Heaps of trouble

First, let me apologize for my long absence. I’ve been playing with statistics, building a migration model, and fighting a cold (I lost). Fortunately, there have been a few moments to spare, and those have been spent puzzling over the Greeks. More precisely, over Greek puzzles.

If you ask a typical person about Greek puzzles, odds are that they will know about the Gordian knot but won’t recognize it as both a puzzle and a historical fact [1]. Somewhat fewer will recognize Zeno’s paradoxes [2]. But they had any number of subtle and interesting questions, many of which still trouble us nearly five millennia after they were first asked.

Take, for example, the Ship of Theseus. Start by building a ship. Now replace one of the timbers you used to build it with a new timber. Is it still the same ship? OK, replace another one. And another. Is it still the same ship? Keep doing that until all of the timbers have been replaced. What you’ll have is a ship that almost everyone will agree is still the same ship that you started with and a pile of timbers. Now use that pile of timbers to build another ship. Which is the original ship? The one with the all-new timbers? Or the one that used the original timbers but was broken apart for a bit?

This question is important if you are thinking about cloning something. If I take a cow and clone it [3], which is the original? The cow or the clone? Does it matter how soon after the first cow comes into being? What if I take the original embryo and split it, creating twins. Is one of the twins the original and the other a mere clone [4]? It also applies if you are thinking about teleportation – have you died and a new being with all of your memories come into being elsewhere? Or is it you that steps out of the teleporter [5]. And it applies if you buy artwork. Is a reproduction of a statue the same as the original? What about a second casting? Or a reprint of a famous photograph?

Another good example is the “sorites paradox” (Greek for “piled up problems”). Take a heap of sand (Or, if you would rather argue about obscure philosophy than politics over this year’s Thanksgiving dinner, use the bowl of mashed potatoes.). Get everyone to agree that it is a heap. Now take away one grain of sand (or spoonful of potatoes).  Is it still a heap? Keep doing that until only one grain remains. Is it still a heap? If not, then when did it stop having “heapness”? Can you build it back into a heap by adding more sand? If so, how much is required [6]?

This question was at the center of the recent push to declare gametes “people” in Mississippi. The central argument of the “pro” camp was that all it takes is one viable cell to make someone a person. The central argument of the “anti” camp was that life is somewhat more complicated than that; for example, if the morula never implants in the uterus, then there is no possibility of further development and no possibility of a person being born. And other cultures have taken the argument further, from those who declared that sentient/human life begins at age 13 to those who insisted that only those in the army were people (everyone else was either a slave or a wife) to those who argued that certain races were only 3/5 alive.

And now that I’ve given you something to puzzle over, I’ll be bowing out again for a bit. I’ve got some statistics to play with, you see…



[1] Remember that it was a knot that couldn’t be untied, supposedly put in place by the father of King Midas in honor of Dionysus (Bacchus) who led the farmer into town and made him a king. Alexander the Great “untied” it using his sword.

[2] Which aren’t really paradoxes, but examples showing the limits of the then-current mathematical language. We still run into versions of the “paradox of place” when discussing cosmology.

[3] As high school students are now wont to do.

[4] In some parts of the world, they get around this by declaring both twins to be evil and killing them. In others, they declare both twins to be demigods, and celebrate them. Oddly enough, the two areas are on the same continent.

[5] Always assuming that there were no flies in the ointment.

[6] Don’t be surprised if people think that heapness comes later when building a pile than it does when destroying it; i.e., that a heap of sand that is losing grains is smaller than a heap when it is adding grains. People are funny that way.

5 thoughts on “Heaps of trouble

  1. Sorry you’ve been feeling theIck. Hopefully, you’re much improved since you’ve been pondering. I went to the first link and found lots of red and blue circles and some multi-colored bars. I’d think you’d get tired of drawing them but if that’s your thing…

    When it comes to Personhood, my old mentor always said, “Abortion should be legal til the embryos reach the age of 21 years.” I’m not sure that was medically correct.

    Be safe, have fun and rest your sinuses!

    • At least you only have to look at it once. The evil bastard makes me proof these things while he’s writing them. I’m not sure if it’s because he thinks I’m smart or because he thinks I represent the average idiot on the street. 8:-)

      • Ooo! Is it “John’s and Evil Bastard Day?” Nobody told me, I’d have baked a cake. Suppose he’ll get pumpkin pie tomorrow, anyway. Hiya!

        I think he’s trusting you to point out his booboos before they’re made public (cos you’re smart AND a good friend).

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