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Conversations with a six-year-old on functional programming

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Re: Conversations with a six-year-old on functional programming

#131

Post by sidlls »

gowld wrote: post #111
wahern wrote: post #90

Earlier quoted context omitted.

Such precociousness is often[1] an indicator of abnormalities and handicapped general intelligence. For example, if our son independently began to read too early the initial reaction of my spouse, a Speech-Language Pathologist, would be to freak out rather than to be filled with pride. Perhaps you know this and used "gifted" in its more euphemistic sense. In any event, I mention this not to correct you but to address…

The comment above is condescending and misleading. Being precocious doesn't mean autism, and no professional SLP would "freak out" at an early reader. Being smart is an "abnormality", and autism is not "handicapped general intelligence". Warning signs for autism include obsession with letters and numbers without understanding meaning , not being able to reason about math and discuss mathematical topics.

It isn't misleading or condescending. In fact as a parent of an autist I find your comment to be the condescending one. The person you're responding to didn't say autism was the same as handicapped general intelligence, but that extreme precociousness is often correlated with atypical development in other contexts.

Re: Conversations with a six-year-old on functional programming

#133

Post by ummonk »

coldtea wrote: post #35
thaumasiotes wrote: post #18

Earlier quoted context omitted.

This and this: >> I think he was just stuck on the idea of the function doing something arithmetical to the input, and was having trouble coming up with some sort of arithmetic procedure which would result in 6 no matter what you put in don't really seem, to me, like they can explain what's happening -- f(x) = 6 is trivially easy to express in terms of arithmetic operations being applied to x. If you assume that a fu…

> what's wrong with a function that multiplies by 0? Obviously the fact that it doesn't seem to have any visible effect on the input -- and people expect the input to be affected.

I think it's more that it doesn't make use of its input. If you aren't using the input, why is the input in its type signature?

Re: Conversations with a six-year-old on functional programming

#134

Post by craftyguy »

jason_slack wrote: post #132

I'm taking a discrete math class right now. How is this read: \lambda x.\, x - 3 and what is a simple example? In a discrete math perhaps it is the same as "All x, x is an integer such that...."?

The '\lambda x' is just another way of saying "f(x)"

So '\lambda x., x-3' --> 'f(x): x-3'

Also, I really enjoyed my discrete math courses! The proofs were.. tedious.. but the amount and breadth of 'stuff' covered was excellent.

Re: Conversations with a six-year-old on functional programming

#135

Post by AndrewKemendo »

dyladan wrote: post #3

What is truly astounding about this is the patience to even attempt to explain free theorems to a 6 year old. Most parents would likely answer "math" and that would be the end of it. I don't (yet) have kids, but when I do I hope I have the wherewithal to recognize and take advantage of moments like these.

I have three very inquisitive kids and I love trying to explain complex topics, like reinforcement learning, to them in a way that they can understand. The best thing I get out of it is clarity for my own understanding, or gaps/lack of clarity, so it's a valuable exercise.

People don't give children enough credit for what they can really understand.

I remember distinctly teaching my oldest daughter how to do a basic cipher - like direct substitution and she got it immediately. I also taught my son how to do pin bumping and pin counting/picking on locks with my lockpick set. I even bought him a transparent set of master locks to practice on and he would sit for an hour at the age of 4 picking those locks. The obvious downside now is that he knows how to get into everything!

Very cool to watch what are basic principals being applied at the very basic level.

Re: Conversations with a six-year-old on functional programming

#136

Post by jason_slack »

craftyguy wrote: post #134
jason_slack wrote: post #132

I'm taking a discrete math class right now. How is this read: \lambda x.\, x - 3 and what is a simple example? In a discrete math perhaps it is the same as "All x, x is an integer such that...."?

The '\lambda x' is just another way of saying "f(x)" So '\lambda x., x-3' --> 'f(x): x-3' Also, I really enjoyed my discrete math courses! The proofs were.. tedious.. but the amount and breadth of 'stuff' covered was excellent.

It is a difficult course! We are doing graph theory right now.

Re: Conversations with a six-year-old on functional programming

#137

Post by jimbokun »

ams6110 wrote: post #49
dyladan wrote: post #3

What is truly astounding about this is the patience to even attempt to explain free theorems to a 6 year old. Most parents would likely answer "math" and that would be the end of it. I don't (yet) have kids, but when I do I hope I have the wherewithal to recognize and take advantage of moments like these.

It's an immense amount of effort to do it consistently. And it gets harder with each kid, at least for me. One of the things you figure out is that some kids aren't interested. And if your kid isn't interested in thinking about prime numbers, you're going to be hard pressed to change that. Conversely they will have interests that you don't share, and it's going to be harder for you to participate meaningfully in that…

My teenage son is a musician and is taking AP Music Theory right now.

I ask him to tell me about what he is learning, and he patiently tries to explain it to me, but I just nod along because I have no idea what he's talking about.

Re: Conversations with a six-year-old on functional programming

#138

Post by _fq4v »

wahern wrote: post #90
heinrichhartman wrote: post #34

I had a somewhat similar encounter with a 4 year old (!), who blew me away with his ability to solve arithmetic puzzles: http://heinrichhartmann.com/blog/2016/06/12/Box-Counting-Ari... It's a great joy to work with such gifted young minds.

Such precociousness is often[1] an indicator of abnormalities and handicapped general intelligence. For example, if our son independently began to read too early the initial reaction of my spouse, a Speech-Language Pathologist, would be to freak out rather than to be filled with pride. Perhaps you know this and used "gifted" in its more euphemistic sense. In any event, I mention this not to correct you but to address…

I mean... honestly, understanding functions is not overly difficult. The only reason we don't expect children to understand them is because we don't teach it to them. On the other hand, we teach them bizarrely detailed and extensive algorithms for doing all sorts of computations on the rational numbers, and expect them to be able to do them perfectly.

Re: Conversations with a six-year-old on functional programming

#140

Post by tathougies »

mmirate wrote: post #75

Functions? Algebra? How is comprehending any of that, possible without the sort of abstract/counterfactual thinking that develops around age 12?

Uh... what? Counterfactual thinking develops well before the age of twelve. Kids that I know are asking 'what if' questions in pre-K and kindergarten. It's a natural thinking mechanism that children engage in all the time.
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