October 09, 2015

2:43 PM | abc and foundations
Now that Davide Castelvecchi’s lucid Nature article on Mochizuki’s “impenetrable” work on the abc Conjecture has been reprinted by Scientific American, many of us can expect our non-expert friends to ask us what’s going on.  (It has already happened to me.)  If your non-expert friends happen to be sociologists, please advise them to review Castelvecchi’s […]
1:05 PM | The beauty (?) of mathematical proofs -- explanatory persuasion as the function of proofs
By Catarina Dutilh NovaesThis is the fifth installment of my series of posts on the beauty, function, and explanation in mathematical proofs (Part I is here; Part II is here; Part III is here; Part IV is here). In this post I bring in my dialogical conception of proofs (did you really think you'd be spared of it this time, dear reader?) to spell out what I take to be one of the main functions of mathematical proofs: to produce explanatory persuasion.==================Framing the […]
12:09 PM | Friday Potpourri Served Up
Again, plenty to choose from.... 1)  David Brooks (no, not THAT David Brooks) continues his search for interesting sequence-generating integers: http://aperiodical.com/2015/10/guest-post-sequence-numbers/ http://sequencenumbers.blogspot.co.uk/ 2)  Chess fans, fabulous post from Jason Rosenhouse reviewing the new Bobby Fischer docu-drama ("Pawn Sacrifice"), and including other Fischer

October 08, 2015

4:40 PM | Moving gently on …
I’m planning to go to a couple of lecture courses this term (including Peter Johnstone’s famed, take-no-prisoners, category theory course), and probably a weekly reading group too. I also need to do quite a bit of other reading over the … Continue reading →
12:59 PM | The beauty (?) of mathematical proofs -- explanatory proofs
By Catarina Dutilh NovaesThis is the fourth installment of my series of posts on the beauty, function, and explanation in mathematical proofs (Part I is here; Part II is here; Part III is here). In this post I present a brief survey of the debates in the literature on what it means for a mathematical proof to be explanatory.=============Quite a bit has been said on explanation and mathematical proofs in recent decades (Mancosu & Pincock 2012). Although the topic itself has an old and […]
12:30 AM | In defense of statistical recipes, but with enriched ingredients (scientist sees squirrel)
Evolutionary ecologist, Steven Heard (Scientist Sees Squirrel) linked to my blog yesterday. Heard’s post asks: “Why do we make statistics so hard for our students?” I recently blogged Barnard who declared “We need more complexity” in statistical education. I agree with both: after all, Barnard also called for stressing the overarching reasoning for given methods, and that’s in sync with […]

October 07, 2015

10:00 PM | Forgetfulness Of Purpose • 7
Re: Peirce List Discussion • Sungchul Ji I invited readers to consider Ashby’s example of a regulation game as a triadic relation whose triples are given by either one of the following tables. Sungchul Ji asked a rather good question … Continue reading →
4:32 PM | The Aïda of our dreams?
Aïda is perhaps one of those operas where the performance of our dreams is likely to beat any staging: we turn up the headphones, and our imagination does the rest. The much heralded new studio recording of Aida, conducted by … Continue reading →
1:30 PM | The beauty (?) of mathematical proofs -- beauty and explanatoriness
By Catarina Dutilh NovaesThis is the third installment of my series of posts on the beauty, function, and explanation in mathematical proofs (Part I is here; Part II is here). In this post I start drawing connections (later to be discussed in more detail) between beauty and explanatoriness.===========================A hypothesis to be investigated in more detail in what follows is that there seems to be an intimate connection between attributions of beauty to mathematical proofs and the idea […]

October 06, 2015

12:23 PM | The beauty (?) of mathematical proofs - methodological considerations
By Catarina Dutilh NovaesThis is the second installment in my series of posts on the beauty, function, and explanatoriness of mathematical proofs (Part I is here). I here discuss methodological issues on how to adjudicate the 'dispute' between the reductive and the literal accounts of the beauty of proofs, discussed in Part I.==========================================But what could possibly count as evidence to adjudicate the ‘dispute’ between the literal/non-reductive camp and the […]
8:27 AM | Git, for the rest of us?
Git is a widely used version control system, much used e.g. by software developers. But others, even writers of one-author paper or book projects,  swear  by it too. Thus Richard Baron writes: The last time the Open Logic Text was discussed on … Continue reading →
3:40 AM | Forgetfulness Of Purpose • 6
Just enough time for an incidental observation. Consider the table Ashby uses to describe his first example of a regulation game. A table like that is a compact way of describing a triadic relation, in this case a relation whose … Continue reading →

October 05, 2015

2:24 PM | The beauty (?) of mathematical proofs - reductive vs. literal approaches
By Catarina Dutilh NovaesI am currently working on a paper provisionally entitled 'Beauty, function, and explanation in mathematical proofs', and so this week I will post what I have so far as a series of blog posts. Here I start with a discussion on the current literature on the presumed beauty of some mathematical proofs. As always, comments very welcome!=============================It is well known that mathematicians often employ aesthetic adjectives to describe mathematical entities, […]
1:54 PM | Book Note: The Open Logic Text, #2
Continuing from the previous post: Part III: Computability (pp. 105-158) Ch. 9 is on Recursive Functions, and is reasonably clear but brisk (I think that non-mathematicians encountering this material for the first time will not find it easy and will need … Continue reading →

October 04, 2015

10:51 AM | Will the Real Junk Science Please Stand Up?
Junk Science (as first coined).* Have you ever noticed in wranglings over evidence-based policy that it’s always one side that’s politicizing the evidence—the side whose policy one doesn’t like? The evidence on the near side, or your side, however, is solid science. Let’s call those who first coined the term “junk science” Group 1. For […]

October 03, 2015

1:16 PM | Book Note: The Open Logic Text, #1
It has been nine months since I really looked at the Teach Yourself Logic 2015 Study Guide. It’s time to start thinking about a 2016 update. So over the coming weeks I’ll be tinkering with the current version, while reading, dipping, … Continue reading →

October 02, 2015

7:30 PM | Forgetfulness Of Purpose • 5
Recall the game between R and D determined by the following data. Here is Ashby’s analysis of how it all plays out. Examination of the table soon shows that with this particular table R can win always.  Whatever value D … Continue reading →
12:45 PM | Math From the Week
Math here and there: 1)  RJ Lipton reviews "The Curious Incident of the Dog in the Night-Time" (the play, about an autistic math savant): https://rjlipton.wordpress.com/2015/09/28/a-curious-inversion/ 2)  Terry Tao's latest math-splash (Erdös proof) via Scientific American: http://www.scientificamerican.com/article/maths-whizz-solves-a-master-s-riddle/ ...and Erica Klarreich explains Tao's
7:27 AM | Le Monde promotes socially responsible mathematics
You know you’re a Parisian intellectual when you are invited to make a totally gratuitous comment in Le Monde.  That has never happened to me, so however I may walk, talk, and quack, Brendan Larvor’s diagnosis of my status remains hypothetical.  And I can’t really say that Leila Schneps, whom I strongly suspect for numerous […]

October 01, 2015

7:00 PM | Forgetfulness Of Purpose • 4
Ashby now invites us to consider a series of games, beginning as follows. 11/3.   Play and outcome.  Let us therefore forget all about regulation and simply suppose that we are watching two players, R and D, who are engaged in … Continue reading →
3:09 AM | Oy Faye! What are the odds of not conflating simple conditional probability and likelihood with Bayesian success stories?
ONE YEAR AGO, the NYT “Science Times” (9/29/14) published Fay Flam’s article, first blogged here. Congratulations to Faye Flam for finally getting her article published at the Science Times at the New York Times, “The odds, continually updated” after months of reworking and editing, interviewing and reinterviewing. I’m grateful too, that one remark from me remained. Seriously I […]

September 30, 2015

8:30 PM | Forgetfulness Of Purpose • 3
Here is the first part of Ashby’s setup for the schematic example I had in mind. Requisite Variety 11/1.   In the previous chapter we considered regulation from the biological point of view, taking it as something sufficiently well understood.  … Continue reading →
2:12 PM | A Friendly Introduction to Mathematical Logic
If you have read the Teach Yourself Logic 2015 Study Guide, then you will know that I there particularly recommend as an admirably lucid and, yes, friendly introduction to first-order logic Christopher Leary’s 2000 book, A Friendly Introduction to Mathematical … Continue reading →
11:00 AM | Shared paths to Infinity
My last post focused on the kinds of problems that can develop when abstract objects, created within mathematics, increase in complexity – like the difficulty of wrapping our heads around them, or of managing them without error. I thought it would be interesting to turn back around and take a look at how the seeds [...]

September 29, 2015

8:00 PM | Forgetfulness Of Purpose • 2
I had planned to get down to brass tacks as quickly as possible, with an object example from Ashby’s Cybernetics that made an impression on me at an early stage in my thinking about intelligent systems.  But while I was … Continue reading →

September 28, 2015

3 years ago… MONTHLY MEMORY LANE: 3 years ago: September 2012. I mark in red three posts that seem most apt for general background on key issues in this blog.[1] (Once again it was tough to pick just 3; many of the ones I selected are continued in the following posts, so please check out subsequent dates…) September 2012 (9/3) After dinner Bayesian […]
11:07 PM | The art of not reading
Wise words, found in my twitter stream: The art of not reading is a very important one. It consists in not taking an interest in whatever may be engaging the attention of the general public at any particular time. When some … Continue reading →
9:29 AM | Easy as 1, 2, 3 ? -- Wittgenstein on counting
By Catarina Dutilh Novaes(Cross-posted at NewAPPS)“A B CIt's easy as, 1 2 3As simple as, do re miA B C, 1 2 3Baby, you and me girl”45 years ago, Michael Jackson and his troupe of brothersfamously claimed that counting is easy peasy. But how easy is it really? (We’ll leave aside the matter of the simplicity of A B C and do re mi for present purposes!)Counting and basic arithmetic operations are often viewed as paradigmatic cases of ‘easy’ mental operations. It might seem that we are […]

September 27, 2015

5:54 PM | PHQ in astonishing form, again
To the Wigmore Hall this morning, to hear the Pavel Haas Quartet play Schubert’s “Rosamunde” Quartet and Beethoven’s “Serioso”. An extraordinary short concert, with the PHQ at their unsurpassed best. Of recorded performances of the “Rosamunde”, I perhaps know the … Continue reading →
4:00 PM | Forgetfulness Of Purpose • 1
Naturally I had purposes and reflected on my purposes for as long as I can remember but I don’t think I thought about the concept of purpose in a systematic way until I began taking courses on cybernetics and systems … Continue reading →
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