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# Posts

### May 24, 2013

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Last time, I posted about Jim Joyce's argument for Probabilism.  At its heart lies a mathematical theorem.  In this post, I state this mathematical theorem and prove it; then I generalize it and prove the generalization.  The frameworkRecall from last time:$\mathcal{F}$ is a finite set of propositions.  (It is the set of propositions about which our agent has an opinion.)A credence function is a function $c : \mathcal{F} \rightarrow [0, 1]$. Throughout the present post, we [â€¦]
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This week (May 20-May 24) I am in Palo Alto, at the American Institute of Mathematics, for the third year of a SQuaRE meeting on Descriptive aspects of Inner model theory. The previous two meetings are mentioned here and here. See also this post on some of our results. This time two other SQuaRE meetings […]
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Martin Conference, Berkeley, May 27-28, 2001. (If someone has a version in higher resolution, or pictures of the conference, please contact John Steel, or myself.)
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Lowell Trott, one of the theory students here at UCI, successfully defended his thesis yesterday. Lowell's Ph.D. advisor is Mike Goodrich, but I've also worked with him on several publications related to both social networks and road networks. (Although the vertices in road networks are not people, the networks still come from a social structure.) Specifically, he:Showed that road networks have the property that any line of sight crosses only a small number of roads, both empirically and in a [â€¦]

### May 23, 2013

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At last—a textbook on category theory for scientists! And it’s free! • David Spivak, Category Theory for Scientists. It’s based on a course the author taught: This course is an attempt to extol the virtues of a new branch of mathematics, called category theory, which was invented for powerful communication of ideas between different fields […]
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(via disneyville) È inutile che spieghi l'importanza di Topolino per la cultura italiana. Studiosi ben più qualificati di me lo fanno e lo faranno. Vi posso però dire che cosa significa per il sottoscritto. Quando negli anni '80 ero un bambino, Topolino per me non era solo uno svago. Su quelle pagine ho visto Paperino venire assunto come manager di Rockerduck, per poi scoprire che non serve a nulla il successo se non hai nessuno con cui condividerlo. Ho visto l'eroismo dell'uom... papero [â€¦]
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In light of my new position as a HarvardX Research Fellow, I have been thinking about the role of data in improving online learning experiences (aka MOOCs) at edX. Can data tell us everything about the ideal learning experience of tomorrow? Can product developers at edX come up with the best version singe-handedly? Or, maybe, [...]
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I just read two very different science books, Daniel Kahneman's Thinking, Fast and Slow and Scott Aaronson's Quantum Computing since Democritus. Not much to connect the two except both deal to some extent about probability and computation and I want to write a blog post for each chapter, for much I disagree with both authors. But that's what makes them so much fun, so rare to find science-oriented books both worth reading that have the guts to say things that one can disagree with. In full [â€¦]
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Questions/answers  about Gold OA: (please add your answers and other questions) 1. Is the author a customer of a Gold OA publisher? I think it is. 2. What is the author paying for, as a customer? I think the author pays for the peer-review service. 3. What offers the Gold OA publisher  for the money? […]
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Patient M: It’s impossible —- no one could urinate into that bottle -— at least no woman could. I’m furious with her [these are the patient's emphases] and I’m damned if I am going to do it unless she gives me another kind of bottle. It’s just impossible to use that little thing. Analyst: It […]
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Methodology and Ontology in Statistical Modeling: Some error statistical reflections–uncorrected  Our presentation falls under the second of the bulleted questions for the conference: How do methods of data generation, statistical modeling, and inference influence the construction and appraisal of theories? Statistical methodology can influence what we think we’re finding out about the world, in the […]

### May 22, 2013

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Since the fields are so closely related, a lot of people who study math also end up studying at least a little bit of physics. I always wanted to take a physics class when I was an undergrad, but I … Continue reading →
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Re: Kilvington’s Sophismata Comment 1 On the one hand Aristotle gives us the logic of analogy (παραδειγμα). On the other hand he cautions us that different paradigms may have no common measure. It seems these Immortals are always getting ahead … Continue reading →
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This is a quick comment on the issue about Mochizuki's claimed proof of the abc conjecture that Catarina wrote about a couple of days ago. (I don't know much about this number theory stuff.)Are proofs cognitive entities? Is every proof cognized? Known? Knowable?Cognitive Reductionism about ProofsEvery proof P of a mathematical claim is cognizable by some one (or more) agent.This claim is analogous to certain verificationist claims more generally (e.g., every truth is knowable). I believe that [â€¦]
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Cognitive Reductionism about languages is the following (empirical) claim:Every language L is spoken/cognized by some one or more speakers.That is, the claim that languages can be reduced to cognitve states of some one or more speakers. However, I think that cognitive reductionism is deeply mistaken. There are languages which are not spoken, or cognized.So, on my view, statements of the form:Agent A cognizes language LAgents A and B cognize the same ("shared") language L. are contingent [â€¦]
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Having spent time in the Air Force and then developing software as a government contractor, I’ve survived more than my share of bad presentations. During this time I began reading the works of the statistician Edward Tufte[wiki]. I’d like to … Continue reading →
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Vitaly Bergelson, Tamar Ziegler, and I have just uploaded to the arXiv our joint paper “Multiple recurrence and convergence results associated to -actions“. This paper is primarily concerned with limit formulae in the theory of multiple recurrence in ergodic theory. Perhaps the most basic formula of this type is the mean ergodic theorem, which (among […]

### May 21, 2013

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When watching Jeopardy with Darling if I get a question correct that is NOT in my usual store of knowledge (that is NOT Ramsey Theory, NOT Vice Presidents, NOT Satires of Bob Dylan) Darling asks me How did you know that? I usually reply I do not know how I knew that. Recently I DID know and I'll get to that later, but for now the question arises: Do you know how you know what you know? As an undergrad I learned mostly from taking courses. Hence I could say things like I Know Group theory from [â€¦]
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Knowledge is like an irregular blob. (thanks due to Jon Awbrey for the following quote) Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions, and virtually […]
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Now I’m back from my Bahamian break, I’m intermittently doing some reading, preparing for another version of the Teach Yourself Logic Guide to be put online at the end of the month. I’ve just been taking another look at Enderton’s … Continue reading →
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A Science publications is one of the best ways to launch your career, especially if it is based on your undergraduate work, part of which you carried out with makeshift equipment in your dorm! That is the story of Thomas M.S. Chang, who in 1956 started experiments (partially carried out in his residence room in […]
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The previous section covered the case of $f \in L^2(\Omega^n, \pi^{\otimes n})$ with $|\Omega| = 2$; there, we saw it could be helpful to look at explicit Fourier bases. When $|\Omega| \geq 3$ this is often not helpful, especially if the only “operation” on the domain is equality. For example, if $f : [...] + Last year, a couple of thousand people downloaded Gödel Without (too many) Tears, and the notes continue to be downloaded at the same rate. Which makes me think I could usefully update/expand the notes so that, for a start, they integrate … Continue reading → + In questo periodo sto provando a preparare una quinta all'esame di stato. Il provare dipende essenzialmente dal fatto che la classe non sembra essere particolarmente interessata ad arrivare all'esame e sto arrivando alle minacce di insufficienze. A parte questi problemi, però, sto al momento affrontando il secondo problema del compito d'esame dello scorso anno, in particolare il quesito in cui viene richiesto il volume di un solido$W$. Data una regione$R$del piano$xy$, base del solido$W\$, [â€¦]
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I see metasemantics has having two major components (cf, David Lewis 1970, "General Semantics"). One component studies languages, what their properties are, how they're individuated, etc. The other component studies how languages are "cognized".On the first issue, for the metasemantics I prefer, languages are finely-individuated mixed mathematicalia, whose intrinsic syntactic, phonological, semantic, pragmatic, orthographic properties are essential. The corresponding individuation [â€¦]
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For the past few years I've been carrying around a small notebook to jot down notes from talks, research ideas, expenses, etc. (I guess I could do it on my phone but I prefer pen and paper.) I like writing with fountain pens, but don't care to carry around an expensive one: I don't feel I need to impress people with how much I spend on accessories, and I don't want to worry about losing it. I had been using disposable Pilot Varsity pens, but occasionally (especially if I took them on airplanes) [â€¦]

### May 20, 2013

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Saranno tre quarti d'ora che passeranno in fretta e molto leggeri. Tutto vi sembrerà, alla fine, molto chiaro e interessante. Buona visione e buon ascolto!
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I recently finished reading Brandon Sanderson’s Mistborn series. Sometimes I wonder what is wrong with me. Why can’t I just read a book and enjoy it for once? Instead, I became obsessed with the religious symbolism of the books and … Continue reading →
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Today, I am passing through New York City on my way to Princeton’s Center for Computational Intractability for a workshop on Natural Algorithms and the Sciences (NA&S). The two day meeting will cover everything from molecular algorithms for learning and experiments on artificial cells to bounded rationality in decision-making and the effects of network topology […]
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Writing a blog like this, a strange and often puzzling exercise[1], does offer a forum for sharing half-baked chicken-scratchings from the back of frayed pages on themes from our Onto-Meth[2] conference from two weeks ago[3]. (The previous post had notes from blogger and attendee, Gandenberger.) Several of the talks reflect a push-back against the idea that […]
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