the spectrum start becoming especially successful and blow up and crowd out the space between them. It's why, for example, any former intermediates between grizzly bears and polar bears are gone even though reproduction is still possible and their ranges still overlap.)You can distinguish between light and dark colored individuals but wherever you draw the line is an arbitrary choice. Go from north to south and you will find that the local people get gradually darker until you reach the equator.
The general issue with both skin color and your number line analogy, as well as any other trait we could come up with, is that the fact that there's a range of possibilities (such as different skin colors or different pebble digits) that could exist, instead of some kind of simple dichotomy, doesn't mean anything by itself. Gradients instead of strict absolute dichotomies are to be expected in all kinds of traits throughout the animal and plant kingdoms. They're how evolution works. If they meant anything at all about about different groups not really being different from each other, then there would only be one species in the world, no taxonomy at all, because even cases that look like sharp dichotomies are just different positions along gradients where some of the intermediates are missing now. There's nobody anywhere claiming smooth gradients don't exist or making any other case that indirectly depends on such an idea. So when you bring them up, you're not countering any part of anybody else's case. You're just mounting a strawman by acting as if somebody else's case depended on some absurd alternative that nobody believes.
At best, the gradient argument only brings up a question that would need to be answered separately in separate cases: how the real-world population(s) is/are distributed along the given gradient. If it's like the first pile of pebbles I described above with the even counts, then that's what it is. If it has a two-peaked distribution like the last pebble pile I described above, then that's what it is. But you have to actually measure things in order to know which; what you can't honestly do is just say "Well, there's a gradient, so the distribution must be perfectly smooth (like the former, not the latter)". Reality actually yields a variety of answers in different cases. And the answer in human populations has been found, and it isn't what the people who keep dredging up this gradient stuff say it must be.