By "beach" we don't mean "many grains of sand." The parent analogy using grains does no more gets us a beach than using gears and pulleys or RAM and CPU's gets us a brain.
Do you really argue that beaches have some sort of, well, “magic”, I guess, property which makes them a beach? That seems entirely unnecessary for something as simple as beaches. You can map all the grains of sand, you can map all the molecules of water and confidently identify when something is a beach. We know how to explain beaches in terms of grains of sands and molecules of water.
We cannot yet explain all properties of brains (most notably consciousness) in terms of, say, neurons but just because we cannot yet doesn’t mean we never will.
†What those configurations are depends entirely on your definition of “beach”. Sand or water might also no play a role at all, again, depending on your definition.
And yet your caveat at the bottom illustrates that what a beach is isn't a trivial problem. Leibniz just wanted to avoid the regressive mechanical discussion by positing substances or monads as a solution to answering the question "What's a beach?". This isn't to say he's right than to say your trivialization doesn't work and that there's room for his speculation.
Definitions don’t make the problem hard. There is just no one true definition of beach, that’s fine. We can agree to use the one most commonly used or you can pick one, it doesn’t matter as long as we communicate the definition we are using.
I again and again find it astonishing that so many people have problems understanding what definitions are all about. They are about communication. Arguing about definitions is rather pointless, at least if you goal is to learn something about the world. (Good definitions make communication easier so there is room for argument about definitions but not really in this case.)
I'm not sure "scientific" properties do much better for the sort of ordinary human purposes for which the property of beachness tends relevant, e.g. distribution of persons, water quality, presence of tiki bars, etc. In other words, replacing ordinary language with descriptive formalism throws the baby out with the bath water, i.e. no matter how accurate the description of neuron firings is, it will not touch upon what it is like to tuck one's child into bed at night.
No matter how accurate the description of neuron firings is, it will not touch upon what it is like to tuck one's child into bed at night.
Great strawman! I don’t think anyone ever claimed that.
Incidentally, the claim that the distribution of Tiki Bars is normally a component of the scientific definitions of "beach" is the most patently absurd use you have made of a sophomoric definition strategy so far in this discussion.
As to your second point, you brought Tiki bars up. I don't think Tiki bars feature prominently in the definitions of beaches in the scientific literature but that doesn't really matter. What matters is that the distribution of Tiki bars (and other properties they might have) is accessible to the scientific method. You can't claim that your definition of "beach" which apparently includes Tiki bars is not accessible to science (at least with the examples you gave for extending the definition).
I mean absolutely nothing of the sort. What I am talking about is the ordinary use of the word "beach" in the ordinary grammar of the English language not its use in some game in which one attempts to translate ordinary terms with "scientific" propositions based a set of logical transformations which ignore the implications of context and connotation.
So long as one insists that the computer simulation is isomorphic to what it simulates, one is doomed to stay in the cave.