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On Sat, Feb 15, 2014 at 3:24 PM, Rustom Mody <rustompmody at gmail.com> wrote: >> I could have three six-sided dice, all made from the same >> mould, and yet each one is a separate object. If I hold all three in >> my hand and toss them onto the table, can I recognize which one is >> which? No, they're identical. Are they distinct objects? Yes. > > In the case of physical objects like dice there is a fairly > unquestionable framing that makes identity straightforward -- > 4-dimensional space-time coordiantes. If the space-time coordinates of > 2 objects are all equal then the objects are identical, else not. Not once you roll them, which is why I specifically used dice. This exact situation comes up in roleplaying games - suppose you want to get a random number from 0 to 999 (or 1 to 1000, by declaring that a result of 0 is interpreted as 1000). The most common way to do this is to roll 10-sided dice for the digits; you can either roll one d10 three times, or three dice all at once. In the latter case, you somehow need to pre-declare which one is the hundreds digit, which is the tens, and which is the units, which means you need some way to distinguish the three dice after you roll them (as you can't recognize by position). This is why dice exist in a variety of colors [1]. Indistinguishable yet distinct dice... and it's actually possible to merge all three into a single object (which is what happens when you roll one three times instead of rolling three once), just as Python is allowed to do. By the way, if you get into quantum physics, you can't depend on three dimensions of space and one of time to distinguish objects. You also need spin. And I think you also need insanity, because you'll be given it on arrival if you don't have enough. ChrisA [1] Well, that and to look cool. I don't know that any system other than FATAL requires you to roll d1,000,000 on six dice, so three colors would normally be sufficient. But it's fun to have the full spectrum.

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