5 ms·

When my son was around five or six, I did a similar exercise to explain the difference between prime and composite numbers. I told him that a number X is compo

by jawns 9y ago

When my son was around five or six, I did a similar exercise to explain the difference between prime and composite numbers. I told him that a number X is composite if you can fit X apples into buckets and end up with the same number of apples in each bucket. I drew 6 apples and asked whether they could be divided into buckets with an equal number of apples in each. It was immediately obvious that they could. My son circled one group of three apples, then another group of three apples. Then I drew 7 apples. He realized that you couldn't divide 7 apples into baskets and have each basket contain the same number of apples. Voila! A prime number. Then we started talking about the frequency with which prime numbers occur on the number line, how important they are to fields such as cryptography, and the existence of dense Bragg peaks among primes in judiciously chosen intervals. By the end of the conversation, he had discovered a new recursive prime generator and submitted a paper on it to arXiv. Who knew?!?

k__ 9y ago
lol, is this some elaborate troll?
- platinumrad 9y ago
  >troll Yes >elaborate No
kazinator 9y ago
> I told him that a number X is composite if you can fit X apples into buckets and end up with the same number of apples in each bucket. Wrong; X is composite if you can fit X apples into buckets and end up with the same number of apples in each bucket, with at least two apples in each bucket. "You gotta tell the children the truth. They don't need a whole lot of lies. Cause one of these days, baby, they'll be running things." - Jimi Hendrix, "Straight Ahead"
- jawns 9y ago
  Very true, and I did actually explain that to him. In my rush to tell a good story I left out the pedantic part.
  - gameshot911 9y ago
    We'll forgive you - this time. ;)
- tome 9y ago
  And at least two buckets.
- ianamartin 9y ago
  This is something I saw over and over again long before I had a serious interest in technology or science at all. It’s an attitude that’s rampant in liberal arts courses. There are “kiddie” versions of everything from History to to Music Theory to Grammar. It used to really frustrate me in undergrad how many things taught as almost moral absolutes were upended the following semester. I sort of get it that even in junior high and high school, the teachers don’t really know anything beyond the kiddie version, so that’s what gets taught. But at the college level, there’s no excuse for that. There’s a certain amount of science envy that some liberal arts professors have. They want to be able to say that there is one and only one way to understand a historical event or way to compose music. Milton Babbit was famous for this in the music composition world and argued that music needed to be “elevated to a higher form like that of math or physics” and that no one expects advanced math to be accessible to lay persons. Therefore music shouldn’t be comprehensible by anyone who doesn’t have a PhD in music theory or composition. This was actually a pretty popular attitude in the “classical” music world from the 1950s to the early 80s, and the music written during that time reflects it. Sorry to get so far off on a tangent, but while that specific fad has come and gone in music composition, there remains an inferiority complex among liberal arts academia that is extremely problematic and a general attitude among professors of all stripes that some people just can’t handle the truth: that outside of religion, there are no absolute truths. Getting back to the Hendrix quote, I absolutely agree. Teach children as much of the truth as you know. They can take it. In my own experience teaching violin, I’ve found that I get the best response when I treat the students the most like adults. About 20 years ago I started bringing in little vignettes about music theory and history with my youngest students (4-6 years old) as a break between lesson segments where we were focusing very intensely on specific violin techniques. When I realized that they enjoyed both the context switch and the color commentary about why exactly we do these kinds of things, I brought more and more of that to the table, and it’s been very successful. Obviously, this isn’t a robust study, it’s not meaningful in a larger scale, and it doesn’t prove anything at all. But if the theory is that young students can handle a lot of uncertainty and a lot of advanced material at a young age, then my experience is, at least, not evidence that it’s false. Deep down inside, I think that we need to be a lot less careful, protective, and hand-holdy about what we expose our children to. They can handle it.
  - 9y ago
- joeframbach 9y ago
  The original is correct, it says "apples" not "apple(s)".
  - e12e 9y ago
    Indeed it says "apples" and "buckets". [Now, why op didn't use pidgins and pidgin holes, I'll never know... ;-) ]
dsnuh 9y ago
> Who knew?!? Your six year old came up with a new recursive prime generator over the course of a conversation introducing him to the concept of primes, and then submitted this as a paper to arXiv? Do you have a link to this paper on arXiv?
- otp124 9y ago
  > Do you have a link to this paper on arXiv? This part was sarcasm.
  - dsnuh 9y ago
    It was a strange context switch if it was sarcasm...
    - ballenf 9y ago
      It was self-deprecating humor aimed at acknowledging that all parents are pretty sure their children are the smartest humans to have ever walked the earth. At least that was my reading and it gave me a chuckle.
      - dmix 9y ago
        Basically an "apple falling on Newton's head = discovered gravity" kind of story people eat up about invention and science. Which always seems to gloss over the endless hard work and constant failure and self-doubt they went through. Plus the incidental ancillary work done in related fields which helped spawn the initial seeds. Although there may be a useful metaphor here that the solutions are often easier or more "obvious" than they seem, and people often get lost in the details and busywork, missing the forest for the trees. So having a simple (but receptive) wall to bounce ideas off of (such as a 6yr old) helps break through the noise to focus on core / fundamental / primitive ideas from which more complex breakthroughs spawn.
      - dsnuh 9y ago
        My apologies, I was just slow on the uptake, and this being HN, although I was incredulous, I was also fully prepared for you to come back with a link! I get the joke, now that I know it was a joke. You never know who's on the other side of the wire, and for all I know you might have some genius kid. My 5 year old is into Nerf guns and Mario, but again, this _is_ HN... Anyway, I'll take my downvotes and move on. Thanks for sharing the story, I might try explaining it like this to my kids! Edit: oops thought I was replying to jawns
gowld 9y ago
FWIW, "rectangles" is a visually/geometrically natural way to express "buckets of equal size". And "1xN doesn't count" can be expressed nicely as "it can't just be a line", or "the line must be folded up into a shorter rectangle [because more compact shapes are nicer]"

by jawns 9y ago

k__ 9y ago

lol, is this some elaborate troll?

platinumrad 9y ago
>troll Yes >elaborate No

kazinator 9y ago

> I told him that a number X is composite if you can fit X apples into buckets and end up with the same number of apples in each bucket. Wrong; X is composite if you can fit X apples into buckets and end up with the same number of apples in each bucket, with at least two apples in each bucket. "You gotta tell the children the truth. They don't need a whole lot of lies. Cause one of these days, baby, they'll be running things." - Jimi Hendrix, "Straight Ahead"

jawns 9y ago
Very true, and I did actually explain that to him. In my rush to tell a good story I left out the pedantic part.
- gameshot911 9y ago
  We'll forgive you - this time. ;)
tome 9y ago
And at least two buckets.
ianamartin 9y ago
This is something I saw over and over again long before I had a serious interest in technology or science at all. It’s an attitude that’s rampant in liberal arts courses. There are “kiddie” versions of everything from History to to Music Theory to Grammar. It used to really frustrate me in undergrad how many things taught as almost moral absolutes were upended the following semester. I sort of get it that even in junior high and high school, the teachers don’t really know anything beyond the kiddie version, so that’s what gets taught. But at the college level, there’s no excuse for that. There’s a certain amount of science envy that some liberal arts professors have. They want to be able to say that there is one and only one way to understand a historical event or way to compose music. Milton Babbit was famous for this in the music composition world and argued that music needed to be “elevated to a higher form like that of math or physics” and that no one expects advanced math to be accessible to lay persons. Therefore music shouldn’t be comprehensible by anyone who doesn’t have a PhD in music theory or composition. This was actually a pretty popular attitude in the “classical” music world from the 1950s to the early 80s, and the music written during that time reflects it. Sorry to get so far off on a tangent, but while that specific fad has come and gone in music composition, there remains an inferiority complex among liberal arts academia that is extremely problematic and a general attitude among professors of all stripes that some people just can’t handle the truth: that outside of religion, there are no absolute truths. Getting back to the Hendrix quote, I absolutely agree. Teach children as much of the truth as you know. They can take it. In my own experience teaching violin, I’ve found that I get the best response when I treat the students the most like adults. About 20 years ago I started bringing in little vignettes about music theory and history with my youngest students (4-6 years old) as a break between lesson segments where we were focusing very intensely on specific violin techniques. When I realized that they enjoyed both the context switch and the color commentary about why exactly we do these kinds of things, I brought more and more of that to the table, and it’s been very successful. Obviously, this isn’t a robust study, it’s not meaningful in a larger scale, and it doesn’t prove anything at all. But if the theory is that young students can handle a lot of uncertainty and a lot of advanced material at a young age, then my experience is, at least, not evidence that it’s false. Deep down inside, I think that we need to be a lot less careful, protective, and hand-holdy about what we expose our children to. They can handle it.
- 9y ago
joeframbach 9y ago
The original is correct, it says "apples" not "apple(s)".
- e12e 9y ago
  Indeed it says "apples" and "buckets". [Now, why op didn't use pidgins and pidgin holes, I'll never know... ;-) ]

dsnuh 9y ago

> Who knew?!? Your six year old came up with a new recursive prime generator over the course of a conversation introducing him to the concept of primes, and then submitted this as a paper to arXiv? Do you have a link to this paper on arXiv?

otp124 9y ago
> Do you have a link to this paper on arXiv? This part was sarcasm.
- dsnuh 9y ago
  It was a strange context switch if it was sarcasm...
  - ballenf 9y ago
    It was self-deprecating humor aimed at acknowledging that all parents are pretty sure their children are the smartest humans to have ever walked the earth. At least that was my reading and it gave me a chuckle.
    - dmix 9y ago
      Basically an "apple falling on Newton's head = discovered gravity" kind of story people eat up about invention and science. Which always seems to gloss over the endless hard work and constant failure and self-doubt they went through. Plus the incidental ancillary work done in related fields which helped spawn the initial seeds. Although there may be a useful metaphor here that the solutions are often easier or more "obvious" than they seem, and people often get lost in the details and busywork, missing the forest for the trees. So having a simple (but receptive) wall to bounce ideas off of (such as a 6yr old) helps break through the noise to focus on core / fundamental / primitive ideas from which more complex breakthroughs spawn.
    - dsnuh 9y ago
      My apologies, I was just slow on the uptake, and this being HN, although I was incredulous, I was also fully prepared for you to come back with a link! I get the joke, now that I know it was a joke. You never know who's on the other side of the wire, and for all I know you might have some genius kid. My 5 year old is into Nerf guns and Mario, but again, this _is_ HN... Anyway, I'll take my downvotes and move on. Thanks for sharing the story, I might try explaining it like this to my kids! Edit: oops thought I was replying to jawns

gowld 9y ago

FWIW, "rectangles" is a visually/geometrically natural way to express "buckets of equal size". And "1xN doesn't count" can be expressed nicely as "it can't just be a line", or "the line must be folded up into a shorter rectangle [because more compact shapes are nicer]"