Quantcast
Browsing latest articles
Browse All 67 View Live

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 Article


The 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 Article


Lex 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...

View Article

Image may be NSFW.
Clik here to view.

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...

View Article

Image may be NSFW.
Clik here to view.

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 Article


The 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 Article

Lex 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...

View Article

Image may be NSFW.
Clik here to view.

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 Article


Lex 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...

View Article


Image may be NSFW.
Clik here to view.

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 Article

Lex 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 Article

Ricordo 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...

View Article

Image may be NSFW.
Clik here to view.

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...

View Article


Image may be NSFW.
Clik here to view.

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 Article

Sleeping 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 Article


Arguments 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 Article

The 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 Article


My 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 Article

Google+

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 Article

The 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...

View Article

Image may be NSFW.
Clik here to view.

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 Article


Sleeping 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 Article


One 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...

View Article

Back in hospital

I spoke too soon

View Article

Christmas in hospital

View Article

Browsing latest articles
Browse All 67 View Live