Re: Epistemology 201: The Science of Science

From: Wolf Kirchmeir (wwolfkir_at_sympatico.ca)
Date: 03/13/05 

Date: Sun, 13 Mar 2005 11:42:25 -0500

Allan C Cybulskie wrote:
> "Wolf Kirchmeir" <wwolfkir@sympatico.ca> wrote in message
> news:TPjXd.11985$fW4.407771@news20.bellglobal.com...
>
>>Allan C Cybulskie wrote:
>>
>>>"Wolf Kirchmeir" <wwolfkir@sympatico.ca> wrote in message
>>
>>[...]
>>
>>>>What operations are different? Are you suggesting that you can/can't add
>>>>octals, etc? Or are you referring to the mechanics of carrying, etc?
>>>>Can't be the former, as it would be sheer nonsense. Must be the latter.
>>>
>>>
>>>I'm claiming that you add -- with the mechanics of carrying as one
>>>example -- the different bases differently. You cannot add a decimal
>
> and an
>
>>>octal using straight decimal addition.
>>
>>[...]
>>
>>That's true enough, but so what? The rules of manipulating the
>>characters representing the numbers represent addition. That's the only
>>way they make sense.
>
>
> The point was basically that you cannot simply do 15 decimal + 17 octal and
> get 32. That was all I was trying to say.

Yes, you could. You could also get 40 octal. An algorithm for doing so
is easy to specify, to whit: Transform each string into binary
representation of the number represented, add, transform the result into
octal and/or decimal representation. Isn't this transform - add -
transform algorithm how computers add decimal numbers?

Note that those addition operations you learned in primary school are
algorithms for maniuplating strings. That's all. (And IMO the reason
that most people find arithmetic so hard is that it is the manipulating
of strings, which is not as intuitive an operation as manipulating piles
of objects. But that's another issue.)

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