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Topic: Non-Euclidean Arithmetic
Replies: 108   Last Post: Sep 13, 2012 3:39 PM

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kirby urner

Posts: 2,000
Registered: 11/29/05
Re: Non-Euclidean Arithmetic
Posted: Sep 6, 2012 7:13 PM
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On Wed, Sep 5, 2012 at 12:24 PM, Robert Hansen <bob@rsccore.com> wrote:

> 1. Is it appropriate to introduce multiplication to 8 year olds as repeated
> addition?
> 2. Is multiplication repeated addition?


<< snip >>

> Btw, the answers to those two questions are Yes and No respectively.
>
> Bob Hansen


I think your "No" answer to 2 could be misinterpreted. I think a
better answer would be "sometimes it is, yes".

In a way, that's the same as "no" as "sometimes" is not the same as "yes".

However, I don't see a need to claim there's some essential core
logical "thing" that multiplication "really is" across the board.

I would consider that an elementary mistake.

Talk of "family resemblance" might enter, i.e. we call both of these
operations "multiplication" because.... and then we talk about
similarities.

Multiplying two matrices, multiplying two complex numbers, multiplying
two integers.... these have similarities but they're not all pointing
to some abstract Platonic "idea of multiplication" that's is the
essence of all three. Or at least I see no need for such overhead /
fantasies.

In many notations, the multiplication operator is exactly what's used
to get repetition of any string, such as "#".

print(20 * "#") results in "####################" which "#" + "#" =
"##" (concatenation). In this language game, I'd say multiplication
very definitely is repeated addition.

Kirby


Date Subject Author
9/1/12
Read Non-Euclidean Arithmetic
Jonathan Crabtree
9/1/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/2/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/3/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/3/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/3/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/4/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/4/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/4/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/5/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/5/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/6/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/1/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/1/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/1/12
Read Re: Non-Euclidean Arithmetic
Wayne Bishop
9/1/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/2/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/3/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/3/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/5/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/3/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/3/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/5/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/3/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/3/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/4/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/5/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/5/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/5/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/5/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/5/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/5/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/5/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/5/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/5/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/6/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/8/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/7/12
Read Re: Non-Euclidean Arithmetic
Jonathan Crabtree
9/8/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/8/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/10/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/10/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/10/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/10/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/10/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/8/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/8/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/8/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/8/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/8/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/8/12
Read Re: Non-Euclidean Arithmetic
Jonathan Crabtree
9/9/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/8/12
Read Re: Non-Euclidean Arithmetic
Clyde Greeno @ MALEI
9/8/12
Read Re: Non-Euclidean Arithmetic
Jonathan Crabtree
9/8/12
Read Re: Non-Euclidean Arithmetic
Jonathan Crabtree
9/8/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/8/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/9/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/9/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/9/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/9/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/9/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/9/12
Read Re: Non-Euclidean Arithmetic
Robert Hansen
9/10/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/10/12
Read Re: Non-Euclidean Arithmetic
Wayne Bishop
9/10/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/9/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/10/12
Read Re: Non-Euclidean Arithmetic
Clyde Greeno @ MALEI
9/9/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/9/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/9/12
Read Re: Non-Euclidean Arithmetic
Wayne Bishop
9/9/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/10/12
Read Re: Non-Euclidean Arithmetic
Wayne Bishop
9/10/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/9/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/9/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/10/12
Read Re: Non-Euclidean Arithmetic
Clyde Greeno @ MALEI
9/10/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/10/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/10/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/10/12
Read Re: Non-Euclidean Arithmetic
Clyde Greeno @ MALEI
9/10/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/11/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/11/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/11/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/11/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/11/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/11/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/11/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/13/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/13/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/13/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/11/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/11/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/11/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/11/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/11/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/11/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/11/12
Read Re: Non-Euclidean Arithmetic
israeliteknight
9/11/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/11/12
Read Re: Non-Euclidean Arithmetic
Jonathan Crabtree

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