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Gershom B
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Gershom B

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Haskell.org Survey on Crowdfunding

The haskell.org committee (http://www.haskell.org/haskellwiki/Haskell.org_committee) oversees how haskell.org funds are spent. Up until now, this has consisted simply of paying for hosting services, funded mostly by proceeds from our involvement in the Google Summer of Code program. 
Now that we are set up to accept donations (http://www.haskell.org/haskellwiki/Donate_to_Haskell.org), we are exploring additional ways to more proactively benefit the open source Haskell community.  In particular, if there is work that the community is willing to fund, haskell.org can serve as a funding conduit and organizing force to make that work happen.

By filling out this survey, you can help us gauge community interest and learn where we can make the biggest impact.
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haskell.org funding surveyThe haskell.org committee (http://www.haskell.org/haskellwiki/Haskell.org_committee) oversees how haskell.org funds are spent. Up until now, this has consisted simply of paying for hosting services, funded mostly by proceeds from our involvement in the Google Summer of Code program. Now that we are set up to accept donations (http://www.haskell.org/haskellwiki/Donate_to_Haskell.org), we are exploring additional ways to more proactively benefit ...
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So this is pretty neat: Some people decided to study the structure of the primes by treating the natural numbers as a stochastic process.

Here's the idea: You can think of the natural numbers as being a giant network, with composite numbers connected to their prime factors. You can use the ordering of the naturals to think of this as a graph that's growing over time -- each number gets added in, one by one, connecting to all its prime factors if it has any, and getting labeled as "prime" if it doesn't.

What this paper does, is it gives a very simple and intuitive randomized algorithm for generating structures that look kind of like this graph. It turns out that the structures that are generated share a lot of the large-scale structure of the primes! For example, they obey the Prime Number Theorem (http://en.wikipedia.org/wiki/Prime_number_theorem), as well as a few other theorems about the distribution of primes.

From the article it seems like this is a pretty major step forward as far as probabilistic models of the primes go; it mentions a couple of issues (notably in modeling small-scale structure; the model assigns nonzero probability to consecutive primes, oops) but overall it sounds pretty awesome.
Abstract: Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive.
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rip -- that track / riddim is a mighty legacy
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How many ways can a tie be tied?

What if I told you: there are 177147 distinct ways in which a normal necktie can be tied, including the exotic knots worn by the character Merovingian in the Matrix films? That's according to a recent paper (http://www.arxiv.org/abs/1401.8242) by Hirsch, Patterson, Sandberg and Vejdemo-Johansson.

The paper builds on work from 2000 by Fink and Mao, who identified 85 distinct tie knots. However, Fink and Mao were only interested in tie knots with trivial façade, meaning that the visible parts of the tie look like a standard tie knot. Since then, interest in more exotic tie knots has increased. This is in part because of the knots worn by the character Merovingian (also known as “The Frenchman”) in the films The Matrix Reloaded and Matrix Revolutions. The knot in the picture is an example of one of the knots Merovingian wears; note that it does not resemble a standard tie knot, even superficially. This means that the Merovingian knot does not have trivial façade, and does not appear in the Fink-Mao classification.

What Hirsch et al do is to classify the tie knots that take up to 11 moves to tie and that are anchored by a single depth tuck. A single depth tuck means that the tuck only passes under the most recent bow made over the knot. The possible moves used to tie the knot are denoted by T (clockwise), W (anticlockwise/counterclockwise) and U (tuck); the letters themselves stand for “Turnwise”, “Widdershins”, and “Under”. The number 11 is somewhat arbitrary, and was chosen because the well-known Eldredge tie knot uses 11 moves.

Hirsch et al develop a tie-knot language, which they use to classify their possible necktie knots. Each knot has to end in a tuck move, or the knot would fall apart under gravity. They prove that the tie-knot language is regular, which means that it can be recognised by a finite-state automaton. The automaton is shown in the top right of the picture. The basic idea is to follow a path that starts and finishes at the double circle in the middle of the picture, following the arrows and taking note of the sequence of letters so obtained. 

An example of an acceptable necktie knot by the authors' definition is the sequence TWWuWWuTTuTTuTTU, which appears in the paper as sequence L-447. This is an acceptable sequence because it is possible to trace a path in the diagram that (a) starts and ends at the middle and (b) follows this sequence of letters, and furthermore, there are at most eleven occurrences of T and/or W in the sequence.

The paper lists 2046 sequences like the one above. The lower case occurrences of U denote places where it would be possible to make a more complicated tuck than a single depth tuck. This means the number of possible knots is much bigger than 2046, which is where the figure of 177147 comes from. However, the final tuck is always a single depth tuck, and is therefore denoted by a capital U.

If you'd like to know how to tie the Merovingian knot in the picture, there is a nice stop-motion animated video on YouTube showing how to do it (Animated How to Tie a Necktie Merovingian Knot for your Necktie aka Ediety Knot - How to Tie a Tie).

#mathematics #scienceeveryday #spnetwork arXiv:1401.8242
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It may be the case that you have seen Inside Llewyn Davis or intend to, and yet do not know much of the music of Dave Van Ronk. In which case you may enjoy this.
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There is a lot of discussion in various online mathematical forums currently about the interpretation, derivation, and significance of Ramanujan's famous (but extremely unintuitive) formula

1+2+3+4+... = -1/12   (1)

or similar divergent series formulae such as

1-1+1-1+... = 1/2 (2)

or

1+2+4+8+... = -1. (3)

One can view this topic from either a pre-rigorous, rigorous, or post-rigorous perspective (see this page of mine for a description of these three terms: http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/  ).  The pre-rigorous approach is not particularly satisfactory: here one is taught the basic rules for manipulating finite sums (e.g. how to add or subtract one finite sum from another), and one is permitted to blindly apply these rules to infinite sums.  This approach can give derivations of identities such as (1), but can also lead to derivations of even more blatant absurdities such as 0=1, which of course makes any similar derivation of (1) look quite suspicious.

From a rigorous perspective, one learns in undergraduate analysis classes the notion of a convergent series and a divergent series, with the former having a well defined limit, which enjoys most of the same laws of series that finite series do (particularly if one restricts attention to absolutely convergent series).  In more advanced courses, one can then learn of more exotic summation methods (e.g. Cesaro summation, p-adic summation or Ramanujan summation) which can sometimes (but not always) be applied to certain divergent series, and which obey some (but not all) of the rules that finite series or absolutely convergent series do.  One can then carefully derive, manipulate, and use identities such as (1), so long as it is made precise at any given time what notion of summation is in force.  For instance, (1) is not true if summation is interpreted in the classical sense of convergent series, but it is true for some other notions of convergence, such as Ramanujan convergence, or a real-variable analogue of that convergence that I describe in this post: http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/#comment-265849

From a post-rigorous perspective, I believe that an equation such as (1) should more accurately be rendered as

1+2+3+4+... = -1/12 + ...

where the "..." on the right-hand side denotes terms which could be infinitely large (or divergent) when interpreted classically, but which one wishes to view as "negligible" for one's intended application (or at least "orthogonal" to that application).  For instance, as a rough first approximation (and assuming implicitly that the summation index in these series starts from n=1 rather than n=0), (1), (2), (3) should actually be written as

1+2+3+4+... = -1/12  + 1/2 infinity^2   (1)'

1-1+1-1+... = 1/2 - (-1)^{infinity} /2 (2)'

or

1+2+4+8+... = -1 + 2^{infinity}  (3)'

and more generally

1+x+x^2+x^3+... = 1/(1-x) + x^{infinity}/(x-1)

where the terms involving infinity do not make particularly rigorous sense, but would be considered orthogonal to the application at hand (a physicist would call these quantities unphysical) and so can often be neglected in one's manipulations.  (If one wanted to be even more accurate here, the 1/2 infinity^2 term should really be the integral of x dx from 0 to infinity.)  To rigorously formalise the notion of ignoring certain types of infinite expressions, one needs to use one of the summation methods mentioned above (with different summation methods corresponding to different classes of infinite terms that one is permitted to delete); but the above post-rigorous formulae can still provide clarifying intuition, once one has understood their rigorous counterparts.  For instance, the formulae (1)' and (3)' are now consistent with the left-hand side being positive and diverging to infinity, and the formula (2)' is consistent with the left-hand side being indeterminate in limit, with both 0 and 1 as limit points.  The fact that divergent series often do not behave well with respect to shifting the series can now be traced back to the fact that the infinite terms in the above identities produce some finite remainders when the infinity in those terms is shifted, say to infinity+1.

For a more advanced example, I believe that the "field of one element" should really be called "the field of 1+... elements", where the ... denotes an expression which one believes to be orthogonal to one's application.
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Gershom B

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Haskell.org Survey on Crowdfunding

The haskell.org committee (http://www.haskell.org/haskellwiki/Haskell.org_committee) oversees how haskell.org funds are spent. Up until now, this has consisted simply of paying for hosting services, funded mostly by proceeds from our involvement in the Google Summer of Code program. 
Now that we are set up to accept donations (http://www.haskell.org/haskellwiki/Donate_to_Haskell.org), we are exploring additional ways to more proactively benefit the open source Haskell community.  In particular, if there is work that the community is willing to fund, haskell.org can serve as a funding conduit and organizing force to make that work happen.

By filling out this survey, you can help us gauge community interest and learn where we can make the biggest impact.
Drive
haskell.org funding surveyThe haskell.org committee (http://www.haskell.org/haskellwiki/Haskell.org_committee) oversees how haskell.org funds are spent. Up until now, this has consisted simply of paying for hosting services, funded mostly by proceeds from our involvement in the Google Summer of Code program. Now that we are set up to accept donations (http://www.haskell.org/haskellwiki/Donate_to_Haskell.org), we are exploring additional ways to more proactively benefit ...
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College Junior? Like Functional Programming? Want to be an intern in New York this summer? Maybe this will be of interest.
[Haskell-cafe] Portfolio Analytics group at S&P CapitalIQ Hiring Summer Interns for 2014. Gershom B gershomb at gmail.com. Wed Feb 26 21:29:38 UTC 2014. Previous message: [Haskell-cafe] Berlin HUG meeting at Tuesday, March 4th; Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ...
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Registration is open for the 1st ever New York City Haskell Hackathon!
Info: www.haskell.org/haskellwiki/Hac_NYC
#haskell   #hackathon   #nyc 
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Good news, everybody!
 
Playing around with Haskell in https://cloud.sagemath.com

Auto-indent and syntax highlighting thanks to CodeMirror; haskell thanks to Linux :-). 

(I just added this -- aggressive browser refreshing may be required.)
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Tnx. I just found "new->terminal" and it works fine on salvemundo.hs. It would be great if fpcomplete and this site managed to  synchronise continuous build library sets.
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These are Howard's original notes (well, a later published version of them) that established the well known Curry-Howard correspondence and the "propositions as types" principle in 1969.

Now a great deal of work was done on realizing proofs as mathematical objects prior to Howard's work (and the notes themselves cite some). But not only had the connection to types not been made, but it seems that type theory itself had fallen by the wayside between Church's work through the early 1940s and Howard's notes in 1969. 

Is that the case? What happened to types  during their "years in the wilderness"? Anything?
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I believe what is linked is in fact the version as published in 1980. That volume ("To H.B. Curry") is quite hard to come by, but I believe contains foundational work by e.g. Scott, Lambek, etc. as well. I would love to see it digitized and made available in its entirety on the web.
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NYC Haskell Hackathon. April 4-6. Boom.

(announcement as reposted from haskell-cafe follows)

On behalf of the organizers, I am pleased to officially announce the
first Hac NYC, a Haskell hackathon/get-together to be held April 4-6
in New York City.  Space will be provided by Etsy on Saturday and
Sunday.  Details for Friday will be announced as they become
finalized.  We want to stress that everyone is welcome---you do not
have to be a Haskell guru to attend!  Helping hack on someone else's
project could be a great way to increase your Haskell-fu.

If you plan on coming, you must officially register by filling out our
registration form [1].  Other details for travel, lodging, etc can be
found on the Hac NYC wiki [2].

We're also looking for a few people interested in giving short (15-20
min.) talks, probably on Saturday afternoon.  Anything of interest to
the Haskell community is fair game---a project you've been working on,
a paper, a quick tutorial.  If you'd like to give a talk, add it on
the wiki [3].

Hope to see you in April!

-The Hac NYC Team

[1] https://docs.google.com/forms/d/1taZtjgYozFNebLt1TR2VnKv-ovD2Yv5sOdSZzmi_xFo/viewform
[2] http://www.haskell.org/haskellwiki/Hac_NYC
[3] http://www.haskell.org/haskellwiki/Hac_NYC/Talks
1 About. The NYC Haskell Hackathon (aka Hac NYC) is an international, grassroots collaborative coding festival with a simple focus: build and improve Haskell libraries, tools, and infrastructure. This event will be held April 4-6, 2014. It is open to all -- you do not have to be a Haskell guru ...
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Education
  • University of California, Berkeley
    Electrical Engineering and Computer Science, 1997 - 2001
  • Boston University
    African American Studies, 2004 - 2005
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