Re: 2button, 1op RPN calculator, again

I think it's pretty clear that *eml *is useless both for computation and as
a symbolic representation.

What are the axioms about *eml* that you need to prove that addition is
commutative and associative (working entirely in eml-world)?

Why are we beating this dead horse?

On Tue, May 5, 2026 at 1:23 PM Richard Fateman <[email protected]> wrote:

> This is just a curiosity.  I thought I'd point out its uselessness
> for encoding computation of scientific use.
>
> What is the precision and accuracy of eml?
>
> If it is not specified, it should be clear that it is useless.
>
>  If it is specified, then examples for which the result
> is arbitrarily incorrect can be devised.
>
> If eml were used (say) for plotting, the picture could be arbitrarily
> wrong.
>
> Maybe the original author addresses this?
> RJF
>
> On Tue, May 5, 2026 at 1:12 PM Stavros Macrakis <[email protected]>
> wrote:
>
>> It has to have some way of entering other inputs if you want to denote
>> anything but constants. Or maybe you pre-push the inputs onto the stack, in
>> general multiple instances of them so that they'll be available at the
>> right place.
>>
>> On Tue, May 5, 2026 at 12:14 PM Henry Baker <[email protected]> wrote:
>>
>>> I just realized that this calculator doesn't have any 'regular' buttons
>>> at all; the only 2 buttons are the parentheses '(' and ')'.
>>>
>>> The '(' button pushes '1' onto the stack; the ')' replaces the top 2
>>> elts of the stack with the single object eml(x,y), where x,y were the top
>>> two elements of the stack.
>>>
>>> Clearly '(' increments the stack length by 1, while ')' decrements the
>>> stack length by 1, so we have a *parenthesis language*, and only properly
>>> paired parentheses are allowed.
>>>
>>> The stack comes initialized with a single object '1', because *every*
>>> legal computation has to start with a push, and the only constant that can
>>> be pushed onto the stack is a '1', so we needn't bother with that first
>>> push instruction at all !
>>>
>>> The number of legal instruction sequences of length 2n is Catalan(n) =
>>> binomial(2*n,n)/(n+1).
>>>
>>> This means that the fraction of legal instruction sequences approaches
>>> zero as the length of the sequence grows, so the bit efficiency of ANY
>>> RPN-type representation isn't going to be particularly good.
>>>
>>>
>>>
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