# Devnology podcast interview

When I was in Amsterdam earlier this year, Daan van Berkel interviewed me for the Devnology podcast. We talked about my winding career path, the overlap of math and computing, bringing math and computing closer together, formal methods, etc.

The podcast was posted this afternoon here.

Related post: Looking like you know what you’re doing

Starting next week, @MedVocab will post two tweets a day, once in the morning and once in the afternoon (CDT).

I’ve stopped posting to @DailySymbol. It was a fun experiment, but it was time to wrap it up.

My most popular account, @CompSciFact, now has over 100,000 followers. It’s interesting how some Twitter accounts take off and some don’t. CompSciFact has done quite well but I’ve shut down several other accounts that never gained much of a following.

You can find a list of my accounts here with a very brief description of each. Some of the accounts are a little broader than the name implies.

# Panel discussion on writing for developers

AirPair is hosting a panel discussion entitled Developer Writing Tips & Tricks as part of AirConf on August 25. I’ll be one of the panelists.

The AirConf events will be broadcast via G+ hangouts.

# Engineering a waterpark

This weekend my family went to Schlitterbahn, a waterpark in New Braunfels, Texas. (The German-sounding name of the park and the city are evidence of the large number of Germans that settled in this part of Texas.) I thought about several engineering questions while we were there.

Most of the rides involve sitting in an inner tube and floating down a course with rapids, waterfalls, swells, etc. At many points there are back currents. You could be headed toward a fall but then find yourself reversing direction. It’s surprising to have to work to make yourself go downhill. At most if not all these points there are employees standing in the water to grab hold of rafts and pull people in the right direction who need a little help.

One question I had is what causes the back currents. Ultimately you could solve Navier-Stokes equations, but it would be nice to understand at a more rule-of-thumb level how these currents work. It would also be interesting to see whether a park could reduce the number of guides while keeping the rides as fun. The guides also serve as lifeguards, so the park may need to position people in all the same spots even if they didn’t need as many guides.

The slowest person in the family was consistently yours truly. I’d start out in front and inevitably end up bringing up the rear. I was curious how I could be so inept at a mostly passive activity.

I was also curious how they designed the rapids to be so safe. You’re repeatedly tossed straight toward rocks — perfectly smooth artificial rocks, but still not not things you want to hit your head on — at a fairly high speed, and yet you never hit one. It has something to do with how they position jets to push you away from the rocks, but that would be interesting to understand in more detail.

Another thing I was curious about is what the park does with its water in the off-season. Schlitterbahn in New Braunfels is actually two parks, an older park that uses untreated water from the Comal river, and a newer park that uses treated water. When the parks close for the season, the older park must just let its water return to the river. (At least one of the rides ends in the river, so they’re already returning water to the river.)

The question of what to do with the treated water in the new park is more interesting. I assume they cannot just dump a huge volume of chlorinated water into the river. Aside from ecological consequences, I wonder whether they’d even want to dump the water. Is it economical to store the water somewhere when the park closes for the year? If not, do they store it anyway because they have no way to dispose of it, or do they treat it so that they can dispose it? I suppose they could circulate the water occasionally while the park is closed, though that seems expensive. I wonder whether different waterparks solve this problem different ways.

If I could propose a new ride for Schiltterbahn, it would be a video presentation about how the park was designed followed by Q&A with a couple engineers. This would be a terrible business decision, but a few visitors would love it.

# Goldilocks software

Aaron Evans condensed a good deal of software engineering experience down to less than 140 characters:

It’s amazing how much cleaner your code looks the third time writing it. First time, hack; Second over-engineer; Third = goldilocks.

# Origins of category theory terms

From Saunders MacLane:

Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: “Category” from Aristotle and Kant, “Functor’ from Carnap …, and “natural transformation” from the current informal parlance.

# Software development becoming less mature?

Michael Fogus posted on Twitter this morning

Computing: the only industry that becomes less mature as more time passes.

The immaturity of computing is used to excuse every ignorance. There’s an enormous body of existing wisdom but we don’t care.

I don’t know whether computing is becoming less mature, though it may very well be on average, even if individual developers become more mature.

One reason is that computing is a growing profession, so people are entering the field faster than they are leaving. That lowers average maturity.

Another reason is chronological snobbery, alluded to in Fogus’s second tweet. Chronological snobbery is pervasive in contemporary culture, but especially in computing. Tremendous hardware advances give the illusion that software development has advanced more than it has. What could I possibly learn from someone who programmed back when computers were 100x slower? Maybe a lot.

Related posts:

# Haskell analog of Sweave and Pweave

Sweave and Pweave are programs that let you embed R and Python code respectively into LaTeX files. You can display the source code, the result of running the code, or both.

lhs2TeX is roughly the Haskell analog of Sweave and Pweave.  This post takes the sample code I wrote for Sweave and Pweave before and gives a lhs2TeX counterpart.

\documentclass{article}
%include polycode.fmt
%options ghci
\long\def\ignore#1{}
\begin{document}

Invisible code that sets the value of the variable $a$.

\ignore{
\begin{code}
a = 3.14
\end{code}
}

Visible code that sets $b$ and squares it.

(There doesn't seem to be a way to display the result of a block of code directly.
Seems you have to save the result and display it explicitly in an eval statement.)

\begin{code}
b = 3.15
c = b*b
\end{code}

$b^2$ = \eval{c}

Calling Haskell inline: $\sqrt{2} = \eval{sqrt 2}$

Recalling the variable $a$ set above: $a$ = \eval{a}.

\end{document}


If you save this code to a file foo.lhs, you can run

lhs2TeX -o foo.tex foo.lhs

to create a LaTeX file foo.tex which you could then compile with pdflatex.

One gotcha that I ran into is that your .lhs file must contain at least one code block, though the code block may be empty. You cannot just have code in \eval statements.

Unlike R and Python, the Haskell language itself has a notion of literate programming. Haskell specifies a format for literate comments. lhs2TeX is a popular tool for processing literate Haskell files but not the only one.

# A subway topologist

One of my favorite books when I was growing up was the Mathematics volume in the LIFE Science Library. I didn’t own the book, but my uncle did, and I’d browse through the book whenever I visited him. I was too young at the time to understand much of what I was reading.

One of the pages that stuck in my mind was a photo of Samuel Eilenberg. His name meant nothing to me at the time, but the caption titled “A subway topologist” caught my imagination.

… Polish-born Professor Samuel Eilenberg sprawls contemplatively in his Greenwich Village apartment in New York City. “Sometimes I like to think lying down,” he says, “but mostly I like to think riding on the subway.” Mainly he thinks about algebraic topology — a field so abstruse that even among mathematicians few understand it. …

I loved the image of Eilenberg staring intensely at the ceiling or riding around on a subway thinking about math. Since then I’ve often thought about math while moving around, though usually not on a subway. I’ve only lived for a few months in an area with a subway system.

The idea that a field of math would be unknown to many mathematicians sounded odd. I had no idea at the time that mathematicians specialized.

Algebraic topology doesn’t seem so abstruse now. It’s a routine graduate course and you might get an introduction to it in an undergraduate course. The book was published in 1963, and I suppose algebraic topology would have been more esoteric at the time.

# Bringing bash and PowerShell a little closer together

I recently ran across PSReadLine, a project that makes the PowerShell console act more like a bash shell. I’ve just started using it, but it seems promising. I’m switching between Linux and Windows frequently these days and it’s nice to have a little more in common between the two.

I’d rather write a PowerShell script than a bash script, but I’d rather use the bash console interactively. The PowerShell console is essentially the old cmd.exe console. (I haven’t kept up with PowerShell in a while, so maybe there have been some improvements, but it’s my impression that the scripting language has moved forward and the console has not.) PSReadLine adds some bash-like console conveniences such as Emacs-like editing at the command prompt.

# Making change

How many ways can you make change for a dollar? This post points to two approaches to the problem, one computational and one analytic.

SICP gives a Scheme program to solve the problem:

(define (count-change amount) (cc amount 5))

(define (cc amount kinds-of-coins)
(cond ((= amount 0) 1)
((or (< amount 0) (= kinds-of-coins 0)) 0)
(else (+ (cc amount
(- kinds-of-coins 1))
(cc (- amount
(first-denomination
kinds-of-coins))
kinds-of-coins)))))

(define (first-denomination kinds-of-coins)
(cond ((= kinds-of-coins 1) 1)
((= kinds-of-coins 2) 5)
((= kinds-of-coins 3) 10)
((= kinds-of-coins 4) 25)
((= kinds-of-coins 5) 50)))


Concrete Mathematics explains that the number of ways to make change for an amount of n cents is the coefficient of z^n in the power series for the following:

Later on the book gives a more explicit but complicated formula for the coefficients.

Both show that there are 292 ways to make change for a dollar.

Learn basic medical vocabulary a little at a time by following my new account @MedVocab on Twitter.

See the full list of my daily tip Twitter accounts here.

The icon for the site is taken from one of Leonardo da Vinci’s anatomical drawings.

# A puzzle puzzle

Jigsaw puzzles that say they have 1,000 pieces have approximately 1,000 pieces, but probably not exactly 1,000. Jigsaw puzzle pieces are typically arranged in a grid, so the number of pieces along a side has to be a divisor of the total number of pieces. This means there aren’t very many ways to make a puzzle with exactly 1,000 pieces, and most have awkward aspect ratios.

Since jigsaw pieces are irregularly shaped, it may be surprising to learn that the pieces are actually arranged in a regular grid. At least they usually are. There are exceptions such as circular puzzles or puzzles that throw in a couple small pieces that throw off the grid regularity.

How many aspect ratios can you have with a rectangular grid of 1,000 points? Which ratio comes closest to the golden ratio? More generally, answer the same questions with 10^n points for positive integer n.

More puzzles:

# Ellipsoid surface area

How much difference does the earth’s equatorial bulge make in its surface area?

To first approximation, the earth is a sphere. The next step in sophistication is to model the earth as an ellipsoid.

The surface area of an ellipsoid with semi-axes abc is

where

and

The functions E and F are incomplete elliptic integrals

and

implemented in SciPy as ellipeinc and ellipkinc. Note that the SciPy functions take m as their second argument rather its square root k.

For the earth, a = b and so m = 1.

The following Python code computes the ratio of earth’s surface area as an ellipsoid to its area as a sphere.

from scipy import pi, sin, cos, arccos
from scipy.special import ellipkinc, ellipeinc

# values in meters based on GRS 80
# http://en.wikipedia.org/wiki/GRS_80

phi = arccos(c/a)
# in general, m = (a**2 * (b**2 - c**2)) / (b**2 * (a**2 - c**2))
m = 1

temp = ellipeinc(phi, m)*sin(phi)**2 + ellipkinc(phi, m)*cos(phi)**2
ellipsoid_area = 2*pi*(c**2 + a*b*temp/sin(phi))

# sphere with radius equal to average of polar and equatorial
r = 0.5*(a+c)
sphere_area = 4*pi*r**2

print(ellipsoid_area/sphere_area)


This shows that the ellipsoid model leads to 0.112% more surface area relative to a sphere.

Source: See equation 19.33.2 here.

Update: It was suggested in the comments that it would be better to compare the ellipsoid area to that of a sphere of the same volume. So instead of using the average of the polar and equatorial radii, one would take the geometric mean of the polar radius and two copies of the equatorial radius. Using that radius, the ellipsoid has 0.0002% more area than the sphere.

# Pi and The Raven

Michael Keith rewrote Edgar Allen Poe’s poem The Raven to turn it into a mnemonic for pi. Keith’s version follows the original quite well considering his severe constraints. The full poem has 18 stanzas. Here I include only the first and last. The full version can be found here.

***

Poe, E.
Near a Raven

Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore,
During my rather long nap — the weirdest tap!
An ominous vibrating sound disturbing my chamber’s antedoor.
“This,” I whispered quietly, “I ignore.”

So he sitteth, observing always, perching ominously on these doorways.
Squatting on the stony bust so untroubled, O therefore.
Suffering stark raven’s conversings, I am so condemned, subserving,
To a nightmare cursed, containing miseries galore.
Thus henceforth, I’ll rise (from a darkness, a grave) — nevermore!

***

The number of letters in most words encodes a digit of pi. Words with 10 letters encode a zero. Words with more than 10 letters encode two consecutive digits of pi. The poem encodes the first 740 digits of pi.