Agreed, but it depends. The analogy can make things harder if you're not intimately familiar with the analogy. Take the below, an excerpt from the explanation on prime numbers for example, and consider you know 0 chemistry (not unlikely if you're reading an intro on prime numbers):
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> I'm no chemistry expert, but I can see a relationship to the primes. Chemical elements have properties based on their location in the periodic table of the elements:
Atoms in group 8A (Neon, Argon) are the noble gases. They don't react and won't blow up in your face.
Atoms in group 4A (Carbon, Silicon) bond well. They're great building blocks for other elements.
Atoms in group 1 (Sodium, Potassium, etc.) are very reactive. Drop 'em in water and see them explode.
And in organic chemistry there's an idea of a functional group: several atoms can determine the class of the entire molecule. For example:
Alcohols are a certain carbon-hydrogen chain with an OH group at the end.
Methanol, ethanol, and other alcohols share similar properties because of this OH functional group.
Those are the basics, if I didn't mess it up. Now let's see what happens when we treat numbers like chemicals.
First Example: Guessing Evenness
In general, an organic chemical contains carbon (not quite, but it's a good starting point). No matter what elements you mix together, if you never add any carbon then you can't create an organic compound.
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Anyway, a single example doesn't negate your point. I love analogies in learning, but one has to be careful to pick analogies from a level of understanding (way) below what you're trying to explain. I guess kids are introduced to primes and chemistry at roughly the same age, but I'd have picked a non-academic analogy to explain an academic concept. But even then, it's tricky. For example I've been confused by my fair share of 'sports analogies' in secondary school books, for sports I happened not to have ever tried or knew the rules for. But really, the analogy should be completely supplemental, and if possible marked off in a side box that people can, but not should, read for better understanding if it helps them. I find many school books do this really well, but I haven't seen it translated to web content as much somehow. For example, on Evenness he'll continue by explaining how if you have a factor of 2 in your number (e.g. 24 = 2^3 * 3), then no matter what, the number is even, likening it to an organic chemical which contains carbon no matter what (though, noting a caveat without going into it). I don't think that analogy is very strong, it's confusing if you don't know chemistry, and it's pretty redundant if you do. In fact I'd personally be better of without it, and understood Kalid's normal explanation without issue. Yet I had to read through something about Atoms in group 4A and their properties, unsure whether I could just skip it or whether it was important to grasp some larger point. Anyway I was already familiar with primes but my 12 year old self probably would've been confused with the chemistry analogy.
Thanks for the feedback! Agree analogies are context (and time) sensitive. As soon as you make a reference the clock starts ticking about how long it would remain relevant.
For this specific example, I was writing to a high-school version of myself who wanted to really get an intuition for primes. What can we deduce from a prime factorization, are there other ways to think about it? (Number theory is studied later, even though numbers are introduced early.)
For a younger child, I'd probably use Lego or Minecraft to show how numbers can have "building blocks". And if you didn't use any Redstone as a building block, there won't be any Redstone in the result. (I.e., a number which never had the "2" building block added, will never be even.)
----- > I'm no chemistry expert, but I can see a relationship to the primes. Chemical elements have properties based on their location in the periodic table of the elements:
Atoms in group 8A (Neon, Argon) are the noble gases. They don't react and won't blow up in your face. Atoms in group 4A (Carbon, Silicon) bond well. They're great building blocks for other elements. Atoms in group 1 (Sodium, Potassium, etc.) are very reactive. Drop 'em in water and see them explode. And in organic chemistry there's an idea of a functional group: several atoms can determine the class of the entire molecule. For example:
Alcohols are a certain carbon-hydrogen chain with an OH group at the end. Methanol, ethanol, and other alcohols share similar properties because of this OH functional group. Those are the basics, if I didn't mess it up. Now let's see what happens when we treat numbers like chemicals.
First Example: Guessing Evenness In general, an organic chemical contains carbon (not quite, but it's a good starting point). No matter what elements you mix together, if you never add any carbon then you can't create an organic compound. -----
Anyway, a single example doesn't negate your point. I love analogies in learning, but one has to be careful to pick analogies from a level of understanding (way) below what you're trying to explain. I guess kids are introduced to primes and chemistry at roughly the same age, but I'd have picked a non-academic analogy to explain an academic concept. But even then, it's tricky. For example I've been confused by my fair share of 'sports analogies' in secondary school books, for sports I happened not to have ever tried or knew the rules for. But really, the analogy should be completely supplemental, and if possible marked off in a side box that people can, but not should, read for better understanding if it helps them. I find many school books do this really well, but I haven't seen it translated to web content as much somehow. For example, on Evenness he'll continue by explaining how if you have a factor of 2 in your number (e.g. 24 = 2^3 * 3), then no matter what, the number is even, likening it to an organic chemical which contains carbon no matter what (though, noting a caveat without going into it). I don't think that analogy is very strong, it's confusing if you don't know chemistry, and it's pretty redundant if you do. In fact I'd personally be better of without it, and understood Kalid's normal explanation without issue. Yet I had to read through something about Atoms in group 4A and their properties, unsure whether I could just skip it or whether it was important to grasp some larger point. Anyway I was already familiar with primes but my 12 year old self probably would've been confused with the chemistry analogy.