tag:blogger.com,1999:blog-74465942014-04-22T03:19:24.296-07:00Bob WaltersRobert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.comBlogger203125tag:blogger.com,1999:blog-7446594.post-68579282577415712802014-04-22T03:14:00.003-07:002014-04-22T03:19:24.327-07:00On the algebra of processesThe following is an abstract submitted to a conference (only half a page was permitted). I would like expand a little here on the matter in the next day or so.<br /><br />--------------------------------------------<br />Abstract: On the algebra of processes<br /><br />Process algebras were introduced by Hoare, Milner and Bergstra-Klop to extend the theory of sequential computation to include parallel and concurrent computation. The basic idea of Milner was to add a parallel operation symbol to the successful algebra of Kleene of regular languages. Notice that Kleene's algebra is an algebra of behaviours rather than of programs/automata/machines. Milner's algebra inherits that fact, and is more concerned with observation of systems rather than systems themselves.<br /><br />In 1997 Katis, Sabadini and I proposed the category Span(Graph) as a parallel algebra of automata, and (in 2000) Cospan(Graph) as the associated sequential algebra. The ideas were successively developed with collaborators, including R. Rosebrugh. In 2004 at the meeting in Vancouver I proposed with Sabadini the more abstract notion of a process (in a topos <b>C</b>) with parallel and sequential interfaces, namely an object G together with four objects A, B, X, Y and four arrows d0:G->X, d1: G->Y, g0:A->G , g1:B->G. Such a diagram may be regarded as a span of cospans or a cospan of spans. It exists as an arrow in two monoidal categories: Span((A+B)\<b>C</b>) (with parallel operations), and Cospan(<b>C</b>/(XxY)) (with sequential operations). Both of these categories have commutative Frobenius structures on the objects. Processes may be combined in parallel in the first category and in sequence in the second. Alternating these operations leads to hierarchical systems.<br /><br />We will describe recent developments including distributive laws between the parallel and sequential operations, which permit the flattening of hierarchy. In fact, the combined algebra forms a kind of <i>ring</i> of processes.<br />-------------------------------------Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-65185669256453291842014-04-20T00:11:00.002-07:002014-04-20T00:12:20.588-07:00Villa Carlotta, Lake ComoTo visit in late April.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-_1nnbw8jmoc/U1Nydfi4pEI/AAAAAAAABnk/9iSsph2fogI/s1600/2014-04-18+15.32.24.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-_1nnbw8jmoc/U1Nydfi4pEI/AAAAAAAABnk/9iSsph2fogI/s1600/2014-04-18+15.32.24.jpg" height="320" width="240" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-LzNVoe34B6Q/U1Nyg6EF4sI/AAAAAAAABnw/jC4tM1rHvco/s1600/2014-04-18+16.14.58.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-LzNVoe34B6Q/U1Nyg6EF4sI/AAAAAAAABnw/jC4tM1rHvco/s1600/2014-04-18+16.14.58.jpg" height="320" width="240" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-Pg5-YNVaLL0/U1NydJk-2nI/AAAAAAAABng/cAorwcabalc/s1600/2014-04-18+16.16.08.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-Pg5-YNVaLL0/U1NydJk-2nI/AAAAAAAABng/cAorwcabalc/s1600/2014-04-18+16.16.08.jpg" height="320" width="240" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-g4ZA9poEUJk/U1NyvRvRwrI/AAAAAAAABn4/FrCD7MOYleQ/s1600/2014-04-18+16.17.29.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-g4ZA9poEUJk/U1NyvRvRwrI/AAAAAAAABn4/FrCD7MOYleQ/s1600/2014-04-18+16.17.29.jpg" height="320" width="240" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-o4neaW5RvTs/U1NyxxsxnrI/AAAAAAAABoA/MUSPMlriv3o/s1600/2014-04-18+16.23.01.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-o4neaW5RvTs/U1NyxxsxnrI/AAAAAAAABoA/MUSPMlriv3o/s1600/2014-04-18+16.23.01.jpg" height="240" width="320" /></a></div><br />Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-90943028379593822522014-04-14T08:00:00.002-07:002014-04-15T03:56:00.314-07:00How to coil a hoseI just bought a hose to water the newly planted roses at our mountain house. Here is one Nicoletta planted last year:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-3kbR7zumXNo/U0vsfFKDzgI/AAAAAAAABk0/pZzgq3mzdas/s1600/2013-06-23+19.26.41.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-3kbR7zumXNo/U0vsfFKDzgI/AAAAAAAABk0/pZzgq3mzdas/s1600/2013-06-23+19.26.41.jpg" height="240" width="320" /></a></div><a name='more'></a><br /><div class="separator" style="clear: both; text-align: left;"></div><a href="https://www.blogger.com/null" name="more"></a>The hose came rolled so:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-ebDvcDXoalc/U0vyt9t1K0I/AAAAAAAABlE/Hxc61J6quT0/s1600/2014-04-14+16.32.12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-ebDvcDXoalc/U0vyt9t1K0I/AAAAAAAABlE/Hxc61J6quT0/s1600/2014-04-14+16.32.12.png" height="150" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">After unrolling it looked like this:</div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-lwdo3wrvtj0/U0zzCQALNLI/AAAAAAAABm8/zkkFNtMpcjE/s1600/2014-04-15+09.56.44.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-lwdo3wrvtj0/U0zzCQALNLI/AAAAAAAABm8/zkkFNtMpcjE/s1600/2014-04-15+09.56.44.png" height="117" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">and no water issued. This is a well-known problem in <a href="http://en.wikipedia.org/wiki/Mountaineer's_coil">mountaineering</a>, sailing, in the <a href="http://en.wikipedia.org/wiki/Over/under_cable_coiling">storing of electrical cables</a> etc.</div><div class="separator" style="clear: both; text-align: left;">They recommend that you coil rope/hoses/cables either like:</div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-EuGIkwFrkWA/U0v6hI9s0bI/AAAAAAAABls/EjvQgZcDAXw/s1600/2014-04-14+17.08.49.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-EuGIkwFrkWA/U0v6hI9s0bI/AAAAAAAABls/EjvQgZcDAXw/s1600/2014-04-14+17.08.49.png" height="128" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: left;">or like this:</div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-BBVtZg5zcKY/U0v0KQQh-II/AAAAAAAABlc/NvoKLKGTMhU/s1600/2014-04-14+16.31.23.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-BBVtZg5zcKY/U0v0KQQh-II/AAAAAAAABlc/NvoKLKGTMhU/s1600/2014-04-14+16.31.23.png" height="202" width="320" /></a>.</div><div class="separator" style="clear: both; text-align: left;">A simple calculation in the braided monoidal category of tangles shows that these expressions are equal to the identity braid (whereas the expression of the first is the composite of 2n twists).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">You may have noticed that I have not blogged for months. That is because the family has had a sequence of serious illnesses over the last two years. The last was the most stressful.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I hope we are back to a period of tranquility.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://lh3.ggpht.com/-E-_TI05FAWU/U0zca-o_VLI/AAAAAAAABmo/Ebbg33K1xwA/s1600/2014-04-15%25252008.42.05.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> </a> </div>Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-65775192272344085922013-12-11T00:52:00.001-08:002013-12-11T01:37:17.974-08:00Old posts: Max Kelly 2007With the closing of our offices in via Carloni the <a href="http://dscpi.uninsubria.it/">web server</a> of the old department was offline for a time and I suspect will not be reliable in future. I have decided to transfer material from the server to this blog or to the <a href="http://comocategoryarchive.com/Archive/">Como Category Archive</a>. <br />The first item is a post made when Max Kelly died in 2007.<br /><br /><a name='more'></a><br /><br />---------------------------------------<br />Max Kelly died on the 26th January 2007. I have known Max since, as a graduate student in Canberra of Bernhard and Hanna Neumann, I travelled to Sydney to see him one day about my developing interest in Category Theory. It must have been 1968.<br /><br />After I returned from Chicago in 1970 to a position at the University of Sydney, I attended with Don Cartwright a course of Max's at the University of New South Wales and then in 1971 Max went on leave, Ross came to Macquarie, we started the Category Seminar. The seminar, first called the Sydney Category Seminar, and now the Australian Category Seminar, with Max and Ross, and with the visitors who came, and the students, was the basis of my research life. I had many struggles with Max over the years. I am very pleased that at the end we were writing a paper together with Richard Wood and Aurelio Carboni. <br /><br />I was deeply saddened by his death. <br /><br />I include some of the letters written to the Categories mailing list after his death was announced. <br />-----------------------------------------------<br />From: Bill Lawvere <br />To: categories@mta.ca <br />Date: sabato 27 gennaio 2007 16.31.58 <br /><br />I am deeply saddened by the loss of Max. In our field he was a rock of reliability and a fountain of imagination. I will miss my lively, warm, kind, and sometimes mischievous friend. <br /><br />Bill Lawvere <br />---------------------------------------------<br />From: Eduardo J. Dubuc <br />To: categories@mta.ca <br />Date: domenica 28 gennaio 2007 17.39.02 <br /><br />I am deeply saddened by the death of Max Kelly. When I saw the subject in Ross posting, and before opening the message, my heart already felt anguish. I am more saddened with his loss that what I have been by the loss of any other member of our category theory community. In fact, I loved Max. I admired his courage, his independence of thought, his lack of hypocrisy, and I loved him simply by the way he was. I am proud that he considered me his friend. For me, our community is not the same without Max. <br />--------------------------------------------<br />From: Richard Wood <br />To: categories@mta.ca <br />Date: lunedì 29 gennaio 2007 21.11.43 <br /><br />Max Kelly, a master of coherence <br /><br />We would like to add to Bill and Eduardo's letters also our feelings of deep sadness at Max's death. <br /><br />Max Kelly's Last Work <br />===================== <br /><br />In due course Max's last work will appear in a four-author paper. While it is not usual for coauthors to divulge who contributed what to a paper the present circumstances seem to warrant such, as an appreciation of Max's extraordinary talents and tenacity. Carboni, Kelly, Walters, and Wood, [CKWW] have for some time been extending the Carboni and Walters notion of `cartesian bicategory' to the general case of bicategories that are not necessarily locally ordered. <br /><br />A cartesian bicategory B ultimately has a tensor product, a pseudofunctor *:BxB--->B that is naively associative and unitary. It is natural to ask whether such (B,*) is a monoidal bicategory, in other words a one-object tricategory in the sense of [Coherence for Tricategories; Gordon, Power, and Street]=[GPS]. Early in 2005 [CKWW] had shown that _if_ a bicategory A with finite `products' -x- and 1, in the bilimit sense, has (A,x) a monoidal bicategory then a cartesian bicategory B has (B,*) monoidal. In the course of polishing the paper it came to Max's attention that nobody had _proved_ the <br /><br />Theorem: A bicategory with finite products is monoidal.<br /><br />Nobody doubted the truth of this. In fact, experts in higher dimensional category theory said that if it were not true then the definition of tricategory is wrong! But when you consider the rather large amount of data that must be assembled and the many equations (some merely implicit in words such as pseudonatural and modification) that must be verified from the apparently rather weak universal property of finite products in the bilimit sense, it seemed like a rather thankless task to write out the details. <br /><br />This was to Max a completely unacceptable state of affairs. If nobody doubts the statement then it must be possible to find a good proof! Now Max had no intention of redrawing any of the diagrams in [GPS]. <br /><br />For the last few years Max, with little central vision left as a result of macular degeneration, has been doing Mathematics using an 8-fold magnification monitor. This allowed him to see only a few square centimetres of a page at a time. Many [GPS] diagrams consume an entire page. His proof, that we were privileged to receive in the last few weeks, has _no_ diagrams (though doubtless we will incorporate a few in a publishable version of the paper). Max attributed the key idea in his proof to Ross Street. <br /><br />Briefly, this is how it goes: For X a finite family of objects in the bicategory A, write A(X) for the bicategory of product cones over X. Thus an object of A(X) consists of an object b of A, together with a family of arrows p_i:b--->X_i, such that for all a, the induced functor A(a,b)--->Pi A(a,X_i) is an equivalence of categories. <br />Lemma: !:A(X)--->1 is a biequivalence <br />(Recall that to say B--->1 is a biequivalence is to say that: i) there is an object b in B ii) for any objects c and d in B, there is an arrow f:c--->d iii) for any arrows g,h:c--->d in B, there is a unique 2-cell g--->h. It follows that in a bicategory biequivalent to 1, every arrow is an equivalence and every 2-cell is an isomorphism.) <br /><br />Next, Max observes that if A has finite products then, for any B, the bicategory [B,A] of pseudofunctors, pseudonatural transformations, and modifications also has finite products, given `pointwise' by the products of A. -x- is an object of [A^2,A]. <br />We can use (a x b) x c and a x (b x c) as names for objects in [A^3,A] and applying the Lemma to [A^3,A](a,b,c) deduce the existence of the associator equivalence, pseudonatural in a,b, and c. The associator gives rise to two arrows (abbreviating somewhat) ((ab)c)d ===> a(b(cd)) in [A^4,A](a,b,c,d) and between these we have a unique invertible modification, the pi of [GPS]. <br />The coherence of pi is chiefly the Stasheff non-abelian 4-cocycle condition (again see [GPS]) and for this we need only apply the Lemma to [A^5,A](a,b,c,d,e) to see that the two modifications in question are equal. Of course the other data and equations are handled with similar appeals to the Lemma. <br /><br />Max was not content to stop here. In his last few days he had been learning the rather subtle definition of _symmetric_ monoidal bicategory and constructed the requisite braiding equivalence and syllepsis isomorphism for a bicategory with finite products. Everything follows from the universal property but Max has shown us _how_ so that we can calculate with these things. His insights show us the way to deal with coherence issues arising from birepresentability generally and weak n-representability when the need arises. <br /><br />Max's personal copy of [GPS] was autographed by Ross with the words ``To Max Kelly, a master of coherence''. Yes, he was. <br /><br />Aurelio Carboni, Robert Walters, and Richard Wood <br />------------------------------------------<br />From: George Janelidze <br />To: categories@mta.ca<br />Date: lunedì 29 gennaio 2007 12.15.06 <br /><br />Gregory Maxwell Kelly was one of the great mathematicians of our time, so perfect in his research and vision of mathematics, and in every aspect of academic life. <br /><br />And he was so exceptionally kind to everyone. It is hard to imagine that Max is not with us anymore, and it is a great pain for his family and for all of us, his friends and colleagues... <br /><br />George Janelidze <br />---------------------------------------------<br />From: Andre Joyal <br />To: categories@mta.ca <br />Date: mercoledì 31 gennaio 2007 21.17.42 <br /><br />Letter to Max Dear Max, I feel deeply sad that you have left. Now that you are gone, I realise how much you mean to me.<br /><br />I regret not telling you that.<br /><br />I wish to repair that by writing you this letter. If I send it to Imogen and to your friends, it will reach you in some way. <br /><br />Your work has been a constant source of inspiration for me. It combines beauty, rigor and depth. It is fundamental, I use it every day. It will last forever. You were a great mathematician. <br /><br />I also want to thank you for inviting me to Australia. I did some of my best work there. You were a great host. I made many friends. <br /><br />I wish we could meet again. <br /><br />I will talk with you in my dreams. <br /><br />Yours, Andre<br />---------------------------------------Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-41748202623876722072013-12-11T00:07:00.000-08:002013-12-11T00:09:12.476-08:00Tributes to Aurelio CarboniI have placed in the Como Category Archive some <a href="http://comocategoryarchive.com/Archive/conferences/aurelio-carboni/tributes/">articles</a> about Aurelio Carboni, which are based on lectures given at the <a href="http://math.unipa.it/metere/Aurelio2013/index.html">conference in memory of Aurelio</a>, June 2013, in Milan. They will be appearing in a volume of the journal Protagora, edited by Fabio Minazzi of the University of Insubria, Varese.Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-39438128472961952642013-11-28T06:24:00.000-08:002013-11-28T06:31:42.284-08:00Last days IIAs I mentioned in an earlier post, my last days as professor at the University of Insubria, Como, were complicated by a sudden change of office. I don't remember whether I mentioned that I also had to complete a course on security obligatory for all teachers and staff of the university, the final date of which was my last working day. Although not relevant for me since I have no duties regarding safety in the university after my retirement I was afraid there might be legal consequences if I did not complete the course as specified.<br /><br />I thought these complications were an aspect of Italian life, but I see now similar problems occur in England. In Peter Cameron's blog he<a href="http://cameroncounts.wordpress.com/2013/11/25/moving-out/"> racounts</a> being removed from his office, and losing his status as a lecturer before his course ended. He had my problem of what to do with all the books and papers.<br /><br />(When I decided to leave the University of Sydney in 1998 I was careful not to tell anyone about it till the last moment exactly for fear of being regarded prematurely redundant.)Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com1tag:blogger.com,1999:blog-7446594.post-61381423676129286632013-11-26T04:23:00.001-08:002013-11-26T12:51:15.094-08:00A walk near LeccoA few days ago I was going to write a post about how depressing I find November with its lack of light. Today however we went for a walk along the Adda in delightful weather. Here are some photographs made with my phone:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-jXeAjrOW7_k/UpSRobg4weI/AAAAAAAABgE/_hcHAwiq63Y/s1600/2013-11-26+08.48.12.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://4.bp.blogspot.com/-jXeAjrOW7_k/UpSRobg4weI/AAAAAAAABgE/_hcHAwiq63Y/s320/2013-11-26+08.48.12.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">The next photograph has Grigna in the background.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-eQWJmNLAmSo/UpSR4jHLcBI/AAAAAAAABgM/W7QxPOs-IyY/s1600/2013-11-26+08.53.10.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://1.bp.blogspot.com/-eQWJmNLAmSo/UpSR4jHLcBI/AAAAAAAABgM/W7QxPOs-IyY/s320/2013-11-26+08.53.10.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">In the centre background of the next is Resegone:</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-9wNiznBzGNQ/UpSSYR1NPRI/AAAAAAAABgU/h7uLi73UxNc/s1600/2013-11-26+09.20.53.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://3.bp.blogspot.com/-9wNiznBzGNQ/UpSSYR1NPRI/AAAAAAAABgU/h7uLi73UxNc/s320/2013-11-26+09.20.53.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Another photograph of Grigna with Lago di Olginate in the foreground:</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-RT7Dxm9K1X4/UpSSqr0dMtI/AAAAAAAABgc/NySlCh-uUOU/s1600/2013-11-26+09.40.27.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-RT7Dxm9K1X4/UpSSqr0dMtI/AAAAAAAABgc/NySlCh-uUOU/s320/2013-11-26+09.40.27.jpg" width="240" /></a></div><div class="separator" style="clear: both; text-align: left;">A last photograph of Grigna and Resegone (with swan):</div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-DhabtYRSNrY/UpUJh_rRUxI/AAAAAAAABgs/zSgafVZjSUw/s1600/2013-11-26+09.20.43.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://4.bp.blogspot.com/-DhabtYRSNrY/UpUJh_rRUxI/AAAAAAAABgs/zSgafVZjSUw/s320/2013-11-26+09.20.43.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><br /><br /><br />Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-77702926508166824122013-10-17T08:21:00.001-07:002013-11-02T11:16:59.416-07:00Yoneda Structures<div dir="ltr">Going through my papers I found notes of a lecture I gave on Yoneda Structures in December 1971, at a meeting (13-17 December) at the University of New South Wales while Peter Freyd was visiting. A pdf file may be had by following <a href="https://dl.dropboxusercontent.com/u/92056191/Archive/temporary_new_material/yoneda.pdf">this link</a>.</div>Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-35010262747492601432013-10-25T20:56:00.001-07:002013-11-02T01:51:05.961-07:00Sydney Mathematics Department <div class="separator" style="clear: both; text-align: left;">Below is a list found amongst my papers of staff and students of the University of Sydney Mathematics Department from 1935 till 1968, the period in which T.G. Room was professor. You may notice that in one year Ross Street, Brian Day and Vaughan Pratt were students together. A little earlier Graeme Segal was a student. Max Kelly was on the staff, and had been a student earlier. I miss out in two ways: before 1935 my great uncle Horatio Scott Carslaw was Professor for many years, and in 1970 I joined the staff. I think the list was compiled by Sam Conlon.</div><a name='more'></a><br /><div style="text-align: center;"><br /></div><div align="center" dir="ltr"><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-dA4mUdreSww/Umu_Cu6G5-I/AAAAAAAABeo/Dz7Ja9anZdg/s1600/2013-10-25+11.27.03.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://3.bp.blogspot.com/-dA4mUdreSww/Umu_Cu6G5-I/AAAAAAAABeo/Dz7Ja9anZdg/s200/2013-10-25+11.27.03.png" width="121" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-56-voiwEmz0/UmyunHc_jZI/AAAAAAAABe4/vFzxBUveG7U/s1600/2013-10-25+21.29.29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://4.bp.blogspot.com/-56-voiwEmz0/UmyunHc_jZI/AAAAAAAABe4/vFzxBUveG7U/s200/2013-10-25+21.29.29.png" width="133" /></a></div><a href="http://1.bp.blogspot.com/-zw19g3DZuUw/Ums8dXc8RoI/AAAAAAAABdY/w7pa8MboWqA/s1600/2013-10-25+12.29.15.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://1.bp.blogspot.com/-zw19g3DZuUw/Ums8dXc8RoI/AAAAAAAABdY/w7pa8MboWqA/s200/2013-10-25+12.29.15.png" width="130" /></a><a href="http://4.bp.blogspot.com/--clAdN5d2V0/Ums8pO3HEeI/AAAAAAAABdg/0IJaKnyGnVA/s1600/2013-10-25+21.29.29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-65CJ7DTj_qg/Ums80BBz3WI/AAAAAAAABdo/Qj2E99p87MA/s1600/2013-10-25+21.31.51.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://3.bp.blogspot.com/-65CJ7DTj_qg/Ums80BBz3WI/AAAAAAAABdo/Qj2E99p87MA/s200/2013-10-25+21.31.51.png" width="119" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-Ue975Apa7uU/Ums8-s2Mz3I/AAAAAAAABdw/pl9MXcTW9jY/s1600/2013-10-25+21.33.12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://2.bp.blogspot.com/-Ue975Apa7uU/Ums8-s2Mz3I/AAAAAAAABdw/pl9MXcTW9jY/s200/2013-10-25+21.33.12.png" width="133" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-wRDj-NYQsbo/Ums9K3hSdDI/AAAAAAAABd4/_M-y9VfCj4o/s1600/2013-10-25+21.34.26.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://1.bp.blogspot.com/-wRDj-NYQsbo/Ums9K3hSdDI/AAAAAAAABd4/_M-y9VfCj4o/s200/2013-10-25+21.34.26.png" width="125" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-zhZD9zlFvKA/Ums9WHeI9nI/AAAAAAAABeA/ffJVOMu9HdM/s1600/2013-10-25+21.35.29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://2.bp.blogspot.com/-zhZD9zlFvKA/Ums9WHeI9nI/AAAAAAAABeA/ffJVOMu9HdM/s200/2013-10-25+21.35.29.png" width="135" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div dir="ltr"><br /></div>Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-23181442265933941652013-10-31T10:03:00.001-07:002013-10-31T10:15:05.800-07:00Castiglione Olona<div dir="ltr">We go frequently to Varese but last Saturday I visited for the first time the beautiful mediaeval village of Castiglone Olona, a few kilometers from the centre of Varese. Here is a detail of frescoes by Masolino in the battistero of the Collegiata church (taken before I realized that taking photographs was forbidden)</div><div class="separator" style="clear: both; text-align: center;"> </div><div class="separator" style="clear: both; text-align: center;"><a href="http://lh4.ggpht.com/-rHfj2oP2sTc/UnKNQkRPEfI/AAAAAAAABfQ/H90nV6LMjL8/s1600/20131026_102822.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="http://lh4.ggpht.com/-rHfj2oP2sTc/UnKNQkRPEfI/AAAAAAAABfQ/H90nV6LMjL8/s200/20131026_102822.jpg" width="200" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">On a different matter, I used to accommodate guests at a beautiful ex-monastery in Calolzio-Corte until I discovered that some were allergic to bells.</div><div class="separator" style="clear: both; text-align: left;"> </div>Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-29021522466854080242013-10-16T11:00:00.001-07:002013-10-26T13:42:59.685-07:00Como has chosen: it wants to be a university city<div dir="ltr">Yesterday the Provincia di Como had this photograph on the front page:</div><div class="separator" style="clear: both; text-align: center;"><a href="http://lh5.ggpht.com/-WSRKPZIEUYg/Ul681KQSzEI/AAAAAAAABc0/y86gCgWkvdo/s1600/Screenshot_2013-10-16-18-16-27-1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"> <img border="0" height="204" src="http://lh5.ggpht.com/-WSRKPZIEUYg/Ul681KQSzEI/AAAAAAAABc0/y86gCgWkvdo/s320/Screenshot_2013-10-16-18-16-27-1.png" width="320" /> </a> </div><div class="separator" style="clear: both; text-align: left;">I thought I had been teaching at a university in Como for 15 years. </div>Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-45344643812177393792013-10-13T04:48:00.001-07:002013-10-13T04:53:00.088-07:00Last daysI've mentioned before that I am retiring as professor at the University of Insubria, Como at the end of this month. I thought my last days would be tranquil, an opportunity to put my papers in order.<br /><br /><a name='more'></a>Not so. The university is closing the building in which we have offices. We heard rumours of this I think at the beginning of September but no official communication until a brief letter from the Rector on the 18th of September. This was reassuring because it said we would be leaving the building by (entro) December 2013 (though others of us had a deadline of 30th September).<br /><br />On Friday Patrizia came to collect Aurelio Carboni's papers. We discovered they had been removed from his locked room and placed in an unlocked storeroom next to the parking area where anyone could remove them. So I did.<br /><br />But we also discovered (rumour only) that next week there will be workmen knocking down walls, and repainting our offices, before which clearly all our papers must be removed. No official notice and no indication of new offices. Judging by Patrizia's experience it seems likely my last days at Insubria will be anything but tranquil.Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-38291570024759131912013-10-02T09:35:00.002-07:002013-10-02T10:09:44.135-07:00Interview with Bill Lawvere by Felice Cardone 2000Going through my papers I found this mail-interview by Felice Cardone of Bill Lawvere made in 2000, on the role of cartesian closed categories in foundations. The interview contains important historical information and is particularly relevant today to developments in type theory. For the pdf file click this <a href="https://dl.dropboxusercontent.com/u/92056191/Archive/temporary_new_material/lawvere-cardone-2000.html">link</a>.Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-44214735719866759232013-09-29T01:06:00.001-07:002013-09-29T23:58:43.936-07:00On Topos TheoryI hesitate to write about Topos Theory since I am not an expert in this area. However it seems to me a subject of great importance which is being presented in a distorted fashion of late.<br /><br />Grothendieck introduced toposes as a notion both of space and of categories of space, a notion which permits spatial intuition to be applied to widely different parts of mathematics. It is a huge conceptual advance on Hausdorff's notion of topological space.<br /><br />Lawvere and Tierney extracted elementary axioms of toposes which also served as an algebra of higher-order predicate logic, as boolean algebras are an algebra of propositional logic through Lawvere's discovery that both higher-order and quantifiers arise as adjoints.<br /><br />Grothendieck's work lead, for example, to Deligne's proof of the Weil conjectures used in such concrete results as Zhang's theorem on gaps in the primes.<br /><br />Lawvere and Tierney's work lead to a revolution in logic, but also to the possibility of a further development of Grothendieck's notion of space for teaching and progress in geometry.<br /><br /><a name='more'></a><br /><br />I mention now three developments which seem to miss the point of the great conceptual development introduced by Grothendieck.<br /><br />Such projects as<a href="http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes"> polymath8</a>, attempting to extract the best possible constants in Zhang's Theorem, instead of taking advantage of the conceptual progress of topos theory, seek to eliminate it from applications by special arguments.<br /><br />Another recent claim is that by concentrating on the axiomatic method in developing topos theory there have been a very limited number of applications in concrete mathematics, and that it would be better to use toposes as a tool to study relations between sites.<br /><br />A third current opinion strongly supported is that topos theory should be supplanted by infinity-topos theory.<br /><br /><br /><br />(This is how I understand the situation. I have not worked directly on applications of topos theory, though I have used various of the exactness properties in my research into the foundations of computer science. I have done a little work on the abstract theory of toposes, the introduction of lex total categories with Ross Street - see the earlier<a href="http://rfcwalters.blogspot.it/2013/09/isle-of-thorns-1976.html"> post</a> about the Isle of Thorns 1976 - and the characterization of relations in an elementary topos with Aurelio Carboni.)<br /><br /><br /><br /><br /><br /><br />Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-71951879070905476892013-09-26T04:25:00.002-07:002013-09-29T00:37:31.490-07:00Ross Street's OrientalsI recently had a look at one of Jacob Lurie's expositions (in 111 pages) on<a href="http://www.math.harvard.edu/~lurie/papers/cobordism.pdf"> the clasification of topological field theories</a> - very briefly and with little comprehension. I find it difficult to read mathematics in which not even formal definitions are given: Lurie himself says "In many instances, we have not attempted to give precise definitions, let alone careful proofs".<br /><br />I have always been interested in lower category theory (up to symmetric monoidal bicategories) but only once have ventured beyond. Always we had the idea that natural transformations were like homotopies, and that one could consider homotopies between homotopies and so on, and so one would get higher categories. Thinking about axiomatizing higher categories, in particular higher associative laws lead Ross Street to considering the free n-category on an n-simplex. Mike Johnson and I also worked on this problem.<br /><br />Following this<a href="https://dl.dropboxusercontent.com/u/92056191/Archive/temporary_new_material/Orientals.html"> link</a> there is an early picture produced by Ross of an oriental.<br /><br /><br />This seems to me still an interesting problem but I don't see where it has gone in Joyal and Lurie's work.<br /><br />In any case infinity-category theory seems to be a distinct subject from category theory. Category theory should resist the attempted takeover.Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-49167576483183536412013-09-21T05:22:00.000-07:002013-09-23T08:04:52.735-07:00Isle of Thorns 1976<div class="separator" style="clear: both; text-align: center;">The rest of the abstracts will be put shortly on the<a href="https://dl.dropboxusercontent.com/u/92056191/Archive/temporary_new_material/Isle-of-Thorns-1976.pdf"> Como Category Theory Archive</a>.<a href="http://lh3.ggpht.com/-s9DKv6QDjww/Uj2OuuDDkiI/AAAAAAAABcI/leyKI4LgtEg/s1600/2013-09-21%25252014.11.01.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://lh3.ggpht.com/-s9DKv6QDjww/Uj2OuuDDkiI/AAAAAAAABcI/leyKI4LgtEg/s320/2013-09-21%25252014.11.01.png" width="240" /></a></div><a href="http://www.blogger.com/null" name="more"></a><a href="http://lh3.ggpht.com/-s9DKv6QDjww/Uj2OuuDDkiI/AAAAAAAABcI/leyKI4LgtEg/s1600/2013-09-21%25252014.11.01.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> </a> <br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://lh5.ggpht.com/-9WkMRNFhs4c/Uj3Ix06Iv2I/AAAAAAAABcg/4pNQGbvwCzk/s1600/2013-09-21%25252018.23.05.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> <img border="0" height="240" src="http://lh5.ggpht.com/-9WkMRNFhs4c/Uj3Ix06Iv2I/AAAAAAAABcg/4pNQGbvwCzk/s320/2013-09-21%25252018.23.05.png" width="320" /> </a> </div>Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-30681991185853351992013-08-27T01:31:00.002-07:002013-09-23T07:07:23.028-07:00Gavia PassA photograph taken by my daughter of the lake (Lago Bianco) at Gavia Pass:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-xpTzNtMm5vo/Uhxj8HORo3I/AAAAAAAABa8/XFSLMWiWBKw/s1600/2013-08-25+21.01.12.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="http://4.bp.blogspot.com/-xpTzNtMm5vo/Uhxj8HORo3I/AAAAAAAABa8/XFSLMWiWBKw/s320/2013-08-25+21.01.12.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">I think a part of the Forni glacier is visible.</div><div class="separator" style="clear: both; text-align: left;"></div><a name='more'></a><br /><br /><div class="separator" style="clear: both; text-align: left;"><b>Later:</b> I realize that, as an Australian, I have not thought clearly about the definition of glacier. The glacier you see in the picture is probably the Dosegu glacier. If a glacier is the abstraction of water flow over the landscape (as I described a river in the last post about the Black Forest) the extent of the glacier is all that ice which flows together to a stream. The Forni glacier flows into the Frodolfo whereas the ice you see flows first into the Gavia which then joins the Frodolfo, a tributary of the Adda, which is itself a tributary of the Po.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><br />Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-16489473634039085722013-09-21T04:23:00.000-07:002013-09-21T04:23:15.335-07:00As others see us<div dir="ltr">Here a drawing by some students in Milan, before the moustache became white:</div><div class="separator" style="clear: both; text-align: center;"><a href="http://lh4.ggpht.com/-VpqVxPftbKg/Uj1mc9lPkDI/AAAAAAAABb4/Nk9Ysfd3DWA/s1600/2013-09-21%25252011.08.06.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> <img border="0" height="307" src="http://lh4.ggpht.com/-VpqVxPftbKg/Uj1mc9lPkDI/AAAAAAAABb4/Nk9Ysfd3DWA/s320/2013-09-21%25252011.08.06.png" width="320" /> </a> </div>Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-65148079769879790342013-09-20T05:43:00.000-07:002013-09-20T05:43:41.326-07:00Evaluation of researchThe Italian government has recently engaged in a procedure for the evaluation of research. The committees set up to do the evaluation have considered thousands (or tens of thousands) of publications. I have just seen the (private) evaluations of my recent papers. Poppycock!Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-37163096052521960602013-09-20T05:36:00.002-07:002013-09-20T05:36:49.031-07:00Memories of primary schoolI lived in Brisbane for 24 years, in Canberra for 3 years, in Sydney for 29 years, and now for almost 15 years in Italy. My memories of the early years are not very clear. However recently some have come back to mind as a result of a visit from a classmate in primary school at Eagle Junction State School, Queensland. His name is Ross and he has been visiting Italy for years with his wife. Last year there was a reunion of the class and he found out from my childhood friend David my whereabouts and visited us.<br /><br />The visit was a pleasure because names, faces, incidents started coming back to me from the long forgotten past, cut off from me by my travels.<br /><br />Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-83355837270038415382013-09-19T00:03:00.001-07:002013-09-19T23:25:37.503-07:00Collocamento a riposoA few days ago I received from the Rector of the University of Insubria my letter of "collocamento a riposo" - that is, on the 1st November 2013 I will no longer be a professor at the the university.<br /><br />I admit to a certain relief.<br /><a name='more'></a><br /> Last week boxes arrived unannounced for the transport of the contents of our offices to a new uncertain location. Yesterday I spent the day packing my papers.<br />Late in the afternoon we in via Carloni 78, Como, received a letter with information about the closing of our offices. I was reassured to find that in fact I do not have to relocate before retirement.<br /><br />It seems I do have to do something else unexpected in my last days at Insubria - all staff members must complete a course on security by 31st October, to assume some responsibility for security in the university.<br /><br />What I am really thinking about in my last days at Insubria is the writing I intend to do. We just finished revising an article for possible publication responding to referees' comments and I realised that the referees were not familiar with the preceding papers. It is clear that the work we have been doing on the algebra of automata has not been well understood by the intended audience. I think the work is very good but journal articles are too hard and we haven't written well. It is true that in mathematics it often takes years or decades for work to be appreciated, but in an interdisciplinary area the problem is even greater. The upshot is that I want to write some books with a leisurely exposition of our work - the students in my courses have not had difficulty understanding.Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-73643424854819658882013-06-30T11:12:00.001-07:002013-08-28T01:06:18.920-07:00Racks and Tangled CircuitsThis is just a link (<a href="https://dl.dropboxusercontent.com/u/92056191/walters-aurelio-talk-24062013.pdf">https://dl.dropboxusercontent.com/u/92056191/walters-aurelio-talk-24062013.pdf</a>) to the slides of the lecture I gave at the conference this week in Milan in memory of Aurelio Carboni. The lecture starts with some memories of working with Aurelio (I said more at the conference!) putting some recent work in context.<br /><br />I noticed while writing the slides that I had not separated the properties of racks sufficiently from those of the new notion of irack - I will probably write up a clearer version for arxiv.<br /><br />Update: The promised arxiv paper is at <a href="http://arxiv.org/abs/1307.5404">http://arxiv.org/abs/1307.5404</a>.Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-22213523937809063752013-08-27T01:26:00.001-07:002013-08-27T07:05:41.718-07:00Black ForestComing back from a conference in Germany we passed the river Breg<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-_9Iac4-Wsr0/UhxfFT7VCFI/AAAAAAAABao/oXg3HTySZqg/s1600/2013-08-11+11.25.51.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://2.bp.blogspot.com/-_9Iac4-Wsr0/UhxfFT7VCFI/AAAAAAAABao/oXg3HTySZqg/s320/2013-08-11+11.25.51.jpg" width="320" /></a></div>whose water flows into the Danube and hence to the Black Sea, and close by the river Gutach<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-UAaKo7_qYs0/UhyW4lGweTI/AAAAAAAABbM/-7ZzsuFQdXI/s1600/2013-08-11+09.28.08.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://1.bp.blogspot.com/-UAaKo7_qYs0/UhyW4lGweTI/AAAAAAAABbM/-7ZzsuFQdXI/s320/2013-08-11+09.28.08.jpg" width="320" /></a><a href="http://1.bp.blogspot.com/-FEZdo7sM_L0/UhxfhR8fxNI/AAAAAAAABaw/aiNbNm_NI7w/s1600/2013-08-11+10.30.59.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>which joins the Rhine and hence the North Sea. (I read however that some of the water flowing towards the Danube is captured by the Rhine through underground channels.)<br /><br />I was struck by the similarity between the graph of an endomorphism of a finite set, and a map of river systems. A river sytem is already a (partially discrete) abstraction of the flow of water over a landscape. A further discretization of space and time yields an endomorphism of a finite set.Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-34153241996114204562013-07-05T23:40:00.003-07:002013-08-27T02:25:38.580-07:00CT2013 Sydney, 7-13 JulyThe annual category theory conference begins tomorrow in Sydney.<br /><br />I had planned to attend taking the opportunity to visit Australia after many years of absence. Unfortunately May and June were terrible months for our family with two of us in hospital and convalescence.<br /><br />I managed with some difficulty to attend the conference in memory of Aurelio in Milan but not the long trip to Australia. The first time I made that trip was in the Orient Line ship Otranto in 1953 (from Sydney to London and back through the Suez canal visiting Ceylon, Aden, Naples and Marseille).<br /><br />Not this year.<br /><br />Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0tag:blogger.com,1999:blog-7446594.post-73716185815265758612013-04-12T05:31:00.002-07:002013-04-15T13:01:47.846-07:00So it goes1. The political movement which proposes e-government in Italy has just announced that a vote conducted by them has been hacked, and must be repeated with tighter security.<br /><br />2. Tim Gowers has conducted an experiment on his readers by asking them to comment on some mathematical proofs, without first informing them that some of the proofs were written by his computer program.<br /><br />3. The project to use toposes as bridges in Mathematics, Physics, Computer Science, Linguistics and Philosophy continues to receive publicity.<br /><br />4. The Bulletin of the American Mathematical Society has an article on the Cobordism Conjecture in which the notion of category is defined, but functors are renamed as homomorphisms. Infinity categories are not defined. The words theorem and definition are (explicitly) used in a new sense. The bibliography is (practically) disjoint from that of Ross Street's article, An Australian conspectus of Higher Category Theory.<br /><br />5. Tim Gower's blog now has a link to another blog called "Stop Timothy Gowers! !!!" in which blog it is stated that the Green-Tao paper about arithmetic progression of primes is not really about prime numbers.<br /><br />6. The "ten greatest living Italian scientists", Edoardo Boncinelli, Enzo Boschi, Sergio Carrà, Giulio Giorello, Marino Golinelli, Margherita Hack, Danilo Mainardi, Piergiorgio Odifreddi, Luigi Luca Cavalli Sforza, and Umberto Veronesi , have been interviewed on a television programme.<br /><br />7. Fact or fantasy? Taken at random from a physics blog: 380,000 years after the Big Bang, the Universe cooled down enough for protons and electrons to settle down and combine into hydrogen atoms.<br /><br />8. One of the programming language most commonly taught to computer science students has multiple vulnerabilities according to the US Department of Homeland Security (March 2013).<br /><br />9. The Princeton Companion to Mathematics has just over two pages devoted to Category Theory of its thousand pages.Robert Waltershttp://www.blogger.com/profile/11168659017114792898noreply@blogger.com0