From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/228 Path: news.gmane.org!not-for-mail From: Patrik Eklund Newsgroups: gmane.science.mathematics.categories Subject: RE: Monads Date: Mon, 6 Apr 2009 06:33:17 +0200 (MEST) Message-ID: Reply-To: Patrik Eklund NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=iso-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1239038549 8583 80.91.229.12 (6 Apr 2009 17:22:29 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 6 Apr 2009 17:22:29 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Mon Apr 06 19:23:47 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1LqsXu-0007lh-Cd for gsmc-categories@m.gmane.org; Mon, 06 Apr 2009 19:23:42 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LqrvV-0007gK-Bb for categories-list@mta.ca; Mon, 06 Apr 2009 13:44:01 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:228 Archived-At: [Note from moderator: this thread has strayed; although this post is allowed, comments closer to categories (not Kant's) are preferred.] Reference to Leibniz is nice, and so is going back even more in history.=20 Going forward into modern history leads to problems of who actually cause= d=20 what. Probably because we then tend to mix history and politics. Anyway, also having googled, I found this about Leibniz: =A7. 1. Die Monaden (Das Worte Monade oder Monas) wovon wir allhier reden= =20 werden / sind nichts anders als einfache Substanzen / woraus die zusammen= =20 gesetzten Dinge oder composita bestehen. Unter dem Wort / einfach /=20 verstehet man dasjenige / welches keine Teile hat. "sind nichts anders als einfache Substanzen" "is nothing but simple substances" They are, but it is not a mathematical statement. "woraus die zusammen gesetzten Dinge oder composita bestehen" "using which you put them together or compose(!) them together" Now he is cooking. Monad compositions are important. Leibniz and Beck=20 working together, I like it. This is closer to mathematics. "verstehet man dasjenige / welches keine Teile hat" "is to be understood as something which doesn't have subparts" I am sure there are non-trivial monads which are not composed (in Beck's=20 sense) by other non-trivial monads. But more interestingely, composed=20 monads are indeed monads, and even worse (from leibniz point of=20 view) submonads do exist, like the filter monad being submonad to the=20 ultrafilter monad (with the astonishing fact, yes, I know, I am repreatin= g=20 myself, that their respective algebras are Scott lattices and compact=20 Hausdorff spaces). So, basically I like Leibniz, even if he was wrong at this point. History= =20 is not easy. We say "Rome was destroyed" and we frequently say by the=20 goths. Saying that leads us to ask "how could it be destroyed". Seldom do= =20 we hear "how could it stay alive so long". Best, Patrik PS "Monas" seems mostly to be used for a sailing boat, the "Kiel", and=20 "the Mona" is Louvre in Paris.