From mboxrd@z Thu Jan 1 00:00:00 1970 Received: (from majordomo@localhost) by pauillac.inria.fr (8.7.6/8.7.3) id CAA17615; Wed, 2 Jan 2002 02:47:46 +0100 (MET) X-Authentication-Warning: pauillac.inria.fr: majordomo set sender to owner-caml-list@pauillac.inria.fr using -f Received: from concorde.inria.fr (concorde.inria.fr [192.93.2.39]) by pauillac.inria.fr (8.7.6/8.7.3) with ESMTP id CAA17581 for ; Wed, 2 Jan 2002 02:47:45 +0100 (MET) Received: from sol.wwwnexus.com (sol.wwwnexus.com [209.150.128.86]) by concorde.inria.fr (8.11.1/8.11.1) with ESMTP id g021li521095 for ; Wed, 2 Jan 2002 02:47:44 +0100 (MET) Received: from developer1-2k.einfo.com (12-234-40-136.client.attbi.com [12.234.40.136]) by sol.wwwnexus.com (8.11.6/8.11.6) with ESMTP id g021les00498; Tue, 1 Jan 2002 19:47:40 -0600 Message-Id: <5.1.0.14.2.20020101173614.031c16c0@einfo.com> X-Sender: einfo@einfo.com X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Tue, 01 Jan 2002 17:53:30 -0800 To: Shannon --jj Behrens From: Byron Hale Subject: Re: [Caml-list] Kernel in OCAML using native compiler Cc: caml-list@inria.fr In-Reply-To: <20011231230117.90704.qmail@web10702.mail.yahoo.com> References: <5.1.0.14.2.20011231135432.02ec0b30@einfo.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: owner-caml-list@pauillac.inria.fr Precedence: bulk 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 ------------------- Bug reports: http://caml.inria.fr/bin/caml-bugs FAQ: http://caml.inria.fr/FAQ/ To unsubscribe, mail caml-list-request@inria.fr Archives: http://caml.inria.fr