The history of mathematics…

July 31, 2008 at 4:30 pm (science) (, , , )

“The history of mathematics is a Markov Chain”.  This is a joke (probably not apparent to non-mathematicians!), but like the best jokes, is based in truth.

Because not everyone here knows what a Markov Chain is, I should explain.  A Markov Chain describes things that change in a way that has no memory.  What happens in the future doesn’t depend on what happened in the past.  Picture a drunk, staggering home after a night out.  Each step he takes is in a random direction.  He might recognise the local shop, and walk towards it – but if he gets lost, and finds the shop again, there is nothing to stop him making the same mistake twice and walking in circles – because he can’t remember where he’s been, but only where he is.

The joke says that mathematics reinvents the same concepts over and over – which is true of this concept.  It was independently invented in physics by Einstein for his description of Brownian Motion, and in mathematics by Andrey Markov in work on probability theory.

A post at Scienceblogs reminded me of this, and it is interesting because (as they argue well) all of Science is like this.  Scientists are not Historians, so we only remember what is important enough to get into textbooks.  If it doesn’t make it it – the next generation don’t know about it, and it becomes forgotten, doomed to be repeated again and again.

I wonder if the Internet will help us overcome this?  When (say) PhD students of 2050 do a literature search for some obscure gene, will they find information from now about it in databases and papers, and will that be of any use to them?  Can we use this to allow science to progress in useful directions, by remembering those that were failures?  Or will failures of the past be viewed as caused by ignorance or lack of equipment, that enlightened folk of “today” can deal with without problem?

Without it, Science will be doomed to proceed as a Drunkard’s Walk, lurching between discoveries on the same old path of failures.  We can easily explore the area around the pub like this, but it takes an awfully long time to stumble back home.

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2 Comments

  1. evsuan said,

    Perhaps we can also picture this Markov chain through an analysis to the game of Monopoly. The past moves of each player no longer affects, or is irrelevant to the, present state. (This is different to the card games, which its past state is necessary to the present state for the player to win the game.)

    I like the joke about the history of math as a Markov chain. Perhaps, few mathematicians are not historians, but that does not mean — I think you will agree — that all mathematicians do not know certain history of mathematics. Our current age is an age of information and cyberspace, thereby transforming mathematicians into historians!

    Nice post by the way!

  2. thinkingdan said,

    I like the monopoly analogy – the current state is who own which properties, how many houses they each have, etc. It doesn’t matter how each player ended up with those properties.

    I’ve “rediscovered” past mathematics at great effort – I’m sure its pretty common. Luckily in my case, I also managed to add something new, but I was pretty gutted for a while! Part of the problem is changing notation, and different names for equations – there is not currently any reliable way to search for information on a problem, let alone a solution to the problem. But the internet has got to help! I suppose there is a difference between knowing the history of a subject (meaning the significant contributions), and knowing the insignificant contributions that you may by chance rediscover.

    On a related subject, a friend once said that you can make a great career out of taking old forgotten papers from obscure journals and jazzing them up for Nature and Science 🙂

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