The seeds of homotopy type theory
I was recently very surprised to find a lecture (http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/2014_IAS.pdf) of Vladimir Voevodsky explaining his motivation for working on...
View ArticleThe algebra of processes XI
We have been thinking about categorical algebra for computer science now for 25 years. I want to discuss the problems of thinking seriously about two distinct disciplines, and how one might avoid the...
View ArticleLex total categories and Grothendieck toposes
In the very valuable volume Sketches of an Elephant, A Topos Theory Compendium, Volume 1, Peter Johnstone mentions a lecture of Andre Joyal at the 1981 Cambridge Summer Meeting where he listed seven...
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Span(Graph) I
I have decided to write a series of tutorial posts about Span(Graph) since I think this work has been unfairly neglected. I am simultaneously introducing a little TeX into the blog, at the...
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The sleeping beauty problem: how philosphers and physicists calculate...
Recently there have been surprising discussions and disputes amongst philosophers and physicists about an elementary probability problem called the Sleeping Beauty problem. The following remarks are,...
View ArticleThe sleeping beauty problem: how some statisticians calculate probability
This problem was drawn to my attention by calculations of physicists and philosophers (see my last post), but I see that some eminent statisticians are also convinced that the answer is $1/3$.What I...
View ArticleLex total categories and Grothendieck toposes II
I said in the first post in this series that totally complete categories have a strong adjoint functor theorem.Here is the adjoint functor theorem: if $A$ and $B$ are locally small categories, $A$ is...
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Span(Graph) II: Circuits with feedback
Previous Span(Graph) post; next Span(Graph) post.As an introduction to ${\bf Span(Graph)}$ I will describe how to extend the category of straight-line circuits to allow circuits with state and...
View ArticleLex total categories and Grothendieck toposes III
Previous post in this series; next post in this series.Today I want to give an application of the adjoint functor theorem for totally complete categories, namely to show that lex total categories are...
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Span(Graph) III: Circuits with feedback
Previous post in this series; next post in the series.The two main operations in $\bf Circ$ are composition and parallel as for straight-line circuits, and there are a variety of constants.Today we...
View ArticleLex total categories and Grothendieck toposes IV
Previous post in this series; next post.The aim of this post is to complete the proof that well-powered lex total categories are elementary toposes, by proving that they have subobject classifiers.But...
View ArticleRicordo di Aurelio Carboni, Matematico e Filosofo
I have just received a volume of "Il Protagora" in which there is a section devoted to Aurelio's memory.There are four articles all inIl Protagora, Volume XL, July-December 2013, sesta serie, n. 20The...
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Giuseppe Peano
On Saturday I bought for 2 euros at the mercatino of Lavello a little book by Giuseppe Peano of numerical tables. It has an interesting preface by Peano.I suppose Peano is best known for axiomatizing...
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Opera d'abbaco del reverendo padre don Smiraldo Borghetti
Here are some pages from a book I bought some years ago on arithmetic, published in 1594.It is interesting to read that without numbers the world would be without order, and a horrible chaos.Strangely...
View ArticleSleeping beauty problem III
Previous post in this seriesI am writing a third post about the sleeping beauty problem partly because I have seen Sean Carmody's post (26th August) in which he describes the problem and expresses his...
View ArticleArguments for funding
From the blog of Sabine Hossenfelder regarding the argument for funding the next supercollider:"The next argument I keep hearing is that the worldwide web was invented at CERN which also hosts the LHC...
View ArticleThe mess we are in with scientific publishing
I am a little out of the Italian academic scene since my retirement, but if I understood the recent rounds of hiring in Italy they occurred in the following way. It was possible to apply for...
View ArticleMy 1992 FTP site
Don't believe any links, or email addresses. Almost all have disappeared. Notice the strange domain name for mathematics at Sydney. We did not get to see the web until at least 1993 when Mosaic came...
View ArticleGoogle+
I just linked up this blog with Google+. This is a test to see what the effect of that is. I assume my posts will now be visible from Google+.
View ArticleThe mess we are in with scientific publishing II - not in the club
previous post in this series; next post in this seriesI mentioned various problems with scientific publishing in the previous post.I neglected to mention the most discussed problems like the ownership...
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Stephen H. Schanuel and Dietmar Schumacher
Steve and Dietmar are two mathematicians I knew who died earlier this year. I meant to write something earlier but have been distracted by my own health problems.I knew Stephen Schanuel (14 July...
View ArticleSleeping beauty problem IV
Previous post in this seriesI have been waiting to see some conclusions coming from discussions of the problem at the Stubborn Mule blog, however the discussion seems to have petered out without a...
View ArticleOne month away from my computer
I want to explain why I haven't done any posting lately, and why I haven't answered mail.I have just had a month's rest in hospital. A rest which requires another rest to recover from.By the way...
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