To the layperson, the earth is indeed spherical. But… How exact is that? It is correct that the earth is generally spherical. But that is not an exact statement.
The geometric definition of a sphere is basically ‘Every point on the surface is the same distance from the center.” This is clearly not true about the earth as we have large deviations in the distance from the center to points on the surface. So the mathematical definition doesn’t work on this level.
If someone claimed that the earth was a sphere, and from the mathematical definition of a sphere proceeded to argue that therefore there were no elevation changes. They would be wrong. But it wouldn’t follow from that the earth was flat. Photographs of the earth from space showing a rotating circular profile could then be employed, but they still don’t’ give you the information you need.
The earth isn’t an exact sphere. Those who study the matter can truthfully say (and demonstrate) that the earth is not “spherical’ in the true meaning of the term. But again saying that the earth is not spherical does not mean that the earth is flat.
The earth is wider at the equator due to rotational and gravitational effects. The correct term is ‘oblate ellipsoid’. A measurement of the earth around the equator measures some 40 miles more than a measurement taken along any given longitude. And even those measurements are usually running averages of elevations above sea level. ‘Sea level’ really isn’t even the same from one point to another even before tidal forces from the moon are taken into consideration.
For a basic understanding of the shape of the earth, ‘sphere’ is fine. But if you want to actually do something with that information (orbits, navigation, etc.) you have to take into account that the earth isn’t truly spherical.
Specialists specialize for a reason. There is a great deal to know about and no one person can grasp it all. That’s one reason open markets work so well, but I digress…
Great leaders are usually great generalists who know how to use specialists and when to seek their input.
Maybe it’s because of my line of work that this is important to me. I’ve seen it happen far too often where the general picture of how something ought to behave breaks down because of some smaller characteristics that aren’t apparent in the knowledge of the larger picture but are known to someone who specializes in some smaller aspect of a system involved. Say an engineer who works with power distribution will have a wide understanding of electrical theory, but will not be terribly successful in high frequency electronics without the addition of a good deal of schooling and practical experience. By the same token, I wouldn’t give terribly great weight to a decorated admiral’s pronouncements on the use of infantry, or a JAG’s pontifications on the shape of the earth.
Experts should be listened to when they speak on their expertise. Outside their expertise they may not know any more than the average schmo.
Oregon, shessh...
There are nuances, yes, and the analogy was perhaps not the best becasue like all analogies it eventually breaks down.
This one might be better. A mathematical law might say that for all instances where x>0, y>0, and z>0, x+y+z>0. Suppose somebody claimed that when you use numbers that are exact to the thousandth place, the law doesn’t hold true because of rounding - so that the more exact you get, the less the law holds up as being true.
What would you say about that?
A positive number will never round to a negative number so no matter how exact you get, the law would remain true. There is no technicality that can alter the accuracy of the law, and any “rounding” the experts do to come up with a different result is just sleight-of-hand. Sophistry. Which seems to be one of the bragging rights for lawyers, who gain their fame by twisting and maneuvering the evidence and arguments so that an unexpected outcome results.
They say that anything can be proven by statistics, depending on how you twist them. If the minute rules can be twisted to say the opposite of what everybody has always understood them to say (such as a ruling concluding that brigade commanders can lawfully order a foreign invasion without presidential approval, when everybody agrees that brigade commanders can’t do that), there is either a problem with the rules or with the people who are twisting them.
At what point would you question whether the “experts” were engaging in creative sophistry rather than being faithful to the intent and genuine meaning of the rules?