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Comment by tynpeddler | Hacker News Reader

Someone should have asked the kid what they meant by their question. I've noticed that kids generate strange questions in the way you might generate a grammatically correct, but nonsensical phrase using BNF. Asking them to clarify their question either highlights that they actually have no clue what they're looking for, or that their question is much much simpler than it first appeared (for example, maybe the kid just meant what happens if the word "six" didn't exist).

All that being said, the modulo world that the article mentions does't make sense to me. If 6 doesn't exist, how could you have modulo 6?

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> Someone should have asked the kid what they meant by their question.

I honestly think that this answer values the children's point of view more than the article's urge to not ignore them by launching into theses on the deep impossibility of what a missing integer might mean to the universe.

All the adults in the article interpreted the question to mean 'what if six things couldn't exist?' and proceeded to formulate complex mathematical implications.

None of the adults in the story asked, "what do you mean"? And none of the adults said "maybe 3 plus 3 would be 7", or maybe "7 could be pronounced 'six'", or what if the kid was asking about one-handed people after hearing about ancient kings who cut hands off of rule breakers, and was really just wondering in kid style whether it'd be better if we have a base 5 number system instead of base 10.

>Asking them to clarify their question either highlights that they actually have no clue what they're looking for

That wouldn't be very nice towards them, though. Many times children ask questions not because they're interested in their particular questions - quite often they don't really have a clue of what they're asking, as you mentioned - but they ask for the sake of learning something.

At least, that's the usual answer to "why children ask so many questions": because they like to learn, more than because they have a specific question.

My own attitude when I was young was probably kind of akin to feeding random input into a program to try to make it crash - how can I find a bug in reality (or the grownups).

I think teaching children to interrogate their own reasoning is the most useful thing you can teach them. I've met a fair number of adults who ask the same kind of nonsensical questions as children do because they don't know how to analyze their own thinking.

I think the idea is that 6 modulo 6 would just be 0, so in that system the only integers used are 0 through 5. Six is used as a concept in structuring the system, but it would not be present in the usage of the system.

> All that being said, the modulo world that the article mentions does't make sense to me. If 6 doesn't exist, how could you have modulo 6?

It's finite so just write out the addition and multiplication tables: http://www.wolframalpha.com/input/?i=Z%2F6Z

It indeed makes sense to talk about modulo 10 in base 10 and in modulo 10 in base 6. Or would base 6 also not exist?

Take it from the other direction. Assume a world with an integer "sqorkle", between the integers 3 and 4. It's >3, <4, and not equal to any other integer.

In our world that doesn't have sqorkle, what is 3 modulo sqorkle? Since is less than the modulus, it should just be 3, right? 4 modulo sqorkle: 1, I guess, being 1 above sqorkle? OK, so what about 4 mod 3? It's defined as 1 in our world, but in a world where 3+2=4, that can't still be true, right?

Mathematical constructs are based on patterns that we see in the world. Change the nature of the patterns, and you invalidate the mathematical constructs that we've built up. I'd think that since our constructs would be invalid in sqorkle-land, trying to apply them there will just end up with contradiction. Ditto, trying to apply our math to 6-less-land.

Sorry, but I think you mean the integer bleem between three and four. http://strangehorizons.com/fiction/the-secret-number/

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