cokernel

This algorithm didn't appear out of nowhere. Maybe this page should mention the source?

I had pictured this as being essentially Gauss's algorithm, but if Wikipedia is correct, this particular implementation is due to Tomohiko Sakamoto in 1993.

https://en.wikipedia.org/wiki/Determination_of_the_day_of_th...

I thought there might be some interest in knowing how people who were in both the 1st and 5th Congresses voted on the Alien and Sedition Acts. This actually consists of four distinct acts, and I chose to focus on An Act concerning Aliens (the second of the four acts).

The short answer is: Federalists voted for it, and Democratic-Republicans voted against it.

If I'm reading the House and Senate Journals correctly, the relevant legislative history is as follows:

1. 1798-06-08: The Senate approves the bill. https://memory.loc.gov/cgi-bin/ampage?collId=llsj&fileName=0... https://www.govtrack.us/congress/votes/5-2/s99

The bill passed by a vote of 17-6 (GovTrack reports this as 16-7 for some reason). Of the 12 members of the 1st US Congress who were senators in the 5th US Congress, two (John Henry and John Vining) had resigned well before the summer of 1798, and four (James Gunn, John Langdon, Philip Schuyler, and Theodore Sedgwick) did not vote on the bill. The remainder voted on straight party lines:

* Affirmative: Theodore Foster, Benjamin Goodhue, John Laurance, Samuel Livermore. (Federalists)

* Negative: Timothy Bloodworth, John Brown. (Democratic-Republicans)

2. 1798-06-21: The House approves the bill, with amendments. https://memory.loc.gov/cgi-bin/ampage?collId=llhj&fileName=0... https://www.govtrack.us/congress/votes/5-2/h90

The bill passed by a vote of 46-40. Of the 9 members of the 1st US Congress who were representatives in the 5th US Congress, one (William L. Smith) had already resigned at the time the bill was considered, and two others (Thomas Hartley and Josiah Parker) did not vote. The remainder voted as follows:

* Affirmative: Abiel Foster, James Schureman, Thomas Sinnickson, George Thatcher. (Federalists)

* Negative: Abraham Baldwin, Thomas Sumter. (Democratic-Republicans)

3. 1798-06-22: The Senate concurs in the amendments. https://memory.loc.gov/cgi-bin/ampage?collId=llsj&fileName=0...):%230020505&linkText=1

Either there was no vote here, or the yays and nays were not requested. The Senate Journal just says that they took into consideration the amendments and resolved that they concur in the amendments.

Thanks, I've fixed it.

The 1st US Congress had 29 senators and 66 representatives (95 distinct people), not all simultaneously, while the 5th US Congress had 45 senators and 118 representatives (162 distinct people, as Andrew Jackson served as both a representative and a senator during this period)[0].

Of the 95 members of the 1st US Congress, 21 (~22%) of them were members of the 5th US Congress, with the following breakdown:

* 5 senators (~17%) remained senators;

* 9 representatives (~14%) remained representatives; and

* 7 representatives (~11%) became senators.

Notes: John Brown was initially a representative of Virginia, then later became a senator of Kentucky (which was part of Virginia at the time of the 1st US Congress). William Smith (MD; 1st US House), William L. Smith (SC; 1st US House), and William Smith (SC; 5th US House) were all different people.

Method: moderately careful transcription plus grep, perl, sort, uniq, and comm.

EDIT: Thanks for adventured for the correction. I mistranscribed Philip Schuyler's name when copying down the members of the 5th US Congress.

[0] I didn't independently check the lists on Wikipedia[1][2].

[1] https://en.wikipedia.org/wiki/1st_United_States_Congress

[2] https://en.wikipedia.org/wiki/5th_United_States_Congress

The structure of Doron Zeilberger's proof of the Alternating Sign Matrix Conjecture is reminiscent of this, though possibly not directly inspired by it: http://www.combinatorics.org/ojs/index.php/eljc/article/view...

I don't read the authors as saying that intellectual need is the only way to motivate. Rather, they're saying that regardless of motivation, students are unlikely to learn certain concepts unless they directly experience the need for those concepts ("disequilibrium"). (Of course, it's possible to learn to solve a class of problems that "require" certain concepts without learning those concepts.)

Where the MUSIC model addresses motivation, the DNR framework addresses what to do with that motivation. So they seem compatible to me. The teachers described in this article would certainly benefit from studying the MUSIC model. I winced a little at the teacher who said, "Well, you care if you want to get a good grade on your test."

Thanks for this comment. While trying to track down the source of the quote, I ran into this interesting, if a bit oddly formatted, blog post:

http://publicnoises.blogspot.com/2009/02/aristotle-and-accur...

There are a few good comments there, too, followed by a bunch of me-toos.

Linguistic evolution is much like biological evolution in that there is no a priori direction for it to go. There is a sort of natural selection in that words that don't get used don't generally get passed on to the next generation. Text and other media allow some of these words to be recovered in later generations.

If history is any indication, in 100 years American English will have some precise ways of expressing things, some loose ways of expressing things, and various groups of people will be unreasonably upset with one situation or the other.

If you're interested in the mechanisms of language change, I found the (2000) 3rd edition of Jean Aitchison's _Language Change: Progress or Decay?_ both readable and worth reading. There is a 4th edition, published in 2013:

http://www.cambridge.org/us/academic/subjects/languages-ling...

I notice that Sarsons's paper says on the very first page:

"NOTE: Very preliminary – please do not cite without permission. Comments welcome."

I wonder if Cowen sought permission or just ignored that sentence? I am aware that linking to something from a blog isn't exactly the same as citing it (presumably Sarsons is trying to discourage citations in other papers), but Cowen could have mentioned, but didn't mention, the preliminary nature of the paper when quoting the abstract.

Is the thing I've overlooked that there are two As?

It's a nice interface. I'm glad arrow keys, the first thing I tried, work. But you're not going to trick me into looking for a sequence of moves that change the parity of the underlying permutation.

I wouldn't read this expecting a condemnation of (or evidence against) installing using RAM. It's a comedy of errors brought about by the hero's hubris (and tiredness). The author is not really suggesting that you should never install used RAM.

Consider it a longform version of https://xkcd.com/349/ .

Incidentally, 45% of 50 is not an integer. This makes me wonder how many books were actually tested. Or were they just rounding up from 44%?

The URL says "Harvard Law Library sacrifices a trove for the sake of a free database", and the title of the print article is "Sacrificing a Legal Trove for the Digital Age", so perhaps the submitter did not editorialize the submission title. Maybe the online title has just changed since submission.

Presumably they found it more important to preserve the pages than to preserve the volume binding. The FAQ for the linear book scanner indicates that Prototype 1 mangles pages in some way (tears or folds) in about 45% of books it scans.

Moreover, it used to be common to create bound volumes by binding multiple issues of a serial together. (In some cases the bindery would crop pages to fit!) The binding is often so tight that the volume cannot open flat enough for a full scan. Separating the pages from the spine allows for the entire page to be imaged without distortion.

Edit: Incorporated correction. I had accidentally stated the claim more strongly than the FAQ supported; however, my point does not depend on the claim being as strong as the form in which I had stated it.

I don't know why a theory has to be labeled "new" to be worth discussing. (I'm know I'm hyperfocusing on Shermer's phrase "a new theory", sorry.)

Hoffman's argument is remarkably close to Plantinga's (1993) evolutionary argument against naturalism, and Plantinga himself asserted, rightly or wrongly, that "Darwin himself had worries" about the compatibility of natural selection with the ability to reach true conclusions. And of course, the notion of "percepts act[ing] as a species-specific user interface" was discussed in voluminous detail by Kant.

Just to be clear, I don't have any problems with Hoffman proposing this idea, and I don't have any problems with Shermer criticizing it. What I don't like is the suggestion that this is somehow an idea that hasn't already been discussed for centuries.

Edit: I guess I should always make sure I've eaten something before posting. This came out angrier than I intended.

It took Wiles seven years to prove the thing (and the proof needed to be patched!), so I wouldn't be discouraged if it takes a while to understand. A nice thing about mathematics is, it waits for you.

If you're interested in the mathematics behind this, I'm not sure a direct attack on the FLT proof is the best route to take. The paper that proves a famous conjecture is normally sitting on a mountain of prior work, which means the final paper (1) assumes familiarity with that mountain and (2) is highly technical because all of the understandable things have already been tried.

So instead, why not start learning about the mountain?

The truth of FLT follows from the two claims:

(1) Taniyama--Shimura--Weil conjecture: "Every elliptic curve is modular."

(2) Ribet's Theorem: "If FLT has a counterexample, then such and such an elliptic curve is not modular."

As it happens, TSW was originally believed to be too difficult to prove, but I suppose the connection with FLT motivated people. Taylor and Wiles proved the absolute minimum of TSW that they could get by with and still get a contradiction from Ribet's theorem. (My understanding is that TSW is now fully proved -- the "modularity theorem".)

If you're wanting to "get" FLT, I'd encourage you to look into elliptic curves, modular forms, and their relationship. I wonder if working on the mathematics of elliptic curve cryptography might be a good way to get a feel for elliptic curves.

However, if you do want to take the direct route, I believe that Faltings's highly compressed article provides a syllabus. Once you can read and completely understand every sentence of that article, it is highly likely that the Wiles and Taylor and Wiles papers will make sense. I... would really not recommend this route.

This analysis was written by Thomas M. Cooley, who was Chief Justice of the Michigan Supreme Court at the time. It was mentioned in passing in a Guardian article discussed here recently: https://news.ycombinator.com/item?id=10401416

The first page is here: https://archive.org/stream/jstor-3303981/3303981#page/n1/mod... Not sure why the link shows the final page as the thumbnail.

A minor nit: Thomas Snell et al. v. The Atlantic Fire and Marine Insurance Company is the opinion which follows Thomas M. Cooley's opinion you are quoting here.

Thomas M. Cooley's 1879 analysis of privacy of telegraphic correspondence (the "hampered by fears" link in the Guardian article) is fascinating: https://archive.org/details/jstor-3303981/

I haven't tested this, but the package https://github.com/subokita/Robust-Text-Detection apparently implements methods described in the paper "Robust Text Detection in Natural Images with Edge-Enhanced Maximally Stable Extremal Regions." by Chen, Huizhong, et al. (http://web.stanford.edu/~hchen2/papers/ICIP2011_RobustTextDe...), which sounds like it might be the sort of thing you want.

In particular, the figure on the first page of the paper shows detection (not OCR) of a textual logo in a photo.

The article explains that these items can unexpectedly shed light on historical questions, giving as an example a letter from Marat that seemed to demonstrate he was not in an English prison at a time when most historians thought he was.

Items in archives are like fossils: remarkably rare, incredibly personal to the entity involved, but potentially of great import to the rest of us because of what we can learn from them.

I admit I'm a little tone-deaf and didn't notice any hyperbolic language, but I would encourage you to give the article another chance.

As the article points out, the Mass Shooting Tracker tracks mass shootings (at least four people shot), not mass murders.

I'm way out of date. The proof (discretized using hypermaps instead of graphs) was completely formalized in Coq in 2005: http://research.microsoft.com/en-us/um/people/gonthier/4colp...

The standard proof does use nodes and arcs (or vertices and edges, which I am taking to mean the same thing). A proper coloring must assign distinct colors to neighboring vertices, but this doesn't mean that vertices with the same color are identified.

Here's an overview of the simplest version of the proof as of 1998: http://www.ams.org/notices/199807/thomas.pdf . This should shed some light on why the proof is as complicated as it is. (See especially the section on equivalent formulations.)

It's worth devoting a portion of classroom time (in my opinion, a substantial portion) to discussion of the topic, perhaps focusing on particular problems and generalizing from there. For example, you might select random students each day to present problems from homework. If you've ever noticed that you learn something better once you teach it to someone else -- well, it works for your students, too.

Moreover, if you create a non-judgmental environment in which people are free to talk about their approaches to problems and get feedback not only from you but from other students as well, then just by watching carefully, you will learn some of the more common gaps in understanding. (Note that some students will not talk in these situations unless forced, but that does not mean they do not benefit from following the discussion.)

If you're anything like I was when I was first TAing courses like this, you might think that if you do this, you won't have enough time to "cover the material". But I put it to you that a lecture that is not absorbed doesn't cover anything.

At my (American, liberal arts, flyover country) university, linear algebra was my first real mathematics course. (The prior classes were calculus and a "proof" class, AKA intro to intro to number theory.) I'd been introduced to the determinant, Gauss--Jordan elimination, and so on, in high school, but all in a very mechanical way.

I think this transition between mechanically generating solutions to problems using pattern matching and some basic algorithms on the one hand, and the more mathematically mature approach of exploring problem spaces using pattern matching, some basic algorithms, and intuition can be difficult for many people.

It's not necessarily the material -- you can get used to almost anything, and even convince yourself it's easy or obvious with enough familiarity -- but the lack of intuition. When you're first learning linear algebra, its fundamental unity is not obvious, especially if the instructor does not take pains to point it out. (And even if the instructor does take pains to point it out -- well, it's hard to understand why the instructor is saying we could do this computation this way or that way.) So in the absence of existing intuition or any perception of unity, linear algebra becomes another target for pattern matching and basic algorithms.

As it happens, I've never, ever felt like I didn't "get" linear algebra. However, I almost always feel like I "get" it now and all my prior conceptions of it were a confused muddle.

"Kind of harsh" is an understatement. Insulting the reader like this is not acceptable. Mathematics is already difficult enough to learn by its very nature. Authors, you don't need to help make it more difficult. We already have a hard enough time convincing people that they can learn something this difficult.

In case it helps, this is literary theory (aka "theory"), not philosophy. Although there is definitely communication between the two fields, they have their own traditions and their own vocabularies. One of the more obvious differences (and here I am comparing with analytic philosophy specifically) is that literary theory is often quite allusive where an otherwise equivalent philosophical argument would be explicit. I think the reason for the difference here is that in philosophy, the goal is clarification of the argument itself, while in literary theory (from my outside perspective I believe) the goal is a sustained state of aporia.

Note: I am by no means an expert in literary theory, but I thought I would give my reading of the sentence you quote.

Jameson is summarizing the previous few paragraphs of the review, where he describes the "generic problems of political, indeed utopian thought". The basic problem is this: how do you talk about major changes to the way society works? At the time period discussed, just as at any other, there were a lot of big ideas about how society ought to be organized, but they did not come with instructions for implementation. Wittenberg (according to Jameson) says that what Wells brought to the table was a literary device to allow an examination of the alternative organization of society without the need to focus on the transition between the current society and the imagined one, in a way dissolving the problem.

"Differentiation" refers to the notion that a society can be viewed in some ways as an organism which attempts to restructure itself to represent and respond to its surroundings.

So Jameson is just using a fancy but allusive way of restating and generalizing the claim that Wells was introducing a new way for society to talk about changes to itself.

I'm not saying I agree or disagree with this, and I definitely can't comment on whether Jameson is characterizing Wittenberg's book correctly, but I think that's what is being said.

Comma and colon are also quite different.