Is randomness mind-dependent?

Eddie asked:

Is randomness mind dependent? Can any random process possibly be generated in a deterministic world?

Answer by Geoffrey Klempner

In the first year of my BA at London University in the early 70s I had a part-time job as a clerk in the OPCS, the Office of Population Censuses and Surveys in Holborn, London (which later in 1996 became the Office of National Statistics). I was in a small office with four or five clerks and a Senior Executive Officer (SEO). Our job was the most boring imaginable. We had to select addresses from the Electoral Register and compile address lists for interviewers to visit for the UK Government’s ‘General Household Survey’.

For the statistics gathered to be reliable, it was essential that the selection was done randomly. It would have skewed the statistics badly if we’d skipped all the East European sounding names, or names from the Indian sub-continent — or houses with twee names like ‘The Nook’ or ‘Rose Cottage’ — or on the other hand gone out of our way to select them. (I’m not saying this was never done. We were very bored.)

According to our SEO, a young woman who had joined the Civil Service after gaining her degree in Statistics, the only correct way to do the selection was use a mathematical formula to generate random numbers. Using a haphazard method, like throwing dice for example, wasn’t always a reliable way of generating random numbers because you need to be 100% sure that the numbers you produce would not appear to support a prediction.

An example of the dangers of relying on a haphazard method would be a penalty kicker in soccer who before the match uses a coin spin to decide which way he will kick the ball, right or left. He spins his lucky penny a few times: heads for left, tails for right. Unfortunately for him, the last six throws have all landed heads. And this time it’s heads again. The goal keeper, noting the kicker’s seeming predilection for going left in recent games, dives left and saves the goal and the match.

As time was pressing and none of us was sufficiently competent in maths (this was before computers) our SEO said it would be OK to select the last digits from telephone numbers in a telephone directory page opened ‘at random’. I hardly ever saw anyone do this. We just thought up two numbers in our heads. The first number n was the nth address on the Electoral Register for the district the interviewer was due to visit. The second number m was the number of addresses to skip before selecting the m+1th address.

Provided this relatively lazy procedure was followed, with no cheating, then the selection probably would have been sufficiently random for the purpose intended. Our SEO had a story to tell her boss. There was always an open telephone directory in the room so we could claim that we’d got our numbers from there.

What is the point of this story? Randomness is a practical concept, which applies differently in different areas of activity. In statistics, you want your results to be reliable, because policy decisions may depend on the outcome. In a game, you want your actions to be unpredictable. In a lottery, you want the result to be fair with no possibility of cheating. And so on. In none of these areas, or other examples you can think of, is randomness merely ‘mind dependent’. That is because in each case, there are consequences in the real world.

However, randomness in the sense I have described, isn’t purely ‘objective’ either. With sufficient knowledge (you might need to have powers approaching those of a Laplacian Super-Mind) you could predict any supposedly random selection or sequence — in a deterministic world, as you say, otherwise the bets are off.

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