Sunday, July 26, 2015

Mathematicians in the Interwebs


I should be blogging about useful stuff, like my workshop on Dialog that is coming up soon in Barcelona, as part of ESSLLI 2015. But this week by a coincidence there are two great and very different mathematicians making rounds on the interwebs.

One in the Guardian, the other on the New York Times Magazine. Both profiles are very well-written. The mathematicians also write very well, a big bonus.

The Guardian has John Conway, and Andre Joyal just talked about his category of games in WOLLIC 2015, which I helped to organize. I saw Conway a few times in DPMMS in Cambridge, but never talked to him. He was already a big name and I was a shy young phd student and he soon departed for the US.

But there are several other players that appear in the article that I remember well. Prof Cassell's was the head of department when I arrived. Simon Norton was always in the common room and the backgammon ladder was the center of life, the universe and everything. I kept my distance, of course.

The other mathematician is Terry Tao in the New York Times. I only saw/heard Tao once, when he got a prize from Stanford and was around for several lectures. He was every bit as impressive as I expected.

Two different kinds of mathematicians, different styles indeed.
Love the Conway  humble brag joke, not quite self-deprecating, but almost so  “I do have a big ego! As I often say, modesty is my only vice. If I weren’t so modest, I’d be perfect.”

Love the down-to-earth, we can-do-this style of Tao, "The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians. Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all." Tao, I think, then meant to quote Lockheart's Lament, but the quote didn't quite make it, a shame.

But I think I liked best the Charles Fefferman quote on this article "The steady state of mathematical research is to be completely stuck. It is a process that Charles Fefferman of Princeton, himself a onetime math prodigy turned Fields medalist, likens to ‘‘playing chess with the devil.’’ The rules of the devil’s game are special, though: The devil is vastly superior at chess, but, Fefferman explained, you may take back as many moves as you like, and the devil may not. You play a first game, and, of course, ‘‘he crushes you.’’ So you take back moves and try something different, and he crushes you again, ‘‘in much the same way.’’ If you are sufficiently wily, you will eventually discover a move that forces the devil to shift strategy; you still lose, but — aha! — you have your first clue." This just about takes me back to the picture of one of the first posts in this blog.  Indeed,  we fight it!

Tuesday, July 14, 2015

A very old post from May 2013: Learning to love stats

 Last Friday I went to the Symposium described below at CSLI, Stanford. This was very interesting, but I haven't had a chance to digest the contents, properly. Since there was no webpage and there are no slides/papers from the talks, I'm posting the program here, as an 'aide-memoire'.

The main reason why I'm interested is obvious: probabilistic vector space semantics makes a lot of sense as a substitute for what semanticists call the Prime Semantics of Natural Language (origin of the infamous joke: What's the meaning of life?  life prime) but the probabilistic approach doesn't seem to scale so well as far as logical phenomena is concerned: antonyms seem to appear in similar contexts, not in opposite ones; a tiny small word like "not" seems to have a huge effect in meaning; concepts can crisply imply others, whether or not the probablities are similar, etc... One of the ideas I had during the meeting was that maybe what one needs to do is to use some sort of Glue Semantics logical system, with two-tiers: one where we do composition of meanings using say implicational linear logic and one where we do use the vector spaces for the meanings of the constituents themselves, ie nourn phrases, verb phrases and propositional phrases.


The 2012-2013 Cognition & Language Workshop is pleased to announce a
Symposium on Compositional Vector Space Semantics
featuring
   Stephen Clark, Chung-chieh Shan and Richard Socher

  The emerging field of compositional probabilistic vector space semantics for natural languages and other symbolic systems is being approached from multiple perspectives: language, cognition, and engineering. This symposium aims to promote fruitful discussions of interactions between approaches, with the goal of increasing collaboration and integration.

Schedule of Events:
   9:00 - 9:30      Light breakfast
9:30 - 11:00      Chung-chieh Shan (Indiana)
                        From Language Models to Distributional Semantics
                        Discussant: Noah Goodman

11:15 - 12:45      Richard Socher (Stanford)
                         Recursive Deep Learning for Modeling Semantic Compositionality
                         Discussant: Thomas Icard
  
12:45 - 2:00      Lunch
2:00 - 3:30      Stephen Clark (Cambridge)
                      A Mathematical Framework for a Compositional Distributional Model of Meaning
                      Discussant: Stanley Peters  

3:45 - 5:00      Breakout Groups and Discussion 
5:00 -       Snacks & Beverages


Chung-chieh Shan, University of Indiana
Title: From Language Models to Distributional Semantics

Abstract: Distributional semantics represents what an expression means as a vector that summarizes the contexts where it occurs.  This approach has successfully extracted semantic relations such as similarity and entailment from large corpora.  However, it remains unclear how to take advantage of syntactic structure, pragmatic context, and multiple information sources to overcome data sparsity.  These issues also confront language models used for statistical parsing, machine translation, and text compression. 
Thus, we seek guidance by converting language models into distributional semantics.  We propose to convert any probability distribution over expressions into a denotational semantics in which each phrase denotes a distribution over contexts.  Exploratory data analysis led us to hypothesize that the more accurate the expression distribution is, the more accurate the distributional semantics tends to be.  We tested this hypothesis on two expression distributions that can be estimated using a tiny corpus: a bag-of-words model, and a lexicalized probabilistic context-free grammar a la Collins.
  
Richard Socher, Stanford University
Title: Recursive Deep Learning for Modeling Semantic Compositionality
 
Abstract: Compositional and recursive structure is commonly found in different modalities, including natural language sentences and scene images. I will introduce several recursive deep learning models that, unlike standard deep learning methods can learn compositional meaning vector representations for phrases, sentences and images. These recursive neural network based models obtain state-of-the-art performance on a variety of syntactic and semantic language tasks such as parsing, paraphrase detection, relation classification and sentiment analysis.
   Besides the good performance, the models capture interesting phenomena in language such as compositionality. For instance the models learn different types of high level negation and how it can change the meaning of longer phrases with many positive words. They can learn that the sentiment following a "but" usually dominates that of phrases preceding the "but."Furthermore, unlike many other machine learning approaches that rely on human designed feature sets, features are learned as part of the model.
 
Stephen Clark, University of Cambridge
Title: A Mathematical Framework for a Compositional Distributional Model of Meaning
  
Abstract: In this talk I will describe a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types (based on categorial grammar). A key idea is that the meanings of functional words, such as verbs and adjectives, will be represented using tensors of various types. This mathematical framework enables us to compute the distributional meaning of a well-typed sentence from the distributional meanings of its constituents. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model.  
There are two key questions that the framework leaves open: 1) what are the basis vectors of the sentence space? and 2) how can the values in the tensors be acquired? I will sketch some of the ideas we have for how to answer these questions.

  

Saturday, July 11, 2015

Every day is Ada Lovelace's day

I thought it would be a good thing to have a Facebook group for Women in Logic.

First because women need to see other women who do their kind of work. I do remember the buzz and, how moved I was,  going into the room of  my first Women of Vision Awards banquet. Seven hundred mostly women doing computing into a single room? It was awesome!!

Then because logic is a too distributed subject really: some of us do computational logic, some do mathematical logic, some philosophical logic, some logic in linguistics, some logic in physics,  some philosophy of science, you name it. We could do with some assurance that there *are* many of us.

So the group now exists, and if you're reading this and is not disgusted by Facebook, please join in!

Marilyn Walker suggested that the group should produce Wikipedia pages for women in logic in a collaborative way. I think it's a great idea, but I worry about the 'notability constraints' of Wikipedia. So I thought I'd try to get going by creating entry-like blog posts.

This is the first one and is about Maria Laura Mouzinho Leite Lopes (in the picture), as she was the first  Brazilian mathematician with a phd, apparently in 1949.

The following comes from CNPq, one of the BRazilian main funding agency, in the series Female Pioneers in the Sciences.  (and I need to do some more work tidying up the google-translation  a bit more, but later on.)


 Maria Laura was
born in Timbaúba,  Pernambuco, on January 18, 1917 and died on June 20, 2013, aged 94. 


  In 1935, the  Mouzinho family came to Rio de Janeiro and she was enrolled in the Lafayette Institute, in 1936, she completed her junior high school as a student of the College Sion, in Petrópolis (RJ).  In 1941, Maria Laura graduated 'Bachelor of Mathematics' from Faculdade Nacional de Filosofia (FNFi), and then in 1942, completed the "Degree in Mathematical Education".  She spent  the next six years working on her "Habilitation" entitled "Projective  spaces - the lattice  of its subspaces", directed by mathematics Portuguese professor António Aniceto Ribeiro Monteiro. In September 24, 1949  Mouzinho earned  the title of FIRST  woman DOCTOR IN SCIENCE - MATHEMATICS in Brazil.

  In 1949, with physicists César Lattes (1924-2005) and José Leite Lopes (1918-2006), participated in the creation of the Brazilian Center for Physics Research (CBPF). Replacing Professor Oliveira Junior, she went on to teach geometry classes in Engineering Course in the newly created Institute of Aeronautical Technology (ITA), which was attended by Professor Francis Dominic Murnaghan (1893-1976). That same year she traveled to the United States, where she worked for a year at the Department of Mathematics at The University of Chicago. In 1951, she participated in the creation of the National Council for Scientific and Technological Development (CNPq). Together with the most influential mathematicians of Rio de Janeiro and with the teacher Candido Lima da Silva Dias (1913-1998), then professor at the University of São Paulo (USP), in 1952, she help to found the Institute for Pure and Applied Mathematics ( IMPA) where she held the  functionof secretary in the 1952-1956 period, and in March 1952, she was inducted in the Brazilian Academy of Sciences.

 In 1956, she married the renowned physicist and professor José Leite Lopes. In 1961 she was appointed professor at the Technical Education State of Guanabara Professional. In 1967, Maria Laura takes over as Head of the Mathematics Department at FNFi, until it becomes Mathematical Institute of the UFRJ. In 1969, with Professor Leite Lopes, is exiled, banished from the country by the Institutional Act # 5 (AI5). They went first to Pittsburgh, USA, and then to Strasbourg, France, where she started to develop her research in mathematics education  at the Institute de Recherche en Enseignement of Mathematiques (IREM).

In 1974, Maria Laura went back to Brazil with all the experience of IREM and invited by Professor Anna Averbuch became the  Mathematics coordinator at the Brazilian Israelite School Eliezer Eistenbarg and participated in guiding the teaching of Mathematics in the Educational Center in  Niteroi. In 1976 she participated in the foundation of the  "Group of Teaching and Research in Mathematics Education - GEPEM" which was chaired by her, during the first eight years. GEPEM under the agreement with the MEC / INEP, coordinates the first research in mathematics education in Brazil, "Project Binomial Teacher-Student in Introduction to Mathematics Education - an experimental research."

 With the signing the amnesty law in August 1979, still during the military dictatorship, Maria Laura resumes her seat in IM / UFRJ. At the end of 1982, responding to a Ministry of Education's call to the University of Integration Program with the Priaery Grades  education, this group of teachers IM / UFRJ, under the coordination of Maria Laura, presented the "Project Training for Teachers of 1st, 2nd and 3rd grades. " In 1983, along with teams from Biology, Physics, Geography, Mathematics and Chemistry, deploy "Fundão Project," which came to integrate the Education Sub-Program for Science, when the creation of the Support of Scientific and Technological Development Program. 

In order to consolidate the mathematics education in Brazil, January 27, 1988, Professor Maria Laura and a group of researchers, professors and employees, founded the "Brazilian Society of Mathematics Education" (SBEM), and then the regional SBEM / RJ. After 65 years of academic life at UFRJ Professor Maria Laura was awarded, on 1 July 1996, with the title of "Emeritus Professor at the Federal University of Rio de Janeiro" and in 2001 she  was awarded  the title of "Honorary Professor the SBEM ". Acting forcefully and intensely in the continuing education of mathematics teachers Professor Maria Laura has published several articles and books and has maintained the standards of Brazilian Mathematics Education as a benchmark for the world.

    
Author:
Pedro Carlos Pereira, Assistant Professor of UFRRJ,  based on his thesis "The Educator Maria Laura: contributions to the constitution of mathematics education in Brazil."

Wednesday, July 8, 2015

Why is this a Proof? Luiz Carlos Festschrift

The book celebrating Luiz Carlos Pereira's work in Proof Theory and Logic is out!

http://www.collegepublications.co.uk/tributes/?00027
Yay!!

Great title, I thought.

Will post later about contents and my contribution. My copy hasn't arrived from the UK, yet.

(Jean-Baptiste Joinet and Luiz Carlos for lunch in Rio, last year. I need a better iphone.)

Thursday, July 2, 2015

Stanford's Workshop on Logic, Rationality, and Interaction

This isn't my favorite picture of Stanford (the place is very photogenic, it looks beautiful almost always), but it's the one that I associate with the workshops on Logic, Rationality and Interaction. So it's appropriate. Many times I tried to remember something I heard in one of the workshops, so it makes sense to collect at least the programs here.

The first workshop was in 2012. I need to go back to my ideas for “Failure of Interpolation for Intuitionistic Logic of Constant Domains”. I'd like to write it for Grisha. The second workshop was the one where I only managed to go one day, the second one. The third workshop was opened by Chris Potts, now the director of CSLI. This year I was invited speaker, yay!!

Saturday, June 27, 2015

Advice on Constructive Modal Logic

This is a picture of Dana Scott when he wrote "Advice on Modal Logic". The paper is fun (it's from 1970, but not freely available, it seems), the subject is fun and there is an awful lot of more fun things to do with it. One of them is constructive or intuitionistic modal logics. Like Modal Type Theory.

But I am feeling tired of trying to force philosophers and computer scientists to collaborate on the subject. If your friends don't want to talk to your other friends, sometimes you just have to let it go.

At least for a while. Mathematical problems can be like wine or cheese, some are better fresh,  you attack them fiercely and win or lose. Some you need to put away,  to mature (or  not), and hope that the process will improve them.

Together with Charles Stewart and Natasha Alechina, I wrote one more note on that. A very preliminary version is here. And I talked about it in Berkeley's Logic Colloquium in March. Slides are available. For my part, I will concentrate on the  'small picture' now, the details that I think I know do work. Instead of trying to think about why it all hangs together, if  indeed it does.

Frank Pfenning has a lovely slide deck, celebrating Scott's 70th birthday here.

Saturday, June 13, 2015

Plans, plans and expectations

The picture is from Doghousediaries and if I could draw to save my life I would add a few crocodiles to the pond. But I cannot, so the rocks, the ladders and the hail will have to do.

Also the fact that it took me the best part of four hours to find this cartoon again, would be a good indicator that I don't give up easily. yes, I don't.

But sometimes it's good to remind oneself that there is always a different way of doing things and given enough time, I will find it.
Here are slides of a talk I gave in October 2012. The picture is very appropriate.