General Question

nikipedia's avatar

Can you solve the pile of sand problem?

Asked by nikipedia (27519points) July 30th, 2008

(Better known as Sorites paradox, first posed by Eubulides of Miletus.)

Start with a pile of sand. Take away a grain. Is it still a pile? Okay, take away another grain. How about now? And another? And another? At what point does it cease to be a pile?

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29 Answers

kevbo's avatar

@niki, is this a segue into a Spring Break story?

flyawayxxballoon's avatar

It’s no longer a pile when there are no grains of sand left.

Pile- a quantity of things heaped together
Quantity- an indefinite amount or number

robmandu's avatar

Wow. Them there ancient Greeks had a lot of time on their hands.

Here. Let me solve this for everyone.

A heap is two or more items where half or more of the items are piled on top of one another. Further, a heap implies some randomization in the structure. If the items were placed neatly one atop another, that would be a stack. If none of the items lay atop one another, then you don’t have a heap or a stack, you have a mess.

Allie's avatar

This reminds me of Theseus’ paradox.
And this might not make sense, but I think once you cannot hold the mass of sand in your hand it becomes a pile, before that it’s a handful.
Robmandu: So you could have a heap and a pile with just two things? And you don’t give any specification about how those two things have to be. So can you put one grain of sand on top of the other and still call it a heap/pile? Edit: You answered this with your edit. But can’t a mess still be a heap? And can’t a stack be a pile?

flyawayxxballoon's avatar

@Allie ; But then it’s simply a pile in your hand. Regardless of the location, it’s still a pile.

girlofscience's avatar

The biggest problem seems to be that, at most cutoffs, the number of grains above and below that number does not appear that different. (Example: If someone said the cutoff should be 1000 grains, does 1001 really look different enough from 999 to be considered two different things? A pile and a nonpile?)

To overcome this issue, I would test individuals and determine the point at which 75% could correctly identify the two groups of grains of sand. (If 75% of people could tell that the group of grains of sand with 47 grains was smaller than the group of grains of sand with 49 grains, then 48 would be the cutoff.)

nikipedia's avatar

@girlofscience: Why not 74%? Or 76%? Isn’t this transferring the same problem to a different medium?

girlofscience's avatar

@nikipedia: In psychophysics, 75% is a universally accepted threshold. 50% is chance (as it would be a forced two-choice design), so 75% is the midpoint between “chance” and it just being way too obvious.

La_chica_gomela's avatar

This sounds like a semantics issue to me. The question is basically, “how do you define the word “pile”?” Why is that a big deal?

marinelife's avatar

To me, two is a pile, a small pile to be sure, but a pile.

Indy318's avatar

metaphorically speaking, this paradox could represent an issue or problem, it made me think of crime and terrorism. When is the world truely considered safe from terror. Is there a universal number of criminals that draws a line between peace and chaos. If each grain were a criminal, would it make a difference if a pile were a million or just a thousand grains. I believe the pile no longer exists only when all the grains have disappeared. Analogously, the world can on be considered safe until every criminal is removed. In both cases, the line is drawn differently according to how people percieve the issue.

nikipedia's avatar

@robmandu: How can you have two grains of sand piled on top of each other without them meeting your definition for “stack”? Is your answer to the larger question about the vaguenesses of language simply that we can eliminate the vagueness by establishing arbitrary guidelines? (If so, I don’t necessarily disagree.)

@La_chica_gomela: Because defining words accurately is crucial to being able to communicate effectively with each other. It’s important to be able to draw a line in the sand. (Woh, woh, woh.) And I think this problem might extend beyond the vagueness of language to the vagueness of decision-making in general, but I’m hoping the thread evolves in that direction (as a side-conversation already has) before I go saying something stupid.

Hobbes's avatar

I think, as humans, we like to classify things into groups: human and inhuman, good and evil, black and white, pile and not-pile. We’ve evolved to see clear distinctions between things because it’s useful to see a rock as distinct from the ground so that you don’t trip on it. However, the real world isn’t as clearly defined as we like to think it is. At the quantum level, for example, there are no real distinctions between one object and another, and an observer at that scale couldn’t tell you where the rock ended and the ground began.

Similarly, we looked for a “missing link” in biology for a very long time before we realized that there was no clear distinction between humans and their ancestors. There was no point where we became human, just as there isn’t a point where a pile becomes not-a-pile, because “human” and “pile” are internal labels that we use to divide the world into discrete pieces, even when there really isn’t a clear dividing line.

I know that only tangentally answers the question, but it’s the best I could do – this is my third re-write!

La_chica_gomela's avatar

Indy, thank you for answering my question. That’s a great point (and that GA is from me)

robmandu's avatar

@niki, well, the point of my answer was to show that the guidelines need not necessarily be arbitrary. The difference between 999, 1,000, and 1,001 is arbitrary as they’re indistinguishable to the human perception. The difference between 1 and 2 is absolute.

There is some vagueness is how I describe the piling. However, you can easily demonstrate what I had in mind with a couple of books. Place one haphazardly on top of the other and it’s a heap. Line up all the edges and it’s a stack.

Indy318's avatar

@la chica, your welcome and thanks for the lurve.

drhat77's avatar

i’m thinking a pile is when it would be too inconveinaint to count the individual grains.
Now we get into “what’s conveiniant?” good question, smart-person. Long answer once again boils down to what 75% of people would say would be too inconveieniat. it might be small. 50 grains, ok, 51 grains too much, so it’s a pile.

short answer, i dunno.

kevbo's avatar

I think the standard smallest unit of measure for piles is dog shit pile. Just count down from three dog shit piles… two dog shit piles… then when you get to one dog shit pile, that’s the smallest you can go. The next grain of sand removed makes it too small to measure in units of dog shit pile.

For example, this discussion is about 6 dog shit piles. If you removed every answer but the first answer, you’d have one dog shit pile, but once you remove the first answer, then it’s no longer measurable in units of dog shit pile. It’s just a collection of words that make for a decent question.

lifeflame's avatar

What a pile of….

whiteowl's avatar

World consists of “piles”!
every thing consists of little, tiny things…
this is why we rare notice changes in this world…
have to be attentive to everything!

Tone's avatar

It ceases to be a pile when you remove enough grains to leave only a single layer, regardless of how many grains are left. The definition of pile isn’t concerned with quantity (as long as it’s more than one), it’s about relative position (i.e. stacked).

whiteowl's avatar

dont understand you,Tone

PhilGood's avatar

Tone makes the best point on this topic I have noticed thus far, one that is necessary for this conversation to progress beyond bickering over quantity and percentages. Decreasing the pile doesn’t have so much to do with adding and removing the grains of sand as it does re-arranging them. We can have the same number of grains in a pile as we can not in a pile aka in ‘order’. Thus, we must progress into the qustion of whether or not it is possible to achieve any kind of ‘order’ without destroying (removing grains) all but one viewpoint (grain).

To go back to what Indy said about crime being like the pile. I like where you have gone with this analogy, but it needs to be clarified we do not ‘remove’ and disgard criminals from society (with the exception of the death penaly). This would be too simple, instead we make an attempt to “organize” them. I.e. put them in prison & rehabilitate in an attemt to create order, to unpile them in this way.

robmandu's avatar

If I may offer a variance to this theme (now that a couple of us feel like we’ve got a handle on the whole pile business)...

How many trees does it take to make a forest (or a wood or a glade or a jungle, whatever)? Ignore the kind of trees, their geographic locale, etc.

I’ll think this is in the spirit of Niki’s original pile question, but without the layering aspect.

nikipedia's avatar

@robmandu: but without the layering aspect.

Not so! If you have one row of trees, even if it’s infinitely long, no one’s calling that a forest!

But…what about two rows?

Three?

Four?

One misaligned not-really row?

I think the layering solution (and this comment) might be an extension of your initial point. The difference between one grain and two—or one layer and two, or one row and two—is something absolute, quantifiable, and measurable. Our descriptor (pile, heap, forest, glade, whatever) starts to get messy when stop being able to easily quantify it. But I think that’s the point of having words like that. We need something that describes “a chaotic, not easily quantifiable amassing of something”.

I think.

robmandu's avatar

Ack! Foiled yet again.

(‘scuse me whilst I return to vacation mode. No more so-called “thinking” for me today.)

robmandu's avatar

Double ack! Back for more…

@Niki, you’re right, a single row of trees, no matter how many, will not be called a forest… but here’s the rub… how many rows would be needed (in addition to the number of actual trees)?

Unlike the pile, I don’t think 2, 3, or even 10 would qualify. The higher the number (whatever it is), the more seemingly arbitrary whatever value is proposed… right?

arnbev959's avatar

Rows aren’t forests. Forrests are ranndom. SO are piles

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