Secondary Qualities

Well, as long as that's clear

2009-11-06T18:51:00.000-05:00

I mean, I was worried that intelligent design was just creationism in disguise. But now we don't have to worry about it, because Bill Dembski rationally, intellectually defends intelligent design…from a bible. Wait…

TeX articles moved to the blog

2009-11-05T14:56:00.000-05:00

As you can see, I've packed up the LaTeX articles from the "Technology" section of my website and moved them over here to my blog. Two main reasons – first, they don't really fit the rest of my professional website (they're more like blog content, if you will), and secondly, I'm about to redesign my professional website, and I don't want to make room for them.

So those three articles will be available for posterity here. I'll be writing a few more in the coming weeks and months – I'm slowly being converted over to XeLaTeX, with its slick handling of OpenType fonts, and I'll probably write something up about it, since it smoothes over what's probably the single most annoying feature of old-fashioned PDFLaTeX.

Advanced LaTeX Typesetting

2009-11-05T14:53:00.000-05:00

So, this is essentially the saga of how I typeset my Princeton undergraduate senior thesis. Several people have expressed interest in seeing how it was done, so I figured I’d write up my collected wisdom as an article here. I’ll present this material as an annotated version of the document preamble.

\documentclass[10pt,twoside]{book}

I decided to use the book class here, as I needed chapter divisions. Article would have worked just as well. The 10pt specifier really isn’t used, but it’s what I started with, so I left it in.

% This implements margin kerning and font expansion to tweak the
% visual layout just a touch
\usepackage[activate={true,nocompatibility},final]{microtype}

This is a package that implements a few really ingenious extensions in PDFLaTeX. If you’re using that to produce your output PDFs (and you should be), this will implement margin kerning (allowing certain letters to stick outside the margin to trick the eye into perceiving a straight margin) and microtypographic font size changes (making a few individual letters larger and smaller by fractions of a point in order to make the “color” of the page more uniform overall). Also used for letterspacing (but see the caveat below).

% Page size
\usepackage[pdftex]{geometry}
\geometry{scale=1,paperwidth=6in,paperheight=9in,
bindingoffset=0in,top=.6667in,inner=1in,width=4in,height=6.8in}

This is a simple call to the geometry package to set the page size. I chose to typeset the book in 6x9 inch format, and use what is an approximately golden-rule proportioned main text block.

% Font packages: Sabon for text, Euler for math, include the RSFS
% font for the \mathscr environment, and drop caps.  Add a command
% to enable lining figures.  Also, Fourier ornaments.
\usepackage[LY1]{fontenc}
\renewcommand{\rmdefault}{psb}
\usepackage[LY1]{eulervm}
\renewcommand{\rmdefault}{psbj}
\usepackage{mathrsfs,lettrine}
\newcommand{\textpl}{\usefont{LY1}{psb}{m}{n}}
\DeclareMathSizes{11}{11}{6}{4}
\usepackage{fourier-orns}

This is the selection of my fonts. I purchased Adobe Sabon, and followed something like this OpenType font installation guide for converting the fonts into PostScript. The first command enables the LY1 font encoding, and the second temporarily sets the default font to the proportional-number (full-height numbers) version of the font. Then, the Euler math font package is loaded, as it balances well with Sabon. The proportional font package is loaded before this so the Euler math packages takes the full-height numbers from that font for use in math mode. Then, the proper old-style figure font is selected.

UPDATE 5/12/09: If you’re using Sabon, and particularly the Sabon OpenType fonts that I mention above, I can now very highly recommend Michael Gaehrken’s page with really nice packages for both Sabon itself and a really fine-looking Sabon math mode.

Several things could make this process a little different. First, if you don’t use the Euler math font package (others include the Mathdesign package that has Utopia, Garamond, and Charter math, or the Minion Pro math package), your math package might provide its own numbers. Alternately, you might want to see if you like the Euler numbers themselves, by adding the “euler-digits” option to the eulervm package. Regardless, if you don’t need the digits from your text font, you don’t need to set twice—just set it to “psbj” (or the appropriate code for your font) after ading the fontenc package.

Also, one reported source of problems when creating a new set of TeX fonts is an incomplete .fd file. In my TeX installation, the .fd files are located in tex/latex/sabon under the local TeX tree. The .fd file should contain many lines of the form “”, with psb perhaps substituted for your own font family. The two options after “psb” (the “m” and “n” above) are the various font weights and shapes, respectively. Unless you have a very complete font package (like the phenomenally extensive, beautiful, and pricey Sabon Next), you will probably only have fonts for the varieties “m/n”, “m/sc”, “m/it”, “b/n”, and “b/it”. This, however, is not enough to satisfy TeX. You’ll need to have aliases such that all the following varieties are available:

m/n
m/sc
m/it
b/n
b/it
m/sl
b/sl
bx/n
bx/it
bx/sl

The shape “sl” above is “slanted,” which I’ve generally aliased to “it”, and the “bx” weight is “bold extended width,” which I’ve aliased to “b”. An individual alias line should look something like:

\DeclareFontShape{LY1}{psb}{b}{it}{ <->ssub * psb/b/n}{}

In this line, I’ve aliased psb/b/it (bold italics) to psb/b/n, since the version of Sabon I purchased doesn’t contain a bold-italic variant. Make sure your font has all the appropriate varieties defined, and you should save yourself much headache later.

Finally, we load a few generic packages (mathrsfs for the calligraphic font and lettrine for large initial capitals), and define a command for when we want to temporarily switch to proportional figures. The DeclareMathSizes command increases the size of sub- and superscripts, which seemed a touch too small throughout the work. Finally, fourier-orns includes a nice selection of ornaments, one of which appears on the title page.

% Letterspacing
\newcommand{\spacecaps}[1]{\textls[200]{\MakeUppercase{#1}}}
\newcommand{\spacesc}[1]{\textls[50]{\textsc{\MakeLowercase{#1}}}}

This sets up commands that will letterspace both capitals and small caps, something that should be done for all extended runs of all caps and small caps in a work. NOTE! The textls command is provided by the microtype package, and uses letterspacing implemented in the core of PDFLaTeX. However, this requires a VERY NEW version of PDFLaTeX—you will either need to compile a new binary from the PDFTeX source, or download at least version 2007 of TeX Live. Otherwise, you can try to use the older and significantly more liable to break “soul” package. I warn you, though, that downloading the latest PDFLaTeX build will save MUCH consternation.

% Paragraph indentation
\parindent=11pt

Set the paragraph indent to 1em.

% AMS math classes
\usepackage{amsmath,amssymb}

Not sure if I ever used anything in these packages, but I include them in every document I write.

% Nice tables, and the ability to set them sideways
\usepackage{tabularx,booktabs,rotating}

The tabularx package allows natural table column sizing, and the booktabs package documentation should be required reading for anyone who ever typesets a table. The rotating package allows one to set a table sideways, and it also automatically knows to rotate a table to the “outside” of a two-sided work like a book.

% Format the ToC
\usepackage[titles]{tocloft}

This is a great package for controlling the formatting of the table of contents. See its usage below.

% Figures and graphics
\usepackage[captionskip=11pt]{subfig}
\usepackage{graphicx}
\usepackage[all]{xy}

I use the subfig package for subfigures, and the standard graphicx package for graphics. The XY-pic package is great for making small on-the-fly line drawings using nothing but TeX source.

% Proper title formatting
\usepackage[rm,tiny,raggedright]{titlesec}

This is the package that allows one to easily change the formatting of section titles. The more detailed configuration for that formatting is below, but the default options here set titles to text-size by default, turn off bold-face, and set ragged-right.

% Footnote config
\usepackage[norule,splitrule,multiple]{footmisc}
\makeatletter
\renewcommand\@makefnmark{\@textsuperscript{\@textsuperscript{\@thefnmark}}}
\renewcommand\@makefntext[1]{%
     \parindent 1em%
    \noindent
    \hb@xt@1.3em{\hss\normalfont\@thefnmark.} #1}
\def\splitfootnoterule{\kern-3\p@ \hrule width 1in \kern2.6\p@}
\makeatother
\renewcommand\footnotesize{\fontsize{8}{10} \selectfont}
\renewcommand{\thefootnote}{\textpl{\arabic{footnote}}}

This block configures the typesetting of footnotes. First, we load the footmisc package, whose sole purpose is to make the horizontal rule above footnotes behave properly—the rule should only appear above a footnote that has been continued from a previous page, unlike the normal TeX method of placing a rule before every block of footnotes. The redefinition of makes footnote numbers smaller (by making them double-superscript). The redefinition of changes the body of the footnote itself to actually display as “1. Text” instead of “Text”. The “splitfootnoterule” command sets the width of the footnote rule. The “footnotesize” sets a proper size for footnotes, and the “thefootnote” command causes the footnote numbers to be set in proportional (not old-style) figures.

% Bibliography and its configuration
\usepackage[round,comma,authoryear,sort&compress]{natbib}
\makeatletter
\let\@internalcite\cite
\def\cite{\citep}
\def\shortcite{\citeyearpar}
\makeatother
\renewcommand{\bibsection}{\chapter*{Bibliography}
  \addcontentsline{toc}{chapter}{\numberline {}Bibliography}}
\setlength{\bibhang}{0.25in}
\setlength{\bibsep}{13pt}
\bibpunct{(}{)}{;}{a}{}{,}

The natbib command sets up the first part of the bibliography formatting. I wanted to use author-date citations, and allow the ability to remove the author’s name from the citation and print only the year. The command is redefined to print (Author 2007) and the command will produce just (2007). That effect is produced by the natbib package options, the redefinition of the cite commands, and the bibpunct command. Finally, the bibsection redefinition does a complicated method to make the bibliography properly appear in the table of contents, and the bibhang and bibsep commands are cosmetic formatting options.

% So I can change dash type at will later if I so desire
\newcommand{\h}{ -- }

On the advice of Robert Bringhurst [editorial comment: READ THIS BOOK], I decided early on to give up the long em dash in place of the spaced en dash. I wanted the ability to change my mind later, so I defined the command. It’s no longer than typing the dash in by hand to simply type in the command itself, so I decided to leave it in.

% Headers
\usepackage{fancyhdr}
\fancypagestyle{empty}{
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\fancyhf{}}
\fancypagestyle{plain}{
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\fancyhf{}}
\fancypagestyle{main}{
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\fancyhf{}
\fancyfoot[LE,RO]{\thepage}}

The fancy headers package just sets up normal book-style headers, with no gigantic rules.

% Whenever I call cleardoublepage (or, chapter starts call
% cleardoublepage), I want the cleared facing page to have no headers
% or footers.
\makeatletter
\def\cleardoublepage{\clearpage\if@twoside \ifodd\c@page\else
  \hbox{}
  \thispagestyle{empty}
  \newpage
  \if@twocolumn\hbox{}\newpage\fi\fi\fi}
\makeatother

See the comment. Whenever is forced to insert a blank page, I don’t want that page to have headers, footers, page numbers, and so on.

% Section formatting, et. al.
\titleformat{\chapter}[display]
  {\fontsize{11}{13} \selectfont}
  {\spacecaps{CHAPTER {\textpl{\thechapter}}}}
  {1em}
  {\spacecaps}
  [\vspace{13pt} \hrule]
\titlespacing*{\chapter}{0pt}{13pt}{13pt}
\titleformat{\section}[hang]
  {\fontsize{11}{13} \selectfont}
  {\thesection}
  {1em}
  {\spacesc}
\titlespacing*{\section}{0pt}{13pt}{13pt}
\titleformat{\subsection}[hang]
  {\fontsize{11}{13} \selectfont \itshape}
  {\thesubsection}
  {1em}
  {}
\titlespacing*{\subsection}{0pt}{6pt}{7pt}
\newcommand{\parasep}{\begin{center}*\hspace{6em}*\hspace{6em}*\end{center}}
\newcommand{\runinhead}[1]{\textit{#1.}\hspace{1em}}

Here’s the section title formatting. Chapter titles are two lines, one saying “CHAPTER N”, letterspaced all caps, and the next with the title of the chapter, letterspaced all caps, with 13pt leading before and 13pt leading after. Section headers are formatted letterspaced small caps, with the section number without a period (i.e. “1 SECTION”), 13pt leading before and after. Subsections are italic u&lc with 6pt leading before and 7pt after. I define a “parasep” command to insert a three-asterisk text separator, and a “run-in header” command to put a run-in paragraph header.

% Table of contents formatting
\setcounter{tocdepth}{0}
\renewcommand{\cftdotsep}{\cftnodots}
\renewcommand{\cftchapfont}{}
\setlength{\cftchapnumwidth}{2.25em}
\renewcommand{\cftchapleader}{\quad}
\renewcommand{\cftchappresnum}{\itshape}
\renewcommand{\cftchapaftersnum}{}
\renewcommand{\cftchappagefont}{\normalfont}
\renewcommand{\cftchapafterpnum}{\cftparfillskip}
\setlength{\cftbeforechapskip}{13pt}

This is my set of commands for tocloft to configure the table of contents. I only include chapters (that’s the tocdepth command), remove the dots as separators, and I do NOT right-align the page numbers. See the PDF file for how it turns out.

\begin{document}

% No extra spacing after periods
\frenchspacing
% Font sizing
\fontsize{11}{13}
\selectfont

This is the only code that needs to come after the beginning of the proper document. Set the “frenchspacing” command to disable extra spacing after periods at the end of sentences. This is an old, antequated typesetting convention, and shouldn’t be used in modern documents. Then we set the actual font size, and away we go!

The only other thing that one might find interesting is the custom bibliography style I produced for this. It’s based loosely on the Journal of Symbolic Logic bibliography format, and I updated it to set a three-em dash on repeated authors, and standardize things a little better across quite a few document types. Again, see the thesis PDF for how it looks in the end.

Download the BST file.

LaTeX and Tableaux

2009-11-05T14:48:00.001-05:00

For my PHI 340 at Princeton, I found myself needing to typeset lots of tableaux-style proofs in the style of our textbook, Possibilities and Paradox, An Introduction to Modal and Many-Valued Logic by Beall and van Fraassen. The same sorts of tableaux proofs appear in Tomassi’s Logic. Here's a tutorial teaching you how to typeset them in LaTeX, using a couple of freely-available packages.

First of all, it’s assumed that the reader is already familiar with the LaTeX typesetting system and its various and sundry intricacies. It’s a fairly difficult thing to learn, but once you’ve got it, it’s incredibly useful. For those looking to get started, I just happen to have a tutorial published on this very blog.

Qtree, the tree-making package I’m using in this document, is part of TeX Live. If you aren’t using TeX Live, however, you’ll need to download qtree from the author’s site. For *nix users, drop this file into your texmf tree, usually located at /usr/share/texmf, in the tex/latex/qtree folder, and do whatever you need to do to make your TeX distribution update its filename cache. For MiKTeX on Windows, assuming you took the default install location of the texmf folder (c:\texmf), make a new directory at c:\texmf\tex\latex\qtree and drop qtree.sty there. Then, go to Start -> Programs -> MiKTeX -> MiKTeX Options and click “Refresh Now” under “File name database” on the first screen.

With that out of the way, we’re ready to actually start creating some documents. The qtree syntax takes a bit of getting used to at first, but all in all, the structure of the LaTeX document pretty effectively mirrors the final structure of the tree.

To begin, create a basic LaTeX document in your normal manner. I’d recommend 12pt in the document type, or you’ll run into some readability problems.

In case you’ve never typeset any sort of formal logic in LaTeX before, here’s the full set of logical connectives and symbols that you should be concerned with:

$\neg$ : unary not (the "hook" variety)
$\mathord{\sim}$ : unary not (the "tilde" variety)
$\square$ : modal "box"
$\lozenge$ : modal "diamond"
$\lor$ : wedge
$\land$ : caret
$\supset$ : horseshoe
$\equiv$ : tribar

$\otimes$ : circled X (closed tree branch)

UPDATE 2/4/08: I’ve added a formatted symbol (using the custom math symbol commands) thanks to Kevin Klement that provides a proper “tilde” unary-not symbol, in addition to the “hook” unary-not symbol that was already listed. Thanks!

Two more notes I almost forgot: to get this full set of symbols, you’ll need to be sure to include the amssymb, latexsym, and amsmath packages. Also, qtree uses PostScript specials, which means PDFLaTeX refuses to process such documents. You’ll need to do standard LaTeX and then run dvi2pdf or ps2pdf to get PDF files (both those programs should come with any reasonably decent TeX implementation).

With the preliminaries now fully out of the way, let’s start creating some trees. First a big, relatively daunting example from my latest problem set:

Which is generated by the following block of LaTeX:

\vspace{\baselineskip}
\Tree
[.{\framebox{$\neg(\lozenge(p \lor q) \supset (\lozenge p \lor \lozenge q)), w_0$}}
[.{\framebox{$\lozenge(p \lor q), w_0$} \\
\framebox{$\neg(\lozenge p \lor \lozenge q), w_0$}}
[.{$w_0 R w_1$ \\
\framebox{$p \lor q, w_1$}}
[.{\framebox{$\neg \lozenge p, w_0$} \\
\framebox{$\neg \lozenge q, w_0$}}
[.{$\square \neg p, w_0$ \\
$\square \neg q, w_0$}
[.{$\neg p, w_1$ \\
$\neg q, w_1$}
[.{$p, w_1$} [.$\otimes$ ] ]
[.{$q, w_1$} [.$\otimes$ ] ]
]
]
]
]
]
]
\vspace{\baselineskip}

As I said above, this is meant to look relatively daunting. The actual construction of trees such as this is relatively simple. Let’s walk through writing the tree given as an example on p. 40 of BvF, which tests the following argument: is the following set satisfiable (in a language with no restrictions on the world-relationship R)?

So, to begin, we start by writing the following code, which sets out our premises on the trunk of the tree:

\Tree
[ .{$(p \supset q)$ \\
$(r \lor \neg q)$ \\
$\neg r$ \\
$\neg p$}
]

A few things to be careful of here: Note that the entire contents of a tree node must be surrounded by curly braces (a convention not entirely unfamiliar to LaTeX users), and also note the period before the starting curly brace. The best way to continue the explanation is by example. Now, following standard tableaux rules for CPL, we box the first formula and create the two branches at the lowest level of the tree:

\Tree
[ .{\framebox{$(p \supset q)$} \\
$(r \lor \neg q)$ \\
$\neg r$ \\
$\neg p$}
[.{$\neg p$}
]
[.{$q$}
]
]

Notice that we simply start two new branches after the closing brace of the contents of the current node. Both of these branches look exactly the same as the trunk, beginning with a period and with their contents surrounded by curly braces. Also note the \framebox command to box the first formula, and the fact that even in nodes with only one formula, I go ahead and return/indent the closing bracket of the node, which makes it easier to add subnodes later on. Now, box the second formula, and add those new branches to the two lowest levels of the tree in exactly the same manner as before:

\Tree
[.{\framebox{$(p \supset q)$} \\
\framebox{$(r \lor \neg q)$} \\
$\neg r$ \\
$\neg p$}
[.{$\neg p$}
[.{$r$}
]
[.{$\neg q$}
]
]
[.{$q$}
[.{$r$}
]
[.{$\neg q$}
]
]
]

Of course, at this point, branches one, three, and four are closed off, with branch two remaining open (and thus this set is satisfiable). The tree is finished like so:

\Tree
[.{\framebox{$(p \supset q)$} \\
\framebox{$(r \lor \neg q)$} \\
$\neg r$ \\
$\neg p$}
[.{$\neg p$}
[.{$r$}
[.$\otimes$ ]
]
[.{$\neg q$}
]
]
[.{$q$}
[.{$r$}
[.$\otimes$ ]
]
[.{$\neg q$}
[.$\otimes$ ]
]
]
]

Not too terribly hard, no? For the sake of examples, I’m going to provide the TeX files both for a basic introduction that is essetially a LaTeX form of this document.

TeX source

PDF output

If you have any questions, feel free to e-mail me. Happy typesetting!

An Introduction to LaTeX

2009-11-05T14:38:00.001-05:00

So you want to typeset a document with lots of math, and you don’t want it to look like x + y^2 = 4z. No, you actually want it to look like your textbook. Well, you’re in luck. In all likelihood, the program the authors of your textbook used to write it is a handy little tool called LaTeX (‘LAY-tech’). There’s all sorts of history here involving LaTeX’s author (Knuth), the programming of TeX, the book that is the TeX source code (yes, the entire source code to TeX is actually a book that you can buy), but that’s for another time and place. Or some kind of computer science lecture or something. You just want to draw pretty integrals, right? Right. So let’s get to it.

Before we start, a brief note. This isn’t necessarily the easiest thing to do in the world, nor is TeX the easiest thing to learn. However, if you don’t have too solid of computer skills, this is a great time to start learning— especially if you’re going to be in the sciences or in math, you’ll have to use computers in a relatively advanced manner, all the time. So, even if you have to struggle through this, it’ll be good for you. No, really. Like eating your vegetables.

To get LaTeX, go to the TeX Live website if you have Windows, the MacTeX website for a Macintosh (running OS X), and either the TeX Live website or your package manager if you’re running Linux. Get the full TeX Live package, and install it (warning: this is a large download and a long install).

Now you need a good editor in which to write TeX documents. If you’re on Windows, you have to go fetch one—I like WinEdt, and people have recommended TeXnicCenter. On Mac, you got TeXShop for free with your TeX installation, which works pretty nicely. On Linux, you probably already have a favorite text editor (Emacs has really nice TeX support, as does vim), and you probably know how to use the terminal, so you’re set.

So, with that, let’s write our very first TeX document. Fire up your editor and fill a new document with the following:

\documentclass[letterpaper,12pt]{article}

\usepackage[left=1in,right=1in,top=1.25in,bottom=1.25in]{geometry}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amsthm}
\usepackage{amsfonts}
\usepackage{amssymb}

\newtheorem{thm}{Theorem}
\newtheorem{prp}{Proposition}
\newtheorem{lem}{Lemma}

\title{How to Take Over the World in 30 Days}
\author{Dr. Claw}

\begin{document}
\maketitle

\section{Getting Started}

Firstly, you need a world-domination plan. These may be
purchased at your local bookstore, or the very creative
can come up with one on their own.

\end{document}

Save this file as paper.tex (I‘d recommend having a different folder somewhere on your computer for each TeX document you make, because TeX will produce a lot of output files). Now, compile the document. [WinEdt: click the brown-dog-thing with a red curly-cue behind it; Mac: click the ’Typeset’ button; Linux: go to the command-line and type pdflatex paper.tex.] This will magically create a PDF file out of the above document. [WinEdt and TeXShop will open it for you automatically, Linux users run xpdf paper.tex.] Astute readers will immediately recognize the font here as that in which every single PDF set of lecture notes for every math class is written. Several things about the template we’ve already got. The first line tells LaTeX that you’re writing an article, which is the right kind of document for most academic papers, and sets the font size and paper size. The next block of five lines loads up packages, which, in TeX parlance, are add-ons that do different things. The first sets page margins, the second is a technical upgrade for nicer fonts, and the last three load useful math packages. The \newtheorem lines create things we’ll use later to write Theorems, Propositions, and Lemmas (shock). The title and author lines are processed by the \maketitle command below to produce the title block on the first page, so set them accordingly. The \begin{document} and\end{document} are the first and last lines of the actual paper. Right after \begin{document} should always be \maketitle, so TeX can write your title block/title page in your document. Now, we get to actually writing LaTeX.

First off, your document is divided into sections by the \section command. We’ve defined one section right off. You can define as many as you want—try copying and pasting the section command/paragraph and changing the section header. You’ll note that TeX numbers them automatically and formats them specially, all without you actually having to tell it how to do that formatting. Starting to see the beauty of the system? Good. Now, straight text in LaTeX is pretty easy. First of all, you can’t add white space between lines or paragraphs just by pressing return. Try typing the following lines to get a feel for how the paragraphs work in TeX:

 This
 is
 all
 on
 one
 paragraph

 This is all on a new paragraph.

 This too is a new paragraph. Note the blank line between
 the lines of text. That makes it start a new paragraph.
 But one
 return
 doesn't.

 See though, even though I try to put



 Lots of space between paragraphs



 It doesn't do anything.

This is one of the guiding principles of TeX—how you format things in your TeX file has little or nothing to do with the exact formatting of the final document. Get used to it, it’s actually kinda nice.
Okay, I hear you say, now I can write great English essays in this thing, but where’s the math? Right, right, here we go then. First off, you should know that there are basically three ways to type math in a TeX file. Here’s a little demonstration:

This math will be typeset $x+5 = y-3$ right in the middle
of the paragraph, or what's called ``inline''. Also, notice that
those quotation marks are funny. That makes TeX make nice
typographically-correct quotation marks, so use those things
instead of shift-apostrophe. This formula coming up will be
numbered and centered:

\begin{equation}
x^2 + 4(x - 5)^4 = 3^{x^2}
\end{equation}

If you don't want it numbered, add a star to the equation
environment, like this:

\begin{equation*}
x^2 + 4(x - 5)^4 = 3^{x^2}
\end{equation*}

Note that the math code between $$ is inline, and between \begin/end{equation} is typeset in the middle of the page, but there’s absolutely no difference between the math code between those delimiters— i.e. if you see me write somehwere else in the document that you do something between dollar signs or between equation tags, you can still use it between equation tags or dollar signs, respectively—these just change how the math is placed on the page. There’s also a more complicated environment you can use to write multiple equations in a row and line them up vertically on their equals sign, but it’s beyond the scope of this guide. Google “latex align” and you’ll find it.

So there’s a lot of math syntax to digest there. First, you can see that the simple syntax for raising things to a power is x^2 (that’s caret, or shift–6 on your keyboard). Also, if you want to raise to a power that’s not just a number, you have to put the argument in curly braces, like 3^{x^2} or a^{(p - 1)/2}. You should also be shocked at how automatic all of the formatting of this math is—you don’t have to do anything but type the formula. Now, I think more math formatting is best taught by example, so here we go. I’d recommend you copy these examples into your TeX file, compile it, and read the PDF along with the TeX source:

Here's one with some greek letters and subscripts, so
you get an idea of how those work. The subscripts use an
underscore instead of a caret, but work basically the same way.
Note how the subscript-superscript combo works:

\begin{equation}
2^\alpha = \phi_0 = b_0^2
\end{equation}

Now for number theory. First, to obtain the symbols for integers,
rationals, etc., we type $\mathbb{Q}$, $\mathbb{C}$,
$\mathbb{R}$, or $\mathbb{Z}/p\mathbb{Z}$. You get the
idea. LaTeX has a builtin mod function, but it produces horrible
output, so the thing to do is as follows. Note importantly the
space after ``mod'' inside the text command, and that equiv
creates the fancy triple-bar equals:

\begin{equation}
a \equiv 1 (\text{mod } p)
\end{equation}

Here's an integral. Note that you set definite integral limits with
sub and superscripts just like a variable. Also, using the sin with
the backslash makes it typeset properly. The backslash-comma
adds a little bit of space between the sin x and the dx to make it
look right. Also note the square root.

\begin{equation}
0 = \int_0^{2\pi} \sqrt{ \sin x }\, dx
\end{equation}

Here's a summation, which works basically the same way. Also
notice here we introduce how to do real fractions, which also
works for the Legendre symbol:

\begin{equation}
\sum_{k=1}^n k^2 = \frac{1}{2} n (n+1)
\end{equation}

And, if you're doing any advanced calculus, here's how to a
second derivative of u with respect to x, and then a second
partial derivative of u with repsect to x:

\begin{equation}
\frac{d^2 u}{dx^2} = \frac{\partial^2 u}{\partial x^2}
\end{equation}

The same subscripting technique as before also works for
limits:

\begin{equation}
\lim_{x \to \infty} \frac{1}{x} = 0
\end{equation}

If you need some kind of random symbol that’s not listed above, it’s almost certain that it’s available in LaTeX. Download [this massive PDF file](ftp://tug.ctan.org/pub/tex-archive/info/symbols/comprehensive/symbols-letter.pdf], and you’ll have a list of basically everything you could ever want.

This is about all the examples that I can think of right now. Google is your friend with LaTeX—much has been written about how this system works, and it’s pretty easy to find more information. Of course, if you have questions, you can always e-mail me. If you can think of some kind of problem you want to typeset that you can’t figure out (or that you can figure out, that you think should be on this page), e-mail it to me and I’ll add to the example collection! I hope this managed to make some sense, and you’ll find it useful. LaTeX is the best computer program since the C compiler, and I hope you find using it as easy and as holistically life-fulfilling as I do. Or something. Go write brilliant math!

Ah, Ayn Rand…

2009-10-25T12:58:00.003-04:00

In case anybody ever feels like asking me about her, things like this post right here are why Ayn Rand is (a) not a philosopher, and (b) hilariously ludicrous.

A message to the universe

2009-10-21T11:44:00.003-04:00

Dear universe, and particularly my students (past, present, and future):

Homo sapiens is not plural. The singular of Homo sapiens is "one member of the species Homo sapiens," not "a Homo sapien."

Thank you. That is all.

On Wasting Time

2009-08-25T16:46:00.002-04:00

Think philosophy is a waste of time? Read this. [Maverick Philosopher, via Leiter.]

The Scopes Trial and Flea Medicine

2009-05-22T21:05:00.003-04:00

Aww, cute puppies:

The original.

WHAT

[Thanks to Betty Smocovitis's talk for this gem.]

Website Maintenance with Pandoc and Markdown

2009-05-12T11:31:00.004-04:00

I've been struggling for a long time with how to properly and simply maintain a website. The eternal dilemma seems to be this: If you want to keep the HTML simple enough to be readily editable in a text editor, you're stuck with keeping the styling really simple. On the other hand, a nice theme has lots of header and footer material, which makes it a nightmare to deal with editing a page on a regular basis. You can smooth over the problem, but only if you have some heavy server power available to use stuff like PHP or server-side includes, and since my professional website is hosted on academic web servers, I don't have any control over what's happening server-side.

I finally think I've got a solution, using Pandoc. More below the fold.

I've known about Pandoc for a while now -- I'm using it to generate the user manual materials for Logos. But it only just dawned on me that a cautious use of Pandoc could make for a great easy-maintenance website system. So I've got a website tree set up like this:

/
/research
/teaching
/source
/source/research
/source/teaching

In the source directories are a bunch of files with ".mdtext" extension, written in Pandoc's extended Markdown language (the extension of Pandoc's which I use the most is the title block, which lets you do custom page titles).

Then, at the root of the source directory, I have a bash script, which recursively does the following: (1) calls pandoc on every .mdtext file in /source/, using a different HTML header and footer depending on whether or not the page is the main index (which has a slightly different theme), (2) moves the output to the appropriate place in the directory tree, (3) runs HTML Tidy over it to sanitize Pandoc's pretty heinous HTML source, (4, and most importantly) computes the depth in the directory tree at which the .mdtext file is located, builds a string of "../../" characters, and runs sed over the HTML output, replacing $TOP with the dots.

Why are the dots so important? Well, I don't want to use any static path names in my code, since there's multiple addresses you could be using to get to my website (charlespence.net, as well as whatever current host it's on, ND at the moment). So I need to be able to do things like refer to the stylesheet in each document, using a relative path. But the header and footer for all the documents is the same. So I set the href in the link tag to "$TOPstyle.css", and then have the script turn this into "style.css" or "../style.css" or "../../style.css" as the occasion requires.

Finally, I can mount the Notre Dame web host using SFTP and Fuse, and use rsync (rsync -crLO -T /tmp --progress --delete) to copy the files from my local directory to the server mountpoint. And finally I have a website system that makes things easy to maintain!

Watch this space -- I'm planning to put up a little collection of history of biology resources, now that I'm teaching a course this summer and can easily do such a thing.

Richard Dawkins in Oklahoma

2009-03-07T16:36:00.003-05:00

I don't normally just re-post content, but, honestly, this is hilarious. So, Richard Dawkins is going to give a lecture in Oklahoma, and the Oklahoma Legislature decides to condemn him. The video of his response, however, is more than worth the watching.

Blogging the APA Central: Day 3

2009-02-23T15:40:00.006-05:00

I was late getting into Chicago due to a crazy snowstorm, so I only managed to catch the last bit of a morning session on experimental philosophy and naturalism, mostly filled with a talk that was at great pains to establish the following two uncontroversial claims: (i) occasionally, philosophical naturalists speak loosely, which might lead one to believe that they thought that ID and its ilk ('God Hypotheses') were actually scientific, and (ii) if one actually does think that such God Hypotheses are scientific, then one is being self-contradictory in espousing philosophical naturalism. In point of fact, I agree with both. Of course, there hasn't yet been presented a God Hypothesis that actually is scientific, so as of yet the argument is moot.

Over lunch there was a meeting of the North American Nietzsche Society, which featured arguments for (Richard Schacht) and against (Maudemarie Clark) the claim that Nietzsche was a Lamarckian. [Note: for any historians or philosophers of biology, they don't really mean Lamarckian -- they only mean belief in the inheritance of acquired characters. Nietzsche would have been nothing less than an actual Lamarckian, as the inherent notion of progress built into Lamarck's notion of evolution would have driven Nietzsche batty.] A good exchange, one that I regard as rather inconclusive. Perhaps yet another point where Nietzsche couldn't quite make up his own mind.

The highlight of the day was the debate between Plantinga and Dennett on the relationship between science and religion. Plantinga's argument is, of course, bad, but it was presented particularly poorly (and rebutted fairly poorly as a consequence) on this occasion.

Plantinga's main points, with my editorial commentary:

The claims that the earth is ancient and that descent with modification are the mechanisms of the evolution of life are compatible with theistic belief. [I agree.]
The claim that the mutations which underly evolution are completely unplanned and unguided is incompatible with, at least, Christian theistic belief. [I'm not sure if I agree or not. I probably don't. But I don't have a horse in that race, so I'm not very concerned with this claim. At least in part, Plantinga's argument here seems to rely on the claim that a mutation-directing God is not part of an organism's environment, which seems absolutely preposterous.]
Further, evolutionary theory doesn't require such completely random mutations. [Indeed, in some sense. See Dennett's reply below.]
The claim that evolution undermines the argument from design, and thus the only really tenable reason for believing in God, is false, due to the work of people like Michael Behe. [Oh jeez. Yeah, he really did refer to Michael Behe. Dennett will tear this to shreds in a little while.]
The claim that evolution is a particularly bad case of the problem of evil isn't valid, because it's no worse an example of the problem of evil than anything else. [This is probably true.]
The claim that positing a theistic designer is unnecessary, in the Ockhamist sense, is false. [Plantinga's defense of this seems to hinge on the claim that there's no "further Ockamistic cost" for someone who already believes in God to posit a designer. That's true, but that's also completely evasive of the point.]
Even if evolution were contrary to theistic belief, theistic belief wouldn't automatically become irrational or unwarranted. [If by this he means it wouldn't become any more irrational or unwarranted than it already is, then I agree with that. Its warrant seems to have little to do with empirical fact.]
Conclusion of this first part of the talk: the supposed conflict between theistic religion and evolution is, in fact, a chimera.

So much for Part I. Now for Part II.

The probability that our cognitive faculties are reliable (i.e., that the content of most of our well-formed beliefs is true), given that naturalism and evolution are both true, is quite low. [This seems to me to be a really problematic claim, for lots of reasons. First of all, Plantinga said nothing in his talk about what the content of a belief is, how that content can be true or false, and so forth. I'll come back to this claim with the help of Dennett, below.]
If you accept that the probability is low, you have a defeater for every belief. [I don't see how this is true whatsoever. I accept that the probability of my own existence is low. I was born premature, and required quite a bit of medical intervention to reach adulthood. In this sense, the probability that I have reliable cognitive faculties is pretty small. I don't thereby have a defeater for my beliefs. Plantinga seems to think this follows straightforwardly.]
This defeater can't be defeated. [Because, I take it, any such defeat would be an argument, which would rely on other premises, which would be defeasible by the defeater already proposed. In other words, if you accept the position I'm trying to attack, you automatically become ineligible to do any philosophy in your own defense. Honestly...]
If you have a defeater for R, you have a defeater for every belief you have, including naturalism and evolution. [Fine, probably true.]
Therefore, the conjunction of naturalism and evolution is self-defeating and can't be accepted.
Plantinga backs up the first claim with some really hasty philosophy of mind, all reliant on the premise that adaptiveness -- in the sense in which our cognitive faculties would have had to be adaptive in order for them to evolve in our ancestors -- doesn't entail truth. [As far as I'm concerned, this claim is transparently false. If it isn't, Plantinga's going to have to give me a very careful account of beliefs, belief content, truth ascription, natural selection, and adaptiveness that makes the point. For my money, here's a good counterargument: (1) on most accounts, the content of our beliefs is fixed by repeatable, causal, physically law-based processes; (2) these processes create correlations between our mental states and the contents of the environment; (3) insofar as these correlations are established by these processes, they reflect the contents of the environment accurately. Now if Plantinga means something else by truth than accurate correlation with environmental stimuli, he'd better tell me what it is.]

Now, Dennett moves in. Three of Plantinga's premises, he says, are accurate, but not in the way Plantinga needs them to be for his argument.

Evolution is compatible with theistic belief. This is true, Dennett argues. Theism is one of a class of reasonably silly beliefs that are nevertheless compatible with evolution. Thus, as supporters of evolution, we have no contradiction upon which to base a rejection of theism. (After all, Dennett argues, finding actual evidence of intelligent design is really, really hard -- compare the "design" of a greyhound with the "design" of a cheetah -- and it's equally really hard to conceptualize natural selection.) On the other hand, with respect to evolution, we can see that theistic design hypotheses are entirely gratuitous. Thus, we have no real reason to accept them.
Evolutionary theory doesn't imply that mutations are random, in the sense of being uncaused. This point of Plantinga's is just flatly correct, despite what some very good evolutionary biologists (like Monod) thought.
Evolutionary theory, by itself, doesn't deny divine design.
- This is true, but only in a very qualified way. Consider two different explanations of a scenario, where one describes a very plausible naturalistic hypothesis, and one ascribes a very simple divine hypothesis. There's just no reason to accept the design explanation.
Naturalism and Plantinga:
- First, if we deny naturalism, Plantinga's doing an injustice (!) to Behe, by placing him among theologians or philosophers, and not scientists.
- Further, Behe's work is a crock. Here's a selection of quotes from Dennett:
  - Behe's work is "neither serious nor quantitative"
  - It is a "transparent concoction of bad science and bad rhetoric"
  - It is "hugely disingenuous propaganda"
- And Dennett already refuted Behe once, with the help of Haig (from Harvard) at a Notre Dame conference. He's not going to do it again.
- No matter how hard the Discovery Institute looks for intelligent design, they aren't going to find any skyhooks.
Naturalism and evolution
- The claim that the probability of reliable cognition given naturalism and evolution is low is simply false.
  - First of all, we can measure the reliability of sense organs and correct when they become unreliable. (Wear glasses much?)
  - Our brains are syntactic, not semantic engines. We clearly track truth syntactically, and such truth-tracking is adaptive. What more do you want? [Parallels my objection above.]
  - After a question by Michael Tooley, challenging Plantinga on this premise: all of the most plausible accounts of brain states have them causally correlated to the environment. Where's the problem here if there's laws of nature doing causal work for us?
Finally, after Murray Gell-Mann told Dennett that the Christian fish was an acronym, he pressed Dennett to come up with an acronym for his Darwin-fish pin. Dennett came up with: "Delere Auctorem Rerum Ut Universum Infinitum Noscas": Destroy the author of things in order to understand the infinite universe.

Plantinga replied and a short Q&A session followed, in which nothing really substantive took place. Among the humor was Plantinga's claim that Behe hasn't been refuted (?!!?).

And thus ended the APA. A good time was had by all.

Blogging the APA Central: Days 1 & 2

2009-02-20T21:48:00.005-05:00

After the first two days of this year's Central APA, I should probably jot a little note here about the proceedings.

Thursday afternoon I sat in on Michael Tooley's John Dewey Lecture, which, after a brief bit of biographical detail, wound up being on one of my favorite philosophical problems. Tooley offered the conclusions, at least, of proofs of the following two premises: (i) if we have a reductive (e.g., Humean) conception of natural law, there's good reason to think we'll never be able to justify induction, and (ii) if we have a strong (i.e., Armstrong/Tooley) conception of natural law, we get a reasonably straightforward justification of induction -- probabilities climb fairly simply with observed instances. I'm looking forward to going through these proofs in fuller mathematical detail.

After the talk, I got a chance to meet Prof. Tooley, as well as famed Spinoza scholar Edwin Curley and Iowa's Evan Fales. I also got the chance to talk with Stephanie Lewis, wife of the late David Lewis, who is both an astute philosopher (far moreso than her self-description as "amateur metaphysician" would imply), and, perhaps more importantly, an incredibly kind and genial woman whom it was a joy to chat with.

After a set of quick talks on reduction, multiple realizability, and complex systems, it was back to South Bend for the night.

Today started with a nice set of talks on causation; my personal favorite being Luke Glynn's discussion of how we might salvage orthodox theories of probabilistic causation (by accepting conditional probabilities as primitive and being careful about our synthesis of objective chance and determinism). After lunch there was an interesting session on the relationship between human freedom and brain and behavioral science, which, for me, mostly served as a primer on the current state of compatibilism, since the free will literature is somewhere I have close to zero experience.

Finally, I attended Peter van Inwagen's Presidental Address. It was mostly combinations of various arguments of Peter's that I'd heard before -- in particular, his claim that the existential quantifier is univocal due to its relationship with counting, combined with his insistence that metaphysical claims, like the truth or falsity of mereological fusions, are valid, non-trivial philosophical problems worth being solved. In this instance, he was defending himself against arguments of van Fraassen -- that many metaphysical problems turn on vagueness in language -- and Putnam -- that the way we count (i.e., whether or not to include fusions in our counts of what there is) is a convention that determines (changes) our use of the existential quantifier. A good paper, very much in van Inwagen's style.

Watch this space tomorrow evening for a report on the Dennett-Plantinga debate on science and religion!

Happy Darwin Day!

2009-02-12T20:17:00.004-05:00

So, I clearly couldn't let Darwin's 200th birthday go by without writing a post. But, as it turns out, neither can the rest of the internet. So let me mention the few articles that, if I were you, I would read in honor of today.

First, a great article from Science News on the man himself, giving a good idea of the breadth of Darwin's work. Next, we have a piece at the NYT that does an incredible job discussing, in broad strokes, the history of the reception of Darwin's work. The latest issue of BBC Focus Magazine, available in a really cool Flash format, has quite a few neat articles (MINI Coopers are referenced on p. 7; my heart sings).

On the cultural front, while Texas manages to score a minor victory, this piece at the Christian Science Monitor talks about the new form we can expect the ID debate to take in the future.

Finally, the singing Darwin scholar.

And, what piece on Darwin could close without the last few paragraphs of the Origin:

It is interesting to contemplate an entangled bank, clothed with many plants of different kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us.

[...]

There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and wonderful have been, and are being, evolved.

That word "evolved" -- the last word of the Origin -- is the only time Darwin uses any variety of the word "evolution." And as the work closes, we feel that the door has been opened -- opened to the entire future of biological science.

Watch this space on Nov. 24, which, in addition to being my birthday, will be the next Darwin holiday -- the 150th anniversary of the publication of the Origin!

Some Presidential humor

2008-10-09T15:11:00.004-04:00

A bit of 1996-style election-time poetry, for your enjoyment. Absurdism somehow seems particularly relevant in the face of the current state of the McCain campaign.

Bob Dole wants to make this
country great again, but I say no. This country
has tried being great, and it
has failed. I want to make this country small,
embarrassed, slightly befuddled. I
want this country to hum to itself as it cleans
its glasses. I want this country to try hopelessly
to learn to play the tuba. I want this country to
watch Jeopardy! every day and get most of the
answers right. I want this country to mumble,
to be shy, to give a limp handshake, to
go days without combing its hair, to
have bad breath. I want this country to
smile again, awkwardly, while carrying a book.
And I will beat that fucker Dole, with his war
stories and his "courage." Who needs courage?
Courage is for cowards. I have something greater
than courage. I am a failure.

-- Sparrow, "Why I Can Beat Bob Dole"