A reply to the email

Last night I got a reply from the email I sent out to the maths and physics graduates. Jonathan Wright, a maths graduate, said:

"In my opinion, there is no such thing as a random event. As an applied mathematician, all physical situations can be modelled mathematically, and as such we can predict all possible outcomes. If we roll a dice in exactly the same way 100 times, 100 times it would give us the same result. If we model the roll of the die, given the starting conditions we could predict the outcome every time.

Predictions are made using models such as this all the time, a classic example being those used by weathermen every day to make their forecasts. Granted, the models can always be improved, but in theory if we had every piece of information (all temperatures, all pressures all over the world etc), and the perfect model, we could exactly predict the future weather.

However, with both the roll of the dice or in predicting the weather, it is this 'knowing' of the starting conditions which creates the randomness that we experience I every day life. In the weather models, if your temperature measurement is off by 0.01 degrees, eventually, perhaps in hours, days or weeks time, the predictions made by the model will become drastically different from those you experience. In fact, this was how chaos was discovered; a seemingly well understood piece of theory, when run on a computer on two occasions, gave two drastically different answers with seemingly the same starting values. The difference was attributed to a difference in the 6th decimal place of the starting values..

And here lies the problem, at some point you reach the limit of your accuracy. If you know the starting position of your dice to 1000 decimal places, the difference in the 1001st decimal place coupled with a similar error in your understanding of the spin the die is thrown with etc may result in a different outcome. A good book on this is by Ian Stewart, Does God Play Dice? The Mathematics of Chaos

Quantum theory on the other hand, may also appear to be random, but similarly I think it is just not fully understood. We may not know the exact position of electrons in an atom, so instead we give electrons a 'probability' of being in certain positions or states. This doesn't mean that the electrons are in a random place, just that we are unable to observe their exact position. (In fact, and here is where you should ask a physicist, I think the very process of looking into an atom changes the states of the electrons..So we dont know.) But does this make it random?

Similarly, is an earthquake a random event?..To someone capable of studying the inner fluid dynamics of the earth, and properties of it's crust etc, then it is not random, in fact with the right models predictable. But will humans ever be able to actually predict such events precisely?..Probably not, because we will never be able to know the starting conditions to the required accuracy.."

So, to conclude, Jonathan Wright believes that pure randomness doesn't exist because probability has allowed us to be able to accurately predict so-called "random" events. Also, he discusses the fact that a random event could be subjective - it really depends on how knowledgeable a person is. Therefore, things that seem random for us right now may just be things that are too mathematically complex for us to understand, or things that we do not have much information about.

This reply has helped me look at randomness for a mathematicians point of view. Jonathan Wright touches upon the different areas of randomness that I will be covering in my dissertation and so all of this will be very helpful to me.