The paradox of the heap is a pretty simple one, but it has interesting implications. Here’s how it goes: Imagine that you had a pile of 1000 grains of sand. You’d have a little heap of sand, spilling out all over your desk. Don’t worry, you can imagine a vacuum later. For now, imagine taking some tweezers and removing one grain of sand. It’s still a heap, right? It’s just a heap of 999 grains, instead of 1000. You can’t even tell the difference. You set the grain aside, and get another grain. Apparently you don’t have much going on tonight, because you continue this process until there are only ten grains of sand on your desk. Is it still a heap? You take seven more, and there’s just a little trio of sand grains. Finally, you get down to one grain. Obviously, this is not a heap anymore. So, when did that change? Was it a heap at 500 grains? Was it a heap at 501, or 499? You can pick any arbitrary number you want, and say, for example, “A pile of more than 100 anythings is a heap,” but come on, really? Look at a pile of 100 things, then a pile of 99 things. Can you really tell the difference? You can try to define ‘heap’ however you want, but it’s impossible to completely nail down. From a purely logical standpoint, heaps make no sense.

Now, at this point, you’re probably going, “What’s the big deal? ‘Heap’ is an inexact, subjective term. So what?” Well, here’s what. As it turns out, lots of things in our lives are types of heaps. If you take the sentence “How many grains make a heap?” you can substitute words in to get at some really deep questions. “How many days of development in the womb make a person?” “How much computing power makes an AI?” “How many work hours makes an expert?” We like to give concrete answers to these things. “16 weeks”. “Passing a Turing test”. “10,000”. But, really, if you have 9,998 hours of experience, are you not an expert? If a computer is just a tiny bit too stiff to pass as a human in conversation, does it not have a mind of its own? Is a 15 week and 6 day-old fetus not worth considering?

I don’t have any answers here. If there was an answer to flip to the back of the book for, this would be a riddle, not a paradox. But I think it’s important to remember, as we move through this world of sliding scales, that even something as basic as a heap of sand can be questioned.

 

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