## A. Burgess: “Clockwork Condition”. A tale on Skinner and Free Will

The real polemic target of Anthony Burgess in The Clockwork Condition (The New Yorker)
(here the Italian translation) was Skinner and behaviorism.
It reminds me of some studies of José Delgado, the brilliant physiologist who implanted electrodes in animal brains to steer their behavior. See his book here (particularly Chap. 11). This is a 1985 CNN Special Report on Electromagnetic Mind Control:

## Science Friction (1)

Mersenne numbers, when they are primes, are routinely used to feed MonteCarlo random number generation. They have the form:

$M_n := 2^{n}-1, \hspace{0.5cm} n \in \mathbb{N}$.

Since not all of them are prime, we can use prime factorization of a sequence of big Mersenne numbers to benchmark our CPU.
The ingredients are fairly minimalistic:
all we need is a Linux bash shell (with the wonderful bench calculator bc), the java compiler (Linux: javac) and the java virtual machine (Linux: java). To factorize we could use for example the Pollard Rho method in this implementation.

import java.math.BigInteger;
import java.security.SecureRandom;

class PollardRho {
private final static BigInteger ZERO = new BigInteger("0");
private final static BigInteger ONE  = new BigInteger("1");
private final static BigInteger TWO  = new BigInteger("2");
private final static SecureRandom random = new SecureRandom();

public static BigInteger rho(BigInteger N) {
BigInteger divisor;
BigInteger c  = new BigInteger(N.bitLength(), random);
BigInteger x  = new BigInteger(N.bitLength(), random);
BigInteger xx = x;

// check divisibility by 2
if (N.mod(TWO).compareTo(ZERO) == 0) return TWO;

do {
divisor = x.subtract(xx).gcd(N);
} while((divisor.compareTo(ONE)) == 0);

return divisor;
}

public static void factor(BigInteger N) {
if (N.compareTo(ONE) == 0) return;
if (N.isProbablePrime(20))
{ System.out.println(N); return; }
BigInteger divisor = rho(N);
factor(divisor);
factor(N.divide(divisor));
}

public static void main(String[] args) {
BigInteger N = new BigInteger(args[0]);
factor(N);
}
}


If processor time has to be accurately recorded, just add the “time” command in front of the java runtime, like this:

for n in seq 101 2 201; \
do echo "[Factoring Mersenne echo 2^$n-1]" ; \ time java PollardRho echo 2^$n -1 |bc ; \
done


The code snippet above loops all the odd numbers $n \in \{101,103,\ldots,199,201\}$, uses them as Mersenne exponent as $M_n := 2^n-1$ and prints prime factors. Check for example that for $n=107$ the Mersenne number is infact a Mersenne prime.