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Topic: Of Sequence and Success
Replies: 17   Last Post: Nov 4, 2012 11:22 PM

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kirby urner

Posts: 1,921
Registered: 11/29/05
Re: Of Sequence and Success
Posted: Nov 3, 2012 1:32 PM
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Consider this:

The "arithmetic" of this culture is all based in string operations,
meaning character strings (not string theory strings).

"aaa" ++ "bbb" -> "aaabbb"

Then they start writing functions like:

reverse [] = []
reverse (x:xs) = reverse xs ++ [x]

And that's algebra. (x:xs) cuts any string but an empty string []
into first character
and the rest.

reverse returns an empty string given an empty string, but otherwise (line 2)
concatenates the first character to the end of a reversed string.

Yes, a recursive definition.

Some kids get really good at concatenating (++) i.e. their arithmetic
is really fine.

But they're not good at writing functions.

The concatenate-only crowd are quite employable and are said to have
"business intelligence".

The function writers are said to "know algebra" and will be given
further training in mathematics.

Kirby


Note: [ ] is an empty list and an empty string because a string is
just a list of characters. (Yes, this is Haskell again, another math
notation, runs on machines).

On Sat, Nov 3, 2012 at 12:25 AM, Jonathan Crabtree
<sendtojonathan@yahoo.com.au> wrote:
> The Greeks were ok at geometry yet bad at arithmetic. I made my own times table the way Euclid, Pythagorus Nicomachus learned their's and it's very hard to learn.
>
> My guess is more people say the Indians via the Arabs gave us the foundation of modern math.




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