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Would it be child abuse to raise your child by teaching them numbers in base 16, so by the time they reach school they can count to twenty, but only in base 16? Would this stunt their growth? Just to clarify for all the people that don't know what this means, it means that they would count like this:

1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10,11... 18,19,1A,1B,1C....

I suppose the main question is, should my child become just as good as anyone else doing basic multiplication and other simple maths if they only learnt in base 16. Surely the base you learn with is arbitrary?

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    Welcome to the site, but: While this is hardly abuse, why would you do this? Apart from it being completely impractical, it's probably impossible to keep a child isolated from the decimal numbering system for longer than its first 2 or 3 years, and the question seems purely hypothetical. I don't think that's a good fit for this site. – Pascal Sep 8 at 22:59
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    Abuse, no (depending on how the child responded.) Very strange, yes. We do allow hypotheticals, but this one seems out of the realm of "normal". Please edit in details (why would this be important to you? Is tis a bet you made with someone? Are you actually entertaining doing tis? Do you have children? Do you want them to "fit in" or not? – anongoodnurse Sep 9 at 2:14
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    If you live in a country which speaks language A (and B & C) should you teach them the numbers 1 to 10 in languages A and D? We did... – Solar Mike Sep 9 at 3:54
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    @SolarMike: Assuming A=German,B=French,C=Italian and D=English, note how these are all natural languages with fairly large speaking populations. Base 16, however, is pretty much only relevant for low-level system programmers ;-) – Pascal Sep 9 at 10:48
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    Not at all abuse. But if you repeatedly pull such stunts there's a significant chance it will (rightfully) hurt his trust in you. There will come a time where he learns the local version of counting that everybody around him - including yourself - is using, is very different from the one he has been taught. Unfortunately, many people intentionally teach their kids "wrong" things because they think it's fun, and it doesn't really make a difference to the kid if you do it for a different reason, because they won't see that difference. – Peter Sep 9 at 17:55
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Surely the base you learn with is arbitrary?

I would argue that if you raised your child in total isolation, meaning that it wouldn't ever encounter the base 10 decimal system, this would hold true. The common assumption why we prefer base 10 is because we have ten fingers, but this never convinced me that base 10 is more "natural" than, say, base 6 (we could hold bigger numbers if we counted using a two-digit system where each hand represented one digit in base 6). Also, not everyone learns to count using their fingers, so it should be possible to teach a child maths in an other base and have it be just as proficient.

should my child become just as good as anyone else doing basic multiplication and other simple maths if they only learnt in base 16

I don't think so. Learning usually isn't an isolated activity. Kids encounter counting long before they go to school, in rhymes, songs, at birthday parties and so on. There are a ton of every-day interactions where mathematical knowledge gets taught to very small children. They hear other people counting balloons or cars or stars in the sky. If your kid expects to hear "A" but people call that number "ten", that's got to lead to a serious amount of confusion. Also, when your kid tells his/her peers that his older brother just turned "C", they're not going to understand and will think he's either very weird or plain stupid (can't even count right). Kids don't want to be different; they want to fit in and be accepted. You make that harder if you teach them to use another numbering system as the default.

Also, since the world is running on base 10, we tend to do things in units of 10 - so the number 10 will appear much more often in the real world than the number 16 (things will often be organized in groups of 10, for example). Multiplication and division are very easy in these cases in base 10, much harder in base 16.

Plus, of course, your child will have to spend the rest of his/her life converting numbers from base 10 to base 16 (and vice versa) just to be able to function in our society. That's a serious amount of work that will slow down your child, even if it can do the actual math just as fast as everyone else (just in base 16).

So, to summarize, if this is a hypothetical question where a child never gets in touch with the real world, then yes, it will most likley perform just as well in base 16. If this is something you actually consider doing, then just don't. You'd make your child's life more complicated without cause.

What I think would happen if you actually tried this is that your child would start out counting in base 16 and then switch over to base 10 when he/she noticed everybody else was doing it in base 10, just to get rid of doing the extra work of converting everything he hears and says. This would happen fairly early (before he/she was ready to learn how to multiply and divide, with the child knowing maybe numbers 1-20 dec). He'd be "bilingual", talking in base 16 with you to make you happy, and using base 10 everywhere else. If you insisted on him learning to multiply and divide in base 16, he'd probably slow down in comparison to everybody else because he'd have to learn to do the same thing in two numbering bases at roughly the same time. There are studies showing that kids who grow up bilingual tend to be less proficient in both languages than monolingual kids, which makes sense to me because they spend their time learning two instead of just one language, which is harder. I'd assume the same is true for doing math in two bases in parallel.

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Let me propose some questions that are, I think, analogous to this one:

  • Would it be child abuse to raise your child by teaching them to exclusively speak an artificial language like Toki Pona or Esperanto, rather than the language spoken in the locale where they live?

  • Would it be child abuse to raise your child by teaching them to read and write every word in the English language from right to left, rather than from left to right? (For example, to teach them to write the words "the dog is red" as "der si god eht")

  • Would it be child abuse to raise your child by teaching them that the word "up" means "down" and the word "down" means "up"? Or that "yes" means "no" and "no" means "yes"? Or that "eat" means "watch" and "watch" means "eat"? ("If you finish watching all of your vegetables, I'll let you eat television later.")

Languages, the direction in which written language is written, and the meanings of words are social conventions -- they are not and cannot be intrinsically "right" or "wrong". However, a child raised using conventions that are completely at odds with the way other people use them would be harmed tremendously. They would be completely unable to communicate with the rest of the world; even simple tasks would be made incomprehensible. They would not be able to understand what people mean when they say things and would not be able to make themselves understood.

In another context, on a different SE site, I once answered a similar question as follows:

I think it's important to stress that the convention is just a convention, and there is no intrinsic reason why one convention is better than another. But at the same time, this particular convention is a nearly universal one, and teaching your students a nonstandard convention is roughly equivalent to a language teacher teaching his or her students a dialect that nobody else speaks. As soon as they leave your classroom they will find themselves in a mathematical world that does things differently, and you are doing them a disservice if they are not thoroughly used to the conventions that everybody uses.

The answer to this question is the same as that, times a million. As soon as they leave your home they will find themselves in a world where nothing makes sense to them, and you would be doing them enormous harm if you do not teach them to use language the way everyone else does.

Having said that, a less extreme version of this question might be:

Would it be child abuse to raise your child by teaching them numbers in base 16, so by the time they reach school they can count to twenty in base 16, in addition to base 10?

This, I think, is more reasonable, and in many ways analogous to raising a child in a bilingual home. Many children grow up speaking one language at home and another outside; if anything, it helps them learn to be more flexible users of language. However, the analogy is not perfect, because in this proposal the written symbol "12" has two different meanings, depending on whether you are at home or outside, and in the case of spoken languages it is unusual to have two words that are indistinguishable both in written and oral form but nevertheless mean different things depending on the language. You would need to have some way of signalling which "dialect" you are using in a given context to avoid confusion. One way to do that would be to use entirely different written symbols and names for base 16... but then we are back to the problem of "nobody outside the house would understand you".

(Parenthetically: Numeration systems are not only written languages, they are also oral languages. how do you imagine, in your hypothetical scenario, that the written expression "12" would be spoken? Would you read it aloud as "eighteen" or as "twelve"? How would you pronounce "AB3"?)

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