Re: [Caml-list] Kernel in OCAML using native compiler

[Byron Hale <byron.hale@einfo.com>]

Yes, I do recall that. Birkhoff and Mac Lane, among others, discuss it. 
Perhaps he did something a bit different from what I thought. Or, perhaps 
it is a tragedy. The publisher was small and maybe his work was not 
properly reviewed. I just checked and his book title wasn't in my pocket 
computer.

It is also worth remembering that Minsky killed early research into neural 
networks. He proved, correctly, that a (single layer, as it turned out) NN 
could not execute an XOR instruction. His proof turned out to be almost 
irrelevant, because multi-layer NNs can perform XORs.

All sets taken together do not form a set. However, in VGB set theory, they 
do form a class and can be discussed as such. It just seems less nihilistic 
to me.

Thanks for reminding me.

Best,

Byron

At 03:01 PM 12/31/2001 -0800, you wrote:
> > By the way, a young Asian mathematics teacher claims
> > to have a trisection
> > construction for the triangle. So, apparently, it
> > wasn't completely
> > foolish, just not so easy.
>
>I hope you're joking!  Abstract Algebra was used to
>prove that the trisection construction for an angle
>was not impossible.  In the same way that you cannot
>get PI by adding or subtracting two integers, so also
>can you not trisect an angle using the standard
>straight edge and compass.
>
>-jj

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