Looking for a human-powered hydrofoil vehicle? Check out Puzey Design’s Pumpabike.

New Scientist’s coverage contains a link to a short video (3.79MB).

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# Month: May 2005

## Hop a Ride on a Puzey Pumpabike

## Is Moralism an Evolutionary Maladaption?

## Solution to SICP Exercise 1.22

## Pakistan Trains Female Fighter Pilots

## Network Theory Study of the U.S. House of Representatives

## Proving Theorem Provers Correct

## Solution to SICP Exercise 1.21

Looking for a human-powered hydrofoil vehicle? Check out Puzey Design’s Pumpabike.

New Scientist’s coverage contains a link to a short video (3.79MB).

Johnnie Moore has been reading Brad Blanton’s Radical Honesty, and applying some of Blanton’s ideas about moralizing to branding, marketing, and improvisation. As usual for Johnnie’s posts, it is well worth a read.

What caught my attention was a quote from Blanton on what he calls the *Disease of Moralism*:

The passing on of learning from one generation to the next is not a bad design, and as an evolutionary development it seems to have triumphed… The ability to act based on accumulated information, and to pass great quantities of new information on, is the primary survival characteristic of the strongest animal on earth.

But, paradoxically, our survival mechanism has proved to be ultimately suicidal.

So is moralism an evolutionary maladaption? It is an interesting hypothesis, and for all I know, could very well be true, but it seems suspiciously oversimplified to me. [I could also very likely be misrepresenting Blanton’s ideas, as I haven’t actually read the quote in context, so take this all with a grain… no, a bag of salt.]

Given how pervasive moralizing is in western culture, I would guess that it probably has some evolutionary advantage, much like what scientists are uncovering with altruism. In fact, I’d guess that moralizing is an enormously beneficial tool; so beneficial that it is often misapplied in situations where it doesn’t work, leading some observers, like Blanton, to believe it is always harmful.

So how could we test the hypothesis of moralism as a maladaption? There’s something to think about.

Solution to Exercise 1.22:

DrScheme does not have a built-in `runtime`

procedure that I could find, so I modified the code for `timed-prime-test`

to use SRFI 19, like so

`(require (lib "19.ss" "srfi"))`

```
```(define (timed-prime-test n)

(newline)

(display n)

(start-prime-test n (current-time time-process)))

(define (start-prime-test n start-time)

(if (prime? n)

(report-prime

(time-difference

(current-time time-process)

start-time))))

`(define (report-prime elapsed-time)`

(display " *** ")

(display (time-second elapsed-time))

(display "s ")

(display (time-nanosecond elapsed-time))

(display "ns"))

I implemented `seach-for-primes`

as follows:

`(define (search-for-next-prime starting-at)`

(if (prime? starting-at)

starting-at

(search-for-next-prime (+ starting-at 2))))

```
```

`(define (search-for-primes find-n starting-at)`

(if (= find-n 0)

null

(let ((next-prime (search-for-next-prime starting-at)))

(cons next-prime

(search-for-primes (- find-n 1) (+ next-prime 2))))))

I could then run some tests:

`(define (time-prime-tests primes)`

(map timed-prime-test primes))

```
```

`(time-prime-tests (search-for-primes 3 1001))`

(time-prime-tests (search-for-primes 3 10001))

(time-prime-tests (search-for-primes 3 100001))

(time-prime-tests (search-for-primes 3 1000001))

This gave the following output:

1009 *** 0s 0ns

1013 *** 0s 0ns

1019 *** 0s 0ns

(# # #)

```
```10007 *** 0s 0ns

10009 *** 0s 0ns

10037 *** 0s 0ns

(# # #)

100003 *** 0s 0ns

100019 *** 0s 0ns

100043 *** 0s 0ns

(# # #)

`1000003 *** 0s 0ns`

1000033 *** 0s 0ns

1000037 *** 0s 0ns

(# # #)

As you can see, all of the tests for prime took no time at all. This is obviously wrong.

I have a feeling that all these processes complete in less time than a single tick of the process clock (which, on Windows, appears to have a resolution in milliseconds).

Let’s magnify the results by calling `prime?`

in `timed-prime-test`

1000 times instead of just once. Here’s the modified definition:

`(define (timed-prime-test n)`

(newline)

(display n)

(start-prime-test 1000 n (current-time time-process)))

(define (start-prime-test i n start-time)

(if (prime? n)

(if (= i 0)

(report-prime

(time-difference

(current-time time-process)

start-time))

(start-prime-test (- i 1) n start-time))))

Now I get the following output:

1009 *** 0s 460000ns

1013 *** 0s 470000ns

1019 *** 0s 320000ns

(# # #)

```
```10007 *** 0s 1250000ns

10009 *** 0s 1410000ns

10037 *** 0s 1090000ns

(# # #)

100003 *** 0s 5940000ns

100019 *** 0s 3910000ns

100043 *** 0s 4060000ns

(# # #)

`1000003 *** 0s 7500000ns`

1000033 *** 0s 1870000ns

1000037 *** 0s 2340000ns

(# # #)

Alright! We have some numbers. Unfortunately, when I run the tests again, I get totally different numbers. Grr! I’m going to consider these numbers representative of many runs, but they probably aren’t. Let’s start with some analysis.

Let’s start by averaging the times for each group. We can multiply this by √10 to obtain an expected time for the following group, which we can compare against the measured time.

Group | Average Time | Expected time (based on lower group) | Difference |
---|---|---|---|

~1000 | 416667 | — | — |

~10000 | 1250000 | 1317616 | -5% |

~100000 | 4636667 | 3952847 | 17% |

~1000000 | 3903333 | 14662427 | -73% |

With a difference of over 70% on the final group, this data clearly does not support the √*n* hypothesis, but it doesn’t disprove it, either. For a definitive answer, we need a larger sample group. We need data for more values of *n* and for several runs. I’m not going to do that here because this post is already too long, and I’m sure you have better things to do.

Boing boing is linking to a BBC story that Pakistan is now training women to be fighter pilots.

In the human factors course that I took as an undergrad years ago, the professor consulted with the military on the several designs. He told us of the stringent anthropometric (body-shape) requirements for fighter pilots. For example, their arms and legs must be a certain length because the seats cannot be made adjustable for G-forces expected in flight. Their torsos cannot be too tall or the canopy window won’t close; nor too short or the pilot won’t be able to see over the control panel.

There is also a weight restriction. The seat ejectors are designed for a very narrow range of weights (if I remember correctly, something like 175-190lbs). If the pilot is any heavier, there is a risk the ejected seat will not clear the aircraft. If the pilot is too light, there is a risk that ejection will cause severe spinal injury and/or death.

Given that women are, on average, lighter than men, I wonder if these women cadets fit the anthropometric requirements for the aircraft that they will be piloting.

A recent paper by Porter, Mucha, Newman, and Warmbrand studies the interconnections of the committees and sub-committees in the U.S. Congress from a network theoretic perspective. They conclude that the distribution of congressmen among the committees is not random — there’s a shocker — that cliques rule over certain parts of the government. For example, there are strong ties between the Select Committee on Homeland Security and the House Rules Committee.

Regardless of the political implications of the study, I found it to be a fun example of network theory.

For those less inclined to read the paper, New Scientist has a summary.

In a Los Angeles Times commentary, Margaret Wertheim writes about one of the growning problems in modern mathematics:

People are now claiming proofs for two of the most famous problems in mathematics — the Riemann Hypothesis and the Poincare Conjecture — yet it is far from easy to tell whether either claim is valid. In the first case the purported proof is so long and the mathematics so obscure no one wants to spend the time checking through its hundreds of pages for fear they may be wasting their time. In the second case, a small army of experts has spent the last two years poring over the equations and still doesn’t know whether they add up.

She claims that mathematics is evolving into a postmodern study where, according to Philip Davis, emeritus professor of mathematics at Brown University, mathematics is “a multi-semiotic enterprise” prone to ambiguity and definitional drift.

What I found interesting was this bit:

The [four-colour map] problem was first stated in 1853 and over the years a number of proofs have been given, all of which turned out to be wrong. In 1976, two mathematicians programmed a computer to exhaustively examine all the possible cases, determining that each case does indeed hold. Many mathematicians, however, have refused to accept this solution because it cannot be verified by hand. In 1996, another group came up with a different (more checkable) computer-assisted proof, and in December this new proof was verified by yet another program. Still, there are skeptics who hanker after a fully human proof.

I don’t know if I buy the postmodern angle, but I believe she’s right about the practice of mathematics changing. It seems to me that as the complexity of mathematical problems grows beyond the abilities of human minds, we are going to require computers to prove our theorems for us. My prediction: the job of mathematicians will eventually turn into proving that theorem-proving software is correct.

Solution to Exercise 1.21:

`> (smallest-divisor 199)`

199

> (smallest-divisor 1999)

1999

> (smallest-divisor 19999)

7